solutions_module4_practice

Module 4 Extra Practice Problems For Questions 1 - 5, choose the best answer. 1. A seller engaging in perfect price discrimination (first-degree price discrimination) A. charges each buyer their maximum willingness to pay. B. charges different prices to each customer based upon different costs of delivery. C. generates a deadweight loss to society. D. charges lower prices to customers who buy greater quantities. E. maximizes consumer surplus. Solution: A firm that engages in perfect/first-degree price discrimination, charges each buyer their maximum willingness to pay for all quantities. As a result, all consumer surplus is captured by the seller and there is zero deadweight loss. 2. Consumers who have a relative high willingness to pay for a good: A. are likely to have a higher consuemr surplus under perfect price discrimination. B. are likely to have a higher consumer surplus under a single-price monopoly. C. are likely to have the same consumer surplus under first-degree/perfect price discrimination and a single-price monopoly. D. are likely to have the same consumer surplus under third-degree price discrimination and a single-price monopoly. Solution: A consumer who puts a high-value on a good will be charged their value under perfect price discrimination–resulting in zero consumer surplus. Under a single price monopoly however, they will pay lower than their willingness to pay (as the monopolist will set MR = MC for the entire market). Similarly, under third-degree price discrimination, the firm will segment the market based on value and the consumer will pay a higher price than under the single price monopolist–resulting in lower consumer surplus. 3. A two-part pricing monopolist A. creates deadweight loss. B. increases market inefficiency. C. captures all consumer surplus. D. decreases total welfare. E. decreases producer surplus Solution: A firm engaged in two-part pricing charges P = MC for all units and an up-front fixed-fee equal to the would-be consumer surplus when P = MC. As a result, the producer captures all the consumer surplus and there is zero deadweight loss (and therefore no market inefficiency).

4. A firm engaging in third-degree price discrimination can sell its output in its domestic market or in a foreign market. Having sold a certain level of output in these two markets, it discovers that its marginal revenue in the domestic market is 42 while its marginal revenue in the foreign market is 40. Assume that the marginal costs of distribution and production are the same in both markets. To maximize profits from the sale of this level of output, the firm for sure should A. have sold more output in the domestic market and less in the foreign market. B. do nothing until it acquires more information on costs. C. have sold less output in the domestic market and more in the foreign market. D. have sold only in the domestic market. E. have sold only in the foreign market. Solution: The firm should allocate sales across market segments such that MR Domestic = MC and MR F oreign = MC . Since MC is the same in both markets, this implies that MR Domestic = MR F oreign at the profit maximizing solution. Since MR Domestic > MR F oreign , ( 42 > 40), the firm should sell more in the domestic market where incremental revenues are higher. 5. Suppose all individuals are identical, and their monthly demand for Internet access from Xfinity can be represented as P = 5 − 0 . 5 Q (or Q = 10 − 2 P ) where P is price in per hour and Q is hours per month. Xfinity faces a constant marginal cost of 1. Which of the following pricing schemes will lead to the highest profit for Xfinity? A. Set a per-unit price = 1 B. Set a per-unit price = 3 C. Set a per-unit price = 1 plus have a fixed-fee = 16 D. Set a per-unit price = 3 plus have a fixed-fee = 4 E. Set a fixed-fee = 25 and allow all goods to be free (P = 0) Solution: The two-part tarrif will always extract the maximum amount of consumer surplus and therefore maximize profit. In a two-part tarrif, P = MC, and the fixed-fee is the would-be consumer surplus at that per-unit price. The other choices all results in lower profit for Xfinity. Choices A & B leave consumer surplus on the table. Choice D captures all possible consumer surplus when P = 3 but results in deadweight loss that could be converted to profit under a two-part tarrif. Choice E is not profit-maximizing as Xfinity would lose on its per-unit sales since P < MC. The graphs below illustrate all of these choices. Remember that profit under each choice will include fixed fees (if any) pluis any revenue earned on the per-unit sales minus any per-unit costs. P P = 1 8 5 MC = 1 10 Profit = 1(8) – 1(8) = 0 Page 2

