PART III: MARKET FOR LEMONS Jessica and Tom are two young professionals looking for a car. They are both rather financially con- strained and decide to orient themselves towards the used car market well-known to our dear Akerlof. Unfortunately, Jessica and Tom are less aware of its workings but still decide to give it a try as prospec- tive buyers. There is a total of N = 1,000 sellers of used cars, and each of them knows the underlying quality of their car and what value they privately attach to it as a result. There are some good quality car sellers (Peaches) in proportion and some low quality sellers (Lemons) in proportion 1 q. However, an uninformed buyer cannot see the quality and need to take the sellers' word for it. Peaches Lemons (Good, ) | (Bad, 1 gq) Sellers | V.7 =10,000 | V; =2,000 Buyers | V.2 = 15,000 | V} =1,000 1. Jessica grew up on a farm and remembers from her youngest age how to fix rusty tractor engines and broken motorcycles. As a result of this experience, she just needs to give a quick look under the hood and can tell right away the quality of the used car. Moreover, she is not afraid of telling the lemon owners that their car is crappy! Suppose that = 0.3 and that there are N7 = 400 customers like Jessica in the market, what is the market clearing quantity? What is the market clearing price (if trade happens in positive quantity)? Hint: Here, there are two separate markets, each with a respective price, as the quality is observ- able. 2. Tom cannot claim such experience with combustion engine vehicles, and is left with having to hear each seller advocate for why their car is in better condition than the seller next door. i. ii. iii. 1v. Derive the supply curve in the market for used car (Q as a function of p), where this time lemons and peaches are combined. Suppose again that = 0.3. Given that Tom cannot give much value to the speeches by the sellers, he uses his economic intuition to try to infer the quality of the car based on the posted price. Based on the supply curve you derived, what is the expected quality of the car given a potential price p 7 What is the expected valuation of Tom as a buyer as a function of p? Hint: Given the range of p, what type of car do you expect will sell and compute the associated expected valuation for Tom. Derive the demand curve supposing that there N7 = 400 customers like Tom and find the equilibrium in the used car market. What does our rational Tom decide to do? Hint: Recall that Tom would be willing to buy if and only if [VB |p} > p. Comment on the type of economic phenomenon happening in this market. What solutions would you suggest to fix the issue? . What would be the minimum g needed so that Tom buyers are willing to take the risk of buying a used car without being sure of the exact underlying quality. 3. Compare the total surplus under perfect information (question 1) and asymmetric information (question 2). Briefly comment