Question

Consider a two-period model of a small open economy that cannot commit to repaying its debt. The endowments are Q1 and Q2 in periods 1 and 2. The world interest rate is r. In period 1, the country can borrow from or lend to the rest of the world, but it cannot commit to repaying its debts. In period 2, if the economy does not repay, then it loses a fraction F of its endowment. The representative consumer has preferences over consumption in periods 1 and 2 given by the utility function U (C1; C2) = log C1 + b log C2. (a) Derive a constraint on the amount of debt that international lenders would be willing to lend to the small open economy in period 1. (b) Suppose that b = 1 2 , r = 0:2, Q1 = 10, Q2 = 60, and F = 1 2 . Solve for the countryís level of consumption in each period and its debt. (c) Would a higher value of b make the debt constraint more or less likely to bind? Explain

Answer 1

a) Q1 and Q2 periods in the Open Economy has representative consumer preferences with utility function U.

Function U = log C1 + b log C2. Let us Period 1 = P1 and Period 2 = P2. Interest Rate = r.

Thus the constraint on the amount of debt can be illustrated by 1 + r = P1/P2 and also endowment reduces to the considerable fraction. i.e. Savings will be nullified here.

b) Level of consumption in P1 = Q1-r/F*b, assuming b=12 is the constant debt price and Q1=10, r=0, F=12.

Then P1 = 10-0/12*12=0.41. (Note:- 0:2, in which 0 is the rate for period 1).

Level of consumption in P2 = Q2-r/F*b, assuming b=12 is the constant debt price and Q2=20, r=2, F=12.

Then P2 = 20-2/12*12=0.75. (Note:- 0:2, in which 2 is the rate for period 2).

Thus the level of consumption can be concluded as P1 < P2.

c) The level of value b makes a high debt constraint.

As Endowment Fraction F have high rate of interest to repay the amount with the described fact of P1<P2.

It was proved in the due course.