HW 8

Why do price discrimination and the existence of slightly different variants of the same product tend to go hand in hand? By introducing slightly different variants of the product, firms that price discriminate are able to

separate buyers based on their willingness to pay. Explanation If a firm wishes to price discriminate, it needs to be able to identify and separate consumers who are willing to pay more from consumers who have a lower willingness to pay. This is a profit-increasing strategy for the firm. Often, in order to separate customers, some minor differences are incorporated into the product that will appeal to customers with a higher willingness to pay, and then a higher price is charged for this slightly different product.

If a monopolist could perfectly price discriminate:

the marginal revenue curve and the demand curve would coincide. Explanation The demand curve and the marginal revenue curve would coincide, because if a monopolist could perfectly price discriminate, he or she would sell each successive unit of output for exactly the reservation price of customer, so the marginal revenue generated from selling each successive unit would equal its reservation price.

Two car manufacturers, Nissan and Honda, have fixed costs of $1 billion and marginal costs of $10,000 per car. If Nissan produces 50,000 cars per year and Honda produces 200,000, calculate the average production cost for each company. Average production cost for Nissan: $_______. Average production cost for Honda: $__________. On the basis of these costs, which company's market share do you think will grow in relative terms?

$ 30,000; $ 15,000; honda Explanation As shown in the following table, Honda's greater production volume gives it substantially lower average production cost, and this advantage helps explain why Honda's market share has in fact been growing relative to Nissan's. Nissan Honda Annual production: 50,000 200,000 Fixed cost: $1,000,000,000 $1,000,000,000 Variable cost: $500,000,000 $2,000,000,000 Total cost: $1,500,000,000 $3,000,000,000 Average cost per car: $30,000 $15,000

TotsPoses, Incorporated, a profit-maximizing business, is the only photography business in town that specializes in portraits of small children. George, who owns and runs TotsPoses, expects to encounter an average of eight customers per day, each with a reservation price shown in the following table. Assume George has no fixed costs, and his cost of producing each portrait is $12. Customer:1,2,3,4,5,6,7,8 Reservation price ($ per photo):50,46,42,38,34,30,26,22 a. Suppose George is permitted to charge two prices. He knows that customers with a reservation price above $30 never bother with coupons, whereas those with a reservation price of $30 or less always use them. At what level should George set the list price of a portrait? At what level should he set the discount price? How many photo portraits will he sell at each price? List price of a portrait: $_____ Number of portraits to be sold at the list price: _____ portraits Discount price of a portrait: $_______ Number of portraits to be sold at the discounted price: _____ portraits b. In this case, what is George's economic profit and how much consumer surplus is generated each day? Economic profit: $________ Consumer surplus: $ 52

$34 5 portraits $22 3 portraits b. Economic profit: $ 140 Consumer surplus: $ 52 Explanation a. The ability to offer a rebate coupon allows George to divide his market into two submarkets. The table of total and marginal revenue for the list price submarket is as follows: Customer:1,2,3,4,5 Reservation price ($ per photo):50,46,42,38,34 Total revenue ($):50,92,126,152,170 Marginal revenue: 50,42,34,26,18 George should set the price at $34 and sell 5 photos per day in this market, since for each of these 5 customers marginal revenue is greater than or equal to marginal cost. In the discount-price submarket, the table of total and marginal revenue is as follows: Customer:6,7,8 Reservation price ($ per photo):30,26,22 Total revenue ($):30,52,66 Marginal revenue: 30,22,14 The discount price should be $22 and George should sell 3 photos in this market, since for each of these 3 customers (customer number 6, 7, and 8) marginal revenue is greater than or equal to marginal cost.b. George's economic profit is now ($34 × 5) + ($22 × 3) − ($12 × 8), or $140. Consumer surplus is ($50 − $34) + ($46 − $34) + ($42 − $34) + ($38 − $34) + ($34 − $34) + ($30 − $22) + ($26 − $22) + ($22 − $22), or $52.

Serena is a single-price, profit-maximizing monopolist in the sale of her own patented perfume, whose demand and marginal cost curves are as shown below.a. Relative to the economic surplus that would result at the socially optimal quantity and price, how much economic surplus is lost from her selling at the monopolist's profit-maximizing quantity and price? Instructions: In the graph, indicate the area that represents the reduction in total economic surplus. Total economic surplus lost: $______per day. b. How much total surplus would result if Serena could act as a perfectly price-discriminating monopolist? Total surplus: $_________per day.

