ISAW Papers 3 (2012)

Rome and the Economic Integration of Empire

Gilles Bransbourg [*]

http://doi.org/2333.1/280gb73f

Abstract:The modern economist Peter Temin has recently used econometrics to argue that the Roman grain market was an integrated and efficient market. This paper gathers additional data and applies further methods of modern economic analysis to reach a different conclusion. It shows that the overall Roman economy was not fully integrated, although the Mediterranean Sea did create some meaningful integration along a few privileged trade routes. Still, it is not possible to identify pure market forces that existed in isolation, since the political structures that maintained the Empire strongly influenced the movement of money and trade goods.

Subjects: Economic history--To 500.

Contents

- Ancient Wheat Prices and Market Mechanisms

- The "Temin Equations" of a Centralized Efficient Market

- The Law of Small Numbers

- Alternative Relationships or Absence of Relationships?

- When Distance to Rome is not a Granted Parameter

- Interim Conclusions

- The Imperfect Pre-modern French Grain Market

- Markets, Geographic Barriers and State Intervention

- Towards the Use of More Prices

- More Thoughts on Roman Prices and Trends

- The Modified Equations

- Towards Partial Grain Market Integration

- Conclusion: Modern Methodologies and Ancient Societies

- Notes

- Works Cited

“Much of the daily buying and selling of processed foods and other raw materials and of manufactured goods in all the cities of antiquity – I should even guess the largest quantity – was carried on without middlemen, through direct sale by individual craftsmen to individual consumers.”[1]

“This allowed a single market for wheat to emerge, whose existence we could verify from surviving prices.”[2]

Ancient Wheat Prices and Market Mechanisms

In several recent publications, Peter Temin has advocated the view that the Roman Mediterranean area was a single market, by studying the credit, labor and goods markets.[3]

In this paper, we will focus on the last of these. This is not to say that the other two topics are of no interest--far from it. But they require, especially for interest rates, specific numerical analysis that we hope to present in a future paper.

The grain market was undoubtedly the largest market by volume in the ancient Mediterranean world, although we cannot be certain it was always the first in value. A single ship engaged in the Indian trade was able to carry close to HS 10 million in value. This is equivalent to about 2.5 million modii of grain at the likely second-century A.D. Italian price and 4 million modii at Egyptian prices. This is about the volume of the entire annual Sicilian first tithe as reported by Cicero.[4]

The relatively low volumetric value of wheat may explain why we have little or no evidence about wealthy merchants specializing in the grain trade, although we have numerous examples linked with the luxury, oil, or wine trades.[5] Numbers from hagiographic sources in the 6th and 7th centuries, for what they are worth, imply that the value of some precious cargos could exceed that of regular wheat loads by a factor of five to fifteen.[6] Eventually, since the administration of the Roman and Constantinopolitan annonae owned a significant share of the grain that was transported by sea, it may well be that, although grain did represent the most important good transported in volume terms, it was not the most important traded good when accounted for in value.[7]

Nevertheless, the sheer importance of grain as the universal subsistence commodity of the Mediterranean area at this period led to some price recording. Although quite scattered and very often linked to crisis situations, these prices or indications of prices of grain in different contexts create a clear temptation for testing whether or not grain price behavior would fit within a global integrated market process. Grain offers the potential for price comparison since its quality and type had necessarily a much more limited impact on its median price than was the case for wine or oil, for instance.[8]

The “Temin Equations” of a Centralized Efficient Roman Market for Grain

In his 2006 article, extended in 2008 with the collaboration of David Kessler,[9] Peter Temin uses various wheat “prices” essentially gathered by Geoffrey Rickman in his influential 1980 book The Corn Supply of Ancient Rome. From these a set of price differences between “Roman” prices and selected prices from outside Rome is built, and a linearity test between price differential and distance from Rome is run. The aim is to produce a linear relationship between price differentials and distances by means of the OLS (Ordinary Least Squares) methodology. This being achieved with a high degree of statistical confidence, the argument leads to the conclusion that the farther we are from Rome, the cheaper the grain becomes, since “the price would have been set in Rome where the excess supplies and the largest excess demand came together” and “wheat outside Rome would be valued by what it was worth in Rome,” the main component explaining the difference being transport costs.[10] This would vindicate the view that Rome and to a lesser extent Italy would have been at the center of an integrated Mediterranean economy.

Free profit-driven traders, having to deal with Roman demand on the one hand and various supply areas on the other, while competing against each other, would have had to purchase wheat where it was the cheapest, transportation costs included. By doing so, they would have encouraged the comparatively cheaper areas to produce more and put pressure on the most expensive producers to reduce their own costs, effectively aligning distance-to-Rome-adjusted wheat prices all across the accessible wheat producing regions of the Mediterranean area. Implicitly, that commercial pressure would have affected wages and other prices altogether, the process of reaching the market equilibrium mainly involving emigration and agricultural shifts in the least competitive regions, while in the best positioned areas more marginal land would have been dedicated to wheat, increasing marginal costs over time. This is how the relationship between price differentials and distance to Rome would prove the existence of a single integrated free market operating at the scale of the entire Imperial area or, to use the author’s own words, “a single monetary market and a single wheat market across the whole Mediterranean.”[11]

An economy of trade centered on the city of Rome and, to a lesser extent, Italy would vindicate the “Tax and Trade” model advocated by Keith Hopkins and further developed by Hans-Ulrich von Freyberg. Rome would benefit from taxation intakes; the influx of liquidities would push local prices higher, making local goods too expensive. Producers from all over the Empire would exploit their comparative price advantage and outperform their Italian competitors.[12]

Temin and Kessler’s figures, showing a broadly negative linear relationship between distances from Rome and grain price differential, can be summarized as follows:

Table 1. Distance from Rome and grain prices according to Kessler and Temin[13]

Region

Distance from Rome (km)

Rome price (HS)

Province price (HS)

Distance from Rome "discount" (HS)

Year

Sicily

427

4.00

2.00-3.00

-1.5

77 B.C.

Spain (Lusitania)

1363

3.00-4.00

1

-2.5

150 B.C.

Po Valley

1510

3.00-4.00

0.5

-3

150 B.C.

Asia Minor (Pisidian Antioch)

1724

5.00-6.00

2-2.25

-3.13

A.D. 80s

Egypt (Fayum)

1953

5.00-6.00

1.5

-4.00

20 B.C. – A.D. 56

Palestine

2298

5.00-6.00

2-2.50

-3.25

A.D. 15

This leads to the following chart between prices differentials and distances from Rome:[14]

Chart 1. Distances from Rome and price for grain

Full size image here ↗

The rather neat linearity observable between price differentials and distance from Rome would imply the following relationship:

(Provincial price – Roman price) = β x (distance from Rome) + α + ε

where β is the multiplicative coefficient linking the distance from Rome to the price differential, α the constant, both factors minimizing the standard deviation between the linear regression results and the actual data, and ε the statistical residual of the equation, i.e.. what is left “unexplained” by the equation produced by the regression computation. The numerical results obtained by the authors eventually fit well with that linearity pattern:[15]

Regression factors

β

α

R^2

Value and statistical quality

-0.001 (-3.9)

-1.10 (-2.2)

79%

This would imply the dominance of market mechanisms, by which prices would be higher where demand is the highest and supply most constrained, whereas remote places far away from the center would enjoy a cheaper life. This is indeed a very seductive vision: Braudelian in the sense that Rome would emerge as the focal point of a wide web of merchant activity, as Bruges, Anvers, Venice, Genoa, Amsterdam, Paris, London, and New York were to become during pre-modern and modern times.[16] Moreover, by introducing statistical treatment and a modern economic approach into the study of the ancient economy, Peter Temin opens the door to a completely renewed approach to ancient history, using numerical analysis, a field where most ancient historians have shown some degree of reluctance.

By doing so, David Kessler and Peter Temin clearly expose themselves to criticisms, of which they seem to be mostly conscious. This is how they address them:

- Ancient data are uncertain. Nevertheless, they can be treated as reliable since they are “mentioned in a surviving document” or because “Polybius was a very careful historian.”[17]

- Distance in itself is not that relevant, in the sense that sea, river and land transportation costs are very different. Hence, the Po valley price is eliminated in a second run.[18]

- Lower prices outside of Rome would have been explained by low monetization.[19] Although this may be true in Lusitania, that factor could not have explained the low prices in Egypt, where coins were very abundant.[20]

- Data may be unreliable, reflecting extreme and crisis conditions as well as being subject to unknown seasonal variations or literary invention. But “travelers were told of the prevailing prices.”[21] Supporting this rebuttal is the fact Rickman was careful to exclude the extreme observed prices from his conclusions regarding average prices.[22]

- The argument could be circular if “we assume the data are sound because they support the hypothesis,”[23] but these prices are simply a true random sample.

- Data are too few. Nevertheless, the level of statistical confidence is compared to minimum levels required for limited samples and degrees of freedom and bodes well.

In reality, most of these issues remain serious hurdles and need to be addressed with a less superficial scrutiny.

The Law of Small Numbers

Everybody is familiar with the Law of Large Numbers, which consists of performing the same experiment a large number of times in order to observe a close approximation of a probabilistic solution. By contrast, there is no such law for small numbers: small samples being less likely to be bulletproof, statisticians try to avoid situations where they have to rely on a dozen or fewer observations. A relatively recent paper went so far as to suggest as a rule of thumb that we should not study samples with fewer than twenty observations when faced with two variables, including the constant.[24] Without entering into technical niceties, the main issue is that few available parameters do not allow the error term in the equation to sufficiently converge towards the true term, implying a significant loss of information.

Even when statistical quality may seem on the surface to be satisfactory, the results might differ from what a larger sample would produce. Because the equations run by Kessler and Temin contain between 5 and 6 parameters and 2 unknown coefficients, we are exactly in that situation.

The second issue that arises when conducting any analysis of that kind is the comparability of the “statistics.” If different measuring tools or concepts are used in gathering the numbers that are to be statistically studied, comparability distortions arise, and results are therefore affected.[25]

The dataset used by Kessler and Temin contains one obvious source of incomparability: most prices are observed in rural contexts, with the exception of Antioch in Pisidia and the estimations for Rome. The sales margin applied by the urban retailers should theoretically be deducted from these two prices to make them comparable. One argument against doing so is that the prefect in Antioch may well have addressed wholesalers’ prices rather than retail and that the Roman retailers’ margin will have been reflected in the constant factor of the equation. We will revert later to that topic.

Another major issue, particularly with limited samples, is what statisticians call the heteroscedasticity of the variables. This occurs when the measurement uncertainty of the observations differs from one to another.[26] The typical way to handle this issue is to run weighted ordinary least squares, where the most uncertain inputs are inversely linked to their reliability by decreasing their impact on the final results.[27]

In the case of these ancient prices, we are clearly faced with such an issue, because of the heterogeneity of the observation process itself. For instance, at Antioch in Pisidia, the customary price is indicated in the Prefect’s edict itself.[28] Egyptian prices are rather well documented as well through numerous surviving papyri, although this does not prevent issues from arising. For instance, the Egyptian price sample selected by Kessler and Temin relates to the years A.D. 45-46. However, there was a famine in 45-47 as a result of the excessive inundation of 45. Temin and Kessler are aware of this but decided to use this sole piece of Egyptian evidence. Interestingly, Dominic Rathbone returned in a more recent work to this topic and opted for a wider and later period of observation, A.D. 80 – 160, which yields a median price of 9 drachmas per artaba. This price, equivalent to HS 2 per modius,[29] is 33% higher than the level used in their equation by Kessler and Temin and illustrates the high variance of the input data.

When we move from primary into secondary sources, the exercise becomes potentially even more unreliable. Although one may argue, with some justification, that Cicero (in the midst of a trial) and Polybius (because of his accuracy) are to be followed, it is quite clear that prices derived from literary sources are of a different nature from prices provided by primary materials recording real transactions.

The case of the Lusitanian price is illustrative: the relevant fragment of Polybius’s Histories has been transmitted through the later 2nd-century A.D. Alexandrian sophist Athenaeus. The price of barley is given as “1 drachma” and the price of wheat as “9 Alexandrine obols.”[30] The word “Alexandrine” is a cause of concern, since it is highly unlikely that the Achaean Polybius would have used the Ptolemaic currency, whose use was restricted to Egypt, to translate a grain price in Cisalpine Gaul while addressing an aristocratic Greco-Roman audience.

Athenaeus might have turned Polybius’s 9 (Attic) obols into 9 “Alexandrine” (Ptolemaic) obols, knowing that the Egyptian currency was at that time locally translated at par against other Hellenistic coinage.[31] In that case we have 1 medimnos = 1.5 drachma = 1.5 denarius = 6 sestertii. Then the modius is worth slightly over 1 sestertius, since 6 modii are a little over 1 medimnos. Alternatively, 9 Alexandrine (Ptolemaic) obols could be equated with 7.5 to 8 Attic obols after taking into account their lower silver content, and the modius would have been worth a figure close to HS 0.85 This is evidently the solution chosen by Rickman, since he writes “just less than 1 sesterce a modius.”[32] As such, this is the figure that Kessler and Temin use.

However, if Athenaeus is paraphrasing Polybius and using the drachma and obol of the Roman Egypt that he and his audience knew, then 9 Alexandrian obols simply means HS 1.5 in the 2nd century A.D., i.e., 3/8 denarius for a medimnos, since at that time 1 Attic drachma = 1 denarius = 4 sestertii = 4 Alexandrian drachmas. In that case, Polybius would have originally written 2.25 (Attic) obols and Athenaeus would have translated this into something more customary to his Alexandrian readers, provided he was aware of the way these different monetary systems were translated into one another. If this is correct, the price of a modius of wheat in Lusitania in the 2nd century B.C. could have been as low as HS 0.25 instead of slightly below HS 1.

But the question is still not exhausted, for when Polybius was writing, the Romans modified their currency system and the denarius was revalued from 10 asses to 16 asses in c. 141 B.C.[33] Since Polybius once approximates 1 obol with 2 asses,[34] it is quite likely that he uses the pre-141 system where the sestertius was worth not 4 asses but 2.5 asses. As the sestertius remained a quarter of a denarius, this does not change the price translation computed by Rickman. Nevertheless, it is legitimate to question whether actual prices in copper currency did not rise by 60% during the years following the moment when the value of the denarius had been adjusted upward by 60% vs. the as. This would undermine the comparative character of the prices stated by Polybius just before the monetary reform.

It is possible that the Roman authorities adjusted their bimetallic monetary system to the actual market rate of exchange between their silver and copper currency at that time.[35] The price computed by G. Rickman could thus be correct. Nevertheless, this example should remind us that ancient “numbers” are not always what they appear to be.

We must also face the issue of prices in the city of Rome. Available estimates offer quite a wide range, from HS 3 to 10 per modius. Rickman, whose work on Roman prices is Kessler and Temin’s nearly unique source, wrote: “the essence of our problem of course lies at Rome,” and “there is no evidence at all for ordinary prices of grain at Rome in the late Republic … The situation is no better for Augustus.”[36]

Indeed, we need to remember that we do not know any wheat price in Rome, and that all these “numbers” derive from scattered indications of State sponsored prices observed during unusual times between the 3rd and 1st centuries B.C., combined with the HS 2 subsidy offered by Tiberius as a reciprocity for capping prices, and the (low) price of HS 3 imposed by Nero in the aftermath of the great fire.[37] Practically speaking, the prices in Rome could have averaged HS 4 or 8 at the beginning of the Principate without modern historians having any convincing way to reduce this level of uncertainty. The closest we can get is by following Richard Duncan-Jones and reducing the price range to HS 6-8.[38] This is still a 30% margin of error and an exceptionally high degree of data instability.

Interestingly enough, the same can be said about the median wheat price in Palestine, which, according to Daniel Sperber, opposing here Heichelheim’s readings, would have been close to 1 denarius (HS 4) per modius. This is twice as high as in Egypt instead of being 50% higher.[39]

The sheer size of the uncertainties surrounding the explicative parameters then leads to even bigger dangers: data errors may be so large that different empirical findings could be supported with the same degree of likelihood.

Contemporary econometrics offer an interesting example of how a single error can significantly modify findings when data samples are small: Christina Romer, in an attempt to correlate wealth with durable goods consumption in the 20th century, was using about 30 pre-war data and a little bit under 45 post-war parameters reflecting the US stock index. The pre-war and post-war results showed significant unexplained differences. The cause of these was eventually found to be a single wrong observation within the post-war S&P 500 series.[40]

If one wrong parameter may have such an influence on a regression supported by about 40 data points, what might happen when the number of explicative parameters is reduced to 5 or 6?

Alternative relationships or absence of relationships?

To test the robustness of the model, I will use most of the parameters of Kessler and Temin, adjusting only those that seem the most clearly debatable. Notably, we will not change the Roman prices at this stage, since their level of uncertainty over the two centuries that are considered is just too wide to easily support any tighter and more relevant median estimate. It could even be argued that the average price does not matter very much, since we are aiming at a relationship between a price differential and a distance. Any shift in the Roman figure would simply translate into the constant factor of the equation, β.

