Chapter 10: Market Power: Monopoly and Monopsony ID: Name: HW #9: Due Monday, 4th July REVIEW QUESTIONS 1. A monopol i s t i s produci ng at a poi nt at whi ch marginal cos t exceeds marginal revenue. How s hould i t adjust i ts output to i ncreas e profit? When marginal cost is greater than marginal revenue, the incremental cost of the last unit produced is greater than incremental revenue. The firm would increase its profit by not producing the last unit. It should continue to reduce production, thereby decreasing marginal cost and increasing marginal revenue, until marginal cost is equal to marginal revenue. 2. We wri te the percentage markup of pri ces over marginal cos t as (P - MC)/ P. For a profit-maxi mi zing monopol i s t, how does thi s markup depend on the el as ti ci ty of demand? Why can thi s markup be vi ewed as a meas ure of monopol y power? We can show that this measure of market power is equal to the negative inverse of the price elasticity of demand. P − MC 1 =− P ED The equation implies that, as the elasticity increases (demand becomes more elastic), the inverse of elasticity decreases and the measure of market power decreases. Therefore, as elasticity increases (decreases), the firm has less (more) power to increase price above marginal cost. 3. Why i s there no market s upply curve under conditi ons of monopol y? The monopolist’s output decision depends not only on marginal cost, but also on the demand curve. Shifts in demand do not trace out a series of prices and quantities that we can identify as the supply curve for the firm. Instead, shifts in demand lead to changes in price, output, or both. Thus, there is no one-to-one correspondence between the price and the seller’s quantity; therefore, a monopolized market lacks a supply curve. 4. Why mi ght a fi rm have monopo l y power even i f i t i s not the onl y producer i n the market? The degree of monopoly (or market) power enjoyed by a firm depends on the elasticity of the demand curve that it faces. As the elasticity of demand increases, i.e., as the demand curve becomes flatter, the inverse of the elasticity approaches zero and the monopoly power of the firm decreases. Thus, if the firm’s demand curve has any elasticity less than infinity, the firm has some monopoly power. It is only the competitive firm that faces a horizontal demand curve who has no market power. EXERCISES 5. The fol l owi ng tabl e s hows the demand curve faci ng a monopol i s t who produces at a cons tant marginal cos t of $10. a. Pri ce Quanti ty 18 16 14 12 10 8 6 4 2 0 0 4 8 12 16 20 24 28 32 36 Cal cul ate the fi rm’s marginal revenue curve. 138 Chapter 10: Market Power: Monopoly and Monopsony ID: Name: To find the marginal revenue curve, we first derive the inverse demand curve. The intercept of the inverse demand curve on the price axis is 18. The slope of the inverse demand curve is the change in price divided by the change in quantity. For example, a decrease in price from 18 to 16 yields an increase in quantity from 0 to 4. Therefore, the slope is is − 1 and the demand curve 2 P = 18 − 0.5Q. The marginal revenue curve corresponding to a linear demand curve is a line with the same intercept as the inverse demand curve and a slope that is twice as steep. Therefore, the marginal revenue curve is MR = 18 - Q. b. What are the fi rm’s profit-maxi mi zing output and pri ce? What i s i ts profit? The monopolist’s maximizing output occurs where marginal revenue equals marginal cost. Marginal cost is a constant $10. Setting MR equal to MC to determine the profit-maximizing quantity: 18 - Q = 10, or Q = 8. To find the profit-maximizing price, substitute this quantity into the demand equation: P = 18 − (0.5)(8) = $14. Total revenue is price times quantity: TR = (14 )(8) = $112. The profit of the firm is total revenue minus total cost, and total cost is equal to average cost times the level of output produced. Since marginal cost is constant, average variable cost is equal to marginal cost. Ignoring any fixed costs, total cost is 10Q or 80, and profit is 112 − 80 = $32. c. What woul d the equi li bri um pri ce and quanti ty be i n a competi ti ve i ndustry? For a competitive industry, price would equal marginal cost at equilibrium. expression for price equal to a marginal cost of 10: Setting the 18 − 0.5Q = 10 ⇒ Q = 16 ⇒ P = 10. Note the increase in the equilibrium quantity compared to the monopoly solution. d. What woul d the s oci al gai n be i f thi s monopol i s t were forced to produce and pri ce at the competi ti ve equi li bri um? Who woul d gai n and l os e as a res ult? The social gain arises from the elimination of deadweight loss. Deadweight loss in this case is equal to the triangle above the constant marginal cost curve, below the demand curve, and between the quantities 8 and 16, or numerically (14-10)(16-8)(.5)=$16. Consumers gain this deadweight loss plus the monopolist’s profit of $32. The monopolist’s profits are reduced to zero, and the consumer surplus increases by $48. 6. Suppose that an industry is characterized as f o l l o w s : C = 100 + 2Q2 MC = 4Q P = 90 − 2Q MR = 90 − 4Q a. Firm total cost function Firm marginal cost function Industry demand curve Industry marginal revenue curve. If there i s onl y one fi rm i n the i ndus try, fi nd the monopol y pri ce, quanti ty, and level of profit. If there is only one firm in the industry, then the firm will act like a monopolist and produce at the point where marginal revenue is equal to marginal cost: MC=4Q=90-4Q=MR 139 Chapter 10: Market Power: Monopoly and Monopsony ID: Name: Q=11.25. For a quantity of 11.25, the firm will charge a price P=90-2*11.25=$67.50. profit is $67.50*11.25-100-2*11.25*11.25=$406.25. b. The level of Find the price, quantity, and level of profit if the industry is competitive. If the industry is competitive then price is equal to marginal cost, so that 90-2Q=4Q, or Q=15. At a quantity of 15 price is equal to 60. The level of profit is therefore 60*15-1002*15*15=$350. c. Graphi cal l y i l l us trate the demand curve, margi nal revenue curve, margi nal co s t curve, and average cos t curve. Identi fy the di fference between the profi t l evel of the monopol y and the profi t l evel of the competi ti ve i ndus try i n two di fferent ways . Verify that the two are numerically equivalent. The graph below illustrates the demand curve (P=90 – 2Q), marginal revenue curve (MR=90 – 4Q), and marginal cost curve (MC=4Q). The average cost curve (AC=100/Q + 2Q) hits the marginal cost curve at a quantity of approximately 7, and is increasing thereafter (this is not shown in the graph below). The profit that is lost by having the firm produce at the competitive solution as compared to the monopoly solution is given by the difference of the two profit levels as calculated in parts a and b above, or $406.25-$350=$56.25. On the graph below, we draw the two profit boxes. The profit box is the difference between the total revenue box (price times quantity) and the total cost box (average cost times quantity) or (P – AC)*Q. The monopolist will gain two areas and lose one area as compared to the competitive firm, and these areas will sum to $56.25. Alternatively this difference is represented by the lost profit area, which is the triangle below the marginal cost curve and above the marginal revenue curve (shaded in dark grey), between the quantities of 11.25 and 15. T his is lost profit because for each of these 3.75 units extra revenue earned was less than extra cost incurred. 140 Chapter 10: Market Power: Monopoly and Monopsony ID: MC D MR 141 Name: