Please help me with all parts of the question! Greatly appreciated.

Exercise 2. Consider a small open economy with 2 periods and one non-storable good. Households receive endowments Y1, Y; 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 carmot borrow or save. Governments can access credit markets and can decide in t = 2 to repay or default (entirely) on its debt. Let D1 be the total face value of the bonds issued by the government in t = 1, to be paid in t = 2, and q1 be the price of a bond of one dollar of face value. International credit markets are populated by risk-neutral foreign investors that can access borrowing [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 govermnent defaults, households receive a xed endowment of Yg = 1'2\"I = 2. If the government repays households receive an endowment Y2 = Y2". From the perspective of period 1, Y; is a random variable Y; uniformly distributed over [3, 5]. A random variable Y is uniformly distributed over [13, b] if and only if Pr(Yy)=::: forge [(1,1)]. (a) Write down the budget constraints for the households and the government in t = 1. (b) 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 govermnent 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, Q1 and the value of debt in t = 1,q1D1. Now suppose that in t = 1, after debt is chosen there is an increase in uncertainty about Y2". Particularly, everybody nds out that Y; is uniformly distributed over [2, 6]. Note that the average of the endowment does not change but the variance increases. (d) Compute the new probability of default and the price of debt in t = 1, Q1 and the value of debt in t = 1, qlDl. Is your answer different from (c)? If so, explain why