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| Because cooking soufflés is incredibly difficult, the supply of soufflés in a small French town is controlled by two bakers, Gaston and Pierre. The demand for soufflés is given by P = 30 – 2Q, and the marginal and average total cost of producing soufflés is $6. Because baking a soufflé requires a great deal of work and preparation, each morning Gaston and Pierre make a binding decision about how many soufflés to bake. a. Suppose that Pierre and Gaston agree to collude, evenly splitting the output a monopolist would make and charging the monopoly price. i. Derive the equation for the monopolist’s marginal revenue curve. ii. Determine the profit-maximizing collective output for the cartel. iii. Determine the price Pierre and Gaston will be able to charge. iv. Determine profits for Pierre and Gaston individually, as well as for the cartel as a whole. b. Suppose that Pierre cheats on the cartel agreement by baking one extra soufflé each morning. i. What does the extra production do to the price of soufflés in the marketplace? ii. Calculate Pierre’s profit. How much did he gain by cheating? iii. Calculate Gaston’s profit. How much did Pierre’s cheating cost him? iv. How much potential profit does the group lose as a result of Pierre’s cheating? c. Suppose that Gaston, fed up with Pierre’s behavior, also begins baking one extra soufflé each morning. i. How does the extra production affect the price of soufflés in the marketplace? ii. Calculate Gaston’s profit. How much did he gain by cheating? iii. Calculate Pierre’s profit. How much did Gaston’s cheating cost him? iv. How much potential profit does the group lose as a result of Pierre’s and Gaston’s cheating? v. Demonstrate that it is in neither Pierre’s nor Gaston’s best interest to cheat further on their agreement. |
Because cooking soufflés is incredibly difficult, the supply of soufflés
A firm with market power faces the demand function q
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| A firm with market power faces the demand function q = 4,000 – 40P. The firm’s total cost function is TC(q) = 10q + 0.001q2 + 1,000. a. If the firm behaves as a single-price monopoly, identify the firm’s optimal price and output level. b. Demonstrate that the single-price monopolist’s profit-maximizing choice of price and output also maximizes producer surplus. c. Identify the output level that would maximize total surplus. d. Identify the output level that a perfect price-discriminating monopolist would produce. |
Owners of a movie theater have determined that the elasticity
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| Owners of a movie theater have determined that the elasticity of demand for movie tickets equals -2.0 for students and -1.5 for adults. a. If the owners of the theater decide to segment the market, who should be charged a higher price, students or adults? Use your knowledge of microeconomic theory to explain why. b. Use the Lerner index as described in the text to determine the ratio of prices. In percentage terms, how big a price premium should be charged to the group that pays the higher price? |
In Problem 5, you found the profit that a promoter
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| In Problem 5, you found the profit that a promoter of a major college basketball tournament would earn if he were to segment the market into adults and students. Suppose that the promoter’s CEO decides that price discrimination presents a poor public image, and announces that everybody will be charged the same price. His resident economist (you) is tasked with figuring out what that price should be. a. Find the total demand for tickets by adding the demand curves of adults and students. b. Derive the inverse demand curve for tickets, as well as the associated marginal revenue curve associated with that demand. c. Find the profit-maximizing quantity of tickets and the corresponding price. d. Determine the promoter’s profit. e. Compare the promoter’s profit when he tries to price for the entire market, to his profit when he simply charges the adult price from the previous problem. Is it better for the promoter to price for the entire market and almost fill the arena, or to price for adults only and have a lot of empty seats? |
Promoters of a major college basketball tournament estimate that the
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| Promoters of a major college basketball tournament estimate that the demand for tickets on the part of adults is given by Qad = 5,000 – 10P, and that the demand for tickets on the part of students is given by Qst = 10,000 – 100P. The promoters wish to segment the market and charge adults and students different prices. They estimate that the marginal and average total cost of seating an additional spectator is constant at $10. a. For each segment (adults and students), find the inverse demand and marginal revenue functions. b. Equate marginal revenue and marginal cost. Determine the profit-maximizing quantity for each segment. c. Plug the quantities you found in (b) into the respective inverse demand curves to find the profit maximizing price for each segment. Who pays more, adults or students? d. Determine the profit generated by each segment, and add them together to find the promoter’s total profit. e. How would your answers change if the arena where the event was to take place had only 5,000 seats? |
Consider the problem faced by the Butterfinger seller in Problem
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| Consider the problem faced by the Butterfinger seller in Problem 3. a. Assume that the seller is able to prevent resale between customers. In the real world, why is the seller still unlikely to be able to perfectly price discriminate? b. Because of the reason you just indicated, the Butterfinger seller decides to segment her customers into two groups, each of which will be charged a different price. In order to maximize profit, should the seller sort by gender or by age? c. Based on your answer to (b), determine who is in each group, and indicate (1) the price the seller should set for each group, (2) the total profit received by the seller, (3) total consumer surplus, and (4) the deadweight loss. d. Is this pricing strategy (segmenting) more profitable to the seller than perfectly price discriminating? Is this pricing strategy more profitable than charging every consumer the same price? e. What happens to consumer surplus and deadweight loss when a single-price monopolist begins segmenting in this way? |
