Question

a) A monopolist faces two totally separated markets with inverse demand p=100 – qA and p=160−2qB respectively. The monopolist has no fixed costs and a marginal cost given by mc= 2/ 3 q . Find the profit maximizing total output and how much of it that is sold on market A and market B respectively if the monopoly uses third degree price discrimination. What prices will our monopolist charge in the two separate markets?

b) Calculate the price elasticity of demand in each market and explain the intuition behind the relationship between the prices and elasticities in these two separate markets.

C)Use the definition of marginal revenue and the definition of the price elasticity of demand to derive an expression for the markup for a monopolist. Use this expression to calculate the markup for the two separate markets in question

Answer 1

ote that when the customers can be segregated, the monopolist can charge different prices to the two groups. The equilibrium quantity and price for each of them can be computed by equilibrating MC=MR, Marginal cost for 1st group is 200 -2 Q₁ while it is 100 -2 Q₁ for the 2nd. MC is given as 40.

This implies Q₁ = 80 and P₁ = 120. Similarly, Q₁ = 30 and P₁ = 70

Consumer surplus is the area of the region above the price line and below the demand curve. This implies, it is the area of the triangle so formed. Consumer surplus is 1/2*(200-120)*80 or $3200 in 1st market and 1/2*(100-70)*30 or $450 in 2nd market

Firm earns a revenue of $9,600 in first market and $2,100 in the second market. Marginal cost is 40 per unit. To produce 110 units in both markets, firm spends $4400. Thus, its profits are $7,300.

b. If total surplus is consumer surplus plus profit, then total surplus in first market is $9600 and $1,350 in the second market.