12. Exchange Rates of Coexisting Moneys

Up to this point we have analyzed the market in terms of a single money and its purchasing power. This analysis is valid for each and every type of medium of exchange existing on the market. But if there is more than one medium coexisting on the market, what determines the exchange ratios between the various media? Although on an unhampered market there is a gradual tendency for one single money to be established, this tendency works very slowly. If two or more commodities offer good facilities and are both especially marketable, they may coexist as moneys. Each will be used by people as media of exchange.

For centuries, gold and silver were two commodities that coexisted as moneys. Both had similar advantages in scarcity, desirability for nonmonetary purposes, portability, durability, etc. Gold, however, being relatively far more valuable per unit of weight, was found to be more useful for larger transactions, and silver better for smaller transactions.

It is impossible to predict whether the market would have continued indefinitely to use gold and silver or whether one would have gradually ousted the other as a general medium of exchange. For, in the late nineteenth century, most Western countries conducted a coup d’etat against silver, to establish a monometallic standard by coercion.46 Gold and silver could and did coexist side by side in the same countries or throughout the world market, or one could function as money in one country, and one in another. Our analysis of the exchange rate is the same in both cases.

What determines the exchange rate between two (or more) moneys? Two different kinds of money will exchange in a ratio corresponding to the ratio of the purchasing power of each in terms of all the other economic goods. Thus, suppose that there are two coexisting moneys, gold and silver, and the purchasing power of gold is double that of silver, i.e., that the money price of every commodity is double in terms of silver what it is in terms of gold. One ounce of gold exchanges for 50 pounds of butter, and one ounce of silver exchanges for 25 pounds of butter. One ounce of gold will then tend to exchange for two ounces of silver; the exchange ratio of gold and silver will tend to be 1:2. If the rate at any time deviates from 1:2, market forces will tend to re-establish the parity between the purchasing powers and the exchange rate between them. This equilibrium exchange rate between two moneys is termed the purchasing power parity.

Thus, suppose that the exchange rate between gold and silver is 1:3, three ounces of silver exchanging for one ounce of gold. At the same time, the purchasing power of an ounce of gold is twice that of silver. It will now pay people to sell commodities for gold, exchange the gold for silver, and then exchange the silver back into commodities, thereby making a clear arbitrage gain. For example, people will sell 50 pounds of butter for one ounce of gold, exchange the gold for three ounces of silver, and then exchange the silver for 75 pounds of butter, gaining 25 pounds of butter. Similar gains from this arbitrage action will take place for all other commodities.

Arbitrage will restore the exchange rate between silver and gold to its purchasing power parity. The fact that holders of gold increase their demand for silver in order to profit by the arbitrage action will make silver more expensive in terms of gold and, conversely, gold cheaper in terms of silver. The exchange rate is driven in the direction of 1:2. Furthermore, holders of commodities are increasingly demanding gold to take advantage of the arbitrage, and this raises the purchasing power of gold. In addition, holders of silver are buying more commodities to make the arbitrage profit, and this action lowers the purchasing power of silver. Hence the ratio of the purchasing powers moves from 1:2 in the direction of 1:3. The process stops when the exchange rate is again at purchasing power parity, when arbitrage gains cease. Arbitrage gains tend to eliminate themselves and to bring about equilibrium.

It should be noted that, in the long run, the movement in the purchasing powers will probably not be important in the equilibrating process. With the arbitrage gains over, demands will probably revert back to what they were formerly, and the original ratio of purchasing powers will be restored. In the above case, the equilibrium rate will likely remain at 1:2.

Thus, the exchange rate between any two moneys will tend to be at the purchasing power parity. Any deviation from the parity will tend to eliminate itself and re-establish the parity rate. This holds true for any moneys, including those used mainly in different geographical areas. Whether the exchanges of moneys occur between citizens of the same or different geographical areas makes no economic difference, except for the costs of transport. Of course, if the two moneys are used in two completely isolated geographical areas with no exchanges between the inhabitants, then there is no exchange rate between them. Whenever exchanges do take place, however, the rate of exchange will always tend to be set at the purchasing power parity.

It is impossible for economics to state whether, if the money market had remained free, gold and silver would have continued to circulate side by side as moneys. There has been in monetary history a curious reluctance to allow moneys to circulate at freely fluctuating exchange ratios. Whether one of the moneys or both would be used as units of account would be up to the market to decide at its convenience.47

• 46For recent evidence that this action in the United States was a deliberate “crime against silver,” and not sheer accident, see Paul M. O’Leary, “The Scene of the Crime of 1873 Revisited,” Journal of Political Economy, August, 1960, pp. 388–92. One argument in favor of such action holds that the government thereby simplified accounts in the economy. However, the market could easily have done so itself by keeping all accounts in gold.
• 47See Mises, Theory of Money and Credit, pp. 179 ff., and Jevons, Money and the Mechanism of Exchange, pp. 88–96. For advocacy of such parallel standards, see Isaiah W. Sylvester, Bullion Certificates as Currency (New York, 1882); and William Brough, Open Mints and Free Banking (New York: G.P. Putnam’s Sons, 1894). Sylvester, who also advocated 100-percent specie-reserve currency, was an official of the United States Assay Office.
       For historical accounts of the successful working of parallel standards, see Luigi Einaudi, “The Theory of Imaginary Money from Charlemagne to the French Revolution” in F.C. Lane and J.C. Riemersma, eds., Enterprise and Secular Change (Homewood, Ill.: Richard D. Irwin, 1953), pp. 229–61; Robert Sabatino Lopez, “Back to Gold, 1252,” Economic History Review, April, 1956, p. 224; and Arthur N. Young, “Saudi Arabian Currency and Finance,” The Middle East Journal, Summer, 1953, pp. 361–80.