6. The Louvre is thinking of offering different ticket prices for admissions to visitors from outside of Paris (hereafter worldwide visitors) and local Parisians (hereafter Parisians), using French national identity cards (known as CNIS), which hold information on the cardholders’ addresses. That is, they are engaging in third-degree price discrimination. The Louvre’s rationale for this policy is that worldwide visitors and Parisians have different demand for visits. One reason for this may be that worldwide visitors have limited time for their visit to Paris and have many of other activities to do, whereas Parisians who visit the Louvre are not time-constrained and have special interests in the collections. The inverse demands per day for worldwide visitors and Parisians are given by: P W orld = 20 − 0 . 01 Q W orld P P aris = 42 − 0 . 03 Q P aris where all prices are in euros ( e ) and Q is number of visitors. The marginal cost for serving worldwide visitors and Parisians are the same at e 6 per visitor. (a) How should the Louvre price their tickets in order to maximize profits? Solution: The Louvre can distinguish the visitor types using the identity card and can engage in price discrimination. As the Louvre has market power, it finds the profit maximizing (Q, P) for each type of visitors at (Q,P) where MR=MC. Marginal revenue curves for each visitor type are: MR W orld = 20 − 0 . 02 Q W orld MR P aris = 42 − 0 . 06 Q P aris Set MR = MC and solve for Q W orld and Q P aris 6 = 20 − 0 . 02 Q W orld 6 = 42 − 0 . 06 Q P aris − 14 = − 0 . 02 Q W orld − 36 = − 0 . 06 Q P aris 700 = Q W orld 600 = Q P aris Using these visitor numbers in each demand curve, we get: P W orld = 20 − 0 . 01(700) = 13, P P aris = 42 − 0 . 03(600) = 24 (b) Now suppose that you find out that free French IDs are being handed out at the entrance to the museum, rendering the discount meaningless. How would you suggest the Louvre price their admissions tickets? Solution: Check the marginal profits at each ticket price and relevant quantity. If the Lourve prices the tickets at e 13, they sell to both the Worldwide customer and the local Parisians (meaning Q = 1300) and make: 13 ∗ 1300 − 6(1300) = e 9 , 100 If the Lourve prices the tickets at e 24, they sell to only the local Parisians (menaing Q = 600) and make: 24 ∗ 600 − 6(600) = e 10 , 800 Therefore the Louvre should price all tickets at e 24 and abandon the worldwide group. Page 4

7. A monopolist sells a product to two consumer types. The individual demand curve for the typical consumer in each segment is: Demand by each “low demand” customer: P = 100 − Q L Demand by each “high demand” customer: P = 130 − Q H where Q is output and P is price per unit (in dollars). The marginal cost of providing this product is constant at MC = $12, with no fixed costs. There are 100 customers in the market: 30 are low demand and 70 are high demand. The monopolist is considering a two-part tariff pricing strategy. There is no segmentation possible, so the monopolist charges all consumers the same up-front fee and the same price P. The monopolist has already decided to set the price at P = $20 and has asked you to calculate the optimal profit-maximizing fixed fee. (a) What is your recommended fixed fee when P = $20? What are total profits for the monopolist? Solution: D Q P P = 20 80 MC = 12 Q P 100 130 Low Demand: 100 – Q L 30 Consumers High Demand: 130 – Q H 70 consumers 110 Profit on each item: (20 – 12) CS = ½(80)(80) = $3200 CS = ½(110)(110) = $6050 At P = 20, Q L = 80 and Q H = 110. CS L = $3200 and CS H = $6050 (calculations shown in graph above) If we set the fee at 3200 per customer, all 100 customers will buy. If we set it at 6,050, only the high demand customers will buy. Profits from setting entry fee = 3200: (3200 ∗ 100) + (20 − 12)(110)(70) + (20 − 12)(80)(30) = 400 , 800 Profits from setting entry fee = 60500: (6050 ∗ 70) + (20 − 12)(110)(70) = 485 , 100 . Therefore, we should set the up-front fee at CS H = $6050 per customer and abandon the low demand market. (b) Is this monopolist currently maximizing his profits? What would be the optimal fixed fee? Solution: No the monopolist is not maximizing his profits. The monopolist can do better by setting P=MC and the fixed fee = the high demand consumer surplus; this would extract all possible consumer surplus. We can show that mathematically below and also further show that it is still better to continue to abandon the low demand consumer. Page 5