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5. Consider a market for used cars, where there are 300 lemons and 600 peaches. Buyers value peaches at $12,000 and lemons at $6,000. (a) If all cars (lemons and peaches) clear the market, what is a condition on the seller's reservation price (willingness-to-sell) for peaches? (b) If sellers value peaches at $1 1,000 and lemons at $4,500, how many peaches sell? (c) Now suppose there are 300 grapefruits on the market (in addition to the 300 lemons and 600 peaches). Buyers value grapefruits at $8,000 and sellers are willing to sell them at $9,000. What types of cars are sold in the market? (d) Given your answer to part c), what is the buyer's new willingness-to-pay for a used car? (e) What types of cars are sold in the market?Consider a market for used cars where each buyer wants to purchase exactly one used car if at all. In case he does not buy a car, his utility is zero. There are two kinds of used cars, good quality, called peaches, and bad quality, called lemons. Let there be 100 lemons with valuation 0 for both buyers and sellers, whereas there are 100 peaches with valuations of 100 for the buyers, and 60 for the sellers. There are 500 buyers, who do not know which car is of which type. a. Explain what type of trade should take place in the efficient outcome. b. Compute the market equilibrium when the buyers know which car is which type. Is the outcome efficient? Explain clearly. c. Now consider the case with asymmetric information; the sellers know the type of their cars but the buyers do not. Explain the market outcome under asymmetric information. Explain clearly whether the market outcome will be efficient.3. (a) In a Solow growth model, with no population growth and no technological growth, what is the Golden Rule level of k, where k is capital per worker? Illustrate this on a graph. (b) Assume that two countries both have the per-worker production function y = ki?, neither has population growth or technological progress, depreciation (8 - 0.05) is 5 percent of capital in both countries, and country A saves 10 percent of output (s-0.10) whereas country B saves 20 percent, (s 0.20), where y (Y/L) and k (K/L) and K is capital and L is labour. What is the steady state level of k, y and c for both countries? (c) Is the steady state level k for country A the Golden Rule Level of k? Explain.Question 4 (6 points) Consider the market for used cars with two types: "lemons" (cars with problems) and "peaches" (cars without problems). Assume that a seller knows whether a car is a lemon or a peach, but a buyer cannot tell until the car is purchased. Suppose that the reservation price of a peach is $6.090 to the buyer and $5:009 to the seller. The reservation price of a lemon is $2.900 to the buyer and $500 to the seller. a. (3 points) Suppose that there are an equal number of peaches and lemons for sale and that buyers know this to be the case. In equilibrium, what proportion of car sales are peaches? b. (3 points) Now assume that the probability of getting a lemon is variable. Suppose that Jorge starts a business to sell tised cars with warranties, In particular, he buys all used cars in the market at $5.000 each (the reservation price of a peach's seller), and sells them at $6.000, of which $1:000 is the cost of The warranty. If the car is a lemon, he refunds the purchase price (that includes the warranty ), and resells the lemon at $2.000 without a warranty. Let p be the fraction of used cars that are lemons, For what range of p is this business profitable for Jorge
