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- Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, cost C=27. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.Brand X is one of many firms in a competitive industry where each firm has a constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase? a. 2 dollars b. 1 dollar c. 0 dollar d. 2/n, where n is the number of firms in the industry e. None of the above.Oligopolies: a) Based on the information in the table, what is the demand function for this market? b) Calculate total and marginal revenues for this market in the table c) if the total cost function for this market is TC = 500 + 10Q2 , calculate the total and marginal costs for each of the quantities in the table d) What are the profit-maximizing quantity, price, and profit for this market? e) If there are two firms Atlas and Bowden in this market with the same earlier total cost function and they engage in Cournot competition, what is each firm's equilibrium quantity, price, and profit? [NB: round quantities to nearest integer to find equilibrium quantity, price, and profit] f) Is this a long run equilibrium? Why or why not?
- Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…Two firms produce goods that are imperfect substitutes. If firm 1 charges price p1 and firm 2 charges price p2, then their respective demands are q1 = 12 - 2p1 + p2 and q2 = 12 + p1 - 2p2 So this is like Bertrand competition, except that when p1 > p2, firm 1 still gets a positive demand for its product. Regulation does not allow either firm to charge a price higher than 20. Both firms have a constant marginal cost c = 4. (a) Construct the best reply function BR1(p2) for firm 1. That is, p1 = BR1(p2) is the optimal price for firm 1 if it is known that firm 2 charges a price p2. Construct a Nash equilibrium in pure strategies for this game. Are there any Nash equilibria in mixed strategies? If yes, construct one; if no provide a justification. (b) Notice that for any given price p1, firm 1’s demand increases with p2, so firm 1 is better off when firm 2 charges a high price p2. What is the best reply to p2 = 20? What is the best reply to p2 = 0 (c) What prices for firm 1 are…1. Two firms compete in a market to sell a homogeneous product with inversedemand function P = 960-6Q. Each firm produces at a constant marginal cost of$60 and has no fixed costs.c. Assuming the firms collude and act as a monopolist, computei. Equilibrium price and quantityii. Total profitsiii. Consumer surplusiv. Total welfare loss relative to perfect competition (if any)
- A country’s market for new motor vehicles is dominated completely by two firms, Fastcars Ltd and Slowcars Ltd. Market revenue is fixed at $10 billion. Each firm can choose whether to advertise. Advertising costs $1 billion for each firm that advertises. If one firm advertises and the other does not, then the firm that advertises receives 100% of market revenue and pays for its advertising. If both firms advertise, they split the market revenue 50:50 and pay for their respective advertising. If neither advertises, they split the market revenue 50:50 but without the expense of advertising. a) What strategy would you advise that Fastcars Ltd should follow? b) What would you predict will be the strategy chosen by each firm? c) Is there an outcome that would make both firms better off? In case you find that there is such an outcome, is it achievable?Demand is assumed to be unit-elastic: X(p) = 1/p. There are m ≥ b2 firms operating in the market with constant marginal cost levels c1 ≤ c2 ≤ ……. ≤ cm. They engage in Cournot competition. a. Show that the equilibrium price implies Lerner indexes Where si is the market share of firm i. b. Using the equilibrium price, show that the profit of firm i is equal to (si)2. c. Show that the industry profit is equal to the Herfindahl index H = Σi(si)2. d. What is the effect of a specific taxt on equilibrium price? How does this tax affect the industry profit and the Herfindahl index?Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, C= 22. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. What is the follower’s total revenue function? Determine the equilibrium output level for both the leader and the follower. Determine the equilibrium market price. Determine the profits of the leader and the follower.
- Four Cournot competitors face an inverse market demand curve of P = 1620 – 8Q, each with identical costs Ci = 4000 + 60qi. Find firm profits, market price, and consumer surplus at a Cournot equilibrium to answer the following questions. a) show that a merger between F3 and F4 will not be profitable if their costs remain unchanged. (Hint: the “n” in the profit formula changes from 4 to 3.)Please include step by step working and derivation of any methods used in the following questions: 1. a) Consider a homogeneous goods industry where two firms operate and the linear demand is given by p(y1 + y2) = a - b(y1 + y2 ), where p is the market price, and y1 (y2) is the output produced by firm 1 (2). There are no costs for firm 1 or firm 2. Derive the best responses (reaction curve) for firm 1 and firm 2. Explain the term best response (reaction curve). Illustrate the best responses in a diagram. b) For the case in (a) determine the Cournot equilibrium (Nash equilibrium in quantities) when firm 1 and firm 2 compete simultaneously in quantities. How large are firm 1’s and firm 2’s profits? What is the industry output? c) Suppose the inverse demand curve in a market is D(p) =a-bp, where D(p) is the quantity demanded and p is the market price. Firm 1 is the leader and has a cost function c1(y1)=cy1 while firm 2 is the follower with a cost function c2(y2 )=. Firm 1 sets its…1. Two firms compete in a market to sell a homogeneous product with inversedemand function P = 960-6Q. Each firm produces at a constant marginal cost of$60 and has no fixed costs.a. Assuming perfect competition, computei. Equilibrium price and quantityii. Profits and producer surplusiii. Consumer surplus and total surplusb. Assuming Cournot duopoly, computei. Reaction functions for each firmii. Profits of each firmiii. Consumer surplusiv. Total welfare loss relative to perfect competition (if any)c. Assuming the firms collude and act as a monopolist, computei. Equilibrium price and quantityii. Total profitsiii. Consumer surplusiv. Total welfare loss relative to perfect competition (if any)d. Rank the output quantities, profits, and total welfare by the three marketstructures above