Exercise 5 Consider a small, open economy where there are two types of goods: tradables, represented by T, and nontradables, represented by N. The representative consumer preferences in this economy are given by UðcT; cNÞ 5 cα

T c12α N ;

where cT represents the domestic consumption of tradable goods and cN represents the consumption of nontradables. In this economy, both tradables and nontradables are produced with the following technologies:

YT 5 ATKρT T L12ρT T with ρTAð0; 1Þ

YN 5 ANKρN N L12ρN N with ρNAð0; 1Þ;

where Yi; Ki; Li represent the amount produced of good i, i 5 T; N, while Ki; Li represent, respectively, the amount of capital and labor used as supplies. Assume that factor K possesses total international mobility, while factor L cannot be transferred from one country to another. However, these two factors possess total mobility between the sectors where goods T and N are produced. Assume that this economy is small, so that the real interest rate of Chapter 5 • The Equilibrium Real Exchange Rate 141 i

 $ 0 is a given and that the international market determines the price of the tradable good.

To simplify, assume that good T is the numeraire, so that pT 5 1.

a. Considering the utility function of the representative consumer, explain why P 5 Pα

T P12α N 5 P12α N is an adequate price index for the economy.

b. What is the share of income the representative individual spends on tradable goods?

What is the portion spent on nontradable goods?

c. Assuming the Law of One Price for the segment of tradable goods, obtain an expression for the real exchange rate between the foreign economy and the domestic economy, as a function of the relative productivity between the two sectors.

d. Applying a condition of zero profit in the sector that produces nontradable goods, calculate the price pN as a function of aT; aN. Evaluate the result when ρT 5 ρN.

e. How does the increase in productivity affect the price index P? In other words, what is the sensitivity of P in relation to aT and aN.

f. How does an increase in the interest rate i affect the price index P?