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., Q1 = 1 and 42 = 2. In order to produce quality in their product, the 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 - where n = N N = (a) Set up the firm's profit maximization problem and list all four constraints. (b) Assume PC and IC 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., Q1 = 1 and 42 = 2. In order to produce quality in their product, the 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 - where n = N N = (a) Set up the firm's profit maximization problem and list all four constraints. (b) Assume PC and IC 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)