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 +... + qn)}q1 - cq1

Others follow

Solutions

Expert Solution

Rahul Sunny answered 1 year ago

Next > < Previous

Related Solutions

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1...

Consider an industry with n identical firms competing a l´a Cournot. Demand is P(Q) = 1 − Q, and each firm’s total cost function is T C(qi) = cqi . (a) Find the limit of the total equilibrium output Q∗ (n) as n goes to infinity. (b) Suppose that n > 3 and 3 firms decide to merge. The new firm has the same total cost function as its predecessors. What is the condition on n that ensures that the...

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 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...

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.

Problem 4 Consider a market for a homogenous product with n identical firms that compete by...

Problem 4 Consider a market for a homogenous product with n identical firms that compete by setting quantities. The cost function of each firm is 8 per unit. The inverse demand function for the product is P = S/Q, where Q is the aggregate quantity and S is a positive parameter. (a) Compute the symmetric Nash equilibrium in the market and the equilibrium profit of each firm. (b) Suppose that one firm can break itself into two independent divisions that...

Consider a competitive industry where all firms have identical cost functions C(y) = y^2 +1 if...

Consider a competitive industry where all firms have identical cost functions C(y) = y^2 +1 if y > 0 and C(0) = 0. Suppose that the demand curve for this industry is given by D(p) = 52 − p. (a) Find the individual supply curve of each firm. (b) Suppose there are n firms in the industry. Find the industry supply curve. (c) Find the price and quantity corresponding to a short-run market equilibrium assuming there are n firms in...

8.6 Investment in the Future: Consider two firms that play a Cournot competition game with demand...

8.6 Investment in the Future: Consider two firms that play a Cournot competition game with demand p = 100 − q and costs for each firm given by ci(qi) = 10qi . Imagine that before the two firms play the Cournot game firm1 can invest in cost reduction. If it invests the costs of firm 1 will drop to c1(q1) = 5q1. The cost of investment is F >0. Firm 2 does not have this investment opportunity. a. ...

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...

Subjects