Question

Short-answer questions 1. Here are some statistics: Inflation Exchange Rates Current Last Year 5 US Japan Mexico Ey/$ 95 Epeso/$ 10.5 100 10 5 (a) List the countries in order of real appreciation (largest appreciation first) relative to the dollar. (b) Taking Last Year's exchange rate as given, what should be the current exchange rate to ensure PPP? (c) Suppose that the movement in the exchange rates were anticipated. According to the UIP, what is the interest rate differential in each country relative to the US? (d) Suppose that PPP will hold in the long run (from now on). Suppose that inflation will be zero in each country going forward. For each country, list whether the nominal exchange rate is expected to appreciate or depreciate in the long run?

Answer 1

The exchange rates provided in the problem are nominal exchange rates (i.e. rates used for converting one currency into another).

a. Real appreciation = domestic inflation > currency depreciation

For Japan, domestic inflation = 0%

Currency depreciation = -5.2%

For Mexico, domestic inflation = 5%

Currency depreciation = 4.76%

So the order is Japan followed by Mexico

b. Japanese Yen

Let us assume a product which costs 100$ last year.

Price this year = 100*(1+5%) = 105$

Converting 100$ to Yen (last year) = 100*100 = 10,000 Yen

Price this year = 10,000*(1+0%) = 10,000 Yen

To ensure PPP, the price of good in one country should be equal to the price in another

--> 105$ = 10,000 Yen

E(Y/$) = 95.24

Mexican Peso

Let us assume a product which costs 100$ last year.

Price this year = 100*(1+5%) = 105$

Converting 100$ to Peso (last year) = 100*10 = 1,000 Peso

Price this year = 1,000*(1+5%) = 1,050 Peso

To ensure PPP, the price of good in one country should be equal to the price in another

--> 105$ = 1,050 Peso

E(P/$) = 10

c. interest rate differential\

Forward rate = spot rate*(1+i_Japan)/(1+i_US)

Forward rate / Spot rate -1 ~= i_{Japan -} i_US

Interest rate differential for Japan = 95/100 - 1 = -5%

Interest rate differential for Mexico = 10.5/10 - 1 = +5%

d. Continuing from part b,

To ensure PPP, nominal exchange rate of Yen E(Y/$) in the current year should have been = 95.24

But the actual nominal exchange rate = 95

To achieve PPP in the long run, Yen will depreciate to reach the rate of 95.24

To ensure PPP, nominal exchange rate of Peso E(P/$) in the current year should have been = 10

But the actual nominal exchange rate = 10.5

To achieve PPP in the long run, Peso will appreciate to reach the rate of 10.