Exercise 1. Consider an small open economy with 2 periods and one non-storable good. Households receive endowments l\"; , Y2 in periods 1 and 2, respectively, and are taxed (lump sum) by the government. Let T1, T2 be the lump sum taxes paid by households in periods 1 and 2, respectively. Households cannot borrowr or save. Governments can access credit markets and can decide in t = 2 to repay or default [entirely]I on its debt. Let D1 be the face value of a zerocoupon bond issued by the government in t = 1, to be paid in t = 2, and q1 be the price of the bond) International credit markets are populated by riskneutral foreign investors that can access borrowingf lending at the international interest rate r. The government is benevolent and chooses debt repayment to maximize consumption in t = 2 for the households. If the government defaults, households loose a fraction I of their endowment in period 2. From the perspective of period 1, output in t = 2 is a random variable Y: uniformly distributed over [0, 2]. A random variable Y is uniformly distributed over [(1,151] if and only if Pr' gm: 2\" foryE [a,b]. c (a) Write down the budget constraints Jfor the households and the government in t = L {b} 1|Write down the budget constraints for the households and the government in t = 2 if the government decides to repay; Write down the budget constraints for the households and the government in t = 2 if the government decides to default; Suppose the equilibrium level of debt in t = 1 is given by D1 = l. {c} Compute the probability of default and the price of debt in t = 1, ql and the value of debt in t = 1, qlDl. Now suppose that in t = 1, after debt is chosen everybody nds out that K; is uniformly distributed over [I], 1] {d} Compute the newr probability of default and the price of debt in t = 1, {J1 and the value of debt in t = 1, 91191. (e) Compute the optimal debt haircut (i.e. percent reduction in face value) that maxi- mizes the value of debt q1(D)D for foreign investors. Now suppose that the original level of debt D, was held equally by N investors, i.e. each of the investors holds debt worth ~ in face value. Suppose a debt haircut as calculated in (e) is proposed to every individual investor. (f) Compute the value of debt for an individual investor that decides to participate in the haircut if all remaining investors also decide to participate. Compute the value of debt for the same investor if he decides not to participate in the haircut when all others decide to participate. For which / will an individual investor prefer to participate in the haircut if all other investors are participating