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Economics 101 L Homework No. 9 – Solution Key (Due in lab Nov. 3, 2008 for sections 1 & 3. Due in lab Nov. 5, 2008 for section 2.) WORTH 100 POINTS TOTAL 1. WORTH 20 POINTS – 5 POINTS EACH a) Is a firm in a competitive industry considered a price taker or a price setter? Explain what this means. Price taker. This means that the firm does not have any power to set the price for the good in the market. Whatever price the market determines is the price that the firm must charge. b) Is a monopolistic firm considered a price taker or a price setter? Explain what this means. Price setter. A firm with monopoly power can charge whatever it wants for a particular price. This is usually because there is only one firm in the industry or only a few. c) Does a firm with monopoly power in a given industry produce more or less output than if the industry was perfectly competitive? Why? Less. Each firm produces where marginal revenue equals marginal cost. However, the marginal revenue curve for a monopoly lies below its demand curve. The intersection of these curves is always at a lower quantity of output than the intersection of the demand and marginal cost curve for a competitive firm. d) Explain what is meant by price discrimination. Price discrimination refers to the ability of a monopoly to charge different prices to different customers so as to realize a higher producer surplus. 2. Table A gives the total costs for a typical firm in a competitive industry. Table B gives the quantity demanded at varying prices in the market. WORTH 30 POINTS Table A Quantity 0 1 2 3 4 5 6 7 8 9 10 Total Cost 20 21 24 29 36 45 56 69 84 101 120 Table B Marg. Rev. 11 11 11 11 11 11 11 11 11 11 11 Marg. Cost 1 3 5 7 9 11 13 15 17 19 Marg. Rev. Monopoly 23 19 15 11 7 3 Quantity 0 1 2 3 4 5 6 7 8 9 10 Price 23 21 19 17 15 13 11 9 7 5 3 Part A 1) Suppose that the price per unit of output is $11. Using excel, add a column for marginal cost and a column for marginal revenue to Table A. 2 POINTS See above table. 2) Graph the inverse supply and inverse demand curves for this firm. (Remember the relationship between marginal cost and supply.) 4 POINTS See Graph Below 2 Supply/Demand 25 Price 20 15 Demand Supply MR 10 5 0 0 1 2 3 4 5 6 7 8 9 10 11 Quantity 3) Add to the graph, the line representing marginal revenue. 2 POINTS See graph above. 4) What is the profit-maximizing level of output? 2 POINTS 6 units 5) Calculate the consumer surplus. 2 POINTS =(23-11)*6*0.5 = $36 6) Is there deadweight loss? If so, how much? 2 POINTS No deadweight loss in perfectly competitive markets. Part B – Now suppose a firm is able to monopolize this industry. 1) The equation for the inverse demand curve for this firm is P = 23 – 2Q. What is the equation for the marginal revenue curve for the monopoly? 2 POINTS P = 23 – 4Q 2) From Table A above, add a column for marginal cost and a column for marginal revenue for this monopoly. Hint: Use the equation you found in the previous question for marginal revenue. Note: Delete any negative values you get. 2 POINTS See table above. 3) Create a new graph for this monopoly including the inverse supply and inverse demand curves as well as the marginal revenue curve. 4 POINTS See Graph Below Monopoly 25 20 15 Price Demand Supply MR 10 5 0 0 1 2 3 4 5 6 7 8 9 10 11 Quantity 4) What is the profit-maximizing level of output for this monopoly? 2 POINTS 3 4 units 5) What price does the monopoly receive for the good at this level of output? 2 POINTS $15 6) Calculate the consumer surplus. 2 POINTS =(23-15)*4*0.5 = $16 7) Is there deadweight loss? If so, how much? (The graph should help you see this.) 2 POINTS Yes. = (15-7)*2*0.5 = $8. 3. Fill in the missing data on a monopolist in the following table: WORTH 20 POINTS – 4 POINTS EACH Quantity of Output 1 2 3 4 5 6 7 8 a) b) c) d) e) Price 20.00 18.50 17.00 15.50 14.00 12.50 11.00 9.50 Total Revenue 20 37 51 62 70 75 77 76 Marginal Revenue 17 14 11 8 5 2 -1 Total Cost 16 20 25 33 42 53 68 88 Marginal Cost 4 5 8 9 11 15 20 Profit 4 17 26 29 28 22 9 -12 At what quantity will the monopolist produce in order to maximize profits? 4 units What will be the price at this level of output? $15.50 What will be the profits? $29 What quantity maximizes total revenue? 7 units Explain in words why the quantity that maximizes profits is not the same as the quantity that maximizes total revenue. Costs must be considered when maximizing profit. Thus, for profit maximization, output is where MR=MC. Maximizing total revenue does not take into account the cost associated with that level of output. 4. Suppose the ethanol industry exhibits monopolistic behavior. The government wants to encourage a monopolist in this industry to produce more ethanol by paying a subsidy (a negative tax) for each unit produced. WORTH 30 POINTS a. Neatly, on paper, draw a diagram (with quantity on the horizontal axis and price on the vertical axis) representing the initial situation before the subsidy is introduced. (Your graph should contain a linear inverse demand curve, a linear marginal cost curve, and a linear marginal revenue curve.) 10 POINTS See graph below (You may also do this problem in excel if you wish—whichever is easier for you.) b. c. d. e. f. g. h. On your graph, label the profit maximizing level of output prior to the subsidy. Call this Qm1 2 POINTS Label the price the monopoly charges prior to the subsidy. Call this P m1 2 POINTS Label the equilibrium price and quantity if this industry was perfectly competitive. Call these Q c and Pc 2 POINTS Now show the effect of the subsidy. Hint: remember how a tax affects a firm’s supply curve and keep in mind that a subsidy can be thought of as a negative tax—having the opposite effect. 5 POINTS Label the profit maximizing level of output after the subsidy is introduced. Call this Qm2 2 POINTS Label the price the monopoly charges with the subsidy in place. Call this P m2 2 POINTS On your diagram, show how deadweight loss changes from the scenario without the subsidy to the scenario with the subsidy. 5 POINTS 4 The deadweight loss is originally the larger brown triangle. After the subsidy, the deadweight loss becomes the smaller yellow triangle. 1.2 MC1 MC2 Pm1 Pm2 Pc MR D 0 0 Qm1 Qm2 Qc 1.2