What matters the most is actually whether the level of general prices in Rome did rise at all between the Late Republic and the Early Empire, since that assumption does have an influence on the actual correlation factor. Kessler and Temin assume a general rising trend that leads from HS 3.5 per modius during the 2nd century B.C. towards 5.5 in the 1st century A.D., finding some support in Rickman and Rathbone’s previous works.[41] I will not challenge that assumption here, although some caution is to be advocated. To quote Rickman: “It is possible that by the end of the Republic and the early Empire, the price of grain in Rome had risen to a regular level of 5 or even 6 sesterces a modius.” As far as Egyptian prices are concerned, Rathbone argues for broad stability between the later first century A.D. and 160. Then his argument develops further, since “even the prices attested before A.D. 50 mostly fall within the later normal band, but they may represent a lower band of prices.”

Even that cautious assumption of a rise is potentially challengeable by the uncertainties surrounding the rate of exchange between the later Ptolemaic and early Imperial Egyptian drachma and the Imperial currency. The weight of silver in the Egyptian tetradrachm dramatically dropped from Ptolemy XII until Nero, from close to 12 grams before 50 B.C. to a 3.4 grams median weight under Tiberius and 3.1 grams under Claudius, before the Neronian reform brought it down to around 2.5 grams. The one to four rate of exchange between the denarius and the drachma is actually only attested from the later 1st century A.D. onward.[42] Strictly speaking, it is thus difficult to prove that Egyptian prices converted in Roman units of value rose at all between the later Ptolemaic/early Imperial period and the 160s. We will come back to that topic.

For the sake of argument, let us nevertheless maintain the Roman price increase as assumed by Temin and Kessler. There remain three prices that they use outside Rome that need some obvious revision: those from Palestine, the Fayyum, and Antioch in Pisidia.

Equation instability with two prices’ adjustment

As previously seen, Palestine’s prices were most likely closer to HS 4 than 2-2.5 per modius. As far as Egypt is concerned, HS 1.5 seems significantly too low: a figure closer to 2 is preferable.[43] This view is reinforced by the specificity of Egyptian sources: most of the time, they are part of estate accounts, whereas literary evidence and administrative injunctions originating from other provinces of the Empire normally deal with local consumption prices. A sales margin or at least some transportation costs must have frequently separated prices measured on estates and local consumption centers.[44] Knowing actual transaction prices for wheat in Oxyrhynchus, Tebtunis or Karanis would suppress that source of heterogeneity. We have unfortunately no such evidence. Finally, in the case of Antioch, we must correct what is probably a typographical mistake in the Pisidian price used by Kessler and Temin. The prices provided by the Prefect’s edict are HS 2 and 2.25. The difference between a Roman price in a range of HS 5 to 6 and that in Pisidia should be HS 3.375 and not 3.13 (they meant 3.125).[45]

The relationship we obtain with these modified data displays a slope coefficient (β) that is -0.00044 instead of -0.001, which is not surprising since moving the Pisidian, the Egyptian and Palestine prices all closer to the Roman prices brings more horizontality to the sample of variables. This is not the worst thing yet; after all, no one would care about the slope as long as it was a statistically relevant number. What actually happens is that the R^2, which expresses the proportion of the variance explained by the equation, dramatically falls from 79% to 10%, while the T-statistics are much too low to be statistically significant.[46] That means we cannot reject the null hypothesis, i.e., the absence of any correlation at all. In simple words, distance and prices could be irrelevant to each other.

At this stage, this does not mean the relationship advocated by Kessler and Temin is necessarily wrong; rather, it is essentially unstable and highly dependent on how a handful of sources are interpreted. This is particularly true of the Judean price: multiplying it by a factor of two effectively destroys the relationship. In that respect we need to keep in mind that Sperber’s work postdates by several decades Heichelheim’s contribution to T. Frank’s ESAR and that his mastery of ancient Jewish sources goes far deeper. Since changing the Judean grain price is sufficient to potentially render the equation irrelevant, we are then exactly in the same situation we described for the post-war S&P 500, where alteration in one unique parameter could kill a numerical relationship.

It is then a true methodological weakness to write, “We assume that the prices we observe are drawn from a distribution of prices in the early Roman Empire.”[47] The reality is that some of these prices are prices, some are testimonies, but some are uncertain reconstructions, and as such may be neither random nor normative.

Thus the equation supporting a market-oriented interpretation of the Roman economy could be the product of pure luck or, worse, careful data selection. The fact that challenging a single parameter leads to entirely different results, or, we should rather say, no result at all, simply means that the equation as formulated cannot be statistically upheld.

When Distance to Rome is not a Granted Parameter

Let us now focus on the other factor: distance to Rome. The authors, aware that land and river transportation are more expensive than sea transportation, ran their equation with and without the Po valley observation.[48] The risk taken here was not big, since that variable nearly fits with the straight line, which means that its removal was unlikely to significantly alter the coefficients. What is more surprising is the way the Lusitania parameter was incorporated. The distance used by Kessler and Temin is exactly the mileage from Madrid to Rome, as can be found on an airline website. Since ancient Romans could not fly, and Madrid is not located in Portugal, it is more relevant to use sea distances instead. The shortest seaborne itinerary between the Douro River mouth and Civitavecchia accounts for 1334 nautical miles, that is 2470 km, and not 1363 km.[49] Once that fact is introduced, the price differentials are visibly no longer aligned according to distance to Rome. The equation again becomes very weak to a point of near irrelevance, even by using the original prices as selected by Kessler and Temin.

Chart 2. Distances from Rome with Lusitania amended, and price for grain

Full size image here ↗

Could landlocked areas trade?

Let’s examine another provenance of one of the sources used by Kessler and Temin: Antioch in Pisidia. This city is located in the Taurus range, at an altitude of 1200 m. (4000 ft.) and is separated from the sea by 200 kilometers of a hilly road, including a couple of steep climbs.[50] Using a ratio of 1: 25 for relative sea: land transport costs,[51] we would translate these 200 km into the equivalent of 5000 km, next to which the 1700 km or so of sea distance would be a minor factor.

Map 1. Antioch in Pisidia – Attaleia road. The map is copyright of the Pelagios Project and published under a Creative Commons Attribution 3.0 license (About).

Full size image here ↗

Reinforcing the view that Pisidian Antioch could not have been fully connected to the Mediterranean sea web is the fact the governor dealing with the grain shortage during the reign of Domitian (from which this figure derives) did not contemplate the possibility of any external help.[52] Similarly, when Dio of Prusa had to defend himself in times of grain scarcity, he claimed that the prices then experienced by the citizens of Prusa were equivalent to the lowest prices of some other towns in the region.[53] Later on, Gregory of Nazianzus writes that it was impossible to import wheat to Caesarea in Cappadocia during a shortage because of high transportation costs.[54] The evidence converges on the fact that little to no price arbitration could have occurred in these landlocked areas, explaining why discrepancies between prices remained in continental provinces like Asia or Hispania.[55] High land transportation costs are certainly the main factors behind the fact that imported pottery sherds are rarely found far from coastal or fluvial areas, although this does not mean either no grain trade at all could occur.[56]

If we now adjust the distance between Antioch and Rome to 6700 km,[57] with all remaining original data being left unchanged (Chart 3), the new equation is still quite irrelevant, with a much lower slope and a very weak R^2 and T-statistics: -0.00015 and 15% instead of -0.001 and 79%.

The following table summarizes the very weak econometric results obtained by adjusting these parameters:

Table 2. Modified econometrics after addressing the most visible data issues

Scenario

Number of parameters

β

α

R^2

Nearly doubling Palestine price from HS 2.25 to 4, moving Egyptian price from HS 1.5 to 2, correcting the price differential in Antioch to HS - 3.375 from – 3.125.

6

-0.00044 (-0.67)

-1.87 (-1.72)

10%

Correcting Lusitania distance, taking into account land distance for Antioch.

6

-0.00021 (-1.18)

-2.02 (-3.51)

26%

Chart 3. Distances from Rome with Lusitania and Asia Minor amended, and price for grain

Full size image here ↗

Interim Conclusion

It could be argued that our demonstration is here circular, in the sense that we modify the parameters we know are the most likely to destroy the relationship. The reality is that the price to distance relationship is just too sensitive to any parametric mistake because there are so few observations. A high degree of caution and care is thus paramount in such a methodological approach. To assume that the ancients could fly from Madrid to Rome is simply the most obvious of a number of unfounded presuppositions that can entirely undermine the conclusions.

A minimal sense of rigor should then lead to the deletion of the Antioch price with a lot more justification than for the Po valley parameter, since we have as much uncertainty regarding the relative sea to land transport costs as we have for the sea to river ratio.[58] We could even go further and state that the clear absence of long distance wheat trade overland in continental Asia Minor means that any relationship between local and outside prices is simply irrelevant, or rather dependent on local agricultural conditions.[59] Then we are left with a set of 4 data points, which is really too limited to be able to draw any sort of statistically robust conclusion.

This is not to say prices in Rome were not generally higher than prices outside Rome. We have numerous ancient literary statements about the high cost of living in Rome. But the linearity suggested by David Kessler and Peter Temin in order to prove not only that Roman prices were high, but also that the Roman Mediterranean market was globally integrated, cannot be accepted on the basis of their simulations. We need more observations.

Let us travel forward in time towards early modern France in order to illustrate the potential weakness of a simple centered integration hypothesis in an economy d’Ancien Régime.

The Imperfect Pre-modern French Grain Market

France and England have preserved extensive records of grain prices through multiple sources, mostly in the form of records from municipalities and royal officials. Starting in the 16th century, the mercuriales, official records of real transactions that occurred in the marketplace, started to be compiled in France.[60] Until the end of the 18th century, they consistently display high seasonal and inter-annual variability in the same location and large discrepancies between locations relatively close to one another during the same period. The available data have to be treated with many precautions: units of measurements, even with the same name, were different from one region to another; the composition of the grain differed as well; and sometimes the exact moment at which prices were recorded is missing.

Chart 4 shows wheat prices measured for three different years in 31 different French cities:[61]

Chart 4.

Full size image here ↗

Paris represents the two last observations. There is some geographic consistency across time: the peaks occur in Provence and in the Alpine region. Paris is very close to the average price for each single year. Grain does not seem to travel from one region to another to take advantage of price gaps, since significant differences are witnessed even between very close locations inside the same regions.[62]

Public purchases manage to alleviate some of the most serious crises, especially in Paris, but are rarely effective in smothering prices on a more regular basis. Between the moment wheat is bought, sometimes from distant locations like Poland, and its arrival, the crisis is normally over and the arrival of fresh wheat has the opposite impact of depressing prices further as local supply has been restored. This happens in 1749 in Charolais, where one year after a serious shortage, local farmers are banned from selling their new grain because of the oversupply resulting from the previous year’s orders.[63]

Many cities try to store grain, but it does not seem very successful in reducing price instability either. In Strasbourg, where between half and three-quarters of the annual consumption needs are kept in storage, prices fluctuate as much as anywhere else. In 1633, Strasbourg’s granaries still include wheat officially dating from 1591, 1525 and even 1439. No doubt this is no longer consumable and points to serious shortcomings in granaries management.[64] Price controls do not work any better: as La Rochelle tries to cap the prices at which Dutch merchants may sell their products, the market simply dries up, as in Antioch a millennium before under Julian. When city councils impose maximum prices on bakers, this leads invariably to more black market transactions.

Interestingly, larger consumer centers are not necessarily at a disadvantage: what matters is the accessibility of additional supplies beyond local production and regular imports to match demand. In that respect, Paris is remarkably privileged, located on a large navigable river at less than 300 km from the sea coast: “A Paris, il venait du grain de partout, jusque de Naples et de Sicile.”[65] The city is more accessible from the Low Countries than from Central or South-Eastern France. As the French economist Adolphe Blanqui noted in 1843, “the villages of Castellane (in the Southern Alps region) were farther away from French influence than the Marquises Islands in French Polynesia. Communications are neither easy nor difficult: they don’t exist.”[66] As such, isolated regions may experience consistently high prices if local productivity is poor, as is the case for most of the southern half of France.

Eventually, discrepancies between regions seem to progressively diminish on average as we progress through the 18th century. A better transportation network from the 1720s onward,[67] higher productivity, and increased population mobility allow a better resource allocation, well before steam boats and railways will dramatically impact these markets by opening new and more distant sources of supply outside of Europe.

In any case, no integrated market hypothesis can be tested successfully before the end of the century. One may argue with some reason that pre-modern France is a poor candidate for testing market efficiency: it has the most continental landmass of Western Europe; few of its rivers are easily navigable; and most do not connect the different regions together. The provinces maintained their own local fiscal system for a long time, adding tolls and duties and effectively discouraging inter-regional trade.

Local excise taxes were the normal practice in the Roman Empire, and even if some of its main coastal cities might have been geographically comparable to the maritime towns of North Western Europe and North America in the 18th and 19th centuries, where price synchronization became progressively a dominant feature,[68] we must not forget that many cities of the Empire were located inland.

What the French example proves is that trying to correlate prices in pre-modern economies can lead tounexpected results. If higher prices serve to locate the French capital, then Louis XIV would have been ruling France from the backwater Alpine valleys or Provence. The French evidence shows that high prices are not necessarily the privilege of a metropolis and could develop as a result of insufficient local supply in areas with limited production and communication capacities.

Markets, Geographic Barriers and State Intervention in the Roman World

Free integrated and efficient markets suppose an absence of significant barriers, whether geographic or institutional. Let us examine some of the patterns displayed by the Roman Empire.

Geographical barriers

In the Roman world, long distance trade is widely attested, as documented by the papyrus and literary evidence dealing with the Indian market, the presence of a Tyrian colony in Puteoli, of Syrians in Gaul and Asians in Italy, or legal writing dealing for instance with the cash settlement of Beirut to Brindisi trade.[69] The finding of similar ceramic types originating from specific regions all around the Mediterranean is still today the most visible witness of that network of merchants that linked together the ancient Roman world.[70]

Whether long-distance trade would have been an efficient market is a highly disputed issue among historians. Gary Reger’s works on Delian prices led him to the conclusion that prices reported at Delos during the Hellenistic period were significantly higher than in Athens, which was doubtless a more important center of consumers. At the same time, prices of different goods like grain, oil, perfume, pitch, and papyrus seem to have followed rather different patterns, building a case against a globally integrated market in the Hellenistic Aegean world: “This result supports the argument that the modernist reconstruction of the operation of a general Greek price-setting market in the early Hellenistic period is indeed mistaken.”[71]

This does not necessarily matter very much, since Delos was a tiny island whose importance grew to a disproportionate level only when Rome decided to punish Rhodes after Pydna in 168 B.C., making it very comparable in a way to modern Singapore or Hong Kong, whose success relies heavily on specific geopolitical conditions and privileges. Similarly, diverging price-series do not necessarily mean inefficient markets: each product depends on its own supply and demand structure, whether yesterday or today. Between March 2010 and March 2011, the main commodity price indices soared by 30%. This did not prevent wheat from rising 67% and even 80% at one point, while cocoa gained only 10% and US crude oil 18%. Moreover, the conclusion that Delos’ wheat prices were in fact that high has been carefully challenged by Joshua Sosin, who concluded that a range of 4 to 7 drachmas per medimnos was certainly proper, hence dividing Gary Reger’s prices by a factor of nearly two and setting them in line with prices in Athens.[72]

When focusing on more local trade, it has been argued that Egypt was most likely a relatively integrated market.[73] Nevertheless, price discrepancies seem to exist between regions close to one another, despite the easy connections offered by the Nile.[74] This could be the result of transportation costs and custom dues, although most trading relationships at Oxyrhynchus, for example, occurred within a short radius of about 200 km around the city, with the exception of trade with Alexandria.[75] Still seasonal prices did not move synchronically from one place to another, failing to show comparable patterns between locations separated by only a few dozens of kilometers of Nile navigation. In that respect, Peter Bang’s comparative study of Egyptian prices illustrates the limits of integration, even for neighboring wheat markets.[76]

In inland areas, grain trading by road rarely exceeded distances of 100 km in early modern Europe, and this must have been mostly the case for the ancient world.[77] Maybe prices were quite similar across Sicily, but this was not the case within Asia or Spain.[78] When local grain markets existed, they seem to have involved producers and consumers rather than professional traders. Cicero does not speak about traders in Sicily, and the only two price-series we possess for 1st-century A.D. Egypt show the average price achieved by some producers to be higher than that paid by consumers, leaving little room for trade-related profit.[79] Evidence for traders is scarce outside of urban environments. Nevertheless, as pointed out by Dominic Rathbone, our prices “relate almost entirely to sales in the countryside at or very near to the point of production,” and “our evidence patently under-represents large-scale transactions and the urban retail market”;[80] “corn dealers existed in Egypt.”[81]

Geographical barriers would explain why consistent regional price differences are recognized by the legal literature (Dig. 13.3.4; 13.4.3; 35.2.63.2). Isolated inland areas such as those around Pisidian Antioch, Bithynian Prusa, or Cappadocian Caesarea would have been structurally excluded from any sort of non-local market activity.

