Question

In: Economics

Consider a market with two firms, where the firms manufacture commodities that are identical in all...

Consider a market with two firms, where the firms manufacture commodities that are identical in all respects. Firm i produces output level qi , i = 1, 2, and q = q1+q2. The market demand curve is p = a−bq where a and b are positive constants. Firm i earns profits πi(q1, q2) = pqi − ciqi , where ci is its unit-cost of production. Assume 0 < ci < a for i = 1, 2. Finally, assume that Firm 2’s costs per unit are twice as high as Firm 1’s. In other words, assume c2 = 2c1.

a = 100,

b = 1,

c1 = 10,

c2 = 20.

(a) Find the best-response functions for both firms.

(b) Sketch of each best response function, first on separate diagrams, then on the same diagram.

(c) Find the Nash equilibrium

Solutions

Expert Solution


Related Solutions

Consider a market with n firms, where all firms produce identical commodities. The market demand curve...
Consider a market with n firms, where all firms produce identical commodities. The market demand curve is p = a − bq where a > 0 and b > 0, and where q = q1 + q2 + · · · + qn, with qi being the quantity produced by Firm i, i = 1, . . . n. Firm i’s profits are πi(q1, q2, . . . , qn) = pqi − cqi , where c is the per-unit...
Consider a market where two firms sell an identical product to consumers and face the following...
Consider a market where two firms sell an identical product to consumers and face the following inverse demand function p = 100 - q1 - q2 but the firms face different marginal costs. Firm 1 has a constant marginal cost of MC1 = 10 and firrm 2 has a constant marginal cost of MC2 = 40. a) What is firm 1s best response function? b) What is firm 2's best response function? c) What are the equilibrium quantities, price and...
Problem 1. Consider a Cournot game with n > 2 firms, where all firms are identical....
Problem 1. Consider a Cournot game with n > 2 firms, where all firms are identical. Assume the linear demand and cost functions. Solve for the symmetric Nash equilibrium. Find the price at which output is sold in the Nash equilibrium and show that the equilibrium price approaches the unit cost of production, as the number of firms increases arbitrarily. Comment on your result. Payoff function for firm 1: ?(q1, q2,...,qn) = {? - (q1 + q2 + q3 +......
Consider a market with two identical firms, Firm A and Firm B. The market demand is...
Consider a market with two identical firms, Firm A and Firm B. The market demand is ? = 20−1/2?, where ? = ?a +?b . The cost conditions are ??a = ??b = 16. a) Assume this market has a Stackelberg leader, Firm A. Solve for the quantity, price and profit for each firm. Explain your calculations. b) How does this compare to the Cournot-Nash equilibrium quantity, price and profit? Explain your calculations. c) Present the Stackelberg and Cournot equilibrium...
Consider two identical firms in a Cournot competition. The market demand is P = a –...
Consider two identical firms in a Cournot competition. The market demand is P = a – bQ. TC1 = cq1 = TC2 = cq2 . Find the profit function of firm 1. Maximize the profit function to find the reaction function of firm 1. Solve for the Cournot-Nash Equilibrium. Carefully discuss how the slope of the demand curve affects outputs and price.
Consider a perfectly competitive market where all firms have identical long-run marginal costs given by LRMC...
Consider a perfectly competitive market where all firms have identical long-run marginal costs given by LRMC = 10. Furthermore, suppose that the market demand curve is given by ? = 3000 − 50?. a. Determine the long-run equilibrium quantity and price in this market. b. Determine the number of firms that operate in this market in the long-run, assuming that a typical firm produces 25 units of output.
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total cost is given by the equation TC = 120 + q2 + 2q where q is the quantity of output produced by the firm. You also know that the market demand for this product is given by the equation P = 1200 – 2Q where Q is the market quantity. In addition you are told that...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total revenue is given by the equation TR = q.p; where q is the quantity of output produced by the firm and p the market price (=P). The market demand for this product is given by the equation P = 5000 – 9Q where Q is the market quantity. In addition you are told that the market...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total revenue is given by the equation TR = q.p; where q is the quantity of output produced by the firm and p the market price (=P). The market demand for this product is given by the equation P = 5000 – 9Q where Q is the market quantity. In addition you are told that the market...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost...
Suppose there is a perfectly competitive industry where all the firms are identical with identical cost curves. Furthermore, suppose that a representative firm’s total cost is given by the equation. TC = 100 + q^2 + q where q is the quantity of output produced by the firm. You also know that the market demand for this product is given by the equation P = 1000 - 2Q where Q is the market quantity. In addition, you are told that...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT