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).

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter18: Asymmetric Information

Section: Chapter Questions

Problem 18.7P

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