Question

In: Economics

In this question you are asked to compute the rationalizable strategies in linear Bertrand duopoly with...

In this question you are asked to compute the rationalizable strategies in linear Bertrand duopoly with “imperfect substitutes.” We have two firms N = {1, 2}, each with zero marginal cost. Simultaneously, each firm i sets a price pi ∈ P = [0, 10]. The demand for the good firm i sells, as a function of p1 and p2) is Qi (p1, p2)=1+ pj − pi. Each firm i maximizes its own profit πi (p1, p2) = piQ (p1,p2).

(a) Given any price pj set by the other firm, what is the best price pBR i for firm i? Plot a graph of best response curves.

(b) Compute the pure strategy Nash equilibrium.

(c) Compute all the rationalizable strategies.

Solutions

Expert Solution

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

) Consider a Bertrand duopoly where ?? , ?? and ??(?? ) = ??? are quantity,...
) Consider a Bertrand duopoly where ?? , ?? and ??(?? ) = ??? are quantity, price and total cost, respectively, for firm ? ∈ {1,2} where ? > 0. Assume neither firm has a capacity constraint. a. Derive the equilibrium quantities and prices if the products are undifferentiated. b. Derive the equilibrium quantities and prices if the products are differentiated such that residual inverse demand for firm ? is ?? = ?? − ???? + ???? given the price...
In the Bertrand duopoly, market demand is Q = ? ? Bp, and firms have no...
In the Bertrand duopoly, market demand is Q = ? ? Bp, and firms have no fixed costs and identical marginal cost. Find a Bertrand equilibrium pair of prices, (p1 , p2 ), and quantities, (q1, q2), when the following hold. a. Firm1 has fixed costs F>0. b. Both firms have fixed costs F > 0. c. Fixed costs are zero, but firm 1 has lower marginal cost than firm 2, so c2 > c1 > 0. (For this one,...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs and identical marginal cost. Find a Bertrand equilibrium pair of prices, (p1 , p2 ), and quantities, (q1, q2), when the following hold. a. Firm1 has fixed costs F>0. b. Both firms have fixed costs F > 0. c. Fixed costs are zero, but firm 1 has lower marginal cost than firm 2, so c2 > c1 > 0. (For this one, assume the...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs and identical marginal cost. Find a Bertrand equilibrium pair of prices, (p1 , p2 ), and quantities, (q1, q2), when the following hold. a. Firm1 has fixed costs F>0. b. Both firms have fixed costs F > 0. c. Fixed costs are zero, but firm 1 has lower marginal cost than firm 2, so c2 > c1 > 0. (For this one, assume the...
Problem 1: Consider the following Bertrand duopoly: two firms (A and B) are operating in a...
Problem 1: Consider the following Bertrand duopoly: two firms (A and B) are operating in a market where they produce identical products and compete on price. Assume that the market demand can be written as ? = 50 − ?. Assume that neither firm is capacity constrained so that either firm can satisfy the market demand at any price. Suppose further that the profit function for each firm can be written as ? = ?? − ?? = (? −...
Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same...
Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same constant marginal cost of MC = $10. There are 2000 identical consumers, each with the same reservation price of $30 for a single unit of the product (and $0 for any additional units). Under all of the standard assumptions made for the Bertrand model, the equilibrium prices would be Group of answer choices $10 for both firms $30 for both firms $50 for both...
Recall the static Bertrand duopoly model (with homogenous products): the firms name prices simultaneously; demand for...
Recall the static Bertrand duopoly model (with homogenous products): the firms name prices simultaneously; demand for firm i's product is a - pi if pi < pj, is 0 if pi > pj, and is (a-pi)/2 if pi = pj; marginal costs are c < a. Consider the infinitely repeated game based on this stage game. Show that the firms can use trigger strategies (that switch forever to the stage-game Nash equilibrium after any deviation) to sustain the monopoly price...
Consider the following asymmetric-information model of Bertrand duopoly with differentiated products. Demand for firm i is...
Consider the following asymmetric-information model of Bertrand duopoly with differentiated products. Demand for firm i is qi(pi,pj) = a−pi + bi ·pj. Costs are zero for both firms. The sensitivity of firm i’s demand to firm j’s price is either high or low. That is, bi is either bH or bL, where bH > bL > 0. For each firm, bi = bH with probability θ and bi = bL with probability 1−θ, independent of the realization of bj. Each...
Why is P = MC the result of Bertrand competition? Explain in terms of dominant strategies....
Why is P = MC the result of Bertrand competition? Explain in terms of dominant strategies. You may use a best-response graph or a pay-off matrix to help your explanation, but neither is required.
Define & explain the following in economic terms: 1)Cournot vs. Bertrand approaches to duopoly 2)Dorfman-Steiner equation...
Define & explain the following in economic terms: 1)Cournot vs. Bertrand approaches to duopoly 2)Dorfman-Steiner equation (for determining optimal amount of advertising for a firm)
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT