Let us consider a market where 10 firms l= {1,2,..,10} compete à la Cournot (quantity- setting competition). The inverse demand function is given by p( Q) =1200-18Q , where Q= Eiqi. The cost function is homogeneous and it is C( q) =10q. 1.the profit functions of eachiEl is: 2.Derive the best reply functions for each firm 3.Derive the market price in the Nash equilibrium of the game.
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- 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.Suppose two firms face market demand of P=150-Q, where q=q1+q2 . Both firms have the same unit cost of C=20. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. a) What is the follower’s total revenue function? b) Determine the equilibrium output level for both the leader and the follower. c) Determine the equilibrium market price. d) Determine the profits of the leader and the follower.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.
- *COULD YOU SOLVE D-F* Suppose the inverse demand function is P = a −bQ, where a is the market price whenQ=0 and b is the slope of the function. Suppose there are two firms, Firm 1 and Firm 2, where their cost functions are denoted by Ci(Qi) = ciQi for i ∈{1, 2}. a) Write the profit function for each firm with price as a function of Q1, Q2 b) Solve for M Ri for i ∈{1, 2}and solve for the Best Response Functions (where M Ri = M Ci) c) Solve for the Nash Equilibrium. Note that your answer will be in terms of (a, c1, c2, b) d) Solve for the price of the market, P using the inverse demand function and your answersfrom part (c). Note that your answer will be in terms of (a, c1, c2, b) e) Solve for the profit for each firm. Note that your answer will be in terms of (a, c1, c2, b) f) If c1 = c2, what value of a will profit equal 0 for both firms?Suppose two firms face market demand of P=130-Q, Both firms have the same unit cost of 30. 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.Consider the following market demand function: Q= 20-2P, where P is the market price. Suppose there are two firms- A,B in the market and they have the same cost function: the per unit cost of producing output is 4. The firms compete by choosing quantities. Find the reaction functions for both the firms if they are maximizing profits. What is the profit maximizing output for each firm and corresponding market price? If there was only one firm in the market how would your answer change?
- Suppose two firms face market demand of P=150-Q, where . Both firms have the same unit cost of C, which consist of your student number a plus 20 (i.e. if your student number a=3, then cost C=20+3=23). 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.Suppose two firms face market demand of P=150-Q, where Q=q1+q2 . Both firms have the same unit cost of 26. Assume the firms compete a la Stackelberg. Firm 1 is the leader and Firm 2 is the follower in this market. (a)What is the follower’s total revenue function? (b)Determine the equilibrium output level for both the leader and the follower. (c)Determine the equilibrium market price. (d)Determine the profits of the leader and the follower (Please write clearly, thank you)Suppose the Boston to Philadelphia airline route is serviced by three airlines – US Airways (Firm A) and JetBlue (Firm B) and Continental (Firm C). The demand for airline travel between these two cities is Q = 150 – p. The cost function is C(Q) = 30Q. The cost function is the same for all three airlines. Assume that the three airlines are making investments in airline capacity. In other words, they are simultaneously choosing quantity. (Cournot Competition) Derive US Airways’ residual demand function given JetBlue’s output, qB, and Continental’s output, qC. What is the Marginal Revenue for US Airways? Derive US Airways reaction function Derive the market equilibrium quantity, Q*, price, p*, and Profit.
- Consider Cournot competition with n identical firms. Suppose that the inverse demand function is linear with P(X) = a - bX, where X is total industry output, a; b > 0. Each firm has a linear cost function of the form C(x) = cx, where x stands for per firm output. It is assumed that a > c. a. At the symmetric equilibrium, what are the industry output and price levels? What are the equilibrium per firm output and profit levels? What is the equilibrium social welfare (defined as the difference between the area under the demand function and total cost)? b. Now let m out of n firms merge. Show that the merger is profitable for the m merged firms if and only if it involves a pre-merger market share of 80 percent. c. Show that each of the (n – m) non merged firms is better off after the merger. d. Show that the m-firm merger increases industry price and also lowers consumer welfare.Suppose the market demand for a homogeneous product is given by Q = a - bP, where a and b are positive constants. The product is supplied by a dominant firm with a constant marginal cost c > 0 and n competitive fringe firms, each of which has a cost function ci(qi) = (qi^2)/(2ki) for i = 1, ... , n, where ki > 0 is a parameter. Suppose the dominant firm moves first by setting a price P, followed by competitive fringe rms setting their quantities, taking the price as given. a). Compute the equilibrium price and quantity level for each firm. b). How does the presence of competitive fringe firms affect the equilibrium price, as compared to the monopoly price by the dominant firm?The market demand and supply function for Pizza in New Town were: Qd = 10,000 – 100P Qs = - 2,000 + 100P A. Determine the equilibrium price and quantity of the Pizza. B. Plot the market and demand curves, label the equilibrium point E, and draw the demand curve faced by a single Pizza shop in this market on the assumption that the market is perfectly competitive. Show also the marginal revenue of the firm on the figure. C. If the total cost function of the firm is TC = 500 + 2Q + Q2, determine the price-quantity combination that will maximize the firm’s profit. D. Determine the profit. What adjustments should be anticipated in the long run?