International Finance Theory and Policy
by Steven M. Suranovic

Finance 30-3

# PPP as a Theory of Exchange Rate Determination

The PPP relationship becomes a theory of exchange rate determination by introducing assumptions about the behavior of importers and exporters in response to changes in the relative costs of national market baskets. Recall, in the story of the law of one price, when the price of a good differed between two country's markets, there was an incentive for profit-seeking individuals to buy the good in the low price market and resell it in the high price market. Similarly, if a market basket, containing many different goods and services, costs more in one market than another, we should likewise expect profit-seeking individuals to buy the relatively cheaper goods in the low cost market and resell them in the higher priced market. If the law of one price leads to the equalization of the prices of a good between two markets, then it seems reasonable to conclude that PPP, describing the equality of market baskets across countries, should also hold.

However, adjustment within the PPP theory occurs with a twist compared to adjustment in the law of one price story. In the law of one price story, goods arbitrage in a particular product was expected to affect the prices of the goods in the two markets. The twist that's included in the PPP theory is that arbitrage, occurring across a range of goods and services in the market basket, will affect the exchange rate rather than the market prices.

The PPP Equilibrium Story

To see why the PPP relationship represents an equilibrium we need to tell an equilibrium story. An equilibrium story in an economic model is an explanation of how the behavior of individuals will cause the equilibrium condition to be satisfied. The equilibrium condition is the PPP equation developed above,

The endogenous variable in the PPP theory is the exchange rate. Thus, we need to explain why the exchange rate will change if it is not in equilibrium. In general there are always two versions of an equilibrium story, one in which the endogenous variable (Ep/\$ here) is too high, and one in which it is too low.

PPP Equilibrium Story 1 - Let's consider the case in which the exchange rate is too low to be in equilibrium. This means that,

where Ep/\$ is the exchange rate that prevails on the spot market and, since it is less than the ratio of the market basket costs in Mexico and the US, is also less than the PPP exchange rate. The right-hand side of the expression is rewritten to show that the cost of a market basket in the US evaluated in pesos, CB\$Ep/\$, is less than the cost of the market basket in Mexico also evaluated in pesos. Thus, it is cheaper to buy the basket in the US, or, more profitable to sell items in the market basket in Mexico.

The PPP theory now suggests that the cheaper basket in the US will lead to an increase in demand for goods in the US market basket by Mexico, and, as a consequence, will increase the demand for US dollars on the foreign exchange market. Dollars are needed because purchases of US goods require US dollars. Alternatively, US exporters will realize that goods sold in the US can be sold at a higher price in Mexico. If these goods are sold in pesos, the US exporters will wantto convert the proceeds back to dollars. Thus, there is an increase in US dollar demand (by Mexican importers) and an increase in peso supply (by US exporters) on the Forex. This effect is represented by a rightward shift in the US dollar demand curve in the adjoining diagram. At the same time, US consumers will reduce their demand for the pricier Mexican goods. This will reduce the supply of dollars (in exchange for pesos) on the Forex which is represented by a leftward shift in the US dollar supply curve in the Forex market.

Both the shift in demand and supply will cause an increase in the value of the dollar and thus the exchange rate, Ep/\$, will rise. As long as the US market basket remains cheaper, excess demand for the dollar will persist and the exchange rate will continue to rise. The pressure for change ceases once the exchange rate rises enough to equalize the cost of market baskets between the two countries and PPP holds.

PPP Equilibrium Story 2 - Now let's consider the other equilibrium story, that is, the case in which the exchange rate is too high to be in equilibrium. This implies that,

The left-hand side expression says that the spot exchange rate is greater than the ratio of the costs of market baskets between Mexico and the US. In other words the exchange rate is above the PPP exchange rate. The right-hand side expression says that the cost of a US market basket, converted to pesos at the current exchange rate, is greater than the cost of a Mexican market basket in pesos. Thus, on average US goods are relatively more expensive while Mexican goods are relatively cheaper.

The price discrepancies should lead consumers in the US, or importing firms, to purchase less expensive goods in Mexico. To do so, they will raise the supply of dollars in the Forex in exchange for pesos. Thus, the supply curve of dollars will shift to the right as shown in the adjoining diagram. At the same time, Mexican consumers would refrain from purchasing the more expensive US goods. This would lead to a reduction in demand for dollars in exchange for pesos on the Forex. Hence the demand curve for dollars shifts to the left. Due to the demand decrease and the supply increase, the exchange rate, Ep/\$, falls. This means that the dollar depreciates and the peso appreciates.

Extra demand for pesos will continue as long as goods and services remain cheaper in Mexico. However, as the peso appreciates (the \$ depreciates) the cost of Mexican goods rises relative to US goods. The process ceases once the PPP exchange rate is reached and market baskets cost the same in both markets.

Adjustment to Price Level Changes Under PPP

In the PPP theory, exchange rate changes are induced by changes in relative price levels between two countries. This is true because the quantities of the goods are always presumed to remain fixed in the market baskets. Therefore, the only way that the cost of the basket can change is if the goods' prices change. Since price level changes represent inflation rates, this means that differential inflation rates will induce exchange rate changes according to the theory.

If we imagine that a country begins with PPP, then the inequality given in equilibrium story #1, , can arise if the price level rises in Mexico (peso inflation), if the price level falls in the US (\$ deflation), or if Mexican inflation is more rapid than US inflation. According to the theory, the behavior of importers and exporters would now induce a dollar appreciation and a peso depreciation. In summary, an increase in Mexican prices relative to the change in US prices (i.e., more rapid inflation in Mexico than in the US) will cause the dollar to appreciate and the peso to depreciate according to the purchasing power parity theory.

Similarly, if a country begins with PPP, then the inequality given in equilibrium story #2, , can arise if the price level rises in the US (\$ inflation), the price level falls in Mexico (peso deflation) or if US inflation is more rapid than Mexican inflation. In this case, the inequality would affect the behavior of importers and exporters and induce a dollar depreciation and peso appreciation. In summary, more rapid inflation in the US would cause the dollar to depreciate while the peso would appreciate.

International Finance Theory and Policy - Chapter 30-3: Last Updated on 7/10/99