The availability of local surpluses

Moreover, another local factor is at play: comparing prices in various locations with those of the main consumer center (Rome) not only supposes that moving goods from one another is materially and financially possible, but also that exchangeable surpluses are always available, since prices in Rome are the determinant overall reference. If we now assume that some areas’ grain carrying capacity was inferior to the needs of their population, linking them all to one unique natural final consumer market like Rome would not reflect the reality on the ground, since more than one location would have been a net grain importer. This could easily explain why prices in Palestine are as high as in some Italian cities: the fact is that both locations might have been purchasing what they needed in grain from the same provider, i.e., Egypt. Then they can no longer be aligned with Rome, since what matters is not the distance to Rome but the distance from Egypt.

This can be easily plotted on a simplified simulation, where P are the Egyptian producers’ prices, M is the constant factor in the margin taken by the merchants exporting Egyptian grain, L is the unit linear cost of transportation by sea plus some proportional sales margin, Pj is the average selling price in Judaea, Pp in Pompeii for instance, D(E-P) the Egypt – Pompeii distance, D(E-J) the Egypt –Judaea distance,

Then we should have:

Pp = P + M + L x D(E-P) and Pj = P + M + L x D(E-J)

Implying:

Pp – Pj = L x (D(E-P) - D(E-J) ).

If prices in Pompeii and Judea were to be related to their distance to Rome, the following relationship would apply as per Kessler and Temin’s initial equations, where Pr is the Roman price, D(R-P) the distance between Rome and Pompeii and D(R-J) the distance between Rome and Judaea:

(Pp – Pr) = α x D(R-P) + β and (Pj– Pr) = α x D(R-J) + β

Then:

Pp – Pj = α x ( D(R-P) - D(R-J) ).

α is obviously equivalent to the linear distance cost factor of Kessler and Temin, with a negative sign since they work with negative numbers by subtracting the Roman price from provincial prices. Then α = - L.

We would get:

( D(R-P) - D(R-J) ) = - ( D(E-P) - D(E-J) ) or ( D(E-P) - D(E-J) ) = ( D(R-J) - D(R-P) ).

The only way such a relationship can be systematically satisfied is if Rome, Pompeii, Judea, and Egypt are situated on the same linear path, since both factors would then equate to D(P-J). If one of them is not, we are dealing with a triangle that has no reason whatsoever to satisfy that relationship, as the following chart shows:

Full size image here ↗

In essence, the assumption that some regions are net importers of grain, competing at a more modest level against Rome as a consumption center, while not being geographically aligned, implies a multipolar set of linear relationships (effectively a matricial system) that cannot mathematically lead to one single linear relationship linking all these provinces together.[82]

Institutional interventions

It would be absurd to minimize the role of merchants and of markets as the normal medium of exchange and of price determination.[83] Even the Emperors had to deal with them to achieve their political aims.[84] If the authorities were monitoring prices, as papyri from Egypt suggest was the case until the very end of the Roman Empire,[85] “there is not one scrap of evidence to suggest that it (this monitoring) was used to intervene systematically in the market-place to compel a given level of price.”[86] We know about the alimentary schemes and official attempts at dealing with shortage situations, but they remained essentially a corrective mechanism offered to more or less willing market participants or landowners.[87] As far as free food distributions to a body of registered citizens, it neither constituted the rule across the Empire [88] nor implied some overall control over prices, since a moderate proportion of the overall tributary grain would have been enough to provide the requested allocation to less than 200,000 citizens of Rome.[89] The Roman authorities’ isolated attempts to regulate prices ended in failures.[90] Sea merchants were so prevalent in the Roman Mediterranean that the Emperor Julian’s rhetoric goes as far as offering to a friend a property distant from the sea in order to escape from their constant solicitations![91]

Nevertheless, institutional interventions brought obvious distortions to trade: beyond customs dues, euergetism, alimenta, and State-engineered purchases, the Roman tribute and distributive schemes must have affected production and consumption patterns in both the originating and final destination areas.

Rome was able to extract wealth by way of moving cash or commodities from the provinces. These two procedures would lead to opposite impacts on prices at both ends of the tributary chain: levying cash meant locals had to sell their surpluses, possibly pushing production higher, eventually removing cash from the local monetary circuit and depressing prices. The cash accumulated in Rome would locally increase the supply of money, pushing prices higher and providing an incentive for traders to bring there cheaper goods purchased in the provinces. Epigraphic and literary evidence points to cash levies in various areas of the Greek East: in Messenia, Cilicia and Syria with a 1% tax levy in cash, or in Asia proper when taxation proceeds in kind were locally sold and the money obtained this way possibly sent to Rome.[92]

The opposite process involves grain levies being transported to Rome. This seems to have been occurring in Asia during the Late Republic, since publicans received custom exemptions for the transportation of the tithe to Rome.[93] Cicero in late Republican Sicily describes wheat levies as well. In Egypt and later in Africa, part of the grain tribute was shipped to Rome. Grain tributes are attested at various points in Roman history in Bithynia, Phrygia, Thrace, Pannonia, and Judea, while there is no strict evidence that Sicily, Sardinia, or Spain ever translated grain into a monetary tax as a matter of rule. The main grain tax, the Egyptian tribute, “can hardly have been much less than 25 or 30 million modii in most years.”[94]

The consequence for prices is then exactly opposite: as grain is removed from the local markets, reducing its supply, provincial prices have to increase, all else being equal. At the level of the individual farmer, levying between 10 and 20% of gross production might have represented most of his available surplus, exhausting his capacity to sell grain. One might argue that Hellenistic kings and Gallic nobles may have extracted from their land as much if not more than Rome did.[95] But the difference after the Roman conquest is that a high proportion of that tribute was shipped abroad, reducing the local supplies. As most cities in provincial Roman territories grew in size, pressure to increase grain production must have been widespread and sometimes massive. Even if technological progress occurred, more marginal lands were necessarily brought under cultivation under the stimulus of higher demand, and the overall impact of the conquest must have pushed both provincial production and price levels higher.

In Rome proper, inflows of tax grain should have lowered local prices. A proportion of the wheat was simply offered to some categories of the resident population, and the market demand will have been reduced as a result. Levying and transporting tribute in kind to Rome must then have reduced the price differential between the provinces and Rome.

Sirks argued that the free distributions might not have represented more than 15% of the needs in Rome.[96] But the arrival of Egyptian, African, and Sicilian tributary wheat not only translated in terms of free grain to some segments of the population: it introduced unpaid supply through the market distribution chain.[97] In Rome, prices will then normally have been pushed lower, since the supply vs. demand equilibrium will have been shifted by the arrival on the local market of levied wheat that might not have been produced and transported to Rome at those market prices if only profit-seeking farmers and merchants had been involved.

Richard Duncan-Jones’ rather maximalist gross Egyptian wheat tax figure of close to 80 million modii would have been sufficient to feed one million people.[98] Whatever losses might have occurred between local usage, transport, and storage, adding the other sources of tax wheat like Africa and Sicily implies that grain belonging to the Roman authorities would have been able to feed the entire needs of the city, effectively evicting long distance private wheat trade from the Roman market if the authorities had been able or willing to directly take over the logistics of feeding the capital.

The existence of a structural excess in grain supply at Rome has been challenged on the basis of the frequency of grain crises in the city. There is no real contradiction here. First of all, the higher purchasing power of the Romans combined with imports of cheap staples from the provinces must have encouraged Italian farmers and landowners close enough to Rome to substitute higher margin cash crops for grain.[99] As a result, Rome became more dependent on navigation conditions. At the same time, cheap or free public grain must have helped Rome to attract more population inflows from rural areas, while the end of the conquests reduced the military attrition rate.[100] A significant number of veterans also returned to Italy in general and Rome in particular, while many slaves were imported into the city, pushing higher the overall population.[101] Grain distributions had such an impact that owners freed their slaves in order to transfer the burden of feeding them to the authorities.[102]

Moreover, one should note that in a pre-modern economy there is no contradiction between generally abundant grain supplies and the repetition of difficult years. Poor harvests, navigation conditions, and finally the great fire of 64 could explain the crises of 23 and 22 B.C. and A.D. 5, 18, 19, 32, 51 and 64.[103] Crises seem to become rare in subsequent years, maybe as a result of the huge investments undertaken in the harbor facilities of Rome by Claudius and Nero.[104] Nero was able to reassure the Roman population by destroying some of the surplus wheat accumulated in the Imperial warehouses, while Trajan was in a position to reduce the amount of wheat necessary to be shipped to the capital, a sign that these efforts eventually paid off.[105]

All this being said, one should not overestimate the role of taxation in supplying Rome. As Jean-Michel Carrié writes: “le blé fiscal n’avait pas vocation à satisfaire la demande alimentaire de l’ensemble de la population de la capitale, mais seulement à couvrir les besoins de l’annone civique(… )”[106]

The reality is that we are not told how the authorities disposed of the tax grain levied in the provinces that was surplus to the needs of the free annona of Rome and military supplies. From the price-related measures taken during the 1st century crises by Tiberius or Nero, it is unlikely that the Imperial authorities would have been selling grain directly to the final consumers or to the bakeries, otherwise the natural course of action would have been to fix an administrative price. The emperors had to interact with merchants to alleviate food crises while not harming farmers’ and merchants’ interests.[107] Similarly, the incentives provided by Claudius and Nero to those who transported grain to Rome were directed at negotiatores.[108] As Rickman writes: “The constant stress in the literary sources of the early Empire on the importance of the corn merchants makes it likely that, ‘state corn’ or not, both the transport and the marketing of grain was very much in private hands.”[109]

We have already noted how Egyptian grain could end in private hands at Puteoli, although we cannot know if this grain originated from the tax proceeds or not. The inherent weakness of the early Imperial bureaucracy compounded with these observations support the view that the proportion of the tax grain that was not given out for free or stored in the imperial warehouses was sold upstream in the distribution chain. This sale could even have taken place in Alexandria itself to agents or associates of Roman-based merchants, the cash being collected by the authorities in Rome, since the Egyptian currency had a lower metallic value. This would have been very similar to the way the socii farming the Asian tribute under the late Republic had to bid and settle their financial commitment in Rome while levying, transporting, and selling the tax wheat themselves.[110]

When wheat was not needed, the authorities could resort to adaeratio, i.e., levying cash instead of wheat, thereby avoiding the burden of levying, storing, and selling grain. The translation into cash would have had to take place at more or less market prices, as recorded once in 1st century A.D. Asia.[111] This is why in the time of Cicero a market price measured in Ephesus could be used by taxpayers who wished to convert their tribute into cash instead of bearing transport costs to the coastal city.[112] Even if, in essence, we are not dealing with free market processes regarding tax grain, the coexistence of different processes adapted to local conditions involving some type of private transactions or at least the use of local market prices at one stage or another is quite obvious.[113] In Egypt proper, the frequent purchases of wheat at fixed prices close to market prices introduced a market component in the cost factor of the wheat shipped to Rome, even if that grain was to remain public until being sold or offered at destination.[114]

The combination of poorly staffed bureaucracy, a high degree of autonomy for provincial authorities, difficult long distance communications, and the involvement of private merchants must then have maintained a degree of relevance for market mechanisms inside the tributary process itself, even if distorted.

Tax privileges

One final exogenous phenomenon has to be accounted for: by providing privileges to merchants involved with bringing grain into Rome, the Imperial authorities were altering their profit function and in consequence the market equilibrium. It is rather difficult to monetize the incentive represented by the bequest of the Roman citizenship or the exemption from the lex Papia Poppaea.[115] But the measure taken by Nero in A.D. 58 is more numerical: the ship of a negotiator was to be deducted from one’s patrimony for tribute assessment purposes, provided he was supplying Rome with grain.[116]

Assuming an average carrying capacity of between 10,000 and 20,000 modii of grain, Rathbone’s calculations based on the Rhodian Sea Law of the 7th century A.D. and different papyri reflecting rental and lease/sales costs suggest that such ships would have cost circa HS 90,000-100,000 to build.[117] This is nearly twice the value of their wheat cargo. If we assume a typical rate of tax extraction during the Principate of 1% of property values,[118] tribute exemption would have increased the profit margin by about 2% of the cargo value. Maybe more important was exempting from public munera those who built ships of more than 50,000 modii of capacity – or enough smaller ships of 10,000 modii to reach the same mark, as expressed by Scaevola in Dig. 50.5.3. Unsurprisingly, people were trying to get these exemptions fraudulently.[119]

These privileges could have contributed to mitigate the cost of ships bound to Rome with grain and oil possibly returning home empty, according to the city of Rome’s capacity to export or, better, to the other commercial opportunities offered by Africa.[120] At the same time, we are not necessarily dealing with an organized corporation of tributary grain carriers, but with a more nebulous group of ship owners and merchants who were simply carrying grain to supply the Roman people as one possible activity among others. What the authorities were doing was simply to provide an additional incentive to grain merchants and ship owners going to Rome for their private business in order to avoid disruptions and excessive price instability, reinforcing the view that a significant proportion of the tax grain might have actually been sold before being shipped to Rome. [121]

It is unrealistic to suppose that these exemptions were only addressing the free distributed public grain. How could transportation costs of state-owned grain have been covered by the simple exemption of the tribute on the value of a ship? Even if we don’t have any actual payment receipt, the ship owners carrying the grain belonging to the State had to be directly compensated, by bidding for transportation contracts through auctions, as described by Columella.[122]

The aim of these exemptions was then to provide grain merchants involved with the trade to Rome of private grain with an additional incentive on top of their existing profit margin in order to decrease the probability of a grain shortage, while the public Treasury only paid the free public grain transportation costs. We are dealing with two different compensation processes, most likely directed at the same type of intermediaries.[123]

What we obtain, therefore, is a rather mixed picture, where geographic isolation, grain deficit in some areas, and a degree of public intervention that varied were interfering with market mechanisms. These factors must bring additional caution when dealing with ancient prices and their relevance to market mechanisms, although it is certainly excessive to consider that bureaucratic involvement moved effective prices very far from their natural equilibrium levels. Roman authorities tended to use traders rather than regulate them.

At this stage, we are able to revert to data testing. Adding new information while taking into account the different hurdles we have identified may lead to a more comprehensive picture.

Towards the use of More Prices

“Perhaps our analysis of these few prices will stimulate other historians to find more price pairs and to provide more evidence for or against our hypothesis.”[124]

Indeed.

We have five inscriptions from Pompeii that bear on wheat prices. One of them clearly states a price of 30 asses per modius of triticum.[125] Another is open to some uncertainty as far as its reading is concerned and seems to lead towards a figure of 12 asses per modius of frumentum.[126] Two others imply a daily bread ration for slaves of 2 asses. A last graffito provides a direct price of bread, 1.5 asses per pound.[127] The key problem is to relate weight denominated bread prices to volumetric grain prices in order to be able to use 3 of these 5 numerical indications.

In a 2001 work, Robert Allen ran a correlation test between skilled wages, grain volumetric prices, and bread prices in 10 cities of pre-modern Europe. A formula was found, linking these prices together when denominated in grams of silver per unit according to the following formula: BREAD = 0.063 + 1.226 GRAIN + 0.017 WAGE (per day).[128]

He applied his findings to Diocletianic prices, disregarding some major issues.[129] We know that according to the quality of the final product, extraction rates between grain and flour can differ by a wide margin. Romans did produce breads of very different qualities, and there is no guaranteed homogeneity between their practice and that of modern Europeans.[130] Another problem is to assume that Diocletianic prices are to be taken at face value: anyone studying the period knows that they were designed to undervalue the price of precious metals that were collected by the authorities through the compulsory reimbursed official purchases of gold and silver.[131] Furthermore Allen’s equations include specific factors linked to each individual modern European city. These variables have a significant bearing on the results, and since no such correlation test could be run for ancient Rome due to a lack of data, any straight projection without this factor towards Antiquity creates a major level of uncertainty. Last but not least, Allen assumes an overall similarity of individuals’ relative budget structure between food, rents, clothing, and tax from Antiquity to early modern Europe that is far from certain.

These shortcomings can easily be demonstrated by applying the general formula to 1st century A.D. Pompeii. We know for a fact that on at least one occasion a pound of bread cost 1.5 asses. After the Neronian reform, where 1 denarius contains about 2.8 grams of silver,[132] this is equivalent to 0.26 g. of silver per Roman pound or 0.81 g. of silver per kilo of bread. If we use as a proxy for the salary of a skilled worker the salary of a legionary before the reform of Domitian, i.e., 225 denarii per year, the daily wage in silver terms would be about 2.1 g. assuming 300 workdays. Multiplying that factor by 0.017 as per Allen’s suggested equation provides us with a wage factor of 0.035. To this we have to add the constant factor, that is 0.063, to obtain 0.099. We just calculated the bread price per kilo to be 0.81 g. Therefore, the wage factor represents slightly over 4% and the constant factor nearly 8%, implying the sole grain component of the final bread price to be 88%, which is certainly too high. The implied result is 2.2 denarii per modius, i.e., HS 8.8, which is very high for a median price in Pompeii, 17% higher than the highest available price of CIL IV 4811 and more than twice CIL IV 1858.

