Part 1 (20 points): Write a short essay on ONE of the following topics.

Topic 1: Two-part tariff.

Provide a definition and at least two examples of two-part tariffs. Illustrate, with the aid of graphs, the optimal two-part tariff and the resulting welfare                    differences with respect to the monopolist’ uniform pricing policy if

-     consumers have an identical demand function

-     consumers differ in their demand functions and there are two possible demand functions.

Topic  2:  Bertrand  competition.  Explain  the  “Bertrand  paradox”  and  how  it differs from a Cournot outcome.   State the conditions under which the paradox holds. Provide detailed examples of two situations in which it does not hold.

Part 2 (80 points): Solve the following three exercises.

Exercise 1: Two firms produce a homogeneous product.   The inverse demand curve for this product is such that the price at which they can sell their output p is given by

p = 100 − Q,

where Q is total output: Q = q1  + q2 .

Assume that the total cost function is the same for both firms and is given by TCi  = 40qi .

a)  Assume that the firms compete in quantity (à la Cournot). Solve for the equilibrium quantities and price, and obtain the profits earned by each firm.

b)  Assume now that the two firms compete in prices (à la Bertrand). Find the equilibrium price and quantities, and obtain the profits earned by each firm.

c)   Suppose that firm 1 can invest in a new technology that would reduce its marginal cost to 25. What is the highest amount firm 1 is willing to pay for this new technology

i.      under Cournot competition

ii.      under Bertrand competition

d)  Assume  firms  have  same  marginal  costs  and  decide  their  quantities sequentially.  Assume  that  firm  1  is  the  leader.  Without  making  any calculation, compare the following equilibrium outcomes under Cournot and Stackelberg

i.       quantity produced by firm 1

ii.      price

iii.      profits of firm 1.

Exercise 2:  An industry consists of two symmetric firms (firm 1 and firm 2)  producing differentiated products. Let good i refer to the product supplied by firm i (i = 1, 2). The demand for product i is given by

qi  = 1000 − 2pi  + pj ,     ( i, j = 1,2 and j ≠ i).

The total cost of production for firm i is given by TC(qi ) = 10qi .

a)  Assume that the two  firms  compete  à la  Bertrand  (in  prices).  Find the equilibrium prices and quantities, and calculate each firm’s profits.

b)  Assume the two firms collude and maximize joint profits. Find the collusive prices, quantities and each firm’s profit.

c)   Assume now that firm 2 commits to setting the collusive price. What price does firm 1 set? Find the profits for each firm in this case and comment on whether firms are likely to stick to the collusive agreement or not.

d)  Prove that the inverse demand function for firm i is given by pi  = 1000 −  qi  −  qj ,     ( i, j = 1,2 and j ≠ i).

e)   Find the Cournot equilibrium and discuss whether the Cournot equilibrium is socially preferable to the Bertrand equilibrium.