Moral hazard in credit markets. A. competitive lender makes loans to a pool of borrowers that are identical. After borrowers have received their loans they choose one of two investment projects. Project G pays the borrower a rate of return of r, with probability pg. With probability 1 Film the entire value of the project disappears, the borrower defaults on the loan, and the lender reeeivm nothing. Project B pays the borrower a rate of return of n; with prolzuibilitgl.r p1,. And with probability 1 * 313,, the entire value of the project disappears, the borrower defaults on the loan, and the lender receives nothing. We assume that ri e: r5, p, 2:- pb, and 13,,[1 + r!) :3- p5[1 + 1],]. The lender can't distinguish between borrower typm and so it charges all borrowers the same interest rate r;. The lender lends an amount L and pays interest rp on funds acquired from depositors. {a} 1Which project would the lender prefer that the borrowers undertake? Explain. {b} Write down an expmesion tor the prot that a borrower tncpmts from Project G. {c} 1Write down an expression for the prot that a. borrower expects from Project B. {d} Suppose r,, = 0.0T, n, = 0.03, p, = [1.99, pi. = {1.5, n; = 0.02, L = 10. Find the value for ff, such that the borrower is indi'erent between projects G and B. Show your work. {e} Plot the lender's expected prot function EhrL} for valum of 1\