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Arbitrage in the Ancient World

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Thales of Miletus made a fortune in the olive market nearly 600 years before the Christian era. But how did he do it?

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MINYANVILLE ORIGINAL Thales of Miletus is one of the earliest Greek philosophers about whom we have some reliable information. About 2,600 years ago, he investigated nearly every branch of knowledge, proposing non-magical explanations expressed in straightforward, testable terms. He probably traveled widely, and linked Egyptian and Mesopotamian observation and practical knowledge to Greek mathematical theory. He is credited with extensive discoveries in both pure and applied mathematics, and he applied his philosophy to both experimental science and practical endeavors. The most famous of those endeavors is described by Aristotle, writing over 200 years later:
There is the anecdote of Thales the Milesian and his financial device, which involves a principle of universal application, but is attributed to him on account of his reputation for wisdom. He was reproached for his poverty, which was supposed to show that philosophy was of no use. According to the story, he knew by his skill in the stars while it was yet winter that there would be a great harvest of olives in the coming year; so, having a little money, he gave deposits for the use of all the olive-presses in Chios and Miletus, which he hired at a low price because no one bid against him. When the harvest-time came, and many were wanted all at once and of a sudden, he let them out at any rate which he pleased, and made a quantity of money. Thus he showed the world that philosophers can easily be rich if they like, but that their ambition is of another sort. He is supposed to have given a striking proof of his wisdom, but, as I was saying, his device for getting wealth is of universal application, and is nothing but the creation of a monopoly. It is an art often practiced by cities when they are want of money; they make a monopoly of provisions.

--Aristotle, Politics, Book 1 section 11, translated by Benjamin Jowett

Although this story is beloved by economics professors and textbook writers, I have never seen any of them point out that Aristotle makes three conflicting claims, and none are credible.

The most explicit claim is that Thales profited by creating a monopoly. The problem is that a monopolist profits by restricting supply. In a "great harvest," all the presses are in use anyway, so there is no advantage to restricting supply. The monopoly is most valuable in bad harvest years.

In a free market, the price for olive pressing services is set by the cost of the marginal producer - that is, the last press put into service. People begin by using the most efficient and convenient presses, but as these reach capacity, the additional olives will be shunted to older, smaller presses that are farther away, require more labor to operate, and produce less and lower-quality olive oil.

To make the point in simple numbers, suppose the olive harvest can be anything from 1,000 to 4,000 tons of olives. Call this value H. Each ton can be pressed for one amphora of olive oil. The price of olive oil is one over the square root of the harvest size in thousands, so one stater per amphora at the minimum harvest and 0.5 stater per amphora at the maximum harvest.

The most efficient press can produce one amphora olive oil for 0.1 stater. Each extra amphora of oil to be produced requires service of a press that costs 0.0001 stater more, so the marginal cost of pressing is 0.1 + H / 10,000. The average cost of pressing is 0.1 + H / 20,000.

The total value of olive oil produced is (1,000H)0.5 which ranges from 1,000 stater (1,000 amphoras at 1 stater per amphora) to 2,000 stater (4,000 amphoras at 0.5 stater per amphora). The total processing cost is H times the average cost, so 0.1H + H2 / 20,000, which ranges from 150 to 1,200 stater.

The free market price for pressing services is 0.1 + H / 10,000, which is the cost of operating the marginal press. Therefore, the total free market revenue for pressing is 0.1H + H2 / 10,000, which goes from 200 at minimum harvest to 2,000 stater at maximum harvest. The total profit for all pressers is revenue minus costs or 0.1H + H2 / 10,000 – 0.1H – H2 / 20,000 = H2 / 20,000. This ranges from 50 stater at minimum harvest to 800 stater at maximum harvest.

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