There are seven consumers, each of whom is hungry for
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| There are seven consumers, each of whom is hungry for exactly one Butterfinger. The consumers’ maximum willingness to pay is given in the table on the right: Consumer (age, gender) Maximum Willingness to Pay Marge (34, female)…………………………….. $2 Homer (38, male) .……………………………. 4 Lisa (6, female) ………………………………. 5 Maggie (2, female) …………………………… 6 Ned (46, male) ………………………………… 1 Krusty (55, male) …………………………….. 3 Bart (9, male) ………………………………… 7 a. Given that each consumer wants one and only one Butterfinger, draw the demand curve for Butterfingers. b. If Butterfingers are priced at $7, only one will be sold. Who buys that Butterfinger? Label the point at $7 on the demand curve with the name of that buyer. c. If Butterfingers are priced at $6, a second buyer will be priced into the market. Who is that buyer? Label the point at $6 on the demand curve with the name of that buyer. d. Continue to label each point on the demand curve with the name of the buyer represented by that point. e. Suppose that you are a monopoly seller of Butterfingers, which you can produce at a constant marginal and average total cost of $2. Suppose you charge every customer the same price for Butterfingers. What price should you set to maximize your profit? How many Butterfingers will you sell? Calculate your profit. Calculate the consumer surplus received by the buyers. Calculate the deadweight loss. f. Suppose that every customer who comes into your Butterfinger store has their maximum willingness to pay displayed in neon on their foreheads. You decide to use this information to increase your profit by practicing first-degree price discrimination. How many Butterfingers will you sell? Calculate your profit. Calculate the consumer surplus received by the buyers. Calculate the deadweight loss. g. Where does the consumer surplus go when you begin price discriminating? h. What happens to the deadweight loss? |
SmacFone is a major provider of pay-by-the-minute, no contract cellphones
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| a. Determine the profit-maximizing price and quantity that SmacFone would like to charge each type of consumer, and show it on the appropriate graph. Then, determine the potential profit that SmacFone could generate from each segment. Because SmacFone cannot tell whether a new customer is an ordinary person or a drug dealer, it decides to use second-degree price discrimination to separate consumers. SmacFone sets a Plan A price of 15 cents per minute, but offers a special Plan B price of 10 cents per minute if a customer purchases 300 or more minutes. b. Determine how much consumer surplus ordinary consumers would receive under Plans A and B. Which plan should ordinary consumers choose if they are trying to maximize their surplus? c. Determine how much consumer surplus drug dealers would receive under Plans A and B. Which plan should drug dealers choose if they are trying to maximize their surplus? d. Is the plan SmacFone derived incentive compatible? (In other words, will the plan successfully direct drug dealers to Plan A and ordinary consumers to Plan B?) How much profit will SmacFone generate with this set of plans? e. SmacFone is considering making some adjustments to their plans. One option is to change Plan B to 11 cents per minute with a 240-minute minimum. Determine whether the new plan selection is incentive-compatible. Why doesn’t SmacFone simply raise the price to 11 cents without altering the 300-minute minimum? How much profit will the new set of plans generate for SmacFone? f. Another option that SmacFone is considering is dropping the price of its ordinary service to 14 cents per minute. Determine whether the new plan selection is incentive compatible. How much profit will the new set of plans generate for SmacFone? g. Why does lowering the price of ordinary service work better at creating an incentive-compatible set of calling plans than raising the price of the large-quantity plan? |
Elaine makes delicious cupcakes that she mails to customers across
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| a. If Elaine is an ordinary monopolist, what price should she charge for cupcakes? How many will each customer order? How much profit will Elaine earn? How much consumer surplus will the buyer get? b. Suppose that Elaine decides to offer a quantity discount according to the following terms: The first 10 cupcakes can be bought for $1.50 each; any cupcake over 10 will be offered at a discounted price. What discount price will maximize Elaine’s profit from this pricing scheme? c. How many cupcakes will customers order at full price? How many at the discounted price? d. What will Elaine’s profit be? How does this scheme compare to the profit she earned as an ordinary monopolist? e. Suppose that Elaine gets super-greedy and decides to implement a three-tiered pricing system. What three prices should she choose to maximize her profit? At what quantities will the price points change? What will her profit be? f. Suppose Elaine decides to charge $2.40 for the first cupcake, $2.30 for the second, and so on. How many cupcakes will she sell, and what will her profit be? g. What happens to consumer surplus as Elaine adds more price points? Where does it go? |
Three consumers, John, Kate, and Lester, are in the market
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| a. If you are a local farmer who can produce dates and eggs for free, what is the optimal price for dates and eggs if you price them individually? How much profit will you generate? b. If you bundle dates and eggs together, what price should you set for a bundle containing one package of dates and a dozen eggs? How much profit will you generate? c. Is there any advantage to mixed bundling in this case? Why or why not? d. Suppose that the cost of producing dates and eggs rises to $1.00 per package and $1.00 per dozen, respectively. Now is there any advantage to mixed bundling? Why or why not? Explain your answer with a numerical illustration. e. What accounts for the change in optimal strategy when costs change? |
