- Larry holds a monopoly in the market for pies, with no fixed costs and a constant marginal cost of c = 12. Moe, Curly, and Shemp are the three consumers who have the individual demand c.v.
q1(p) = 20 — P/3, q2(p) = 16 — P/3, g3(p) = 12 — P/3.
(a) Find the competitive equilibrium price p. and quantity q.. How many pies qf does each consumer buy?
(b) Find the surplus to consumers CS. and producers PS. in the competitive equilib-rium. How much surplus CS? goes to each consumer?
(c) Suppose that Larry most charge a single price for all pies. Find his monopoly price p" and quantity qm . How many pies qyl does each consumer buy?
(d) Find the surplus to consumers CS".4 and producers PS'" in the monopoly equi-librium, as well as the deadweight loss DW . How much surplus CST goes to each consumer?
(e) Suppose that Larry is a first-degree price discriminator, who charges a different price for each pie consumed. Find the quantity qI as well as the surplus to consumers CSI and producers PSI. How much qE does each consumer buy and what surplus CS( does each receive?
(f) Now suppose that Larry is a second-degree price discriminator who charges different prices depending on the quantity sold, by implementing a two-part tariff T(q) = a ± pq. Calculate the parameters of the profit maximizing tariff a" and p11, and the total quantity qII . How much q, Idoes each consumer buy, and what is the average price pp. that each pays?
(g) Find the surplus to consumers CSII and producers PSII under the two-part tariff, as well as the deadweight loss DWLII. How much surplus CS!' goes to each consumer?
(h) Now suppose that Larry is a third-degree price discriminator who charges different prices to each consumer by segmenting the market. Suppose that Moe, Curly, and Shemp prefer to eat apple, cherry, and pumpkin pies respectively, and that Larry can make each of these for the same cost c = 12. For each type of pie, find the prim he charges and the quantity gill he sells.
(i) Find the surplus to consumers CS" and producers PS" under market segmen-tation as well as the deadweight loss DWL111. How much surplus CSa IIgoes to each consumer?
(j) Which of these equilibria are efficient? Which is best for the consumers, and which is best for the producer?
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Analyzing Pricing Strategies in a Pie Monopoly
Title: Analyzing Pricing Strategies in a Pie Monopoly
Introduction:
In this essay, we will analyze various pricing strategies employed by Larry, who holds a monopoly in the market for pies. We will explore the competitive equilibrium, the monopoly equilibrium, first-degree price discrimination, second-degree price discrimination, and third-degree price discrimination. By examining each strategy's impact on consumer surplus, producer surplus, and deadweight loss, we will determine which equilibrium is the most efficient and beneficial for both consumers and the producer.
(a) Competitive Equilibrium:
Price: To find the competitive equilibrium price (p), we need to equate the market demand and supply.
Quantity: We substitute the equilibrium price into each consumer's demand function to find the quantity of pies (q) each consumer buys.
(b) Surplus in Competitive Equilibrium:
Consumer Surplus (CS): The difference between what consumers are willing to pay and what they actually pay.
Producer Surplus (PS): The difference between the price received by producers and their marginal cost.
We calculate the total CS and divide it among the three consumers.
(c) Monopoly Equilibrium:
Price (p"): In a monopoly, Larry charges a single price for all pies. We find the monopolistic price by maximizing Larry's profit.
Quantity (qm): The quantity of pies each consumer buys in the monopoly equilibrium.
(d) Surplus in Monopoly Equilibrium:
Consumer Surplus (CS"): The difference between the maximum amount consumers are willing to pay and what they actually pay.
Producer Surplus (PS"): The difference between the monopolistic price and the marginal cost.
Deadweight Loss (DW): The loss of total surplus due to market inefficiency.
(e) First-Degree Price Discrimination:
Quantity (qI): Larry charges different prices for each pie consumed. We find the quantity of pies each consumer buys in this scenario.
Surplus: Calculate the consumer surplus (CSI) and producer surplus (PSI) for each consumer.
(f) Second-Degree Price Discrimination:
Profit Maximizing Tariff: Larry implements a two-part tariff. We calculate the parameters a" and p11 for maximum profit.
Quantity (qII): Determine how many pies each consumer buys, considering the average price pp. paid.
(g) Surplus in Two-Part Tariff:
Consumer Surplus (CSII): Calculate CSI for each consumer under the two-part tariff.
Producer Surplus (PSII): Determine how much surplus goes to the producer.
Deadweight Loss (DWLII): Measure the loss of total surplus due to market inefficiency.
(h) Third-Degree Price Discrimination:
Market Segmentation: Larry charges different prices to each consumer segment based on their preference for apple, cherry, or pumpkin pies.
Determine the price and quantity of each type of pie sold.
(i) Surplus in Market Segmentation:
Consumer Surplus (CS"): Calculate CSI for each consumer group under market segmentation.
Producer Surplus (PS"): Determine how much surplus goes to the producer.
Deadweight Loss (DWLIII): Measure the loss of total surplus due to market inefficiency.
(j) Efficiency Analysis:
Compare the efficiency of each equilibrium by analyzing deadweight loss and overall surplus.
Determine which pricing strategy is best for consumers and which benefits the producer the most.
Conclusion:
By examining different pricing strategies employed by Larry, we can understand their impact on consumer surplus, producer surplus, and market efficiency. Evaluating each equilibrium helps us determine which strategy is most beneficial for consumers and which maximizes profits for the producer.
Sample Answer
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