4. Consider a firm that wants to offer two different qualities of a good marketed to a low type and a high type consumer. The firm cannot tell the difference between the two consumers, but knows that the high type values the good twice as much as the low type, i.e., 0₁ = 1 and 0₂ = 2. In order to produce quality in their product, the 02 firm faces the cost function c(s) = s³ where s is the quality level. The proportion of low type consumers is y and the proportion of high type consumers is 1 - 7 where N₁ = N. N₁+N₂ (a) Set up the firm's profit maximization problem and list all four constraints. (b) Assume PC₁ and IC₂ bind. Calculate the equilibrium qualities and prices offered to each type of consumer. (c) For what values of y does the firm offer any quality at all to the low type consumer? (Hint: look at si).
4. Consider a firm that wants to offer two different qualities of a good marketed to a low type and a high type consumer. The firm cannot tell the difference between the two consumers, but knows that the high type values the good twice as much as the low type, i.e., 0₁ = 1 and 0₂ = 2. In order to produce quality in their product, the 02 firm faces the cost function c(s) = s³ where s is the quality level. The proportion of low type consumers is y and the proportion of high type consumers is 1 - 7 where N₁ = N. N₁+N₂ (a) Set up the firm's profit maximization problem and list all four constraints. (b) Assume PC₁ and IC₂ bind. Calculate the equilibrium qualities and prices offered to each type of consumer. (c) For what values of y does the firm offer any quality at all to the low type consumer? (Hint: look at si).
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN:9781305506381
Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Chapter3: Demand Analysis
Section: Chapter Questions
Problem 2.5CE
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