Solutions to second problem set 1. The used car supply in a given town consists of 10,000 cars. The quality of these cars range from 5,000 to 15,000 with exactly one car being worth each pound amount between these two …gures. Used car owners are always willing to sell their cars for what they are worth. Demanders of used cars have no way of telling the quality of a particular car. Their demand depends on the average quality of the cars in the market (Q) and on the price P of the cars themselves, according to the equation: D = 1:5Q P (a) If demanders base their estimate of Q on the entire used car market, what will its value be and what will be the equilibrium price of used cars? AVERAGE QUALITY IS 10000. DEMAND = 15000 - P. EQUATING SUPPLY AND DEMAND ONE FINDS P=5000 (b) In the equilibrium described in part a, what will be the average quality of used cars actually traded in the market? ONLY THE CAR WORTH 5000 WILL BE TRADED (c) If demanders revise their estimate of Q on the basis of the average quality of cars actually traded, what will be the new equilibrium price of used cars? What is the average quality of cars traded now? NEW DEMAND IS = 7500 -P. EQUATING SYPPLY AND DEMAND ONE FINDS NEGATIVE PRICE (d) Is there a market equilibrium in this situation at which the actual value of Q is consistent with supply and demand equilibrium at a positive price and quantity? NO. ASYMMETRIC INFORMATION HAS RESULTED IN MARKET BREAKDOWN. 2. There are many entrepreneurs and each has one project that requires an upfront investment of 100. There are two types of projects. The “safe” type of project yields 106 with probability 1 (net return equal to 6). The “risky”project yields either 100 or 110 (a 0 or 10 percent net return), each with probability one half. Entrepreneurs have no funds of their own, and must borrow the entire investment cost of 100 from a bank. Assume that banks are willing to make loans as long as their expected (mean) return is at least 4 percent; entrepreneurs, on the other hand, will borrow if and only if they have some chance of making strictly positive pro…ts. (a) Suppose banks can tell which type of project each entrepreneur has prior to making loans. Show that it is an equilibrium for banks to 1 charge 4 percent interest to safe entrepreneurs and 8 percent interest to risky entrepreneurs. (By ‘equilibrium’ you need to show two things: (1) banks are willing to lend because they are able to make an expected return of 4 percent on their loans, and (2) entrepreneurs are willing to borrow, because they have some chance of making positive pro…ts). RISKY ENTREPRENEURS ARE HAPPY LO BORROW BECAUSE THEY WILL PAY BACK ONLY IN CASE OF SUCCESS. THE BANK’S EXPECTED RETURN FROM A RISKY ENTREPRENEUR IS: 1 1 0+ 8=4 2 2 HENCE BANK IS HAPPY TO LEND (b) Now suppose that banks cannot distinguish safe entrepreneurs from risky entrepreneurs. Assume that the probability of funding a safe (risky) entrepreneur is 50%. i. What will be bank’s mean return be if it o¤ers a 4 percent interest rate to all borrowers? Why isn’t this an equilibrium as de…ned in part (a)? BANK’S EXPECTED RETURN: 1 1 1 1 4 + ( 0 + 4) = 3 2 2 2 2 BANK WILL NOT LEND. ii. Now suppose the bank charges 6 percent to all borrowers. What would the mean return to the bank be if both types of entrepreneurs were willing to borrow at this rate? Will risky entrepreneurs actually be willing to borrow at this rate? Will safe entrepreneurs actually be willing to borrow at this rate? What will the mean return to the bank from charging 6 percent actually be, given the types of entrepreneurs who will actually want to borrow at this rate? Is this an equilibrium as de…ned in part (a)? BANK’S EXPECTED RETURN IF EVERYONE BORROWS: 1 1 1 1 6 + ( 0 + 6) = 4:5 2 2 2 2 ONLY RISKY ENTREPRENEURS WILL BE WILLING TO BORROW. HENCE ACTUAL MEAN RETURN IS: 1 1 0+ 6=3 2 2 BANK NOT HAPPY TO LEND 2 iii. Suppose the bank charges 8 percent to all borrowers. Which type of entrepreneur will be willing to borrow at this rate? What will the bank’s mean return be, given the types of entrepreneurs who will want to borrow at this rate? Is this an equilibrium? ONLY RISKY ENTREPRENEURS. BANK HAPPY TO LEND BECAUSE EXPECTED RETURN IS 4. THIS IS AN EQUILIBRIUM. iv. Explain why the equilibrium in (iii) is ine¢ cient from society’s viewpoint. ADVERSE SELECTION PROBLEM DUE TO ASYMMETRIC INFORMATION 3 Answer to question 3: 4 5 Answer to question 4: 6 7 8