Exercise 5 Consider an endowment economy that exists for two periods. Assume that the representative individual preferences are represented by the following utility function:

U1 5 ffiffiffiffiffi C1 p 1 β ffiffiffiffiffi C2 p

where C1 and C2 represent consumption for periods 1 and 2, respectively. In each period, this individual receives an endowment of 10 units of the only consumer good in this economy. The individual begins with no financial assets, i.e., Bp 1 5 0, and can lend or borrow at market interest rate r 5 10%.

The individual pays lump-sum taxes to the government each period, represented by T1 and T2, respectively. The government does not have any type of financial debt or asset at the beginning of the first period, i.e., Bg 1 5 0. In period 1, the government collects taxes and consumes one unit of consumer good, i.e., G1 5 1. In period 2, the government repeats the same procedure, collecting taxes and consuming G2 5 1. As with the representative agent, the government has access to the financial markets. Assume, moreover, that β 5 ð1=1 1 rÞ.

a. Find the equilibrium values for consumption, trade balance, and current account for each of the two periods.

b. Assume that T1 5 0. Find the value of T2. What is the value of public and private savings in each of the two periods?

c. Assume now that T1 goes from zero to one, while government expenditures remain unaltered. How does this change in taxes affect the current account and fiscal deficit in period 1? Explain your answer.

d. Assume that the government begins to consume two units of consumer goods in the first period ðG1 5 2Þ and that it also doubles the tax burden in the first period, i.e., T1 5 2.

What is the impact of these changes on the current account for period 1? Present an economic intuition for your answer.

96 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS

e. Alternatively, suppose government expenditure increase permanently, i.e., G1 5 G2 5 2.

What is the reaction of the current account in period 1? Compare your result with that obtained in the previous items.