Question

Consider an (inverse) demand curve P = 30 - Q. And a total cost curve of C(Q) = 12Q.

(a) 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?

(c) Instead consider two firms (Firm A and Firm B) competing in this market. They simultaneously decide on the price of the product in a typical Bertrand fashion while producing an identical product.

(d) Both firms face the same cost function: C(qA) = 12qA and C(qB) = 12qB, where qA is the output of Firm A and qB is the output of Firm B.

(i) What will be the Bertrand-Nash equilibrium price (pB) chosen by each firm? Explain.

(ii) What is the equilibrium quantity (qB) sold by each firm and the total market output (QN)?

(iii) What, if any, is the dead-weight loss in this case?

Now consider a typical Cournot duopoly situation such that the market is being served by two firms (Firm 1 and Firm 2) that simultaneously decide on the level of output to sell in the market, while producing an identical product.

The total output of the industry is Q = q1 + q2, where q1 and q2 are the output of Firm 1 and 2, respectively. Each firm has a symmetric cost function: C(q1) = 12 q1 and C(q2) = 12 q2.

1. (i) Write down the (inverse) market demand function for this situation and the resultant profit functions for both firms.

2. (ii) Derive the reaction functions for Firm 1 and Firm 2.

3. (iii) What is the Cournot-Nash equilibrium output level (qN) for each firm? Explain.

4. (iv) Calculate the market price of the product (pN).

5. (v) What will be the total market output (QN) for both firms together?

6. (vi) Calculate the allocative inefficiency resulting from this market structure. Compare it to

   that under the monopoly market in part (a).

What can you say, in general, about the Cournot-Nash equilibrium quantities and prices as the number of sellers (n) competing in the industry rises?

Now, think of two firms colluding to earn monopoly profits by each agreeing to enjoy half the market share.

1. (i) If each firm honors this agreement, calculate each firm’s level of output and the resulting profit enjoyed by each firm.

2. (ii) In general, when can such an arrangement be feasible, that is, when will each firm have an incentive to honor such an agreement?

Answer 1