Burdened by Homework? Let us write your essays and assignments Order This Now
There are 3 questions and 40 points in total
You need to show all steps of your work, only writing the final answer is not enough.
Question 1 [13 points] A seller of a good chooses its price (p ≥ 0) and quality (q ≥ 0). The cost of quality q for the seller is C(q) = q2 .
A buyer can be either of type 1 or type 2. If a type 1 buyer purchases the good of quality q at price p, its net utility is 2q − p. If a type 2 buyer purchases the good of quality q at price p, its net
utility is 3q − p. Any buyer who does not purchase the good gets zero net utility. The seller knows the fraction 1/2 of buyers is type 1 while the remaining 1/2 is type 2.
(a) [4 points] Suppose the seller offers a menu of price-quality pairs ((p1, q1), (p2, q2)) where (pt, qt) is intended for type t for t = 1,2. For the two types, write down the individual rationality
constraints IR1,IR2 and the incentive compatibility constraints IC1,IC2 .
(b) [4 points] From the constraints above, show that q2 ≥ q1 .
(c) [5 points] We know that at any menu that maximizes profit of the seller: IR1, IC2 hold with equality and IR2, IC1 can be ignored (you don’t have to prove these results). Using these results, determine menu that maximizes profit of the seller.
Question 2 [17 points] A credit market has two types of borrowers: s (safe) and r (risky); each has proportion 1/2. Any borrower borrows 1 unit of capital to invest in a project. A project can result in either one of the two outcomes: good or bad. Under bad outcome, the return is 0. Under good outcome, the return is xs = 108 for type s and xr = 111 for type r. The probability of good outcome is ps = 2/9 for type s and pr = 1/6 for type r.
A credit contract is given by interest i (which includes both principal and interest). Under this contract, a borrower pays back i to lender if the outcome is good and pays back nothing if the outcome is bad. The opportunity cost of a borrower is B0 = 12. The opportunity cost of a lender is L0 = 7. Assume the credit market is competitive, so a lender makes zero net profit. Showing all steps of your work, answer the following questions.
(a) [3 points] Find the maximum acceptable rate of interest for each type.
(b) [5 points] Consider the full information case where a lender knows types of individual borrowers. Determine interest rates offered, which type gets loan and the aggregate income.
(c) [9 points] Consider the asymmetric information case where a lender does not know types of individual borrowers and only knows there is proportion 1/2 of each type. Determine interest rate offered, which type gets loan and the aggregate income. Then determine if there is a problem of underinvestment or overinvestment.
Question 3 [10 points] Consider an economy with n = 3 goods. The representative consumer of the economy equally weights the goods. The economy has 7 units of labour that the representative consumer supplies.
There are three sectors 1, 2, 3 in the economy, with sector i producing good i. Each sector has a competitive fringe of firms. Initially firms in all sectors use the existing technology (traditional mode) in which 1 unit of labour can produce 1 unit of good and the wage is 1.
There is a new technology (modern mode) in which 1 unit oflabour can produce t > 1 units of the good. The modern mode pays higher wage 1 + v. It is known that 7 = 400, t = 4 and 1 + v = 2 (so that v = 1).
Suppose sectors 2,3 are non-industrialized (that is, all firms in sectors 2,3 use traditional mode) and sector 1 is industrialized (that is, all firms in sector 1 use modern mode). Showing all steps of your work, determine (i) the income of economy and (ii) the demand for each of the goods 1, 2, 3.
Looking for some help? We have it all. Great price and impressive quality