pls explain this question, thank you so much.

5. Consider the following moral hazard problem with risk aversion. Assume that a risk- everse individual wants to start a business that requires an initial investment L = 3. The individual has no money, thus he asks a risk-neutral lender to lend him the money required for the initial investment. The return on the business is risky; it is either 17 = 10 with probability 7n.3 or Z = 1 with probability 1 are, where e E {0, 1} denotes the effort level of the individual. Specically, let so = 1/4 and 1T1 = 3/4 and suppose that exerting effort is costly to the individual which is given by 1); = 1/2. Suppose the individual receives utility from any transfer t according to the function u(t} = t1\". Finally, suppose the lender does not observe if the individual exerts effort or not1 and the nancial contract consists of repayments {(21 El} to the lender, depending upon whether the business is successful or not. (Note that Mat) = u'1(:r) = 3:3-) (a) Write down the optimization problem of the lender where he induces effort from the individual. Transform this problem to the usual form. [b] Make the necessary substitutions and show that the lender's optimization problem is a proper concave program. (c) Show that both the incentive compatibility and the participation constraints of this problem are binding. (d) Find the optimal repayments that solve the lender's problem. Does the lender nd it protable to lend money to the individual? Explain. (e) Find the second-best cost of inducing effort and verify that the lender prefers in- ducing eifort over not inducing it