In order to relate the cost of daily bread to a grain price, a more traditional approach is to approximate the rate of extraction between grain and flour and then the gross relationship between bread and flour prices. This is how Mrozek finds that HS 4 a modius would be a maximum for Pompeii from a daily ration of bread stated at 2 asses, assuming that a slave would consume at least 1 kilogram of wheat in the form of bread.[133]

Mrozek does not state the basis of his calculation. It is most likely the work of Moritz.[134] Moritz carefully reviewed Jasny’s previous calculations derived from Pliny’s statements on bread, flour, and wheat weights and extraction rates as well as Pliny’s inconsistencies.[135] He eventually used a grain to flour extraction rate close to 60% in order to produce high quality commercial white bread. With bread weighing about 35% more than the flour used in baking it since it absorbs water, one kilo of grain would produce about 800 g. of white bread. Using a daily bread ration of c. 800 g. priced at 2 asses, the kilo of grain would cost at most 2 asses, since bread incorporates some work factor. Assuming that 1 modius weighs approximately 6.74 kilos,[136] we obtain a modius priced at most at HS 3.4, while Mrozek claimed HS 4.

This said, no one knows exactly the quantity of bread included in the daily slaves’ ration in Pompeii. Mrozek’s figure of c. 1 kilo of wheat is certainly based on Cato’s slaves’ monthly rations set at 4 to 4.5 modii a month for those who work in the fields.[137] This is nearly 1 kilo of wheat a day. Now Cato was only providing 3 modii a month to his higher-end slaves not involved with the hard outdoor labor. This leads to about 675 grams of wheat a day. We should assume that urban slaves in Pompeii were closer to that diet, and that they were not more poorly fed than field workers, but that their diet was certainly more diversified and pleasant. Modern studies on ancient nutrition assume daily bread requirements of c. 500-660 g. a day,[138] implying a daily grain ration of c. 700-800 g. if we assume a 1:0.8 weight relationship between grain and white bread.[139]

If the median daily bread ration’s weight was c. 600 g. instead of 800 g., with c. 750 g. of grain being used instead of 1 kilo, since we know that the price of the daily bread ration could be 2 asses for a slave, decreasing the bread component for the same set price would push all implied maximum grain prices up by 33%. We would obtain a wheat price below HS 4.5 instead of 3.4 in Pompeii.

The next uncertainty lies with the quality of the bread provided to slaves. A 60% extraction ratio between bread and flour implies multiple grinding to obtain white bread and must have been reserved for high-end consumers.[140]

Pliny states that military bread weighed one-third more than grain and that a modius of Balearic wheat allowed the production of 35 pounds of military bread, while all the other figures provided by Pliny are between 20 and 25 pounds per modius. Even if that 35 pounds figure is corrupt, it is clear that soldiers (and thus slaves) must have received some kind of whole wheat bread processed through a single grinding with a higher extraction rate from wheat and thus bearing a higher weight than white bread would have for the same quantity of wheat. Moritz, carefully reviewing Pliny’s figures and comparing them to more modern experiments, concludes that a flour extraction rate of 90% is likely. Thus the weight of whole wheat bread would have exceeded its incorporated wheat’s weight by about 25% instead of being lighter.[141] This is broadly consistent with Cato the Elder providing 4 to 5 pounds of bread a day to his chain gang slaves, which is about 30 to 50% heavier than the bread extracted from the 4 to 4.5 modii of grain given to the other slaves working in the fields. If it seems clear that chained slaves digging in the vineyards needed more food than any other slave, a large proportion of that difference in weight must then derive from the low quality of the bread, heavier than the grain used to produce it.[142]

If a lower c. 600 g. of daily bread ration of Pompeian urban slaves incorporates only 500 g. of wheat, for instance, for whole wheat bread instead of the c. 800 g. of the white wheat bread, a price of 2 asses per day for the bread ration would lead to a maximum wheat price of HS 6.75 instead of 4.5. The range would be HS 4.5 to 6.75 before incorporating any processing costs. Using a level close to 15% for the labor and profit factors would lead to a range of about HS 3.9 to 5.9 a modius with a median of HS 4.9.[143]

Finally, we have to deal with the bread price of 1.5 asses per pound in CIL IV 4227. It can only produce a range as far as wheat price is concerned, since there is no way to determine the quality of that bread. Since one pound of bread could have incorporated as little as 0.8 pound of wheat, if whole wheat bread, and as much as 1.25 pounds of grain for high quality white bread, the implied grain price range is HS 5.3 to 8.3 after incorporating a wage and margin component of 15%.[144] In case we are dealing with white bread, the implied price would no longer be “plutôt élevé.”[145] This scenario seems likely, since a price over HS 8 in Pompeii would be quite high indeed.

The average of all the Pompeian prices of HS 3, 7.5, 4.9 and 5.3 per modius works out to be slightly above HS 5.

A daily ration of bread at 2 asses is also to be found for the cost of the bread allocated per person in a collegium at Lanuvium, 24 km south of Rome.[146] It is here unlikely that whole wheat bread is concerned. Rather the higher grain to bread ratio used for white bread would lead to a lower grain price close to HS 4.3, implying a price range of c. HS 4 to 5 per modius in Campania and Latium.

An early 2nd-century A.D. inscription from Forum Sempronii shows wheat provided by a benefactor at a price of HS 4 in time of crisis, which could be considered as standard in assuming subsidized prices under crises to be close to prices under normal conditions.[147]

Under Nerva and Trajan, alimentary schemes operated in many Italian cities: a monthly allocation of cash provided by participating landowners who had received Imperial grants was devoted to the subsistence costs of young boys and girls. Duncan-Jones assumes that three-quarters of that amount would have been used to buy 3 modii of wheat for legitimate boys, and thus relates the HS 16 a month tariff in Veleia to a modius priced at HS 4.[148] There are several issues with that approach. Children were not fed with wheat, but bread. With a daily bread ration set at 600 g., provided under the form of white bread, with bread occupying about two-thirds of the monthly budget with processing costs of 20%, we obtain c. HS 3.6 per modius instead.[149] Eventually, one may argue that using a monthly budget incorporating an unknown proportion of bread simply leads to such a wide range of possible outcomes that the indications provided by the alimenta are useless. We will still use them as an indication of a range, knowing that as such they should play a reduced role in any simulation.

In Terracina, in Latium, 137 km south of Rome, the alimentary scheme monthly rate was HS 20. This would lead to a modius “price” close to HS 4.5 and confirm that areas close to Rome in Latium and Campania would have witnessed higher average prices than in more backwater parts of Italy.[150]

As far as non-Italian prices are concerned, we have another potential parameter, coming from Duncan-Jones’s observation that in late 2nd century A.D. Africa, at Sicca Veneria, the alimentary scheme rates for boys and girls are between 62.5 and 66.7% of the Veleia equivalent levels. Assuming broad proportionality, the wheat price would have been close to HS 2.4.[151]

More thoughts on Roman Prices and Trends

Now that we have at least defined likely ranges for a certain number of additional wheat prices outside Rome, it is time to bring some last adjustments to the data assumed by Kessler and Temin and revert to the question of the prices in Rome proper. This is all the more important as what we need are not prices but price differentials with Rome.

Kessler and Temin have used a chronologically linear scenario, with a price increase from HS 3 to 4 in the 2nd century B.C. to HS 5 to 6 in the 1st century A.D.[152]

We will start with the 1st century A.D., since this is where some indications are available from ancient literature. Besides the low price of HS 3 briefly imposed by Nero after the great fire of A.D. 64, we do have selected indirect information regarding wheat prices during that period. There is one attested bread allocation for a 1st century A.D. Roman collegium at 3 asses.[153] Comparing it to the collegium of Lanuvium and using a simple proportionality relationship would imply a price of HS 6.5 per modius, This is somewhat higher than the HS 5 to 6 range assumed by Kessler and Temin for the 1st century A.D., although still in the likely variability range of ancient wheat prices.

The next indication is provided by Pliny’s prices for flour, between 40 and 80 asses per modius. Using the price of similago at 48 asses as the main type of flour used for processing the common bread, various authors have worked out a HS 6 to 8 range per modius of grain in Rome.[154]

By analogy with the doubling in volumetric prices between raw and milled millet provided by the Price Edict of Diocletian, Duncan-Jones assumes that grain volumetric prices must be about 50% of flour prices. This is how he is able to reduce the HS 8 per modius cost computed by Jasny into HS 6 for Rome proper from Pliny’s flour price indications.

Using millet as a parallel to wheat is not justified: its flour extraction rate is lower, since millet is a husked grain and not wheat .[155] Even if Jasny’s computations may need some refinement, it is extremely difficult not to share his view that a volumetric price of HS 12 per modius of flour implies a volumetric price of wheat that can’t be much lower than HS 10 a modius.[156] We will therefore adjust upward the median level of 5.5 used by Kessler and Temin towards a more likely HS 7 per modius that could still be conservative.

The next step lies with the grain prices in Rome during the Late Republic. Since we have no direct evidence in Rome proper for that period, it is worth exploring whether or not some general rise in prices would have occurred between the Late Republic and the Early Empire.

Once more, Egypt provides some clues. In the later Ptolemaic period before the final debasements of the second half of the 1st century B.C., one tetradrachm purchased between 1 and 1.5 artabas of wheat and included about 12.6 g. of silver.[157] After the reform of Nero, the Egyptian tetradrachm’s silver weight was about 2.5 g.[158] and the artaba was worth about 8 drachmas. Thus 1 g. of silver purchased 0.1 artaba under Ptolemy XII Auletes and 0.2 under Nero. Even if this may be essentially the consequence of the debasement of the Egyptian coinage between Tiberius and Nero, pushing the local purchasing power of silver artificially higher as a result, the Egyptian evidence does not point towards a general inflationary situation in the Mediterranean world between the later 1st century B.C. and the 1st century A.D.

According to a literary source dealing most probably with Spain, 4 asses seem a standard (and low) customary price for a modius of wheat for some inland isolated areas at the end of the 1st century A.D.[159] This is close to the price possibly provided by Polybius for Lusitania more than two centuries before.[160] With Egypt, this would be a second example of overall price stability, this time between the end of the 2nd century B.C. and the 1st century A.D. This does not prove anything for Rome, since its newly established position as the center of the Mediterranean world may well have produced a local leap in prices during that period. Still we may question whether or not Roman prices did jump by as much as 50% between the late Republican period and Imperial times, as assumed by Kessler and Temin.

One clue could come from comparing the various Roman grain subsidies. The Gracchans’ scheme had provided the modius at a low price of 6.33 asses (HS 1.58) in 124 B.C.[161] During the Empire, we have two known interventions on wheat prices during periods of hardship: one under Tiberius, where prices are fixed at some unspecified level while HS 2 per modius are given to the merchants as a recompense; later, Nero imposed a price of HS 3 after the great fire.

If Nero had been simply trying to enforce the price Tiberius had previously enacted, this would imply a customary HS 5 per modius during that period. Since the available information pushes towards an average prices closer to 7 at that period, Nero’s measure would actually have been more aggressive. His subsidized price would have included a discount of nearly 60%, vs 30% for Tiberius. If we assume that similar discounts were applied to the earlier Republican scheme, this would lead to a price range of HS 2.2 to 3.7 per modius in 124 B.C. This is still close to the HS 3-4 range assumed by Kessler and Temin for the mid-2nd century B.C. If the middle of this updated range could be used as an estimate of the median price for that period, it would lead to a HS 3 level for the second half of the 2nd century B.C. When compared to the HS 7 that seems likely during the 1st century A.D., it would point to a more than doubling of wheat prices in Rome between the second half of the 2nd century B.C. and the 1st century A.D., an even more important jump than assumed by Kessler and Temin.

How could such a price increase over nearly 3 centuries be reconciled with the apparent stability in Egypt and Spain during most of that period?

First of all, the Spanish “stability” relies on very weak foundations. Martial’s “price” is a word in a poem that might have been written during a stay in Spain. These epigrams were not intended to be used in some database by “manipulators” of statistics a couple of millennia later. Furthermore we know there is a potential issue with the price for Lusitania given by Polybius through Athenaeus.[162] A “Polybian” price of HS 0.25 a modius is perfectly defendable and would then imply an increase by a factor of 4 between the time of Polybius and that of Martial. However this comparison is potentially meaningless, since there is no precise geographic indication for either of these prices, and we know from Cicero that prices in Iberia differed from one location to another.[163]

Regarding Egypt, it is worth looking more carefully into what occurs during the 2nd century B.C., since we have previously only compared very late Ptolemaic prices to Roman prices. Interestingly, grain prices denominated in “bronze drachmas” (or rather the unit of account on which the bronze coinage was based) multiply 3-fold during a very short period of time between 150-140 and 120-100 B.C., while the price of the Egyptian silver tetradrachm in bronze drachmas remains essentially stable. The purchasing power of silver in grain is effectively divided by 3 during the second half of the 2nd century B.C. Since the bronze coinage weight standards are divided by about the same factor by the end of that period, the relative stability of the purchasing power of bronze leads to the conclusion that silver lost about two-third of its value vs. bronze, grain and maybe other commodities at that time in Egypt.[164]

The other region that provides us with price series is Babylonia, through the “Astronomical Diaries,” whose remaining tablets more or less cover the period 382 to 60 B.C. Interestingly, silver prices for all the listed commodities (Barley, Dates, Mustard, Cress, Sesame and Wool) are increased by a factor of about 3 between the years 175-150 B.C. and 100 – 75 B.C.[165]

There is still another hint of a general fall of the purchasing power of silver-based currencies during the second half of the 2nd century B.C. A retariffing from 10 to 16 asses of the denarius relationship with the bronze coinage takes place around the years 145-140 B.C. in Rome, essentially restoring a stable intrinsic relationship between both coinage since the weight of the as had been divided by a factor of 2, from 1/6th to 1/12th of a pound (uncial) since 211 B.C., the year the denarius was introduced.

After the retariffing, the weight of the as fractions drifts again lower to a de facto semuncial standard while production of the as itself comes to a near halt in 146 B.C. The restoration of the uncial standard by an obviously administrative decision in 116-115 B.C. does not last for long. By 93-92 B.C., the lex Papiria legitimizes the semuncial standard again, as if the authorities were unable to maintain the heavier bronze currency.[166] After a short reversion to a standard close to the uncial standard under Sulla, no significant issue of asses occurs until Augustus, who opts for the semuncial system. Since the denarius : as conversion rate remains stable, the intrinsic purchasing power of the silver contained in the denarius is effectively halved vs. the bronze between 141 and 92 B.C. In other words, the same quantity of bronze buys twice more silver through the official coinage conversion rate. The implied silver : bronze ratio has moved from c. 120 to c. 60.[167]

One possible explanation would be that the Roman authorities had voluntarily increased the level of fiduciarity of the bronze coinage. That looks unconvincing: the issue of bronze coinage is very limited during the second half of the 2nd century B.C. and most of the 1st century B.C., unlike the first phase of debasement during the second Punic war.[168] Why would any monetary authority debase a currency that is barely minted? The second explanation is that the purchasing value of silver as a metal had effectively dropped between the second half of the 2nd century B.C. and the 1st century B.C. In that case, the Roman mint would have essentially kept the metallic value of its currency system close to its intrinsic ratio.

We have no hint regarding grain prices at Rome during that period except for the subsidized Gracchan scheme. Nevertheless, a division by 2 of the weight of the bronze coinage, the stability of the silver to bronze coinage ratio implying a possible drop in the value of the silver, could have led to a general doubling of most commodity prices denominated in Roman currency units during the same period. This would help to explain why political instability really worsened in Rome from the 130s B.C. onward, with a clear focus on financial measures whose aim was to alleviate the cost of purchasing food for the urban classes, through subsidized distributions of grain and land.

Although Egypt, Babylonia, and Rome are far apart and specific political situations may explain price rises here and there, one interesting scenario would be to postulate not a smooth doubling of most prices over nearly 3 centuries, but a general doubling in silver units of most prices all across the wider Mediterranean area during a very narrow period of time at the end of the second half of the 2nd century B.C. In other words, a quick fall in the purchasing power of silver would have pushed all prices higher, followed by a long period of stability.

The key factor here could have been the increase in silver production by the Spanish mines under Roman control during the later 2nd and early 1st century B.C., something that would be reflected by the pace at which the Roman mints in Italy, Iberia, and Macedonia stepped up their own production of silver coinage, with a clear acceleration during the years 130-110 B.C. and a denarius peak in the 80s B.C.[169]

If we retain such a hypothesis, we have to substantially increase the 1st century B.C. Roman prices to a level closer to those of the 1st century A.D., while creating a clear gap between them and those assumed for the 2nd century B.C. We will therefore increase the HS 4 level used by Kessler and Temin for the time of Cicero to HS 6 and use HS 3 for the earlier period.

Moving forward into the 2nd century A.D., we have only one non-Egyptian new price from Sicca Veneria in North Africa. This is a very low price of about HS 2.4 deduced from the local alimenta rate.[170] We need to define a likely level for the prices at Rome during that period as well to estimate a differential.

