Chapter 9 Problems1 Chapter 9 Problems2. State whether the following statements are true or false, and explain why.a. In a perfectly competitive industry the industry demand curve is horizon-tal, whereas for a monopoly it is downward-sloping. False. The demandcurve for an individual competitive firm is horizontal, while the demandcurve for the competitive industry as a whole is downward-sloping (justas it is downward-sloping for a monopoly). An individual competitivefirm is small in relation to the market, so any change in quantity haslittle effect on market price. Since a monopolistic firm is big in relationto the market, changes in production quantity do have an effect on mar-ket price. Not surprisingly, the monopolist’s downward-sloping demandcurve is similar to an industry’s demand curve because, by definition,a monopoly is as big or almost as big as an entire industry.b. Perfectly competitive firms have no control over the price they charge fortheir product. True. Perfectly competitive firms’ product is identical totheir competitors’ product. Thus, they cannot raise their price becauseall customers would buy the same product elsewhere. Thus, competitivefirms are “price takers.” Alternatively, imperfectly competitive firmsare able to differentiate their product from their competitors’ product.Thus, they can raise their price without losing all their customers, be-cause some customers won’t want to buy a slightly different good fromanother producer. Thus, imperfectly competitive firms are, at least tosome degree, “price-makers.”c. For a natural monopoly, average cost dec lines as the number of unitsproduced increases over the relevant output range. True. Fixed costsare spread over more units as output increases, so average cost per unit(fixed + variable cost per unit) declines as output increases.5. Explain why price discrimination and the existence of slightly differentvariants of the same product tend to go hand in hand. Give an exam-ple from your own experience. To price discriminate, there is a needto separate people with different reservation prices. To do this, theproducer must differentiate the product by, for example, quality. Low-reservation-price customers are likely to buy the product at a slightlylower quality, while high-reservation-price customers are willing to pay1higher prices - but only for the higher quality version. Name-brandclothing designers price-discriminate by quality: they sell full-priceditems in boutiques, while “irregular” units are sold at discount pricesduring sales or at discount stores.6. What is the socially desirable price for a natural monopoly to charge?Why will a natural monopoly that attempts to charge the so cially de-sirable price invariably suffer an economic loss? The socially desirableprice equals the marginal cost of the product. This price is found at theintersection of the demand and marginal cost curves (D = MC). Butto price at marginal cost, the monopolist only covers variable cost anddoes not account for any fixed costs that may exist. Instead of settingprice to marginal cost, a monopolist must set price to average total costin order to avoid making a loss. In other words, since ATC = MC +F/Q, setting P to MC makes P less than ATC, so the firm makes aloss.7. TotsPoses Inc., a profit-maximizing business, is the only photographybusiness in town that specializes in portraits of small children. George,who owns and runs TotsPoses, expects to encounter an average of eightcustomers per day, each with a reservation price shown in the followingtable.Customer Reservation price Total revenue Marginal revenueA $50 $50> $42B $46 $92> $34C $42 $126> $26D $38 $152> $18E $34 $170> $10F $30 $180> $2G $26 $182> −$6H $22 $1762a. If the total cost of each photoportrait is $12, how much should Georgecharge if he must charge a single price to all customers? At this price,how many portraits will George produce each day? What will be hiseconomic profit? George should charge $34 to each customer becausemarginal revenue ($18) exceeds marginal cost ($12) up to customer E.At this price, George will produce 5 portraits per day. His profit will be$110 = ($34 * 5) - ($12 * 5) = $170 - $60.b. How much consumer surplus is generated each day at this price? $40.A $50 - $ 34 = $16B $46 - $ 34 = + $12C $42 - $ 34 = + $8D $38 - $ 34 = + $4E $34 - $ 34 = + $0= $40c. What is the socially efficient number of portraits? 8 because MB of $22that the last customer is willing to pay exceeds the cost to George of$12 per portrait.d. George is very experienced in the business and knows the reservation priceof each of his customers. If he is allowed to charge any price he likesto any consumer, how many portraits will he produce each day, andwhat will his economic profit be? In this case, George is allowed toperfectly price discriminate. Thus, he will charge each customer his orher own reservation price. He will produce all 8 portraits, because eventhe customer with the lowest reservation price (H at $22) is willing topay more than George’s production cost of $12.A $50 - $ 12 = $38B $46 - $ 12 = + $34C $42 - $ 12 = + $30D $38 - $ 12 = + $26E $34 - $ 12 = + $22F $30 - $ 12 = + $18G $26 - $ 12 = + $14H $22 - $ 12 = + $10= $1923Summing the individual producer surpluses gained from each customer,and subtracting total production costs, results in a total profit to Georgeof $192.e. In this case, how much consumer surplus is generated each day? Theconsumer surplus is $0 because all surplus is taken by the producerunder perfect price discrimination.9. Suppose you are a monopolist in the market for a specific video game.Your demand curve is given P = 80 - Q/2, and your marginal costcurve is MC = Q. Your fixed costs equal $400.a. Graph the demand and marginal cost curve. See accompanying pdf graph“ch9econ2.pdf”.b. Derive and graph the marginal revenue curve. T R = (P )(Q) = (80 −Q/2)(Q) = 80Q −12Q2. Take the first derivative of TR with regardto Q to get MR, so that MR = 80 - Q. Thus, the vertical intercept ofMR is 80 and the slope of the MR curve is 1. The MR curve hits thehorizontal intercept where MR = 0. So, MR = 0 = 80 - Q means thatQ = 80 at the horizontal intercept.c. Calculate and indicate on the graph the equilibrium price and quantity.QE= 40 and PE= $60. A monopolist’s equilibrium quantity occurswhere MR = MC. MR = 80 -Q and MC = Q. So, 80 - Q = Q whichmakes 80 = 2Q which makes QE= 40. Plugging the equilibrium quan-tity into the demand