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 merger is profitable?

Expert Solution

Rahul Sunny answered 1 year ago

Consider two identical firms competing as Cournot oligopolists in a market with demand p(Q)=100-0.5Q. Both firms...

Consider two identical firms competing as Cournot oligopolists in a market with demand p(Q)=100-0.5Q. Both firms have total costs,TC=10q where 10 is the marginal cost of production. ( Here Q represents total output in the market whereas q represents firm level output.) (b) Now assume that the firms collude. They again play a one-shot game. What is the output that each firm should produce in order to sustain the collusion? Find the market price, and profits of each firm. Are...

Consider an industry with demand Q = a − p where 3 identical firms that compete...

Consider an industry with demand Q = a − p where 3 identical firms that compete a la Cournot. Each firm’s cost function is given by C = F + c q. Suppose two of the firms merge and that the merged firm’s cost function is given by C = F'+C'q, where F<F'<2F (a) Determine each firm’s market share before and after the merger. (b) Suppose that a = 10 and c = 3. Determine the Herfindahl index after the...

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.

1 Consider two Cournot competitive firms – with the following market demand function P=100-Q. The firms...

1 Consider two Cournot competitive firms – with the following market demand function P=100-Q. The firms face constant marginal costs, MC1 = 5 whereas MC2 = 25. However, if they merge then the marginal production costs would fall to 5. Calculate the costs and benefits due to the merger for either firm. Is this merger Pareto improving for the economy? Explain. A Bertrand competition does not necessarily gravitate towards competitive prices in the equilibrium, with imperfect substitutes. In...

In an industry where demand is Q = 120 – P and two identical firms have...

In an industry where demand is Q = 120 – P and two identical firms have MC = AC = 30 find the Cournot and the Stackelberg equilibriums and compare the corresponding market outcomes. Do consumers have a preference for one market structure over the other?

There are N symmetric firms in the industry, facing market demand Q (p) = 250-p Firms...

There are N symmetric firms in the industry, facing market demand Q (p) = 250-p Firms have a constant marginal cost of production of c = 10, and they compete in prices. a) What are the Bertrand equilibrium price, output levels, and profits? b) Suppose that the firms want to sustain the monopoly price using grim trigger strategies. Let each firm produce a share of 1/N of the total demand under collusion. Calculate the critical discount factor as a function...

a.) Two identical firms compete as a Cournot duopoly. The market demand is P=100-2Q, where Q...

a.) Two identical firms compete as a Cournot duopoly. The market demand is P=100-2Q, where Q stands for the combined output of the two firms, Q=q1 +q2. The marginal cost for each firm is 4. Derive the best-response functions for these firms expressing what q1 and q2 should be. b.) Continuing from the previous question, identify the price and quantity that will prevail in the Cournot duopoly market c.) Now suppose two identical firms compete as a Bertrand duopoly. The...

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 +......

Question 1: Demand in an industry is 1200 – Q/10. There are 20 identical firms in...

Question 1: Demand in an industry is 1200 – Q/10. There are 20 identical firms in a competitive fringe, each with the cost function: C(q) = 1000q + q2 . There is also a dominant firm with the cost function C(q) = b*q, where b is a constant, and b<1000. (a) What is the maximum possible value of b such that the fringe produces zero output? (b) Suppose b=500. Work out the equilibrium price and Consumer Surplus. (c) Suppose b=...

Assume that two firms are in a Cournot oligopoly market. Market demand is P=120 - Q...

Assume that two firms are in a Cournot oligopoly market. Market demand is P=120 - Q where Q isthe aggregate output in the market and P is the price. Firm 1 has the cost function TC(Q1)=30 + 10Q1 and Firm 2 has the cost function TC(Q2)=15 + 20Q2. a) Write down the Profit function of Firm 1: Profit function of Firm 2: b) Using the profit functions in part (a), obtain the reaction function of Firm 1 to Firm 2....

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