this is the home work I need help with,

1. (22 marks total) Consider the following modication of the endogenous interest-rate spread model from Section 2.1 of LNG. Suppose that, rather than there only being two possible income realizations in the second period (Le, 32 and 0), there are three: yg 2 3,1}; with probability pH, y2 = 3,3; with probability 391,, and '92 = 0 with probability p0 = 1 pH p1,, where 3);; > y; > 0. All other elements of the model are the same as in LNG, including the fact that the EH is required to repay as much of the loan in the second period as it feasibly can. (a) (6 marks) For a given interest rate 7'3, let GH(Q) denote the amount the HE would actually repay the bank at t = 2 for an initial loan size Q 2 0, assuming their second- period income was '93. Similarly, let GL(Q), and GQ(Q) denote the actual repayment amounts assuming the HHS second-period income was 3;}, and 0, respectively. Write down mathematical expressions for GH(Q), 6'; (Q), and G0(Q)- Draw these three flmctions on the same graph (one with Q on the horizontal axis), being sure to carefully label any important points on the axes