Question

Suppose that a company has a Monopoly in the production of keyboards. Market research shows that it faces a market demand function given by

P (q) = 100 ? (1/4)Q.

Its cost function is

C(Q) = 2000 + 2Q.

a. What would the price and quantity be in this market be if the company behaved as in perfect competition?

b. What is the consumer surplus in the case of perfect competition? Why is it higher than if it was a monopoly case? What is the social cost of monopoly?

Answer 1

Market demand function is . The cost function is . The marginal cost is hence or or .

(a) If the monopoly firm behaved as in perfectly competitive firm, then the equilibrium supply of product would be at where the demand is equal to the MC (which is the supply curve of the firm), rather than where MC is equal to the marginal revenue. Hence, behaving as perfectly competitive firm, we have , ie or units, ie firm would produce 392 units. The price will be setted as , ie dollars.

(b) The graph is as below.

The consumer surplus in case of perfect competition would be the area of triangle ACF, which is , and as CF is quantity produced under perfect competition, which is 392 units, and AC is is 100 minus 2 (labeling origin as O, AC is OA minus OC) which is 98, we have the or dollars.

In case of monopoly, the price would be setted at where the MC is equal to the MR. MR in this case can be found to be , and the profit maximizing quantity is hence at where or or . The price would be setted as or . The price is higher than that of in case of perfect competition due to the fact that the monopoly firm faces negative sloped demand curve, and hence the MR curve is well below the demand curve, which meets the MC curve more sooner than the perfect competition case.

The social cost of monopoly is the deadweight loss caused by it, as the prices below the profit maximizing quantity and above the MC are prices which consumers were willing to pay, and considereing the prices are above the MC, the firm could have given them without incuring any loss, but were not provided as profit maximizing condition met before that. The deadweight loss would be area of triangle EDF, which is or dollars, which is the social cost of monopoly, the surplus that is left in the market.