Since the times of Tiberius and Nero, significant monetary debasements had affected the denarius.[171] This could have fuelled some price increase. Furthermore, the so-called Antonine plague might have had an upward impact on nominal prices as well.[172] Our only other evidence for the later 2nd century is again provided by Egyptian prices, and they did double at some point during the period 165-195.[173] At the same time, by the end of the 2nd century A.D., the silver-debasement of the Egyptian drachma had been much more accentuated than for the denarius, leading to a loss of intrinsic relative value of about 50% compared to the mid-1st century A.D.[174] Most of that relative debasement would have occurred under Commodus.[175] We cannot exactly evaluate the fiduciary value given by locals to their own currency during that period.[176] But the doubling of nominal grain prices expressed in drachmas in Egypt under Commodus could simply be related to the approximate halving of the corresponding relative content of silver vs. the denarius. In that case one may support the view that nominal grain prices elsewhere in the Empire did not follow the Egyptian rise, which would have remained confined within this province.[177] The very low alimenta rate at Sicca Veneria at about the same period does support that scenario.

We are therefore going to assume an overall broad stability for Roman prices between the 1st and the 2nd century A.D.

The Modified Equations

Before trying to visualize what these new parameters may add, let us streamline further our geographic available data:

- The sea distance from Alexandria to Civitavecchia is 2086 km. But the Fayyum is located at about 350 km from the sea by canals and the Nile. Using a 1: 5 sea: river factor to obtain a weighted distance, the rounded figure becomes 3700 km.[178]

- From Ascalon to Civitavecchia, the distance is 2437 km, rounded to 2440. We need not add any land transportation factor, since the most fertile area of Palestine is the coastal plain.

- For the Po Valley, from Venice to Civitavecchia, we have 1742 km. We will add a weighted 500 km for 100 km of downstream Po navigation,[179] leading to 2250 km.

- We have been using Civitavecchia instead of Ostia or Portus in order to get modern easily verifiable distances. We similarly have not taken into account the Tiber upward journey. Since this fixed difference is added to all prices, it won’t change any relationship. But one figure needs some adjustment: Lanuvium, very close to Rome by land. Instead of adding a fixed factor to every other numbers, we decrease its weighted distance to Rome by 27 km of river journey, equivalent to 135 km by sea.

- Forum Sempronii lies 278 km away from Rome, through the Apennines, the equivalent of 6,950 km by sea if we multiply the initial figure by 25 to translate it into comparable sea distance in cost terms. An alternative to the overland route to Rome would have been to carry goods to the coast and ship them by sea. The city (modern Fossombrone) was 30 km away from the coast and was linked by the Via Flaminia to a harbour named Fanum Fortunae, re-founded in 49 B.C. by Julius Caesar, and later a colony under Augustus. Taking into account 1600 km of sea distance to modern Civitavecchia through the straits of Messina, we obtain a more competitive weighted 2,350 km. However, if the harbor facilities at Fanum Fortunae were inadequate, the next nearest harbor, Ancona is situated 95 km by road from Forum Sempronii, and the weighted adjusted figure from Rome becomes 4000 km. This is a huge difference and shows how econometrics are sensitive to assumptions about the way the ancient economy was operating. We will prefer the first number: Fanum Fortunae was a significant city,[180] with a natural harbor still restored by pope Paul V in the early 17th century.

- Terracina is located on the via Appia and more importantly is a coastal city located half way between the cities of Campania and Ostia. There was a small harbor, renovated under Trajan and Antonius Pius, 137 km from the Tiber estuary.

- Sicca Veneria is located inland, at 92 km from the closest seaport, Thabraca, where the distance to Civitavecchia is 600 km, leading to a weighted 2900 km for the entire journey. [181]

- Veleia is located about 30 km south east of Placentia; the latter was 40 Roman miles south of Milan on the road to Rome, itself 433 Roman miles away from Rome.[182] The distance from Veleia to Rome is therefore close to 550 km, equivalent to 13,750 km by sea (!). A less expensive journey would use the 78 km of road linking Veleia to Luna, on the Via Aurelia and close to modern La Spezia, and then the 182 nautical miles to Civitavechia. The overall sea-weighted distance would be 2262 km.

We have now expanded the initial database from 6 to 12 factors, leading to potentially more stable results, notwithstanding the intrinsic weaknesses and uncertainties of these numbers.

Table 3.

LOCATION

ESTIMATED PRICE IN ROME IN HS

PROVINCIAL PRICE IN HS

ESTIMATED PRICE DIFFERENTIAL TO ROME IN HS

WEIGHTED SEA-EQUIVALENT ESTIMATED DISTANCE TO ROME IN KM

DATE

Lusitania

3

0.25

-2.75

2470

About 150 B.C.

Po valley

3

0.5

-2.5

2250

About 150 B.C.

Sicily

6

2.5

-3.5

427

77 B.C.

Pompeii

7

5

-2

300

Before A.D. 79

Fayum

7

2

-5

3700

A.D. 78-160

Palestine

7

4

-3

2440

First two centuries A.D.

Antioch in Pisidia

7

2.125

-4.875

6700

About A.D. 90

Veleia

7

3.6

-3.4

2262

A.D. 98-102

Forum Sempronii

7

4

-3

2350

Early 2nd century A.D.

Lanuvium

7

4.3

-2.7

465

A.D. 136

Terracina

7

4.5

-2.5

137

2nd century A.D.

Sicca Veneria

7

2.4

-4.6

2900

Late 2nd century A.D.

Chart 5. Distances from Rome and price for grain, with an enlarged sample of data (1: Lusitania, 2: Po valley, 3: Sicily, 4: Pompeii, 5: Fayum, 6: Palestine, 7: Antioch in Pisidia, 8: Veleia, 9: Forum Sempronii, 10: Lanuvium, 11: Terracina, 12: Sicca Veneria)

Full size image here ↗

It is graphically obvious that the results will show a lower level of correlation when using the entire sample. We will therefore run two tests: first with these 12 data, and second by restricting a final sample to the broad Egypt-Rome trade axis, into which we incorporate Sicily and Africa.

Table 4. Econometrically modified results

SCENARIO

Number of parameters

β

α

R^2

F-statistic

All modified parameters

12

-0.00041 (-3.56)

-2.43 (-7.57)

56%

12.65

Coastal data sample

6

-0.00072 (-4.96)

-0.93 (-8.65)

86%

24.5

If we now graphically plot the highest quality regression line from the most reduced sample we obtain the following chart:

Chart 6. Distances from Rome and price for grain, with a coastal sample of data

Full size image here ↗

The conclusions are quite straightforward. First of all, the linear relationship is much weaker when taking into account all available prices. The level of 79% of the variances obtained by Kessler and Temin is reached or overtaken only by careful sample selection limited to Rome, Latium, Campania, Sicily, Africa, and Egypt. The overall dataset leads to 56% of the variance being incorporated by the closest possible line. That should not come as a surprise and materializes the fact some of these locations had little to none long distance grain trading relationship. It of interest to note that similar results are achieved when numbers are drawn from the Standford University ORBIS Project (http://orbis.stanford.edu/), which appeared after the above calculations were complete.

This would support the view of quite a dichotomous ancient Roman economy, where consuming and producing regions accessible by sea trade could display truly efficient price behavior, while areas left outside the main trade axes would live an economic life essentially driven by local considerations, at least as far as an essential staple like grain is concerned.

There remains one final issue that has not been addressed so far: the high prices recorded in the Greek world.

The limits of the Rome-centered model

Aegean wheat would have sold at standard prices no higher than 5 to 7 drachmas per medimnos during the Hellenistic period.[183] This would translate into an average close to 1 Roman denarius or 4 sestertii per modius. Although we possess no regular Roman prices for that period, it seems likely that they were lower. After the extremely high prices experienced during the second Punic war, we are told that 4 asses (= 0.4 denarius) and then 2 asses a modius were abnormally low in 203 and 202 B.C.[184] A little less than a century later, 6.33 asses (= 0.4 denarius still since the retariffing had taken place) is a subsidized price. Such indications would not easily be compatible with customary prices close or higher than 16 asses, although we have no firm evidence. Still, it seems likely that prices in some if not most Hellenistic metropolis were higher than prices in Rome under the Republic.

Notwithstanding the impact of the Roman conquest of the East, later imperial evidence points in the same direction: the main cities of the Aegean area remained very expensive throughout the Hellenistic and Roman periods compared to Western prices.

In Ephesus at the time of Trajan, prices of bread were regulated by the local authorities at an average levels of 2 obols per pound for the standard quality.[185] Naum Jasny’s calculations point to a grain price ten times higher than in Antioch in Pisidia, to a point where the author is so surprised by the gap that his conclusion is “not to use the evidence for Asia Minor in that study.”[186] After translating his prices in cents per bushel or British pounds back into ancient units, this is equivalent to HS 19.9 per modius.[187]

However, Jasny does not pay any attention to the peculiarity of the monetary system of Roman Asia during the High Empire. The term obol should normally refer to the subdivision of the regional currency that was minted with a reduced weight standard, the cistophoric drachma, valued at 12 Roman asses. That local tetradrachm was thus worth 3 denarii instead of 4.[188] Then 1 obol is worth 2 Roman asses and not 2.67, and the denarius 8 obols. In order to ensure some symmetry with its own system, a local as, the assarion, whose value was 16 to 18 to the denarius, was introduced.[189] Jasny’s price of HS 19.9 should therefore be corrected into HS 14.9 per modius. For Rome, our computations led to a median price of HS 7 vs. Jasny’s HS 8. Applying the same proportionality would lead to HS 13 per modius in Ephesus.

Another approach could refer to the bread price of 1.5 asses per pound in Pompeii. We had previously computed from this price a grain price range of HS 3.6 to 5.1 per modius. Applying the same method for Ephesus with 2 obols = 4 asses would imply a HS 9.6 to 13.6 range. Since we know here the bread is here of the lower quality (another price is provided for fine bread: 3 obols for 9 ounces), we know we have to use the higher price. This is very close to Jasny’s findings, and it would seem safe to assume that Ephesus’s wheat prices were significantly higher than in Rome by a margin of maybe up to HS 5-6 per modius.

The main issue with these estimations is the uncertainty surrounding the true value of the local obol once translated in Roman Imperial currency terms. In classic Greece, the most widespread relationship follows the Attic standard: 6 obols to 1 Attic drachma. At that time, the obols were small silver coins approximately weighing 1/6th of a silver drachma, or, better, 1/24th of a tetradrachm. Since the Attic drachma equals a denarius, and the cistophoric tetradrachm 3 denarii, this is how we related 1 obol to 2 assaria or 1/8th of a denarius. When Greek states started to mint bronze coins, that relationship was maintained, even though the bronze coinage was effectively overvalued, since its intrinsic value in bronze was lower than the value as indicated by its rate of exchange with the silver coins.[190]

Things are no longer that straightforward during the Hellenistic period: token coinages need a high degree of trust to operate. In 2nd century B.C. Egypt, the bronze drachma became a unit of account most likely defined following the formula 10 “new” drachmas = 1 “old” obol.[191] Something quite similar occurred in Athens after it submitted to Sulla. A heavily overvalued bronze drachma of less than 10 g. was minted, and it seems obvious it was not accepted at face value outside of Athens. After a gap of more than a century, Athens started to mint the same bronze modules again under Hadrian. Then we know from a contemporary inscription in the Agora that 1 bronze drachma was worth not 1 denarius, but 1/6th of a denarius, while a later 2nd century religious law mixes denarii with leptû drachmas[192]

This phenomenon could have been peculiar to Athens or widespread. The reality is that we are very often not in a position to opt for one scenario or another, since Greek coinage normally bore no marks of value.[193] In the 2nd century A.D., Aeginus in the Peloponnesus struck coins marked hemiobols weighing c. 8 g., showing that city had not adopted the debased Athenian system but had stuck to the old standards.[194]

We have reasons to think Athens was not an isolated case and that Ephesus was most likely operating with a similar standard during the Imperial period. Under Trajan, Rhodes struck large bronze coins weighing about 20 g. and marked didrachmon, metrologically quite consistent with the contemporary Athenian coinage.[195]

In Asia Minor, Roman denominations appear on the epigraphic material from Tiberius onward with the Sagalassus inscription, denarii and assaria being often mixed with Greek numerals, drachmas, obols and chalkia. The Trajanic Salutaris inscription in Ephesus as well as the Hadrianic banking regulatory text of Pergamum use denarii and/or assaria, while the tetrachalkia appear under the Flavians. Several other inscriptions from Asia Minor testify to the wide use of the assarion, while obols fade away with the 2nd century. In the 3rd century A.D. at the latest, ancient Greek denominations are absent from the Asia Minor numismatic material. Coins minted in Pergamum of c. 8 and 4 g. in the 2nd century would have been assaria and half-assaria. In Chios, which had struck assaria since the early 1st century A.D. and was the only Greek city to often indicate marks of values, the last appearance of the obol occurs under Hadrian.[196]

The pricing in obols in 2nd and 3rd century A.D. Ephesus is thus somehow anachronistic, unless we are again dealing with a different unit of account. This could be possibly implied by a dossier of Hadrianic inscriptions from 124 and 125 A.D. where denarii and assaria are the normal units of accounts, with the exception of one amount expressed as 300 drachmas: one wonders why both units would be used unless we are dealing with two different units of reckoning.[197] Interestingly, the unique example of the use of the phrase “silver assaria,” obviously referring to a unit of account since there were no silver assaria coins, is to be found in an inscription from early 2nd century A.D. Ephesus, pointing to the fact that silver and bronze likely belonged to two different systems of denomination.[198]

If Ephesus and some other Eastern Greek cities had been following Athens and Rhodes in establishing the drachma and obol as fractional units of account of the denarius, the available bread price would have to be translated at an entirely different rate. In Athens, the bronze “drachma” had replaced the old obol, and the new obol had become 1/36th of a denarius. A similar division by a factor 6 would lead to a denarius being worth 48 new obols since the local silver drachma is lighter by a quarter compared to the silver Attic standard.

In this case, 2 obols a pound for whole wheat bread means 1/24th of a denarius per pound, and 3 obols for 0.75 pound of white bread leads to 1/12th of a denarius per pound. As per the calculations for Pompeii, assuming respectively a 0.8 to 1.25 wheat to bread ratio according to its quality leads to a HS 4.4 to 5.6 range. We will then use HS 5 as an estimate compatible with both prices. This is very different from the previous estimate close to HS 14. This wide level of uncertainty entirely relies on what unit of account the obol is referring to in Hadrianic Ephesus. We believe the lower scenario is better supported by the epigraphic and numismatic analysis.

We have a few more testimonies from Imperial Greece and Asia at times of scarcities. In Sparta, under Hadrian, a grain official provides grain at 1 denarius per hemiekton, i.e., HS 8 per modius, while prices had reached 40 denarii per medimnos (HS 26.67 per modius). At Sebastopolis in Caria in the late 2nd century A.D., a city located inland at about 50 km from the Meander valley, wheat is sold by a private benefactor at 2 denarii per kupros, i.e., HS 4 per modius.[199] If subsidized prices bear a close relationship to standard market prices,[200] these figures fit rather well within the Italian price range.

Next comes Alexandria proper. Although we do not have any price information regarding wheat transactions during the Roman period, there is at least some hint with respect to the price structure in Ptolemaic Egypt. In a year close to 270 B.C., a set of sales accounts concerning wheat being transported from the Herakleopolite nome to Alexandria involves a very high price of 4 drachmas, 5 obols per artaba, whereas the Egyptian average price at that time was 2 drachmas per artaba.[201] Although this sale is not specifically reported to have occurred in Alexandria, the situation described by the papyrus and the price itself point towards such a hypothesis. The implied countryside to Alexandria ratio is about 1:2.4.

That looks certainly too high, since the same papyrus shows barley selling only one third above standard country prices, leading to a very unusual ratio of 1:3 between barley and wheat here, compared with the usual range of 1:1.5 to 1:2. So maybe some temporary disturbance produced that price of wheat out of line with normal. This could suggest that a more normal Alexandrian wheat price was somewhere between 2.5 and 3 drachmas at this period.[202]

Applying such a price structure to Roman Egypt, Alexandria wheat prices would have been close to HS 2.75-3 per modius, with countryside prices of about HS 2. The absence of any evidence for the Roman period will prevent us from trying to use that estimation as the price of wheat in Alexandria.

After computing the distances to Rome, the new chart obtained by adding the additional Eastern locations shows as expected a less linear and as such a less integrated result.

Chart 7. Distances from Rome and price for grain, with additional Eastern data

Full size image here ↗

The picture that emerges is of a more multipolar economy, where a main trade axis does show up between some coastal regions aligned on a broad Egyptian-Italian axis, while other areas do not fit into any linear relationship with Rome.

Greece and coastal Asia Minor are two of the wealthiest regions of the Empire from the late 1st century A.D. onward. As during the time of the Athenian Empire, the area relied on some external grain in order to sustain itself. In periods of shortage, we have evidence of Egyptian wheat imports, although there is no consensus about how casual they were and how restrictive the Imperial authorities were about them.[203] We might keep some doubts about the significant character of the Spartan price, as it seems very high compared to the overall regional average, and that further highlights the fact benefactors might have been in a position to take some profits in selling their reserves at times of scarcity.

