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Economics
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Market demand is given by
P (Q) = (
100 − Q if Q < 100
0 otherwise
Suppose that two firms both have average variable cost c = $50.Assuming that firms compete
in prices, then:
1. Define the reaction functions of the firms;
2. Find the Bertrand equilibrium;
3. Would your answer change if there were three firms? Why

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Related questions

Let the inverse demand curve be p(q) = a - bq. Suppose there are two firms, with a constant marginal cost equal to C.

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

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

B) If the firms have different marginal costs, how does your answer to part A change?

Consider a Bertrand model with two firms facing the market demand Q(p)= 100 - p. Both firms have a constant marginal cost of 20. The firms compete over prices, but each firm has a production capacity of 25 units.

a) If Firm 1 believes that Firm 2 will use up all of its capacity, what price does it charge? In a diagram, show Firm 1 residual demand and the profit-maximizing price.

b) What do you expect the Nash equilibrium to be for this capacity constraint Bertrand competition? Explain your answer.

16 points) Consider a homogenous good market with the following market demand curve: Q=100-p

Two firms produce output at a constant marginal cost = 10. Derive the Nash equilibrium outcome in terms of prices, outputs, and the profits of the two firms under the following alternative situations in a)-d)

a) (3 points) Firms engage in Bertrand price competition with no capacity constraints.

b) (3 points) Firms engage in Bertrand price competition and each firm has a maximum production capacity = 15.

c) (2 points) How would your answer in part (b) change if the capacity of each firm is 90?

d) (5 points) Firms engage in Cournot quantity competition (i.e., determine their capacity assuming that the price is such that market demand equals industry capacity).

e) (3 points) Compare the industry output in cases (a) and (d) to the socially optimal and the monopoly output levels.

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