Question

Consider the following two period, endowment open economy model. A representative consumer with utility represented by U(C₁, C₂). The consumer decides consumption C₁ and C₂, and bond holdings B₁ and B₂. Initial bonds are B₀, and interest rates are r₀ and r₁. Endowments are Q₁ and Q₂. In equilibrium, B₂ = 0 and normalize the prices to one in each period. The consumer’s budget constraint in periods 1 and 2 is respectively:

C₁ + B₁ - B₀ = r₀B₀ + Q₁
C₂ + B₂ - B₁ = r₁B₁ + Q₂

(b) Show that a country that starts as a debtor B0 <0 must have a strictly positive trade balance in either period 1 or period 2 or both.

Answer 1

A country that starts as a debtor must have a positive trade balance in either period 1 or period 2 or both.

Step-by-step explanation:

To show that a country that starts as a debtor must have a positive trade balance in either period 1 or period 2 or both, we need to consider the consumer's budget constraint in each period. In period 1, the budget constraint is given by C₁ + B₁ - B₀ = r₀B₀ + Q₁. If B₀ < 0, then B₁ > B₀, which means the consumer is borrowing in period 1.

This borrowing is possible because the country is a debtor, and the consumer's willingness to borrow implies that the country must have a positive trade balance in period 1 to finance the borrowing.

In period 2, the budget constraint is given by Q₁C₂ + B₂ - B₁ = r₁B₁ + Q₂. Since B₂ = 0, the budget constraint simplifies to Q₁C₂ = r₁B₁ + Q₂. If B₀ < 0, then B₁ > 0, which means the consumer is lending in period 2. This lending is possible because the country is a debtor, and the consumer's willingness to lend implies that the country must have a positive trade balance in period 2 to generate the surplus needed for lending.