Consider a two-periods a small open economy populated by households and firms with a single good each period.

The preferences of the representative household are described by the utility function (12) = (12)2 where 1 and 2 denote consumption in periods 1 and 2, respectively. In period 1, the household receives an endowment of Q1 = 1. In period 2, the household receives profits, denoted by 2, from the firms it owns. In period 1, the household has access to financial markets where they can borrow or lend at the interest rate = 10%. The household has a zero asset holding position in period 1. Let the budget constraint in the first period be 1 + h = .

Firms borrow in period 1 from the international financial market to invest in physical capital and to produce final goods in period 2. Denote by 1 the amount of debt taken by the firm in

period 1. The production technology in period 2 is given by = 40.5, where and 2121

denote output in period 2 and investment in period 1, respectively.

Both firms and households are subject to the same collateral constraint, with 1 denoting the value of the collateral. Suppose that 1 equals 5. Assume that the economy's initial net foreign asset position is zero (b0 = 0).

Question 1: State the maximization problem of the firm, and compute the firm's optimal levels of period-1 investment and period-2 profits. Provide intuition.

Question 2: State the maximization problem of the representative household, derive the associated optimality conditions, and compute the equilibrium allocation of the country consumption, net foreign asset position (b1), the trade balance, and the current account. Provide intuition.

Question 3: Suppose that a financial panic causes foreign banks to lower their assessment of the value of the collateral. Specifically, suppose that 1 falls from 5 to 1 for firms and from 5 to 0 for households. Solve for the equilibrium levels of investment, consumption, the trade balance, the current account, and the country's net asset position in period 1, and output and profits in period 2. Provide intuition.