Defaultable Debt. In this section, you will analyze the problem of a country that is considering defaulting on its debt. 1. (15 marks) Consider the problem of a country with a stochastic income y;, which follows an AR(1) process. They choose consumption ; in each period which they value according to a flow utility function u(c) = 79 /(1 o), they discount the future at a rate 3, and they have the ability to issue debt B;y1 up to some debt limit B, which pays off in the following period. The price of their debt is given by q:- Assume that there is a representative agent who makes all decisions about consumption and debt issuance. For now, let's assume that they must repay their debt (no default allowed) and so the price is depends only on value of the risk-free interest rate 1_}_,_,_, which is constant. We can write their problem recursively (dropping time subscripts, and using the notation that B' is the debt issued for the following period) as: v(B,y) =max u(c) +FE[v(B',y) | y] st. cc+qgB B Borrowing Limit log(y') = plog(y) + Stochastic Process e~ N(0,0.) Set 8 =0.98,0 = 2.0,p =0.945,0. = 0.017, and = 0.017. Use a borrowing limit of B = 1. Now, solve this model, produce whatever diagnostic plots you think are necessary to verify that the solution method is working well, and discuss the choices you've made. Then simulate the model for 100,000 years, ignore the first thousand, and report the average bond holdings, both in absolute terms, and as a share of GDP. Discuss your findings. Hint: You should discretize the income process with Rouwenhorst's Method using 21 points, and solve the consumption-savings problem with a grid search, rather than using continuous methods