Chapter 10: Monopoly Answers to Study Exercise Question 1 a) horizontal; downward sloping b) marginal revenue; marginal cost; equals; is greater than c) greater than d) less than Question 2 a) Total revenue (along the demand curve) is equal to price times quantity demanded. Average revenue is equal to total revenue divided by quantity. So note that average revenue is simply equal to price. The completed table is shown below. Price ($) Quantity Total Revenue ($) Average Revenue ($) Marginal Revenue ($) 20 100 20 100 = 2000 2000/100 = 20 18 125 18 125 = 2250 2250/125 = 18 250/25 = 10 16 150 16 150 = 2400 2400/150 = 16 150/25 = 6 14 175 14 175 = 2450 2450/175 = 14 50/25 = 2 12 200 12 200 = 2400 2400/200 = 12 50/25 = 2 10 225 10 225 = 2250 2250/225 = 10 150/25 = 6 8 250 8 250 = 2000 2000/250 = 8 250/25 = 10 6 275 6 275 = 1650 1650/275 = 6 350/25 = 14 4 300 4 300 = 1200 1200/300 = 4 450/25 = 18 b) Marginal revenue is equal to the change in total revenue divided by the change in quantity. In the table above it is shown for a change from one row to the next. For any given quantity, marginal revenue is less than price. This is because in order to sell more output, price on all units must fall. Thus the price on the new units is not equal to marginal revenue we must subtract from this new price the amount that we lose on the previous units by having to reduce their price.
2 c) The scale diagram is shown below. Note that the MR curve is plotted at the midpoint of the intervals of quantity demanded. d) The scale diagram is shown below. When TR reaches its maximum, an increase in quantity (and a reduction in price) leads to no change in total revenue. Thus marginal revenue at this point is exactly zero. At larger quantities than this, marginal revenue is negative. Question 3 a) The profit-maximizing quantity is where MR=MC, at 400 games per week. The profitmaximizing price is $60 per game.
3 b) The ATC at Q = 400 is $30 per game. c) At the profit-maximizing price and quantity, the profit is given by the rectangle defined by points acef. The total profit is ($30 per game) (400 games per week) = $12 000 per week. Question 4 a) For any firm, profits are maximized at that level of output where marginal revenue equals marginal cost. In the diagram, MR equals MC at output of Q 0. At this level of output, the monopolist charges the price p 4. b) Profits per unit are equal to price minus average total cost. Thus the profits are the rectangle defined by the points p 2 p 4 BC. Since price exceeds average total cost, the monopolist s profits are positive. c) Consumer surplus is the triangle defined by the points p 4 AB. As always, it is the area below the demand curve and above the price line. d) If the industry were instead a perfectly competitive one, equilibrium price and quantity would be determined by the intersection of demand and supply, where the industry supply curve would be given by the summation of the firms MC curves. Thus point D would be the competitive equilibrium, with price p 3 and quantity Q 2. e) Consumer surplus in part (d) would be the triangle defined by points p 3 AD, the area under the demand curve and above the (competitive) price line. Question 5 a) The diagram is shown below. The demand curve and its associated marginal revenue curve are conventional. The monopolist s MC curve is the horizontal axis, since we are told that the firm has no variable costs whatsoever. b) The profit-maximizing output is where MR = MC. But in this case it is where MR equals zero
4 since MC is always equal to zero in this example. In the diagram the profit-maximizing output is Q* and the price is p*. c) The marginal value of the water to society is given by the current market price, p*. The marginal cost to society is zero. Thus allocative efficiency is not achieved with this outcome, as is usual in the case of a monopolist. The problem is that producing more than Q* would benefit society by more than it would cost society, and so society as a whole would be better off if the price were lower and quantity were higher. The monopolist (only part of society) is better off to restrict output and raise price. Question 6 a) The two diagrams are shown below. Note that the horizontal scale is different on the two diagrams. The left-hand diagram shows industry output, Q; the right-hand diagram shows the firm s level of output, q. b) If the farmers could successfully collude to restrict output, they would collectively act like a monopolist, choosing output such that MR equals MC. They would collectively produce output equal to Q M and charge price p M. c) In the right-hand diagram, we see that the cartel s restriction of output requires the typical farmer to produce output equal to only q M. (Since Q M is roughly one-half of Q 0, it must be the case that for the typical firm q M is roughly half of q 0, as shown in the right-hand diagram.) The high price of p M means that the typical farmer earns profits given by the light shaded area. d) Yes, it is definitely profitable for each individual farmer to increase its output rather to leave output at q M. Given that all other farmers are restricting their output, the industry price of p M becomes each individual farmer s MR curve. But MC is much lower than p M, so each individual farmer would like to cheat on the agreement and produce more. e) Given the cartel price of p M, each individual farmer has the incentive to increase output all the way to q*, where the cartel price is equal to MC. In this case, profits for the individual cheating farmer would be the sum of the two shaded areas.
