Exercise 3 Consider the model of an open economy with two periods, with only one good and with no investment. The representative consumer preferences for this economy are represented by the utility function:

94 PRINCIPLES OF INTERNATIONAL FINANCE AND OPEN ECONOMY MACROECONOMICS U1 5 ffiffiffiffiffi C1 p 1 β ffiffiffiffiffi C2 p ;

where, as is usual, Ct represents consumption for period t and parameter β is the intertemporal discount factor. Assume that r 5 0:10 and that β 5 1=ð1 1 rÞ. The representative consumer possesses net wealth in the initial period of ð1 1 rÞB1 5 1, besides receiving an endowment of 5 units of goods during period 1, and 10 units in period 2. There is perfect capital mobility.

a. Compute the consumption in equilibrium for both periods, and the trade balance and the current-account balance for the first period.

b. Now assume that the government imposes a capital control, where it is required that the net international investment position at the end of period 1 is not negative, i.e., B2 $ 0.

Find the equilibrium value of the domestic interest rate for periods 1 and 2, the trade balance and the current-account balance for period 1.

c. Evaluate the impact of the capital controls on welfare. In a more specific way, find the utility level for the representative agent under capital control and compare with the level of utility obtained when capital controls do not exist.

Now consider that the country experiences an increase in endowment for period 1, which becomes Y1 5 9, while the endowment for period 2 remains unchanged.

d. Considering the case of free mobility of capital between countries, compute the effect of this product shock on the equilibrium consumption for periods 1 and 2, the trade balance and the current-account balance.

e. Now consider a situation with capital controls as described in item (b). Is there any change in the behavior of the representative consumer?