Question

Answer the following sub-questions based on the information provided. You will draw

explanatory graphs associated with each market structure as is relevant to the explanation. Consider an (inverse) demand curve P = 30 - Q. And a total cost curve of C(Q) = 12Q.

Assume a monopolist is operating in this market.

1. (i) Calculate the quantity (qM) chosen by a profit-maximizing monopolist.

2. (ii) At the profit-maximizing quantity, what is the monopolistic market price (pM) of the

   product.

3. (iii) Calculate the dead-weight loss (allocative inefficiency) associated with this monopoly market.

Assume the market for this product is perfectly competitive.

1. (i) Calculate the market-clearing output (qPC) and price (pPC) for the product.

2. (ii) Is there any allocative inefficiency in this case?

Answer 1

Marginal cost (MC) = dC(Q)/dQ = 12

(i) and (ii)

Monopolist will maximize profit by equating Marginal Revenue (MR) with MC.

P = 30 - Q

Total revenue (TR) = PQ = 30Q - Q²

MR = dTR/dQ = 30 - 2Q

Equating with MC,

30 - 2Q = 12

2Q = 18

Q = 9

P = 30 - 9 = 21

(iii)

A perfect competitor will equate P and MC.

30 - Q = 12

Q = 18

P = MC = 12

Deadweight loss = (1/2) x Difference in P x Difference in Q = (1/2) x (18 - 9) x (21 - 12) = (1/2) x 9 x 9 = 40.5

In following graph, D, MR and MC are given demand, marginal revenue at marginal cost curves. Monopoly outcome is at point A where MR intersects MC with price pM (= 21) and quantity qM (= 12). Deadweight loss equals area ABC.

(iv) Perfectly competitive price (pPC) is 12 and quantity (qPC) is 18, computed in part (iii).

(v) Allocative efficiency is achieved when Price equals MC, which holds true in profit-maximizing competitive outcome as this one. Therefore allocative inefficiency does not exist.

In above graph, perfectly competitive outcome is at point C where D intersects MC with price pPC and quantity qPC.