Question

Question 5 [20 marks] Foursome Inc. is the monopolist in the four-toe socks market. The product does not sell very well, but some people buy it as a present for their in-laws. In particular, the market demand is given by P = 24 − Q

where P and Q are the market price and quantity of four-toe socks, respectively. The cost function of producing q units is given by the cost function c(q) = 5q^2 . Foursome Inc. practises simple monopoly pricing.

(a) Find the profit-maximising price and quantity for Foursome Inc.

(b) Calculate the profit of Foursome Inc.

(c) Calculate the dead-weight loss associated with the monopoly power of Foursome Inc.

Answer 1

a.)

The cost is given as. -

This means the marginal cost will be given as -

Given the market demand function, since the company is a monopolist, his individual demand function is also the same -

This is the Average revenue curve. We get total revenue as -

From TR, we can calculate the MR as. -

Now, equating MR and MC to find equilibrium price and quantity -

Substituting value of q in the AR equation to get the price -

b.)

The profit is given as the difference between the TR and TC. We get -

c.)

The dedweight loss due to the monopoly can be calculated using the following formula -

This means we take the average of the change in quantity and the change in price, from the perfect competition values.

In perfect competition, we have the MR=MC as the pricing condition as well, and the AR=MR=P

Hence, we get -

Therefore,