Market failure-government failure or both

Question

Problem 1: Behaving optimally

Consider a utility-maximizing consumer who devotes all of his weekly income,1=5720, to purchases of caviar (available at the market price px=S10 per serving) and high-end denim jeans (available at the market price py=S120 per pair). Compute this consumer's optimal consumption of caviar (x) and jeans (y) for each of the following possible utility functions, and show your work:

a) U(x,y) = [2x+13y]²
b) U(x,y) = Min[x,6y]
c) U(x,y) = xy²

Problem 2: Market failure, government failure, or both?

JockMart ovals a large textile factory in a small, remote community. The JockMart factory is the only source of employment for the community, so that the firm enjoys monopsony power. The supply curve for textile workers is described by Ls=160w, where L is the number of workers hired and w is the hourly wage. JockMart's labor demand (or, equivalently, marginal revenue product) curve is given by L^D=1600-80w. Throughout your analysis, assume that JockMart is unable to "price-discriminate" (that is, it will pay the same wage to each of its employees).

a) How many workers will JockMart hire to maximize its profits, and what wage will the farm pay?

b) How many workers would be hired, and what wage rate would prevail, if the labor market were perfectly competitive?

c) Suppose the government implements a minimum wage covering all textile workers at $8 per hour. How many workers will JockMart hire?

d) Illustrate your answers to pans a), b), and c), in a diagram. and compute the deadweight loss associated with the monopsony and minimum-wage outcomes, respectively.