5 f) If all firms cheated in this way, the industry output would rise significantly and the market price would fall below the cartel price p M. This is exactly why cartels tend to be unstable; all individual cartel members have the incentive to cheat on the agreement, and this cheating essentially eliminates the output-restricting behaviour of the cartel. Question 7 Remember that price differences are discriminatory only if not justified by cost differences. a) It seems clear that airline pricing is discriminatory, discriminating against business travellers who travel mostly during the week and have inelastic demands. b) The price differences between business class and economy class are partly discriminatory but are also partly based on cost differences. For example, the use of 50 percent more space would appear to justify prices 50 percent higher. But space occupied is not the only cost. It would be surprising, however, if there were not a good bit of price discrimination included in business-class fares, reflecting the greater willingness to pay on the part of those having expense accounts, or those who like the snob appeal. c) These price differences are clearly discriminatory. The sales personnel are trying to extract as much consumer surplus as possible from each consumer. For those customers that like to bargain and show that they are prepared to walk out the door and purchase from other firms, a lower price is surely available. But for those who dislike bargaining and want to make a quick purchase, their inelastic demand will result in a higher price being paid. In this case of hurdle pricing, the hurdle that must be cleared in order to get the low price is to actively bargain with the sales personnel. d) We cannot tell without knowing how the costs differ in economics and in law which they probably do to some extent. Given that law graduates can expect higher incomes than economics graduates, one would expect the market solution to be to extract some of the consumer surplus for the suppliers of the training. Question 8 a) With perfect price discrimination, the monopolist would choose output where the demand curve intersects the MC curve, and so would sell 600 games per week. The price on the last game would be $40. b) Without price discrimination, the single-price monopoly output yields consumer surplus given by the triangle cde. c) With perfect price discrimination, the consumer surplus is zero because each unit is sold at the highest price consumers are willing to pay for that unit (the height of the demand curve). d) It is difficult to practise perfect price discrimination because the monopolist would need to know consumers willingness to pay for every unit and would also have to be able to prevent arbitrage. More likely forms of price discrimination might include: different prices for different customer "groups" such as business vs. leisure
6 Question 9 different price on different days of the week different prices for different times of the day bulk purchase discounts in which customers buy several games in advance for a lower price per game than is available when customers buy a single game a) The two scale diagrams are shown below. Note that both the vertical and horizontal scales are different on the two diagrams. b) The MR curves are also shown in the diagrams above. Notice that the horizontal intercept of the MR curve is exactly half of that for the demand curve, and that the vertical intercept is the same as that for the demand curve. c) The MC curve is horizontal at $15 in both diagrams. The horizontal MC curve reflects the assumption that the scale of production does not affect Levi s cost for producing an additional unit (though any fixed costs would imply that average costs decline as output rises). d) To solve for the profit-maximizing level of output in each market segment, we must set MR = MC in each segment separately. Since the markets are completely segmented, this problem is just like having two independent monopoly problems, the solution to each being to have MR = MC. Keeping in mind that the MR curve is twice as steep and has half the horizontal intercept as its associated straight-line demand curve, the equations for the two MR curves are: Q D = 75 (0.5)MR E and Q D = 125 2MR A For the European market, we set MR E = 15. This gives Q D = 75 7.5 = 67.5. At this quantity, the price in Europe is given by the demand curve (Q D = 150 p) which gives p* = 82.5. For the American market, we set MR A =15. This gives Q D = 125 30 = 95. At this quantity, the price in America is given by the demand curve (Q D = 250 4p) which gives p* = 38.75.
7 e) Own-price elasticity of demand at the profit-maximizing point is given by: η = ( Q/ p) (p/q) In Europe, the measure of elasticity is η E = ( 1) (82.5/67.5) = 1.22. In America, the measure of elasticity is η A = ( 4) (38.75/95) = 1.63. Thus American demand is more elastic than European demand and, as we explained in the text, the price in America is therefore lower than the price in Europe. Question 10 a) Arbitrage is prevented because the product (movie viewing) is a service rather than a good; an adult can not purchase a senior ticket and then see the movie because the ticket will easily be checked at the theatre entrance. Without price discrimination, seniors would be worse off and adults would be better off because the single price would probably be between the two discriminatory prices. b) This is hurdle pricing, where the hurdle that must be cleared to get the low price is to wait 6-12 months before buying the book. Impatient people (inelastic demand) will buy the hardcover book at a high price; patient people (elastic demand) will wait and buy the paperback book at a low price. Note that in this case the products are also slightly different, and thus the price differential partly reflects differences in cost (hardcover books are more expensive to produce than paperbacks). It is difficult to determine who would be better off and worse off without price discrimination in this case because there is a difference in the products. If publishers were forced to sell only one type of book (at a single price), then the single price would likely be between the hardcover and paperback prices. c) This is hurdle pricing where the hurdle is to reveal that you are prepared to haggle. Each side of the transaction (buyer and seller) typically tries to extract as much surplus as possible from the other side, and the relative success in haggling determines the final price. It is not clear what a single price (no price discrimination) means in this situation, since most garage sales have only one unit of a large number of goods. However, you might wonder what prices would be like if garagesale operators committed to posting a single price for each good and not haggling. That single posted price would probably be less than what would otherwise be the starting price, but greater than what the final (after haggling) price would be. Thus successful hagglers would be worse off with the single posted price, and poor hagglers would be better off. d) Typical business travellers do not want to stay over the Saturday night whereas typical nonbusiness travellers do. The former have less elastic demands, and so this pricing scheme is aimed at segmenting the two groups of customers. Without price discrimination, the single price would probably be less than the discriminatory business price and greater than the discriminatory nonbusiness price. Thus business travellers would be better off and non-business travellers would be worse off without the price discrimination.