Exercise 4. [42 points] Consider a small open economy with 2 periods. Households receive an endowment 2 in period 2 and are taxed 72 (lump-sum) by the government. Households don't have any savings or borrowing. The government has an outstanding stock of government debt B issued in period 1, which implies repaying B(1 + r) in period 2 (if the government decides to repay), where r is the interest rate on government debt. Suppose this debt is held by risk-neutral foreign investors that can access borrowing/lending at the risk-free international interest rate r* = 0%. 3 The government can be of two types: with commitment or strategic. From the perspective of period 1, the probability of each type is p = ;. The government with commitment repays its debt always. The strategic government chooses to repay or default on its debt to maximize consumption in period 2 for the households. If the government repays, its available endowment is Y = 2. If the government defaults, the available endowment for consumption is given by by = 1. Suppose first that the government can choose to default fully on its debt, i.e. not repay anything to investors. (a) [10 points] Write down the budget constraints for the households and the government in period 2 if the government decides to repay. Write down the budget constraints for the households and the government in period 2 if the government decides to default. (b) [10 points] For what levels of debt B does a risk-less debt equilibrium exist? The answer should provide a range of B. (c) [10 points] For what levels of debt B does a risky debt equilibrium (i.e., an equilibrium in which the strategic government defaults) exist? The answer should provide a range of B. (d) [2 points] Is there a region of multiple equilibria? If so, for what values of B? Suppose now that the strategic government can only choose to fully repay or partially default on its debt. In particular, assume that if the government chooses to partially default it only repays 0.5 dollars for every 1 dollar that it owes, i.e., it repays half of the full amount of repayment. (e) [10 points] What is the interest rate / lenders will ask if they expect the strategic government to partially default