The Greek East case is actually similar to what we concluded for Palestine: little to no grain surplus, no direct relationship with Rome, not located on the Roman grain route, rather a competing position as a grain import centre.

Towards Partial Grain Market Integration

What does this tell us? First and foremost, the proportion of grain import vs. local production must have been marginal in most locations of the Empire. As we reflected for Antioch in Pisidia, Prusa, or even cities like Forum Sempronii, the relative value of wheat vs. its weight made it an unlikely candidate for profitable trade. Hence local conditions must have been generally the main factors in explaining the equilibrium price of grain in a given location, or at least played a significant role.

This does not mean that cities in some regions did not tend to develop some common pattern. Italian prices seem pretty much alike, prices being higher in coastal areas and closer to Rome than inside the peninsula. Asia Minor seems to show something of a regional pattern as well: the 3 locations we have information about are graphically rather well aligned. Since their sea distance to Rome is about the same, what matters in that case is their weighted distance to the coast. This would somehow bring some additional information to Cicero’s statement that prices inside the provinces of Asia (and Iberia) could vary, unlike the relative uniformity that would have characterized Sicily: they would vary according to their distance to the coast, and this confirms Cicero’s statement about Ephesus’ prices compared to inland Philomelion.[204]

Does this mean that inland cities could have been directly trading grain with each other? Veleia and Forum Sempronii, or Sebastopolis and Antioch in Pisidia, certainly did not. Nevertheless, a minimum level of capillarity in short-distance land transportation of grain and human mobility itself must have linked adjacent regions, eventually creating mechanisms by which average prices in normal years could not move too far from one another within each province of the Empire. Such a scenario would find another confirmation for the Balkans and Asia Minor, where coastal cities’ hoards show bronze coins minted far away in significant proportions, whereas isolated inland locations display a more local circulation patterns.[205] This is quite consistent with the higher coastal prices vs. the interior that we are highlighting for this region.

Still, the broad comparability of prices in distant areas like Ciceronian Sicily or Pisidian Antioch leads Jean Andreau to suggest that: “(…) toute identité de prix ne révèle pas un phénomène de «marché» (…). Si les conditions de production et le rapport entre l’offre locale et la demande locale sont identiques, le prix peut aussi être identique, sans qu’il existe aucun contact entre les lieux concernés.”[206]

One could question whether more fundamental integrating factors would not have been in play too. Prices in isolated areas might eventually have become broadly aligned with many other areas of the Empire, since migrations and access to the same monetary system and broader cash pool would tend to cap divergences within a single overall continuous price structure. In essence, poorly productive areas would experience population losses through emigration until their supply to demand balance was restored, and vice versa.

That said, maritime areas of the Empire developed some integrated economic patterns as far as the grain trade is concerned: the high linearity of the cities located on the Rome-Sicily-Africa-Egypt axis cannot be dismissed out of hand, while, at a regional level, what seems to matter most is the distance to the coastline.

Another interesting problem is the evolution of the likely price ratio between Egypt and the Aegean world from the Ptolemaic into the Roman period. Since the Aegean average wheat price seems to have been close to 1 denarius per modius during the first two centuries of the Empire, its relative ratio compared to Egyptian domestic prices of about 8 to 12 local drachmas per artaba would have been close to 2 at the official currency exchange rate of 4 Egyptian drachmas per Roman denarius.[207]

During most of the Hellenistic period, the average Aegean price had been around 5 to 7 Attic drachmas per medimnos, i.e. 1 drachma per modius.[208] These prices are mostly from the 3rd century B.C. and the first half of the 2nd century. During that period, Egyptian wheat prices in silver currency terms were close to 2 Ptolemaic drachmas per artaba.[209] Provided the Egyptian kings managed to consistently impose an overvalued parity exchange rate towards the Attic standard, that leads to Egyptian prices of about 45% of the Aegean average.[210]

The cumulative uncertainties of the data and the fact they don’t concern the same Aegean locations don’t allow for a more accurate comparison. Nevertheless, if that order of magnitude were correct, such stability between Hellenistic and Roman ratios would highlight the surprisingly minor impact on the Eastern wheat price structure of the Roman tributary process. Most likely some production increase large enough to stand the impact of the city of Rome’s supply requirements must have happened in various parts of the Roman world, Egypt included.[211] That the Empire was later able to set up a new capital in Constantinople, diverting grain flows from Rome as a consequence, tells us a lot about the most likely production increase that took place in many areas of the West and the East.[212]

To that extent, the Rome-Sicily-Africa-Egypt commercial axis within a generally more fragmented economic “Roman” world did not develop at the visible expense of the other areas. The dividends of the Roman peace would have globally financed the tributary extraction.

Chart 8. Distances from Rome and price for grain, regional patterns

Full size image here ↗

Rather than an integrated single market for grain, the Empire would have been a combination of partially integrated regional or local markets, where the distance to the coastline would have been the main factor, while a major sea-trade axis linking the most productive areas to the most demanding consuming center would have emerged. As far as the role of the State is concerned, rather than by becoming a trading actor itself, it would have contributed to displace the market equilibrium towards a more politically desirable outcome by a combination of incentives and restrictions that would have been more effective than commonly thought.

Public intervention did not exclude traders and markets from the equation. On the contrary, Rome proved materially unable or culturally unwilling to set up a State-run centralized economy. But any equilibrium that the Roman world reached was a combination of the activity of profit-oriented individuals evolving within a more global framework of an Imperial policy aware of the basic economics on which its very existence relied upon.[213]

Conclusion: Modern Methodologies and Ancient Societies

Historians should be grateful for the intrusion of numerical analysis into ancient history. The efforts by Peter Temin to scientifically use ancient “numbers” tell us that such approaches, used with the proper caution, care and methodology, do offer a degree of leverage in helping to understand ancient economies better. Still, it seems to us that the ancient Mediterranean grain market is a difficult environment in which to test the use of numerical analysis. The very limited number of available data along with their level of uncertainty does not lead to very stable results. Any new price discovery could potentially modify all these findings.

Focusing on Egypt as a single province or shifting our attention towards the later Empire could prove promising, however: there are many papyri in the first case, while moving into a later period could partially complete or contradict the present results.

That said, it seems difficult to dismiss the fact the Roman economy did display a certain degree of market integration, particularly alongside some sea trade routes. Economically, the Roman Empire was the true produce of the Mediterranean Sea.

Economics did not start with Adam Smith. The man who wrote: “And the best and greatest art is the art of government which causes the good deep soil in lowlands and highlands to be tilled, and all the seas to be safely navigated by merchantships laden with cargoes to effect the exchange of goods which the countries in desire for fellowship render each other, receiving those what they lack and sending in return those of which they carry a surplus” is indeed not David Ricardo, but Philo of Alexandria.[214]

Notes

[*] Institute for the Study of the Ancient World, New York University, <http://isaw.nyu.edu> and American Numismatic Society, <http://numismatics.org/>.

[1] Finley 1973, 144.

[2] Kessler and Temin 2008, 159.

[3] Temin 2001; Temin 2006.

[4] The mid-II AD so-called Muziris loan, SB XVIII 13167. Italian wheat prices: S. Mrozek 1975, 14 with CIL IV 5380 and 1858, XI 6117. See as well Duncan-Jones 1974, 145-146 and 252-253. Egyptian wheat prices: Duncan-Jones 1976; Drexhage 1991, 20; Rathbone 1997, especially 329 n. 25; Sicilian tithe: Cic., 2 Verr. 3.163.

[5] Pleket 1990, notably pp. 65, 124, and 129; Erdkamp 2005. The fact that grain was not transported inside jars or amphoras works against evidence for grain merchants, since their names would not be preserved in Monte Testaccio for instance.

[6] Mundell Mango 2001. If the average vessel from the patriarchal fleet of Alexandria in A.D. 610-620 were carrying circa 16,000 solidi worth of precious goods, this would have been equivalent to 160,000 artabas, i.e., 720,000 modii of wheat. There is good evidence that 50,000 modii represented the minimal expected capacity of the standard size of ship used for the transport of the annona, larger vessels reaching up to 200,000 modii: Rickman 1980, 123. See as well C. Th. XIII, 5, 14 where 10,000 modii is used as the minimum size of vessel capacity leading to tax exemptions.

[7] Acknowledging the vast literature accumulated on the topic of the more or less “nationalized” nature of those grain flows.

[8] One should not let oneself be misled by the variability of ancient wheat prices: they were more the consequences of shortage and famine than of relative differences in quality. Studies assuming some regional standardization for grain prices are therefore legitimate. Pliny compares wheat types more by weight and flour extraction rate than by taste (NH 18.63-90), unlike what he does for wine (ibid., book 14), even though different grain types did exist: Jasny 1944a. The ratio provided by Pliny between the cheapest and the most expensive flour is 1 to 2 (NH 18.90). The corresponding price ratio for wheat was certainly closer to 20%, since lower extraction and water retention rates when processing the bread from grain would characterize the flour obtained from the finest wheat: Jasny 1947, 191. Median wine prices enjoyed a significantly wider range due to their sole difference in intrinsic quality: 1 to 4, still excluding the priciest wines (Mrozek 1975, 14 ). Even in Egypt, whose wine did not enjoy much praise, a similar ratio is observed: Rathbone 1997, 224-227. Diocletian’s Price Edict characteristically provides one single price for wheat against 17 references for various qualities of wine and 3 for olive oil. The price range is close to 1 to 4 for wine and oil. Later (c. 340), P. Oxy. LIV 3773 provides a 25% range of variability over time for wheat prices, 67% for barley, 70% for wine: Bagnall 1989, 71.

[9] Temin 2006; Kessler and Temin 2008.

[10] Kessler and Temin 2008, 144.

[11] Ibid, 158.

[12] Hopkins 1980; later expanded and revised into Hopkins 2002; von Freyberg 1988.

[13] von Freyberg 1988, 143, table 7.1. All of the data can be found in Rickman 1980, with the exception of the Egyptian price average allegedly taken from P. Mich. II 127 through Rathbone 1997. The actual average of his “seven prices” must include the transaction from P. Mich. II 123 verso and leads to 7.09 drachmas per artaba, equivalent to HS 1.58 per modius. The authors wrongly give 7.5 drachmas at some stage (p. 141, n. 10) but this does not affect the results, since that error does not contaminate the actual data used for the correlation test. These figures date from A.D. 45/46 and not B.C. as wrongly stated, p. 141. For some reason, the date range in table 7.1 becomes 20 B.C. – A.D. 56, although all the prices date from A.D. 45/46. This does not affect the later calculations, however, since the Roman “price” remains in the HS 5-6 range that is used for the entire first century A.D.

[14] Temin and Kessler 2008, 144.

[15] From Temin and Kessler 2008, 145, table 7.2. with 6 active variables including the Po valley. The number in parenthesis is called the T-statistic, or Student Test. The higher that number is, the more likely the coefficient given by the ordinary least square regression is significantly different from 0. A higher T-statistic implies a higher confidence level. The R^2 provides the proportion of the variability of the output observed data (price differential) that is explained by the independent input parameters (distance from Rome). They are the main factors used to assess the statistical quality of the result of an Ordinary Least Square Regression process To simplify, the closer the R^2 is to 100% and the higher the absolute value of the T-statistics is, the better. 79% is a relatively high level for such a simple linear relationship with 1 variable input and 6 observations.

[16] «(…) car le mal éternel des villes capitalistes survoltées, c’est la cherté, pour ne pas dire l’inflation sans répit. Celle-ci tient à la nature même des fonctions urbaines supérieures dont c’est le sort de dominer les économies adjacentes», Braudel 1979, 21.

[17] Temin and Kessler 2008, 149-153.

[18] Ibid, 150.

[19] Even Sicily displayed a rather low level of monetization: out of 770 Greco-Roman sites recently surveyed, only 220 delivered some coins: Puglisi 2011.

[20] Ibid, 152.

[21] Ibid, 153.

[22] Rickman 1980.

[23] Temin and Kessler 2008, 153-154.

[24] Montenegro 2001, 603-605.

[25] These definitions can be found on: http://stats.oecd.org/glossary/detail.asp?ID=395.

[26] In statistical jargon, that means that the conditional variance of the results varies with each different observation.

[27] Studenmund 2011 devotes its entire tenth chapter to heteroscedasticity. Essentially, the squared root of each residual is inversely weighted according to the conditional variance of the corresponding parameter, which means that the more uncertain the data is, the less its distance from the average will influence the final equation.

[28] AE 1925, 126 and 1926, 78 as well as Robinson 1924, 5-20. The prefect Lucius Antistius Rusticus is directly quoted by the ancient inscription saying: ante hanc hibernae asperitatis per severantiam octonis et novenas assibus modium frumenti in colonia fuisse. This is thus a rather accurate price indication with little uncertainty.

[29] Rathbone 1997, 193; Temin and Kessler 2008, 141; Rathbone 2009.

[30] Pol. 34.8.7 from Athenaeus 7.302e.

[31] Le Rider 1986.

[32] Rickman 1980, 147.

[33] Crawford 1974, 144-145.

[34] Pol., 2.15.6.

[35] Buttrey 1957.

[36] Rickman 1980, 149, 151, 239-240, based on Pliny’s flour and bread price indications (Plin., NH 18.90) and Jasny 1944.

[37] Tac., Ann. 2.87; 15.39.

[38] Duncan-Jones 1974, 50-51, 346.

[39] Sperber 1991, 102, 114, 118; Sperber 1966, 248-271, 182-211; Heichelheim 1938. They both use Mishnaic and Talmudic materials. The issue lies with the local volumetric unit, the se’ah, equivalent to 13.131 liters according to Heichelheim and to the Roman modius according to Sperber. We should also note that Heichelheim himself states that Palestinian prices are “50 to 600 percent higher than the Egypt one.” He is, however, using the very wide range of Egyptian wheat prices listed by Johnson 1938, 310-311, including those from upper Egypt under Augustus before the coinage reforms of Claudius and Nero, which are not easily comparable to later prices in monetary terms. Prices extracted from the New Testament range between HS 2 and 4: Pankiewicz 1994.

[40] Romer 1990; He and McGarrity. The S&P 500 is a broad-market U.S. stock index.

[41] Temin and Kessler 2008, 142. See Rickman 1980, 154; Rathbone 1997, 191-192.

[42] The most recent silver measurements are to be found in Butcher and Ponting 2005, 108. The classic reference used to be: King and Walker 1976. The A.D. 72 Jewish poll tax Edfu ostraca illustrate the one to four exchange rate: King and Walker 1976, 155. It is supported by later metrological texts: Melville Jones 1993, 403. The assumption expressed by Walker and King is that this conversion rate appeared under Claudius. Alternatively it could get postponed until the introduction by Nero of a weaker standard around 57/58 or 62/63: Christiansen 1987, 104-108.

[43] If we disregard P. Mich. II 127 and 123, showing an average of 7.1 drachmas per artaba (= HS 1.58 a modius) in 45-46 because of a specific situation there, the other ten private transaction prices recorded by Dominic Rathbone for the period 78-160 lead to 8.76 drachmas, that is HS 1.94 per modius. Official prices were usually set at 8 drachmas, translating into HS 1.78 per modius. For the measure of the artaba at 4.5 modii italici, see Duncan-Jones 1976, 43-52; Rathbone 1983, 265-275; For the later Empire: Bagnall 1993, 332. Note the existence of an alternative strong tradition that equates the artaba to 3.33 modii for the earlier Empire: Johnson 1938; Duncan-Jones 1976, 257-260, who revised his view shortly thereafter; Mayerson 1998, 189-194. Applying that lower ratio would further increase equivalent prices in sesterces to HS 2.5-2.7 per modius.

[44] Although there is little evidence for permanent markets in Egyptian villages and even cities, significant quantities of wheat were travelling for the purpose of short distance trade: Alston 2005.

[45] Kessler and Temin 2008, 143, table 7.1

[46] All these econometric results are summarized in Table 2, infra.

[47] Kessler and Temin 2008, 153.

[48] Ibid, 150.

[49] For sea distances, see http://82.146.41.123/, provided by World Shipping Register TM. In using modern sea distances, we are not immune to significant distortions either, since seafaring with square sails asymmetrically increases distances to cover in comparison to fuel powered ships, although not on a similar scale. We assume that differences between ancient and modern navigation would lead to all distances being divided by a similar factor, which would have no impact on the equations. This is not necessarily true, however, since the wind regimes and the use of cabotage are factors that affect each route differentially. Moreover, we are equating ancient cities with their closest modern equivalent: Ostia is replaced by Civitavecchia, for instance.

[50] See Hendy 1985, 70 and 101 for maps showing Antioch of Pisidia. It is outside the main grain producing area and linked by a road to the coastal city of Attaleia. A major East-West road crosses Antioch: Broughton 1940, 864.

