Please answer

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 (GOOd: 9') (Bad: 1 _ 9') Sellers 11;, = 10, 000 143 = 2, 000 Buyers 1713'; 2 15, 000 17,3 = 1,000 1. Jessica grew up on a farm and remembers from her youngest age how to x 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 a lemon! Suppose that q = 0.3 and that there are N J = 400 customers in the market, all of them just like Jessica (i.e. with the ability to detect a car's quality). 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 observable