A: THE EFFECT ON PPP BY RELATIVE PRICE CHANGES

APPENDIX 7.A: THE EFFECT ON PPP BY RELATIVE PRICE CHANGES

Arbitrage in goods markets makes it easy to understand why price level changes affect exchange rates, but the effect of relative price changes is more subtle. The following example will illustrate how exchange rates can change because of relative price change even though there is no change in the overall price level (no inflation). Table 7.A summarizes the argument. Let us suppose there are two countries, France and Japan, and each consumes wine and sake. Initially, in period 0, wine and sake each sell for 1 euro in France and 1 yen in Japan. In a simple world of no transport costs or other barriers to the law of one price, the exchange rate, E 5 h/f, must equal 1. Note that initially the relative price of one bottle of wine is equal to one bottle of sake (since sake and wine sell for the same price in each country). To determine the inflation rate in each country, we must calculate price indexes that indicate the value of the items consumed in each country for each period. Suppose that initially

Table 7.A The Effect of a Relative Price Change on the Exchange Rate

Price in Quantity

Euros Consumed Wine

in Euros

Consumed

1 9 1.111 8 Sake

1 1 0.741 1.5 Value of consumption

Price in Quantity

Yen Consumed Wine

in Yen

Consumed

Prices and Exchange Rates 147

France consumes 9 units of wine and 1 unit of sake, whereas Japan con- sumes 1 wine and 9 sake. At the domestic prices of 1 unit of domestic currency per unit of wine or sake, we can see that the total value of the basket of goods consumed in France is 10 euros, whereas the total value of the goods consumed in Japan is 10 yen.

Now let us suppose that there is a bad grape harvest, so that in the next period wine is more expensive. In terms of relative prices, we know that the bad harvest will make wine rise in price relative to sake. Suppose now that instead of the original relative price of 1 sake 5 1 wine, we now have

1.5 sake 5 1 wine. Consumers will recognize this change in relative prices and tend to decrease their consumption of wine and increase consumption

of sake. Suppose in period 1 the French consume 8 wine and 1.5 sake, whereas the Japanese consume 0.333 wine and 9.5 sake. Let us further assume that the central banks of Japan and France follow a policy of zero inflation, where inflation is measured by the change in the cost of current consumption. With no inflation, the value of the consumption basket will

be unchanged from period 0 and will equal 10 in each country. Thus, although average prices have not changed, we know that individual prices must change because of the rising price of wine relative to sake.

The determination of the individual prices is a simple exercise in algebra, but is not needed to understand the central message of the example; therefore, students could skip this paragraph and still retain the benefit of the lesson. Since we know that France consumes 8 wine and

1.5 sake with a total value of 10 francs and that the relative price is 1.5 sake 5 1 wine, we can solve for the individual prices by letting

1.5P s 5P w , and we can then substitute this into our total spending equa- tion (8P w 1 1.5P s 5 10) to determine the prices. In other words, we have

a system with two equations and two unknowns that is solvable:

8P w 1 1:5P s 5 10

Substituting Equation (7.A2) into the previous equation, we obtain

148 International Money and Finance

Since P w 5 1.111, we can use this to determine P s :

ð7 :A4Þ Thus, we have our prices in France in period 1. For Japan it is even

1 :5P s 5 1:111 5 . P s 5 1:111=1:5 5 0:741

easier:

0 :333P w 1 9:5P s 5 10

Substituting Equation (7.A6) into the preceding equation, we obtain

ð7 :A7Þ Thus,

0 :333P w 1 6:333P w 5 10 5 . P w 5 1:5

1 :5P s 5 1:5 5 . P s 51 ð7 :A8Þ Given the new prices in period 1, we can now determine the

exchange rate implied by the law of one price. Since sake sells for 0.741 euros in France and 1 yen in Japan, the euro price of yen must

be h/f 5 0.741. In summary, this example has shown how exchange rates can change

because of real economic events, even when average price levels are con- stant. Since PPP is usually discussed in terms of price indexes, we find that real events, such as the relative price changes brought about by a poor harvest, will cause deviations from absolute PPP as the exchange rate changes, even though the price indexes are constant. Note also that the relative price effect leads to an appreciation of the currency in the country where consumption of the good that is increasing in price is heaviest. In our example the euro appreciates as a result of the increased relative price of wine.