Exercise 1 Consider a small, open economy that exists for two periods. This economy has a representative agent who, in the first period, receives an endowment of 6 units of a tradable good ðYT 1 Þ

and 9 units of a nontradable good ðY N 1 Þ. In the second period, this agent receives 13.2 units of the tradable good and 9 units of the nontradable. At the beginning of period 1, the agent possesses neither credit nor debt, so that the net international investment position is B0 5 0.

This country has access to the international financial market, where the current interest rate is i 5 10%. The representative agent’s preferences are given by UðCT 1 ; CN 1 ; CT 2 ; CN 2 Þ 5 lnðCT 1 Þ 1 lnðCN 1 Þ 1 lnðCT 2 Þ 1 lnðCN 1 Þ;

where CT t and CN t represent the consumption of tradable and nontradable goods in period t, respectively, while pTt and pNt represent their prices.

a. Find the demand for tradable and nontradable goods in periods 1 and 2.

b. Find the net international investment position for period 1 ðB

1Þ.

c. For period 2, obtain the equilibrium current-account balance and the relative price of tradable goods in terms of the nontradable. Intuitively explain why pNt changes over time.

d. Let the consumer price index, Pt, be defined as Pt 5 ffiffiffiffiffiffiffiffiffiffiffiffiffi pTtpNt p . Similarly, let the consumer price index for a foreign economy be P

t 5 ffiffiffiffiffiffiffiffiffiffiffiffiffi p

Ttp

Nt p , where the superscript  represents the foreign variables. Nominal foreign prices are denominated in terms of the foreign currency. Assume that the purchasing power parity of tradable goods is valid. Finally, find the real interest rate between periods 1 and 2 that makes the relative price of nontradables in terms of tradables equal to 1 in both periods.