Now suppose that the two firm engage in price competition (set p) instead of qua

Question

Now suppose that the two firm engage in price competition (set p) instead of quantity competition (set q).

1. (Bertrand) If both firms move simultaneously, what are their equilibrium strategies and what is the equilibrium outcome?

2. Compare the efficiency of this outcome to that of Cournot and Stackelberg.

3. If the firms have different marginal costs, how does your answer to part 1 change?

4. Explain the corner solution of one firm pricing at the monopoly’s price.

5. Let the two firms be located at 0 and 1 on the unit interval. There are n consumers located uniformly along the interval, each with a reservation value of V . They incur transportation costs of t per unit of distance traveled from their location to the a store.

(a) What are the equilibrium strategies of the two firms under the assumption the entire market is served.

(b) What is the equilibrium outcome?

(c) In the space of (p1, p2), draw the best-response curves of the two firms. Are prices strategic complements or strategic substitutes?

6. If the firms are both located at 1/2, what are their equilibrium strategies and what is the equilibrium outcome?

Explanation / Answer

ANS:

1.) Bertrand equilibrium:if the two firms have identical marginal cost equal to c, then the Bertrand equilibrium price is equal to c.p1 = p2 = c (stable equilibrium).

Suppose p1 > p2 > c

Firm 2 captures the whole market and earns profits. Firm 1 will match or undercut firm 2’s price.

p2 > p1’ > c

Firm 1 captures the whole market and earns profits. Firm 2 will match or undercut firm 1’s price.

p1’ > p2’ > c

Firm 1 will match or undercut firm 2’s price. The adjustment will continue until p1 = p2 = c.

The outcome in Bertrand equilibrium is the same as the perfectly competitive market. No firm can earn profit.

2.) The Cournot model is a one period game, in which two firms produce an undifferentiated product with a known demand curve. The two firms compete by choosing their respective level of output simultaneously. Each firm chooses Q assuming their opponents’ output is fixed.

In a Cournot game, equilibrium is reached when each firm correctly assumes the opponents output and chooses a level of output Q that maximize its own profits. There is no incentive for either firm to change from this equilibrium. So, given a market demand of: Q (P) and production levels by two producers of Q = Q1 + Q2, then in order to maximize profits, each company has to:

The outcome of Cournot equilibrium is an example of a Nash equilibrium.

The Stackelberg model: This is a one period game, where two firms offer an undifferentiated product with known demand. Firms have to compete by choosing the amount of output Q1 and Q2 to produce, but one of the two firms goes first. Firm 2 can observe what the Firm 1 has chosen for Q1, and choose Q2 accordingly to maximize its profits. Furthermore, Firm 1 knows that Firm 2 will pursue this strategy since it can rely on the other firm’s economic rationality.

In a Stackelberg model, equilibrium is reached when Firm 1 pre-emptively expands output and secures larger profits. Hence the term “first mover advantage”. In fact, Firm 2 is forced to curtail output given that the leader (firm 1) has already produced a large output (“As I produce more, you react by producing less”).

3.) Any pair of unequal prices cannot be the Bertrand equilibrium.The situation p1 = p2 > c is not stable. As long as there is profit for the one who can capture the whole market, both firms will have incentive to undercut the other firm’s price.

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