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Jessica and Tom are two young professionals looking for a car. They are both nancially constrained and decide to purchase a car in the used car market (famously studied by Prof. Akerlof). Jessica and Tom are less aware of the workings of the used car market but still decide to give it a try as prospective buyers. There is a total of N S = 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 q and some low quality sellers (Lemons) in proportion 1 q. Peaches Lemons (Goad: Q) (Bad! 1 _ Q) Sellers VM = 10,000 1/; =2,000 Buyers 1/52,, = 15,000 V,B = 1,000 Tom cannot claim such experience with combustion engine vehicles, and is left with having to hear each seller advocate for why her car is in better condition than the seller next door. That is, Tom cannot detect quality directly. (8-) (b) (C) (d) Derive the supply curve in the market for used car (Q as a function of p), where this time lemons and peaches are pooled in the same market. Suppose again that q = 0.3. Given that Tom cannot trust the sellers' claims, 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 ? What is Tom's expected valuation as a buyer as a function of p? Hint: Given the range of 3), what type of car do you expect will sell? Compute the associated expected valuation for Tom. For price ranges where no car is expected to be sold, you can assume that if a car happens to be offered, then it must be a low-quality type. Find the equilibrium in a used car market made up of N T = 400 customers like Tom. What does each 'Tom' decide to do? Hint: Recall that Tom would be willing to buy if and only if ]E [Vlp] 2 p. What is the minimum q needed so that Tom customers are willing to buy a used car when they're unsure of its underlying quality