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A: Cournot duopoly
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Consider a Bertrand duopoly. Market
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- Consider a Bertrand duopoly where market demand is P(Q)=107-5Q. Each firm faces a marginal cost $18 and no fixed cost. what is one market price that can occur in a Nash equilibrium?Consider a duopoly where firms compete in prices and firms do not have any capacity constraints. Market demand is P(Q)=45-4Q, and each firm faces a marginal cost of $9 per unit. How much is each firm's total variable cost if firms equally divide the market at Nash equilibrium?Consider a market that is a Bertrand oligopoly with 5 firms in the market. Each of these firms produce an identical product and each have the same cost function of C(Q) = 80Q. The inverse market demand for this product is P = 2480 – 2Q. What is the equilibrium market price?
- Consider a market that is a Bertrand oligopoly with 5 firms in the market. Each of these firms produce an identical product and each have the same cost function of C(Q) = 80Q. The inverse market demand for this product is P = 2480 – 2Q. How much does EACH firm produce at the equilibrium price?Consider two firms that compete according to the Cournot model. Inverse demand is P (Q) = 16 − Q. Their cost functions are C (q1) = 2q1 and C (q2) = 6q2 (a) Solve for Nash equilibrium quantities of each firm (b) Suppose firm 2 becomes more inefficient and its cost function changes to C (q2) = xq2 where x > 6. How large must x be to cause firm 2 to not want to produce anything in equilibrium?Suppose a duopoly market can be modeled as a prisoner’s dilemma. Which of the following statements is correct? Group of answer choices -At the equilibrium, firms produce less total output than if there was a monopoly. Consumers are better off than with a monopoly. -At the equilibrium, firms produce more total output than if there was a monopoly. Consumers are better off than with a monopoly. -At the equilibrium, firms produce the same total output as if there was a monopoly. Consumers are better off than with a monopoly. -At the equilibrium, firms produce more total output than if there was a monopoly. Consumers are worse off than with a monopoly. -At the equilibrium, firms produce the same total output as if there was a monopoly. Consumers are worse off than with a monopoly. -At the equilibrium, firms produce less total output than if there was a monopoly. Consumers are worse off than with a monopoly.
- Consider a Bertrand duopoly. Both firms produce an identical good at the same constant marginal cost of $0.80. Demand is given by Q=100−P. If the two firms charge the same price, they share market demand equally. The firms are located in Singapore, where the smallest currency denomination is $0.05. The firms thus can only choose prices in increments of $0.05. a) Suppose that both firms choose the same price, P. What is the profit of a firm as a function of P? b) Now suppose that one firm unilaterally deviates from the arrangement in (a) by charging a price $0.05 lower than P. What is that firm’s profit as a function of P? c) A Nash equilibrium occurs when no firm has an incentive to deviate by lowering its price. Using your answers in (a) and (b), set up an inequality that characterizes the Nash equilibrium. Then solve for the Nash equilibria in this game. (Hint: there are three equilibria)Consider a Stackelberg duopoly with the following inverse demand function: P = 1,200 − 3Q1 − 3Q2. The firms' marginal costs are identical and are given by MCi = 6. Based on this information, the Stackelberg follower's reaction function is Multiple Choice: Q2 = 398 − 0.5Q2. Q2 = 199 − 0.5Q1. Q2 = 398 − 0.5Q1. Q2 = 199 − 0.5Q2.Three electricity generating firms are competing in the market with the inverse demand given by P(Q) = 20 – Q. All firms have constant marginal costs. Firm 1’s marginal cost is MC = 5; it has a capacity constraint of K1 = 5 units. Firm 2’s marginal cost is MC = 8; it has a capacity constraint of K2 = 2.5 units. Firm 3’s marginal cost is MC = 10; it has a capacity constraint of K3 = 2.5 units. A. The three firms compete in the style of Cournot. Please compute the Nash equilibrium quantities. Also compute the price in the Nash equilibrium. B. Which of these firms would have produced a larger quantity if it had a larger capacity?
- Consider a Duopoly model, in which two firms decide a quantity simultaneously. The market demand is given by P=50 - Q, where Q is the total output (Q=Q1+Q2). Each firm has an identical cost function, TCi=6Qi, i=1, 2. If Firm 1 believes Q2=10, Firm 1 should sell Q1= ____ units in order to maximize its profit.Consider a Cournot duopoly with a demand function of p=10-Q(where Q=q1+q2) and a constant marginal cost of c>0. a) Find the two firms’ best-response functions. b) Find the Nash equilibrium output. c) What happens to the equilibrium market price as c increases (assuming that c remains below 10)? d) What happens to the equilibrium market price if c increases above 10?Consider a Cournot duopoly. The market demand function is P = 180 – 2(q₂ + q₂), where P is the market price, q₂ is the output produced by Firm 1 and q₂ is the output produced by Firm 2. The two firms have a constant marginal cost c = 30. What is the total output in this market? Round your answer to the nearest integer (e.g. 50)
