Homework 8 rev.pdf

Homework 8 rev.pdf - Homework 8 1 The variable cost curve...

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Homework 8 1. The variable cost curve of a typical photo developer is given by VC(Q) = .25Q 2 where Q is measured in rolls of film per day. The fixed costs of the developer are $100 per day. a) What are the total costs of the developer? What are the marginal costs of the developer? What are the average costs? What is the optimal scale of the firm? b) Illustrate the marginal and average cost curves. Be sure to indicate the optimal scale of the firm and the minimum average cost of the firm. Suppose that there are currently 10 developers in the industry and each firm is producing 30 rolls per day. Assume that the firms are all perfectly competitive. c) If each firm is producing 30 rolls then what must be the price in the market? When each firm is producing 30 rolls are the firms earning normal, supernormal or subnormal profits? Illustrate the profits of the typical developer when it is producing 30 rolls in your diagram for part (b). d) Do you predict that there will be entry or exit from this market? What will be the long run price for developing a roll of film? e) Suppose that the variable costs of developing film rise by 21%. Will marginal cost rise by 21%? Will average cost rise by 21%? Will the optimal size of the firm increase or decrease? By how much will the price rise in the long run? 2. Consider a market composed of 8 buyers and 8 sellers. Each of the 8 sellers has one unit of the good to sell and each of the buyers wants to buy exactly one unit of the good. The reservation prices of the buyers and the costs of production of each of the suppliers are given in the following table; Buyer Reservation Price Seller Cost of 1 Unit Amelia 12 Arthur 3 Blanche 10 Bob 4 Cary 9 Charles 5 Donna 8 David 6 Edwina 7 Edgar 7 Fanny 6 Fred 8 Georgia 5 Glenn 9 Harriet 4 Howard 10 a) Assume that both buyers and sellers are perfectly competitive. What is the market clearing price? What is the total surplus associated with the market clearing price and quantity? b) Match each buyer with a seller such that each can gain by trading with the other (for example a buyer with a reservation value of 4 can be matched with a seller with a cost of 3 and each could gain by trading with the other). What would be the total surplus generated by this matching of every buyer and seller? Compare your answer with (a). c) Although the surplus is higher in (a) than in (b) are there some traders that would prefer the outcome in (b)? d) Bonus: show that there is no matching mechanism that generates more surplus than the surplus generated by the competitive equilibrium.
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3. Suppose that the daily market demand curve for cheese in Parksdale is Q D (P) = 1600 - 50P .
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