Question

A monopolist sells in two markets. The demand curve for her product is given by p1 = 120 y1 in the first market; and p2 = 105 y2 2 in the second market, where yi is the quantity sold in market i and pi is the price charged in market i. She has a constant marginal cost of production, c = 10, and no fixed costs. She can charge different prices in the two markets.

1) Suppose the monopolist charges different prices in different markets. What type of price discrimination is this monopolist using?

2) Now, suppose the monopolist must charge the same price in both markets. (a) Calculate the aggregate (total) demand. (3p) (b) Write down the total profit function of the firm. (2p) (c) Calculate the profit maximizing price p; total quantity y T ; and quantities y1 and y2 to be produced in market 1 and 2, respectively. (4p) 3) Suppose the first market whose demand is p1 = 120 y1; was perfectly competitive, (hence, several firms can provide the same product) where each firm had a marginal cost of $10. What would be the price and total quantity in this perfectly competitive market? (Give numerical values for this price and total quantity

Answer 1

1) Price discrimination of third degree is being used by the monopolist

2) a)agregate demand is obtained by horizontal summation of individual demand functions.

p1 = 120y1 or y1 = p1/120

p2 = 105 y2 or y2 = p2/105

p1 = p2 =p

Agreegate demand = y1 + y2 = p/120 + p/ 105 =p/56

y= p/56

b) profit = total revenue - total cost

π= p*y - c*y

π= 56y² - 10y ..eq 1

c) first order condition of profit maximisation is

d π / d y = 0

d( 56y² - 10y)/dy = 128y - 10 = 0

y = 10/128 = 0.0892 is the total output

at y = 10/128 , p= 56y = $5

at p= $5

y1= p/120 = 5/120 =1/24 = 0.0416 output sold in market 1

y2 = p/105 = 0.0476 output sold in market 2

3) When market 1 was perfectly competitive,

Equilibrium will be established at price equal to average cost ( = marginal cost )

p = $10

y1 = p1/120 = 1/12 = 0.0833 units of goods would be sold in this perfectly competitive market