Question

A monopolist who sells toys faces the following demand: P(y)=100-2y. The total cost function of the monopolist is given by: c(y)=20y+10y2 . a) Find the price and quantity that maximizes the monopolist’s profit. Also calculate the profit. [3+3] b) If the monopolist can do a perfect price discrimination, then find the consumer and producer surplus.

Answer 1

The profit-maximizing choice for the monopoly will be to produce at the quantity where marginal revenue is equal to marginal cost: that is, MR = MC.

Cost function is 20y+10y2

Hence, Marginal Cost=20+20y.

Price is 100-2y

hence, revenue=y*p=100y-2y2

Marginal revenue=100-4y

At max profit

100-4y=20+20y

y=10/3

P at this quantity

p=100-20/3

=280/3

B. At perfect price discrimination, the consumer surplus is zero.

The producer surplus is the area under the demand curve. Demand curve is given as P(y)=100-2y

Area under this curve

=.5*50*100

=2500