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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.

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Insha Fatima
Insha FatimaLv10
28 Sep 2019
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Related questions

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.

Consider the following Bertrand competition model. Two firms choose their prices simultaneously and the market demand is Q(p). A firm with the lowest price serves the entire market. They split the demand equally if prices are equal. Each firm i = 1, 2 has constant unit of production (i.e., marginal cost) ci > 0 where c1 > c2,and so the firms marginal costs are different. a) Show that p1 = p2 = c1 is not a Nash equilibrium. b) Show that there is no Nash equilibrium where the firms pick the same price (i.e., p1 = p2). c) Is there a Nash equilibrium of this game? d) Suppose now that the prices are discrete and so firm is price must be a multiple of a cent: That is, pi - {0.01, 0.02, 0.03, ..., 0.01n, ...} where n is some positive integer. What is the Nash equilibrium now?

(Assume firms compete over quantity) Two identical firms are serving a market in which the inverse demand function is given by P = 4002Q (P = 4002(q1 +q2)). The marginal costs of each firm are $40 per unit.

A) show and explain, how the Cournot quantities will change when the cost of firm 1, c1 falls to 30? You may skip the calculations for this part, but you must provide the basic intuition.

E) What is the Bertrand Nash equilibrium outcome? What is the price? What are each firm's equilibrium quantities and total equilibrium quantities? What is the total profit per firm?

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