$40 per day. b. $360 per day. Explanation a. The profit-maximizing quantity is 8, the quantity at which MR = MC. The socially optimal quantity is 12, the quantity at which MC = MB (that is, where the MC curve intersects the demand curve). The loss in total surplus when Q falls from 12 to 8 is the area of the shaded triangle below, or $40 per day. Note that half of this loss comes from a reduction in consumer surplus and half comes from a reduction in producer surplus. The horizontal axis labeled quantity in ounces per day ranges from 0 to 24. Points 4, 6, 8, 12, 16 are also marked out on the horizontal axis. The vertical axis labeled price in dollars per ounce ranges from 0 to 60. Points 10, 15, 20, 30, 40, 45, 50 are also marked out on the vertical axis. A line begins at the point (0, 60) goes down to the right passes through the points (4, 40), (5, 30) (8, 20), and ends at the point (12, 0). A line labeled D begins at the point (0, 60) passes through the points (4, 50), (6, 45), (8, 40), (12, 30), (16, 20), and ends at the point (24, 0). A line labeled M C begins at the point (0, 0) goes up to the right through the points (4, 10), (6, 15), (8, 20), (12, 30), and ends at the top right of the quadrant. The area between the points (8, 20), (8, 40), and (12, 30) forms a triangle and is shaded. b. A perfectly price-discriminating monopolist would sell each unit for exactly the buyer's reservation price, so the marginal revenue curve and the demand curve become the same. Serena will thus produce and sell 12 ounces per day. Buyers get no consumer surplus. Total surplus is equal to producer surplus, which is the area of the shaded triangle below, or $360 per day. The horizontal axis labeled quantity in ounces per day ranges from 0 to 24. Points 4, 6, 8, 12, 16 are also marked out on the horizontal axis. The vertical axis labeled price in dollars per ounce ranges from 0 to 60. Points 10, 15, 20, 30, 40, 45, 50 are also marked out on the vertical axis. A line begins at the point (0, 60) goes down to the right passes through the points (4, 40), (5, 30) (8, 20), and ends at the point (12, 0). A line labeled D begins at the point (0, 60) passes through the points (4, 50), (6, 45), (8, 40), (12, 30), (16, 20), and ends at the point (24, 0). A line labeled M C begins at the point (0, 0) goes up to the right through the points (4, 10), (6, 15), (8, 20), (12, 30), and ends at the top right of the quadrant. The area between the points (0, 0), (0, 60), and (12, 30) forms a triangle and is shaded.

TotsPoses, Incorporated, a profit-maximizing business, is the only photography business in town that specializes in portraits of small children. George, who owns and runs TotsPoses, expects to encounter an average of eight customers per day, each with a reservation price shown in the following table. Assume George has no fixed costs, and his cost of producing each portrait is $12.a. Complete the following table. Instructions: If you are entering any negative numbers be sure to include a negative sign (−) in front of those numbers. Enter your responses as whole numbers. Customer:1,2,3,4,5,6,7,8 Reservation price ($ per photo):50,46,42,38,34,30,26,22 Total revenue ($ per day):----------------- Marginal revenue ($ per photo):--------------- How much should George charge if he must charge a single price to all customers? $_______ At this price, how many portraits will George produce each day? _______ portraits What will be his economic profit? $______ per day b. How much consumer surplus is generated each day at this price? $____ c. What is the socially efficient number of portraits? _____ portraits d. George is very experienced in the business and knows the reservation price of each of his customers. If he is allowed to charge any price he likes to any consumer, how many portraits will he produce each day?______ portraits What will his economic profit be? $_______ per day e. In this case, how much consumer surplus is generated each day? $ ___

Total revenue ($ per day):50,92,126,152,170,180,182,176 Marginal revenue ($ per photo):50,42,34,26,18,10,2,-6 $ 34 5 portraits $ 110 per day b. $ 40 c. 8 portraits d. 8 portraits $ 192 per day e. $ 0

Suzanne owns the only kayak rental company in a small resort town. Every day there are 8 people potentially interested in renting a kayak, each with a reservation price shown in the table. The marginal cost to Suzanne of renting out a kayak is $20. Potential Customer:1,2,3,4,5,6,7,8 Reservation Price: $85,$75,$65,$55,$45,$35,$25,$15 a. What is the socially efficient number of kayaks for Suzanne to rent out each day? _____ kayaks b. If Suzanne acts as a single-price monopolist, then how many kayaks will she rent out each day, and what price will she charge for each kayak? _______ kayaks per day at a price of $________ per kayak c. Now suppose Suzanne offers to give a discount to customers who fill out a customer satisfaction survey. People with reservation prices above $45 will never fill out the survey, while those with reservation prices of $45 or less will always fill out the survey. How many kayaks will Suzanne rent out each day? What price should she charge to people who do not fill out the survey? And what price should she charge to people who do fill out the survey? Price charged to those who don't fill out the survey: $____ per kayak Price charged to those who do fill out the survey: $______ per kayak Suzanne should rent out _______ kayaks total. d. Is consumer surplus higher when Suzanne acts as a single-price monopolist (part b) or when Suzanne price discriminates (part c)?

a. 7 kayaks b. 4 kayaks per day at a price of $55 per kayak c. 55,35,6 d. Consumer surplus is higher when Suzanne price discriminates. Explanation a. The socially efficient number of kayak rentals each day is 7 because the marginal benefit of the 7th kayak ($25) is greater than marginal cost ($20), but the marginal benefit of the 8th kayak ($15) is less than marginal cost ($20). b. Suzanne will continue to rent out kayaks as long as the marginal revenue from doing so is at least as great as her marginal cost. As shown in the table below, the marginal revenue from renting out the first 4 kayaks is greater than $20, but marginal revenue falls below $20 after that. Thus, Suzanne should rent out 4 kayaks per day and charge a price of $55 each. c. Suzanne will continue to rent out kayaks in each submarket as long as the marginal benefit from doing so is at least as great as her marginal cost. Thus, Suzanne will rent 4 kayaks a day to people who do not fill out the survey at a price of $55 each, and she will rent out 2 kayaks to people who fill out the survey at a price of $35 each. In total, she will rent out 6 kayaks a day. d. In part b, consumer surplus is $30 + $20 + $10 + $0 = $60 per day. In part c, consumer surplus is $30 + $20 + $10 + $0 + $10 + $0 = $70 per day. Thus, consumer surplus is higher when Suzanne price discriminates than when she acts as a single-price monopolist. Potential Customer:1,2,3,4,5,6,7,8 Reservation Price:$85,$75,$65,$55,$45,$35,$25,$15 Total Revenue:$85,$150,$195,$220,$225,$210,$175,$120 Marginal Revenue($):85,65,45,25,5,-15,-35,-55 Total Revenue in each submarket:$85,$150,$195,$220,$45,$70,$75,$60 Marginal Revenue in each submarket:85,65,45,25,45,25,5,-15

State whether the following statements are true or false. a. In a perfectly competitive industry, the industry demand curve is horizontal, whereas for a monopoly it is downward-sloping. b. Perfectly competitive firms have no control over the price they charge for their product. c. For a natural monopoly, average cost declines as the number of units produced increases over the relevant output range.

a. false b. true c. true Explanation a. False. The industry demand curve is downward-sloping in both cases, but from the individual perfectly competitive firm's point-of-view, the demand curve is horizontal. Because the individual firm is too small to affect the market price, it can sell as many units as it wishes at that price. b. True. Perfectly competitive firms are price takers (i.e., if they try to charge a higher price, they will lose all their business). Similarly, there is no reason to charge a lower price as they can sell any quantity they choose to at the current price. c. True. This is the essential feature of a natural monopoly.

A single-priced, profit-maximizing monopolist:

always charges a price above the marginal cost of production. Explanation The monopolist chooses the output level at which marginal revenue equals marginal cost and then charges a price consistent with demand at that level of output. Since price is greater than marginal revenue for a monopolist, price is also greater than marginal cost. The quantity produced by the monopolist at the monopoly price is exactly equal to the quantity demanded by consumers, so the monopolist does not cause excess demand or shortages (even though the monopolist's profit-maximizing level of output falls below the socially efficient level). And the monopolist has no reason to maximize marginal revenue (which would require producing zero units of output).

What is the socially desirable price for a natural monopoly to charge? A natural monopoly that attempts to charge the socially desirable price will invariably suffer an economic loss because

the price at which the marginal benefit to the consumer equals the marginal cost of production. average cost is higher than marginal cost. Explanation Socially optimal means that the marginal benefit equals the marginal cost. At this point, all goods that are valuable enough to consumers to justify producing are produced; no goods with costs higher than the benefits they provide are produced. The demand curve tells us about the marginal benefits to consumers: at any given quantity on a demand curve, the price that inspires that quantity demanded is equal to the marginal benefit of the good. Therefore, setting marginal benefit equal to marginal cost requires setting a price that is equal to marginal cost and selling to all consumers who demand it at that price. However, this is not a good outcome for natural monopolies, which are usually characterized by very large fixed costs and relatively low marginal costs. The high fixed costs mean that average cost is greater than marginal cost (ATC > MC), so that charging a price equal to marginal cost implies economic losses (because when P < ATC the firm's profit is negative).