[51] The Price Edict of Diocletian would give an average ratio close to 25:1, according to the type of animal used, and what sea route is chosen as a reference. Some scholars have questioned if it would have been in the Imperial interest to lower the sea costs in the Edict to reduce navicularii compensation: Appendix 17 in Duncan-Jones 1974; Laurence 2005, 125-144. This is, however, not necessarily true: the Aphrodisias copy of the Edict adds the mention praeter onera fiscalia quae formam suam optinent to all the tariffs to Rome, implying that the navicularii were subject to a different compensation regime: Arnaud 2008, 131-132. Roger Bagnall recently calculated from Mitteis and Wilcken 1912, n° 321, that transporting wheat over 100 km of desert adds 50% to its price. In the Price Edict, that cost would amount to 30%, showing that transportation prices might have been systematically undervalued, especially since the flat Egyptian desert was certainly easier than any mountain route elsewhere. The sea cost is about 1% per 100 km between Alexandria and Rome. For relative sea and land costs in pre-modern Europe: Chant and Goodman 1999, 73; Masschaele 1993, 273. There are additional late medieval and modern European references in Duncan-Jones 1974, 368-369.

[52] Supra (n. 28)

[53] Or. 46, 10.

[54] Or. in laudem Basilii Magni 34f.

[55] Cic., 2Verr. 3.191-192.

[56] Martin-Kilcher 2004. The fact grain could still be transported by land in Asia Minor is supported by an inscription found in Pisidia and dating from Tiberius’ reign, dealing with transport requisition. The governor edict does indeed mention grain privately transported for being consumed or sold: Mitchell 1976, l. 47-48. As in medieval and pre-modern Europe, the average distance covered by such carriages must have been very limited and the costs very high.

[57] 200 km of land distance translated into 5000 km of sea journey, to which we add the original 1700 km of sea distance.

[58] For the argument about the Po valley data: Kessler and Temin 2008, 150.

[59] Interestingly, Temin was saying the same thing few years ago: “The Roman market for bulk commodities extended only slightly beyond where ships could go”: Temin 2001, 180.

[60] Extensively used by Emmanuel Le Roy Ladurie, Pierre Goubert, Henri Hauser, and Camille-Ernest Labrousse in their landmark works.

[61] Using the monumental synthesis produced in 6 volumes at the beginning of the 20th century by D’Avenel 1910-1914. This has been justly criticized and contains significant mistakes and inconsistencies: Febvre 1932, 585-586. Nevertheless, this is the most extensive single source, and it becomes rather reliable for the 18th century with the use of centrally collected prices from the Ministère des Transports Publics. Prices in livres, sous and deniers are translated into francs.

[62] Wheat prices from d’Avenel 1910-1914 II. About limited regional market integration in modern France: Weir 1989, 209-211. Regarding the imperfect correlations between regions : Gráda and Chevet 2002.

[63] D’Avenel 1910-1914 III, 218-219.

[64] Ibid, 217.

[65] D’Avenel III 1910-1914, 223.

[66] These villages “étaient plus éloignés de l’influence française que les Iles Marquises […]. Les communications ne sont ni grandes ni petites, elles n’existent pas,” quoted from Braudel 1979, 278

[67] Arbellot 1973.

[68] De Vries and Van Der Woude 1997, 418 for a comparative price index chart between Amsterdam and Dantzig in the XVIIIth century.

[69] The Muziris loan: supra (n. 4); Plin., NH 6.101; Strabo 2.5.12; IG XIV, 830;T. R. S. Broughton, in ESAR IV, p. 876; Dig. 45.1.122.1 (Scae.). See as well Dig. 19.2.61.1, dealing with a shipload of wheat sent from Cyrenaica to Aquileia.

[70] The distribution of the SES amphora stamp and its variations over Southern Gaul and Northern Italy is still an emblematic example of the trade web that entangled the Roman Mediterranean area at the end of the Republic: once can for instance refer to Daniele Manacorda 1978, among a vast literature on that topic; more generally, Harris 1993.

[71] Reger 1997. See as well Reger 1993a and 1993b

[72] Sosin 2002.

[73] Rathbone 1997, 197.

[74] P.Oxy. LI 3628-3636 indicate a price range of 240 to 500 myriads of denarii per artaba between several nomes of the province of Arcadia at the same season of the year: Bagnall 1985, 5. p. 5.

[75] Alston 1998, 186.

[76] Bang 2008.

[77] Erdkamp 2005, 201.

[78] Cic., 2Verr . 3.191–192.

[79] P. Mich. II 127 and P. Lond. 131 and Duncan-Jones 1976, 250, 252. For traders in rural and urban situations: Alston1998.

[80] Rathbone 1997, 195.

[81] Duncan-Jones 1976, 250. See as well Wallace 1969, 211-212, discussing taxes on various food dealers, and Johnson 1937, 369-374, commenting on a papyrus relating to bakers.

[82] Pompeii may well have been a net grain importer as well without endangering the possibility of a linear relationship between prices in Egypt, Pompeii, and Rome, since it is located on the same linear itinerary linking Alexandria to Rome – i.e., distance (Rome, Alexandria) = distance (Rome, Pompeii) + distance (Pompeii, Alexandria). On Pompeian wheat supply see Andreau 1994.

[83] The Sulpicii archives show that even Egyptian wheat could be privately purchased: Camodeca 1999, see TPSulp. 51, 52, 67 and 68. Casson even argues that the available Egyptian grain could be freely purchased: Casson 1980, 21-33. In Dig. 19.2.61.1, a ship is hired by an individual to transport oil and grain from Cyrenaica to Aquileia. In a Talmudic text, Egyptian wheat is sold in Palestine: Sperber 1966, 191. As far as price mechanisms are concerned, Cicero observes fluctuating prices set by the supply and demand in Sicily, annona […] pretium (2Verr. 3.227), providing different ranges according to the concerned year and situation. Pliny the Elder uses a similar formulation about average grain prices: pretium huic annona media: NH 18.90.

[84] Tac., Ann. 2.87; 13, 51; Suet., Claud. 18-19. The existence of private speculators, the dardanarii, is recognized by later Roman legislation: Dig. 47.11.6pr. (Ulpian). Legal exemptions sometimes concern ship owners and not traders without being specific – Dig. 50.5.3 for instance. But Dig. 50.6.6.3 covers negotiatores and navicularii alike: see Erdkamp 2005. For the later Empire: C. Th. XIII, 5, 14 (371). For a synthesis about private trade in the Later Empire, Carrié 1994.

[85] P. Oxy. LIV, for instance. We have about 40 price declarations to the logistes at Oxyrhynchus, from the IVth and Vth centuries A.D.

[86] Bagnall 2000.

[87] For a synthesis, Erdkamp 2005.

[88] Carrié 1975; Rea 1973.

[89] Reduction to 200,000: Res Gestae 15.4. One should not forget that the late Republic had been aiming at providing grain rations to 320,000 citizens before reducing that figure to 150,000 at a time when Egyptian grain was rarely granted: Suet., Caesar 42.1.

[90] Nero (Tac., Ann. 15.39.2); Commodus (SHA Com. 14.3); Gallus and Julian in Antioch: Amm. 14.7.2-8 and 22.14.1; Jul., Mis. 368c ; Lib., Or. 1.96.7; 14.47; 15; 18.195, for a list of failures of Emperors trying to impose low prices. The aim of Diocletian’s Price Edict was most likely limited to setting advantageous prices for official purchases and tax aederatio: Carrié and Rouselle 1999, 202.

[91] Jul., Ep. 4 (46), Bidez (ed.) 1972.

[92] IG V, 1, 1432-33; App., Syr. 8.50; in Asia a local official is removed after a complaint. He was visibly forcing some unfair cash conversion rate for grain levies: Magie 1951, 152-154. This does not prevent taxation from being partially levied in kind according to the Imperial requirements: Erdkamp 2005, 219.

[93] Cottier et al. 2008, 55.

[94] Erdkamp 2005, 220-221 for cash and wheat tribute and 231 for Egypt; Duncan–Jones 1990 for tribute; Duncan-Jones 1994, 53, table 4.6 for estimates of the Egyptian wheat tax. For a discussion on the use of the Egyptian wheat: Rathbone 1987.

[95] Romans casually considered that their own tax regime was generally nicer than what had been in place before the conquest or that they simply used what was in existence, as in Sicily with the lex Hieronica. Mark Antony explains to the city of Asia that the tithe system is privileged compared to what their kings used to exact: App., BC 5.1.4; see as well Caesar, BG 6.13, magnitudine tributum, when describing the heavy taxation imposed on the commoners by Gallic nobles. The tax imposed on Macedonia after Pydna is half what the kings were requesting: Livy 45, 18, 7; 29, 5; Plut., Aem. Paul. 28, 3 and the incorporation of Commagene by Tiberius leads to some tax reduction compared to the imposts levied by the local kings: Tac., Ann. 2.56.

[96] Sirks 1991, 21 supports the view that the 8 million units of wheat recorded by Edict XIII of Justinian were expressed in modii of one-third of an artaba, thus dividing by three the most common estimate of available Egyptian tax grain for shipment. Beyond the metrological argument, this seems very low. The cultivable area of ancient Egypt ranged between 6 to 9 million arouras, while the average grain levy for the Constantinopolitan embolè was close to 1.25 artaba per aroura, leading to a 7.5 to 11.25 million artabas range. Even by allowing a quite high overall loss rate of 30% and using the lowest acreage figure, one gets a floor of 5.25 million artabas or over 17 million modii kastrenses. References: P. Cairo.Masp. 67057; Bagnall and Worp 1980, 263-264; Rathbone 1987; Mayerson 2007. Under the Principate, the aggregate grain tax rate would have stood higher at about 2 artabas per aroura: Duncan-Jones 1994, 57, table 4.7

[97] TPSulp. 51, 52, 67, 68 for the evidence of Egyptian grain making its way to Rome and its region.

[98] Duncan-Jones 1994, 53, table 4.6.

[99] Hence Augustus’s desire to abolish free distributions, because they harm farmers’ and merchants’ interests (Suet., Aug. 42.3) and the measures taken by Domitian to restrict further vine planting (Suet., Dom. 7).

[100] Scheidel 2007, particularly pp. 3-5.

[101] Hence the huge investments Augustus undertook in founding overseas colonies, or buying land to ensure veterans would settle as farmers and not as dwellers in the city of Rome. HS 600 million were invested in Italy and 250 million outside to buy land: Res Gestae 16. For the Italian population: Brunt 1971 for a classic synthesis, and Lo Cascio for a higher count: Lo Cascio 1999. For the high count, one can refer as well to Lo Cascio and Malanima 2005. See Scheidel 2007 for a recent synthesis.

[102] Dio 39.24.1.

[103] Dio 54.1; 55.22.3, 26.1-3; 28.1; Tac., Ann. 2.87; 6.13; 15.39.2. Suet., Aug. 42.3 and Claud. 18.

[104] Dio 60.11.3.

[105] Tac., Ann. 15.18.2 and Pliny, Pan. Traj. 29.

[106] Carrié 2003, 170.

[107] When Tiberius offers HS 2 to the merchants, Tacitus makes it clear that the imperial authorities are not selling the grain themselves but have to deal with negociatores: Tac., Ann. 2,.87. Atque ita posthac rem temperavit, ut non minorem aratorum ac negotiantium quam populi rationem deduceret: Suet., Aug. 42.3.

[108] Suet., Claud. 18.2; Tac., Ann. 13.51. Legal sources from the Digest are generally more ambiguous, since they sometimes deal with shipowners without specifying if they are engaged in private trade or not: Erdkamp 2005, 244. Dig. 50.6.6.3 (Callistratus 1 de cogn.) deals with negociatores and navicularii, while Dig. 39.4.9.8 (Paulus, 5 sent.) makes clear that mercatores can get engaged in selling public wheat.

[109] Rickman 1980, 143. The same author notices the absence of agents of the praefectus annonae of Rome in Egypt: ibid, 82.

[110] “The shipment of grain from Alexandria to Puteoli in the first century A.D. was clearly in the hands of Alexandrians”: Rickman 1980, 129. For the tax farmers in late Republican Asia: Cottier et a 2008, 73-74.

[111] Supra,(n. 92).

[112] Cic., 2Verr. 3.191.

[113] Pliny praises Trajan for having alleviated tributary pressure so that the annona would henceforth be purchasing its wheat from the provincials: Plin., Pan. Traj. 29-32. See also Plin., Ep. 10.27-28, where a freedman procurator purchases wheat in Paphlagonia. In Numidia, T. Flavius Macer buys grain for Rome: CIL VIII 5351 = ILS 1435. For legal references regarding public grain purchases: Dig. 7.1.27.3 (Ulp. lib. 18 ad Sab.). As far as the importance for tax levies of respecting local traditions is concerned, we can refer to a later edict sent to Tripolitania in A.D. 366: C. J. XI.48.5.

[114] For a comprehensive list of wheat purchases in Egypt: Rathbone 1997.

[115] Rickman 1980, 76; Tac., Ann. 3.25; Suet., Aug. 14, Dio 56, 1-10. Regarding the law itself, we only possess various legal texts dealing with some of its aspects: see Brunt 1971, 558-566. The lex Papia Poppaea essentially restricted the capacity of unmarried Romans to benefit from legacies.

[116] Tac., Ann. 13.51.

[117] Rathbone 2003.

[118] Rates between 10% and 20% of the grain production are frequently attested for the tributum. With typical return on capital being between 6 and 12%, this would amount to a net levy of around 1% of the capital, a rate actually mentioned for Syria and Cilicia by Appian: Syr. 8.50.

[119] Dig. 50.6.6.6 (Callistratus).

[120] Pliny noted that ships dedicated to the transport of the Egyptian wheat to Rome normally returned empty: Pan. Traj. 31. A century earlier Strabo observed that ships leaving the harbor of Alexandria were heavier than those returning: Str. 17.1.7. Nevertheless, wheat is a bulky and cheap commodity, and we cannot prove that no light luxury cargo would not have been returned from Rome to Egypt as a reciprocity of the Far-Eastern trade, including the newly minted Julio-Claudian gold and silver coins found in India in significant quantities: Bolin 1958; Tchernia 1995; Harl 1996, 303. The presence of African Red Slip Ware in Berenice points as well to the possibility of triangular trade rotes between Rome, Africa and Egypt: Bes and Poblome 2009, 68.

[121] For the distinction between grain bound to Rome as a supply and the specifically free grain distributed to the Roman beneficiaries: Suet., Claud. 18-19; Tac., Ann. 13.51; Gaius, Inst. 1.32c; Dig. 14, 1, 1, 18 (Ulpian 28 ad ed.); 50.5.3 (Scaevola 3 reg.), 50.6.6.3 and 5 (Callistratus 1 de cogn.). These edicts or legal statements normally use annona urbis or populi romani, annona being the generic word for grain supply. The free grain is more specifically called frumentum publicum or frumentatio publica: Res Gestae 15.4; Suet., Aug. 42.3. Gaius, referring to Claudius, is more ambiguous in using the phrase frumentum Romam. Gaius writes under Hadrian or Marcus Aurelius, at a time where the annonae praefectura must have kept ownership of a higher proportion of the tributary grain transported to Rome. Dig. 50.1.8 (Marcinus 1, de indic. public.) uses both annona and frumentum in a local civic context, the first meaning supply, the second the implicitly free grain that is requested by the plebs. See Dig. 48, 12, 3pr. (Pap. 1 de const.) where frumentum, used alone, is the grain and annona the level of (not free) supply of a city.

[122] Col., de r. r. praef. 20.

[123] The responsibility for ensuring free grain distribution remained formally an attribute of the Senate until A.D. 44, long after Egypt was incorporated in the Empire, even though the Emperors became more and more involved: Rickman 1980, 73-76. We witness Augustus periodically supplying the plebs with additional grain (Res Gestae), as if Egyptian wheat was not the usual source upon which the Senatorial quaestor relied. Using non-Egyptian grain would have made sense, since wheat shipped from Sicily or Africa was cheaper to transport to Rome. Maybe the free grain of the early Empire was supplied out of Egypt only to a limited degree at that time. This could explain that much commented upon statement by Josephus, that Africa under Nero supplied Rome during 8 months of the year in contrast to 4 months only for Egypt: Bell. Iud. 2.383-5. Josephus would be talking about the freely distributed grain and not the grain sold in Rome by private merchants, confirming that the Roman authorities in charge of delivering the free grain were avoiding using Egyptian grain as much as they could. We would be dealing with two very different processes between tax grain offered in Rome or sold to traders for eventual sales in Rome or elsewhere. See Virlouvet 2003.

[124] Kessler and Temin 2008, 154.

[125] CIL IV 4811.

[126] CIL IV 1858. The inscription reads as follows in the CIL: FRVMIINTVM H A > IIX. The author notes that the H could be read as IS. The lecture as 12 asses per modius derives in fact from Ernest Diehl: Diehl 1910, 391. Assuming the M stands for modius, H is in reality IS and means 1.5, that the symbol that follows is an A that stands for as, and that the half X was originally a full X, then 1.5 modius is worth 18 asses. This reading is upheld by Breglia 1950, 50, n. 2, and followed by Mrozek 1975, 11, n. 3. Regarding the use of S as sign for half a unit: Varone 2000, 279. I wish to thank Jean Andreau for his kind help regarding that uncertain inscription and its possible meanings.

[127] Mrozek 1975, 10-14, 16, 22, with, CIL IV 5380, 8566, and 4227.

