Economics 101Summer 2008Homework #4Due 6/17/08Please make sure your homework includes your name and the time and day of your discussion section. In addition, please write legibly and neatly and make sure your answer is clearly marked (you might place a box around your answer). Homework shouldbe stapled (there is no stapler at the lecture), and it should be neat. All homework must beturned in on the date it is due in the large lecture and it must be turned in at the beginning of the lecture. No late homework assignments will be accepted. Note: Homework #4 includes questions on perfect competition, monopoly, natural monopoly, price discrimination, and game theory.1. Suppose there is a perfectly competitive market that is initially in long run equilibrium.For each of the scenarios below, identify what will happen in the short run to the equilibrium price, the equilibrium quantity produced by the firm, the equilibrium quantityproduced by the market, and the level of economic profits received by the firm. Then, identify what will happen in the long run to the equilibrium price, the equilibrium quantity produced by the firm, the equilibrium quantity produced by the market, and the level of economic profits received by the firm. Also, identify whether there will be entry or exit of firms in the long run. I have provided a handy summary table for you to enter your answers. Assume the perfectly competitive industries in this question are constant cost industries with respect to current technology and inputs.Summary Table:Scenario A B C DSHORT RUN Firm Price Firm Quantity Market Price Market Quantity Firm’s economic profitLONG RUN Entry or Exit of Firms Firm Price Firm Quantity Market Price Market Quantity Firm’s economic profitSecnarios (assume each scenario is a separate event and that in the short run, the market price is always sufficient to cover the firm’s variable costs of production):a. People decide that this product is good for their health.b. The price of a complement good increases.c. The price of a substitute good increases.d. People’s incomes increase and this good is an inferior good. 2. Suppose there is a constant cost perfectly competitive industry with a market demand curve that can be expressed as P = 100 – (1/10)Q where P is the market price and Q is themarket quantity. Furthermore, suppose that all the firms in this industry are identical and that a representative firm’s total cost can be expressed as TC = 100 + 5q + q2 where q is the quantity produced by this representative firm. The representative firm’s marginal cost is MC = 5 + 2q. a. In the long run, how many units will this firm produce and what price will it sell each unit for in this market?b. What is the total market quantity produced in this market in the long run?c. When the market price of the good is equal to $5, this market does not provide any units of this good. Given this information and all the other information you have either been given or calculated, write an equation for the market supply curve.d. What is the value of FC for the representative firm in this industry?e. At the long run profit maximizing quantity for the representative firm, what is the valueof VC for the firm?f. Compute the value of consumer surplus and producer surplus in this market. What is the value of total surplus in this market?g. Suppose that demand in this market changes and that at every price the quantity demanded decreases by 475 units. What is the new market demand curve? Given this market demand curve, what are the new equilibrium quantity in the market and the new short run equilibrium price in this market?h. Given the price you found in part (g), will this representative firm choose to produce inthe short run?i. For those firms that choose to produce in the short run, what will the level of short run economic profit for the firm equal?j. In the long run what do you think will happen in this market? How many firms will be in the industry in the long run (hint: it is okay if you get a fractional firm)?3. Suppose there is a monopoly serving a market and the market demand curve is equal toQ = 1000 - 10P. The monopolist’s MC is given by the equation MC = 5 + (2/75)Q. Themonopolist’s TC can be found by calculating the area under the monopolist’s MC curve over the relevant range of production.a. What is the equation for the monopolist’s marginal revenue curve?b. What is the profit maximizing level of output for the monopolist? What price will the monopolist sell the product for in this market? (Hint: the numbers are ugly here, so just round to two places past the decimal and use your calculators!)c. What is the value of TR for the monopolist? What is the value of TC for the monopolist? (Hint: remember to find the TC you will want to compute the area under the monopolist’s MC curve from an output of 0 units to the profit maximizing level of output.) What is the value of economic profit for the monopolist? (Hint: these numbers will not be even, whole numbers. Here is a time when you will want to use your calculators!!)d. Compare your answer in part (c) to your answer in problem (2) for the long run equilibrium in perfect competition. In your comparison compare the market price under perfect competition and monopoly, the market quantity under perfect competition and monopoly, and the level of long run economic profits for the industry (hint: to find this for the perfectly competitive industry you need to find the level of profits for a representative firm and then multiply this amount by the number of firms). In addition compare the value of consumer surplus, producer surplus and total surplus for the monopolist versus the perfectly competitive market. What is the value of the deadweight loss due to the monopoly? I have provided you a handy summary table for your comparison. (Hint: the numbers for the monopoly are ugly….use a calculator.)Perfectly CompetitiveIndustryMonopolyMarket Quantity Market PriceEconomic Profit in IndustryConsumer SurplusProducer SurplusTotal SurplusDeadweight Loss4. The following graph illustrates the market demand curve, the average total cost curve, and the marginal cost curve for a natural monopoly.a. On the graph indicate the quantity this monopolist would produce if it was not regulated. Identify this quantity as Qm. On the graph mark the monopolist’s price as Pm. In addition, label the area that corresponds to the monopolist’s profits.b. On the
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