Exercise 3. Consider a small open economy with 2 periods. Households receive endowment 1'2 in period 2 and are taxed T2 [lumpsulm by the government. Households don't have any savings or borrowing. The government has an outstanding stock of government debt B = 1.5 issued in period 1, which implies repaying B(1 + T] in period 2 (if the government decides to repay). Suppose this debt is held by riskneutral foreign investors that can access borrowing] lending at the riskfree international interest rate r'\" = 10%. The government is benevolent and chooses to repay or default (entirely) on its debt to maximize consumption in period 2 for the households. If the government defaults, the 1 3 is the proportional available endowment for consumption is given by YQU C], where c 2 cost of default. From the perspective of period 1, Y2 is a random variable that can take the value of Y2 = 10 with probability 0.5 and Y2 = 6 with probability 0.5. (a) 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. Now we investigate whether an equilibrium with riskless debt exists. (b) If investors expect debt to be repaid in both states, what is the interest rate for the government bonds? ((3) Given the interest rate found above, does the government prefer to repay in both states (when Y2 is high and when it is low)? [(1) Given your answers to (b) and (c), does an equilibrium with riskless debt exist? Now we investigate whether an equilibrium with risky debt exists. (e) If investors expect debt to be repaid only when Y2 is high, what is the interest rate for the government bonds? (f) Given the interest rate found above, in which states does the government decide to repay and in which to default? (g) Given your answers to (b) and (c), does an equilibrium with risky debt exist