Exercise 4 There are two economies, one domestic and the other foreign. There are two types of goods:

tradable and nontradable. Assume that the foreign economy consumes only tradable goods.

The domestic economy, however, consumes both tradable and nontradable goods. The nontradable goods answer for 50% of the consumption basket of the domestic economy. The production function for tradable goods is identical in both countries, given by YT 5 aTLT;

140 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS where YT is the amount produced of the tradable good, LT is the amount of labor employed in the productive process, and aT . 0 is the parameter that measures the productivity of the tradable goods sector. The production function of the nontradables is given by YN 5 aNLN;

where YN is the quantity of the nontradable good produced, LN is the amount of labor employed in the productive process, and aN . 0 is a parameter that measures the level of productivity in the nontradable goods sector.

Both the product and the factors markets are perfectly competitive and labor is fully mobile within each economy, but does not possess international mobility.

a. Assuming that the Law of One Price for the tradable goods segment is valid, derive the expression for the real exchange rate between the foreign and domestic economies, as a function of the relative productivity between the two sectors.

b. Assume that both aT and aN grow at a rate of 3%. What will be the real exchange rate growth rate? Is the relative Power of Purchase Parity valid? Is the absolute Power of Purchase Parity valid? Explain your answers.

c. Now assume that aT grows at a rate of 4% and that aN grows at a rate of 3%. What will be the real exchange rate growth rate? Will the Power of Purchase Parity, in its relative or absolute version, be valid? Explain your answers.