[128] Allen 2001, 418.

[129] Allen 2007. His results are used in Scheidel 2009, for instance.

[130] See Moritz 1958, 151-183. In 2nd and 3rd centuries A.D. Ephesus, the price range between the best and the poorest quality bread is a little over 1:2: IvE 923-24; 3010; see as well Broughton 1938, 879-880; Jasny 1947, 190.

[131] For the gold market price being most likely at least twice its official price: Bagnall 1985, 28. If the Edict were to be followed, the quantity of gold that will be later incorporated in a solidus would buy 3 artabas of wheat, although the 4th century average is 8 artabas per solidus in Egypt. Regarding the compulsory purchases of gold and silver: Bagnall 1977, 322-336; Carrié 1988, 128-130.

[132] Butcher and Ponting 2005, 117.

[133] Mrozek 1975, 11.

[134] Moritz 1958, 191, 197 with tables VIII and X.

[135] Jasny 1944.

[136] From Pliny NH 18.66, where 1 modius weights between 20 and 21 Roman pounds. See Foxhall and Forbes 1982, 43. A Roman modius is worth 8.62 liters: Bagnall 2009, 187, table 8.3.

[137] Cato, de Agr. 56.

[138] Thurmond 2006, 15; Allen 2007, 11, table 2, used by Scheidel 2008, 5, table 1.

[139] Supra (2nd sentence after n. 135).

[140] Moritz 1958.

[141] Ibid, 195-209. This is consistent with more recent experiments: Foxhall and Forbes 1982, 76 and close to Carrié’s calculations where 1 kilo of wheat provides 660 g. of the highest quality white bread, 1 k. of second quality flour bread and 1.32 k. of whole wheat bread (Carrié 1975, 1045-1046).

[142] Cato, de Agr. 56.

[143] In Roman Egypt, milling costs seem a little lower than 10% of wheat price: Drexhage 1991. In later Byzantine sources, the margin that bakers are allowed to charge of top of wheat costs is c. 17% of the bread final price: Koder 1991, 128-130. The difference may well be explained by the quality of the bread produced: a single milling with an extraction rate of 90% between grain and flour would produce a lower quality bread at lower costs.

[144] Jasny’s simulations point to a 10% grinding costs in classical Rome, before taking into account any profit component: Jasny 1944b, 159.

[145] Mrozek 1975, 22-23.

[146] CIL XIV 2112. For a collegium, we will use 500 g. of bread a day as per Allen’s respectability basket: Allen 2007,11, table 2.

[147] CIL XI 6117. We may question whether benefactors tended to sell grain at standard pre-crisis prices or just a little below shortage prices. One piece of Athenian evidence seems to support the it may have been generally the former: during the 4th century B.C., Athenian wheat prices average around 5 to 6 drachmas per medimnos: Heichelheim 1935; during this period Herakleides of Cyprian Salamis is credited for having sold 3,000 medimnoi of wheat at a price of 5 drachmas a medimnos during a food shortage – IG II^2 360 – SIG^3 304.

[148] Duncan-Jones 1974, 51,144-145, 208, N° 1172.

[149] The Egyptian prices used by Scheidel in order to monetize the "Mediterranean respectability basket" imply that bread would have accounted for about 32% of the food costs: Scheidel 2009, 5, table 1. This seems significantly too low, since wheat would have represented about 70-75% of the ancient Mediterranean diet: Foxhall and Forbes 1982, 71. Allen, who first proposed that basket, used the prices for the Edict of Diocletian to compute that bread would cost 37% of food costs: Allen 2007, p. 11, table 2. The bread’s share in calorific intake is then 70%: Ibid. p. 11 with Allen 2001, p. 421. This said, a Roman laborer could have only borne 56% of that’s basket cost for his family when using his total income (Allen 2007, 6-7). The alternative "Bare Bones basket" (p. 12, table 3) proposed by Allen seems then preferable for the poorer classes, where wheat accounts for over 80% of the budget. Poor children raised with state aid must have been closer to the latter situation than to the respectable basket, knowing that wine had to be replaced in their diet as well. Assuming 60-70% for bread in their nutrition budget seems a reasonable assumption. This is why we use a slightly higher daily bread ration at 600 g. compared to the 500 g. of the "respectability basket."

[150] Duncan-Jones 1974, N° 1171.

[151] Ibid, 51. Quoted in Rickman 1980, 148.

[152] Kessler and Temin 2008, p. 143, table 7.1.

[153] CIL VI 10234. A similar amount is known for Ostia: AEp, 1940, 94.

[154] Jasny 1944b; Duncan-Jones 1974, 345-347. appendix 8; Rickman 1980, 239-240 appendix 6. From Plin., NH 18, 89-90.

[155] Traditional rates achieved in Africa and Asia before mechanization reached 75%, while extraction rates for whole wheat are close to 95%. Then, flour volumetric weight for millet and wheat are quite close, although millet is lighter than wheat under its raw form. The result is that flour extracted from millet does not enjoy a much higher volume than the original unmilled cereals, unlike flour extracted from wheat, with the exception of the highest quality of white flour, where the extraction rate is much lower. And this is not that most refined flour that had been used by Jasny, Rickman, and Duncan-Jones to estimate wheat price, since Pliny provided a much higher price for that quality at HS 20 per modius.

[156] Jasny 1944b. That view is shared by Rathbone 2011.

[157] Alessandro Cavagna 2010, 87, 154, 224-225.

[158] Butcher and Ponting 2005, 108.

[159] Mar., Epig. 12.76. Spanish, Martial spent most of his life in Rome but it is likely he wrote this while staying in Spain: Mrozek 1975, 14.

[160] Supra: the 4 paragraphs including and from (n. 30).

[161] Liv., Epit. 60; Cic., pro Sestio, 103. It could have been consistent with the monthly ration of 5 modii being sold for 2 denarii: Rathbone 2009, 304. We know of several earlier exceptional occurrences of very low prices: in 203 B.C., when the aediles sold the wheat stored during the war at 4 asses a modius (Livy, 30.26.5), prices going even to 2 asses in 200 and 196 and to virtually nothing in 202. Livy is most likely using the later Republican monetary standard: Crawford 1985, 18.

[162] Supra The 4 paragraphs including and from (n. 30).

[163] Cic., 2Verr. 3.192.

[164] Cavagna 2010, 224; Faucher and Lorber 2010.

[165] Grainger 1999. See the graphs p. 323-325. The Delian accounts established by the hieropoioi stop in 169 B.C. and cannot be of any use here.

[166] For the references regarding the Roman Republican monetary system: Crawford 1985, notably 147 and 183-185, and Crawford 1974 for the bronze currency weight standards during the 2nd century B.C.; see as well Buttrey 1957.

[167] Regarding the c. 1:110 silver: bronze ratio during the 3rd to 2nd century B.C. Roman monetary history: Crawford 1985, 41, 59, 145. When Augustus resumed the production of a bronze coinage, the implied ratio becomes 1:55: ibid. p. 260.

[168] Crawford 1985, 257-258. On the Punic war debasements: Crawford 1974, 626-628.

[169] Hopkins 1980, 109, Fig. 2; Crawford 1985, 176. The computations by Crawford should not be taken at face value: Buttrey 1993, 335-351. They still provide a general pattern that is unlikely to be profoundly wrong: Hollander 2007, 20. For a recent synthesis on the question of quantification: de Callataÿ 2011, p. 7-29. On mining: Domergue 2008, 85. The 2nd century B.C. to 1st century A.D. period represents a clear peak in Mediterranean silver production, with South-East Spanish mines’ production declining as early as the second half of the 1st century B.C.

[170] Supra (n. 151).

[171] Duncan-Jones 1994, 225, Table 15.5. The metallic analyses of Walker, on which Duncan-Jones had to base his own observations, have been partially renewed since then. Generally speaking, denarii struck after Nero’s reform of c. A.D. 64 contain less silver than previously thought due to some surface enrichment techniques. This does not change the fact the denarius was debased between Nero and Septimius Severus: Butcher and Ponting 2005; Gitler and Ponting 2003.

[172] For a discussion regarding the leap in price inflation or real-terms deflation in Egypt after Marcus Aurelius, Rathbone 1996, 334-335; Bagnall 2002 following Scheidel 2002.

[173] Ibid, 103, based on Rathbone 1996, 329; Rathbone 1997, 197; Duncan-Jones 1976, 246.

[174] A tetradrachm of Commodus would have contained 40% of the silver of a denarius of the same emperor, against a ratio of 67% under Nero, implying a relative loss of 40%: Duncan-Jones, 1994, p. 234, table 15.10. This said, the gap between the tetradrachms and the denarii has been drastically reduced for the period of Nero by more recent research, essentially by lowering the silver content of the denarii : Butcher and Ponting 2005b. The silver ratio between the tetradrachm and the denarius would have been close to 86.5% instead of 67%. We are not aware of any recent analysis of Commodus’s coinage. This said, Walker’s results as summarized by Duncan-Jones pointed to 2.12 g. of silver, whereas we know that the debasement of Septimius Severus brought the silver content down to around 1.55 g. of silver (Gitler and Ponting 2003, 38, table A). It is therefore unlikely Commodus’s denarii would have been significantly below 2 g. of silver. Walker’s metallic analysis found only 0.85 g. of silver in Egyptian tetradrachms of that period. Since the gaps between more ancient and recent methods in determining silver content usually occur for the richer coinage, it seems quite safe to assume that by Commodus the Egyptian billon coinage contained only about 40 to 45% of the silver included in the Imperial coinage. This would imply a halving of the relative silver content of the tetradrachm vs. the denarius between Nero and Commodus.

[175] Caley 1958, 170-171, tables II and III.

[176] Andreau et al. 2008, notably 281-284.

[177] While soldiers’ pay and wheat prices are not necessarily closely correlated, this is worth noticing that until the pay rise under Septimius Severus in A.D. 202 A.D., soldier’s’ pay remained stable for 116 years while the denarius had lost about a half of its intrinsic silver value: Duncan-Jones 1994, 33, 227, revised by Ponting and Butcher 2005a and b. Eventually, the annual number of silver coins struck during the reigns of Commodus seems to have halved – Duncan-Jones 1994, 168 - compared to all previous reigns since Vespasian, which does not support the view of a strong price leap in Rome during that reign. Regarding the potential price stability outside of Egypt during the later 2nd and earlier 3rd century: Bransbourg 2010, 399-408, 456-459.

[178] We know that ancient seamen could not always follow the straightest route, and the distance covered from Alexandria to Rome by following the African coastline as far as Cyrene or edging northwards to Cyprus first increases the distance by a significant factor. We won’t make any adjustment for this, assuming that all our sea routes were somehow affected.

[179] Polybius speaks of the nearby coastal area and of the Po valley itself as a single region.

[180] Mentioned by both Strabo, 5.2.10 and Ptolemy 3.1. See Taus 2006, 330-334 for a virtual map. Vitruvius, 2.9.16, dealing with the transportation of timber down the Adriatic coast from the Ravenna region, mentions the city as a possible destination there, alongside Ancona, implying that a real harbor was available there.

[181] This is the easiest way, knowing that from Commodus onward a classis Africanae had been set-up (SHA Commodus 17.7), and grain was perhaps transported to Carthage first, by sea or directly by land, which would have increased the distance to Rome factor.

[182] Ant. Itin. p. 57, ed. Parthey and Pinder.

[183] Sosin 2002, 142.

[184] Livy, 30.38.5 and 33.42.

[185] Broughton 1940, 879-880.

[186] Jasny 1947, 192.

[187] With an average wheat weight of 60 pounds per bushel.

[188] Burnett et al. 1992, 369-371. The key inscription is the donation of Gaius Vibius Salutaris in A.D. 103/104, where a cistophoric tetradrachm is equated to three denarii: The Collections of Ancient Greek Inscriptions in the British Museum III, 481; see as well Habicht 1975, showing the parallel use of the denarius and of the tetrachalkon normally worth one twelfth of a drachma and here one sixtieth of a denarius. Under Hadrian, cistophoric issues from Mark Antony and Augustus were overstruck. It had most likely no impact on the exchange ratio between denarii and cistophori: Metcalf 1980, 119.

[189] The following references in no way exhaust the vast literature published on that topic: Jones 1963; Mac Donald 1989; Lo Cascio 1981, for an attempted synthesis. We do not encounter the issue at Antioch of Pisidia, since that city was a Roman colony with the ius Italicum and used the Roman Imperial monetary system.

[190] Prince 1968.

[191] Faucher and Lorber 2010, 58.

[192] Price 1987; Kroll 1993, 82-84; 89-91; 118-120; 330; Miller 1972; Howgego 1985, 54-55.

[193] Picard 1998; Johnston 2007, 1-5.

[194] Kroll 1993, n° 733 and Kroll 1996, 52-54.

[195] Howgego 1985, 57-58.

[196] Mitchell 1976, 107; Callu 1969, 58, n. 1; Johnson et al. 2003/1961, doc. 246; Habicht 1975, 4; Melville-Jones 1971; Howgego 1985, 53-60; Johnston 2007, 19-23 and 235; McDonald 1989, 123, n. 15; Mavrogordato 1918.

[197] Wörrle 1988: assaria l. 17 as a minimal interest income; denarii for the donation components and prizes; 300 drachmas in l. 83 for a fine borne by the villagers’ leaders if they were to refuse to provide for the annual sacrifice. The cost of a sacrifice is one bull. Since Roman laws often set fines at twice the cost of the underlying damage, we should infer that a bull cost c. 150 drachmas. We have independent prices from Dacia at about the same period: 5 denarii for a pig, 3.6 denarii for a lamb (Mrozek 1975, 21). Even if regional prices in Dacia could have been relatively low, the implied 30: 1 ratio between a bull and a pig seems high if the drachma had been a denarius. In Egypt, cattle cost an average of 150/200 drachmas i.e., c. 40/50 denarii, and about 10 times the average price for pigs: Jonhson 1936, 231-232. By comparison, in late medieval France and England, bulls cost 3 to 5 times the price of a pig (d’Avenel 1913, IV, 76-83 and 115-121; Rogers 1866).

[198] Heberdey 1912, II, n° 27; A.D. 104.

[199] Broughton 1940, p. 879 with AE 1929, 20 and Robert and Robert 1954, n° 172. The kupros is to be found in Hultsch 1864, 264.

[200] Supra (n. 147).

[201] Cadell and Le Ridier 1997, 28, 32-33; doc. 3, from P. Hibeh I 110.

[202] Personal communication from Roger Bagnall.

[203] Casson 1980, 21-33 and Herz 1988, for the minimalist view of State restrictions regarding Egyptian grain private trade. Erdkamp arrives at quite opposite conclusions: Erdkamp 2005. Regarding the authorizations to import Egyptian grain in Ephesus and Tralles: Boatwright 2000, 92-93. In a similar way, Hadrian rules on Athenian oil trade, restricting its export in order to maintain adequate local supply: IG II^2 1100 and Oliver 1989, 237-238. He also allocates a cash and a grain dole to that city: Dio 76.16.2.

[204] Cic., 2Verr. 3.191-192.

[205] Katsari 2011.

[206] Andreau 2007.

[207] 1 artaba = 10 Egyptian drachmas ⇒ 1 artaba = 2.5 Roman denarii ⇒ 4.5 modii = 2.5 denarii ⇒ 1 modius = 0.55 denarius.

[208] Sosin 2002. See as well Garnsey et al. 1984, 43, n. 55, once Delian prices are adjusted following Sosin.

[209] Cadell and Le Rider 1997, 64; Cavagna 2010, 175-176, 204-205, 224-225.

[210] Le Rider 1986, 45.

[211] As advocated by Rathbone 1983a.

[212] Italian regions, Sicily, and Sardinia never stopped providing supplies to Rome: in the 1st century, T. Caesius Primus purchases wheat in Umbria and Tuscany to sell it in Rome: CIL XIV 2852 = ILS 3696. A curator frumenti publici is attested in Sicily: CIL X 7239. Varro quotes Sardinia as a supplier to Rome: De re agr. 2.3. See the analysis of Pompeii’s pollens showing the importance of local grain supplies: Ciarallo 1994, 137-139. Regarding Rome’s local supplies’ potential role, one must notice that the Tiber’s navigability extended upstream far beyond what was possible in later periods of history: Tchernia 2003. For later periods, the Historia Augusta attributes to Commodus the organization of the African grain fleet: SHA Vit. Com., 17.7. Still later, Pope Gregory the Great frequently deals with the Church’s Sicilian patrimony: Ep. 1.46, and the Church of Ravenna derives from its Sicilian lands 30,000 solidi and 50,000 modii a century later: Lib. Pont. Ecc. Rav., Maurus, III.

[213] Similar mechanisms could apply to the oil market. Finds of amphora stamps from Baetica and Istria are heavily concentrated in the military areas during the first two centuries of the Empire, while nearly absent from Southern Gaul and peninsular Italy for instance, suggesting some official intervention: from A. Tchernia 2011, 115-122 and fig. 1 and 2.

[214] De Leg. ad Gaium, 7.47, trans. Colson 1962 (London).

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