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1. Peach-Lemon problem Consider the market of used cars. Sellers have two types of cars: peaches (cars in good condition) and lemons (cars in bad condition). If a potential buyer is able to identify quality of a car, his is willing to pay $10000 for a peach and $5000 for a lemon. On the other hand, sellers is willing to sell a peach at $7500 and a lemon at $4000. The game unfolds as below: first, sellers choose to sell or not, and at which price to sell, After that, potential buyers choose to buy or not. Find equilibrium decisions in the following situations: a. There are four times as many peaches as lemons (q=4/5); (15 pts) b. There are four times as many lemons as peaches (q-1/5). (15 pts)Problem 3: The market for product Q has many identical firms, each having the short-run total cost function: STC(q) = 400+5q+q?, where q is the firm's annual output. We also know that the market demand curve for Q is given by: Q =262.5 - 0.5P, where P is the market price. Each firm is currently earning zero economic profit. (a) Calculate numeric values for: E the market price, (ii) each firm's output, the number of firms in the market. (b) State the market level supply curve. (c) Draw the market and firm demand/supply graphs and show your results from parts (a) and (b).2. Consider a market containing four identical firms, each of which makes an identical product. The inverse demand for this product is P = 100 - Q. The production costs for firms 1, 2, and 3 are identical and given by C(q1) = 20q where qi is the output of firm i, i = 1,2,3. The production cost function of firm 4 is C(q4) = 30q4. Assume that the firms each choose their outputs to maximize profits given they each act as a Cournot competitor. a) Derive the Cournot equilibrium output for each firm, the product price, and the profits of all four firms. Remark: in answering (a), you can assume that firms with identical costs (firms 1, 2, and 3) will produce the same output. Under this assumption, the system of four equations (i.e., best replies) reduces to two equations in which you need to solve for firm 4's output and the output of firms 1, 2, and 3. Of course, you can also solve the system of four equations sequentially. b) Assume that firms 1 and 2 merge and that all firms continue to act as Cournot competitors after the merger. Confirm that this merger is unprofitable. c) Now assume that instead of merging with firm 2, firm 1 merges with firm 4. Is this merger profitable? What has happened to profits of firm 2 as a result of this merger?Consider a market with two firms each selling an identical product and with identical costs of c(qi) = 12q2 i i= 1, 2 where qi is the output of firm i. The market demand is given by p(Q) = 20 - Q where q is the total market output, Q = q1 + q2. Each firm chooses its own output to maximize their own profit ("Cournot Competition"). Consider a market with two firms each selling an identical product and with identical costs of c(qi) = =9. i = 1,2 where qi is the output of firm i. The market demand is given by P(Q) = 20 - Q where q is the total market output, Q = q1 + 92. Each firm chooses its own output to maximize their own profit ("Cournot Competition"). (a) Write the profit for firm 1 in terms of its own output as well as the output of the other firm: 71 (91, 92). Write out the profit for firm 2 as well: 72(91 , 92). (b) Solve for the Cournot equilibrium quantities (output quantities where each firm is simultaneously producing its best response). What is the market price? e) Is the output efficient? Derive the efficient level of output and com- pute the deadweight loss from the Cournot equilibrium. (Hint: what is the perfectly competitive market quantity with the two firms act- ino as price fakers? What is the difference in total surplus resulting