Suppose we have 2 firms competing on quantity in a homogenous-goods market. The market inverse demand function is P=17-0.5Q, and each firm has cost function TC; = 5 +8q; + ³/q?, for i=1,2.
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In the Cournot equilibirum, what is the market price and units produced by firm 1 and firm 2?
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- Alpha and Gamma are the only two phone handset manufacturers in the world. Each firm has a cost function given by: C(q) = cq + q?, where q is number of phones produced and c=70. The market demand for phones is represented by the inverse demand equation: P = a - bQ where Q = q1 + q2 is total output, a=250 and b=1. Suppose that each firm maximizes its profits taking its rival's output as given (i.e. the firms behave as Cournot oligopolists). a) What will be the equilibrium quantity selected by each firm? What is the market price? What is the profit level for each firm? Equilibrium quantity for each firm , price , profit b) It occurs to the managers of Alpha and Gamma that they could do a lot better by colluding. If the two firms were to collude, what would be the profit-maximizing choice of output for each firm? What is the industry price? What is the profit for each firm in this case? Equilibrium quantity for each firm , price , profit c) What minimum discount factor is required for…There are only two driveway paving companies in a small town, Asphalt, Inc. and Blacktop Bros. The inverse demand curve for paving services is ?= 2040 ―20? where quantity is measured in pave jobs per month and price is measured in dollars per job. Assume Asphalt, Inc. has a marginal cost of $100 per driveway and Blacktop Bros. has a marginal cost of $150. Answer the following questions: Determine each firm’s reaction curve and graph it. How many paving jobs will each firm produce in Cournot equilibrium? What will the market price of a pave job be? How much profit does each firm earn?Suppose market inverse demand function is p(y)=100-Yt where Yt is total production in the market. Assume that there are two firms with following marginal cost MC(firm 1)=Y1 MC(firm 2)=2*Y2+10 Assume that Yt=Y1+Y2 Set up profit function for both firms. What is the best response function of each firm by taking into account action of other firm? What output level is going to be produced by each firm in equilibrium? Assume that Firm 1 is leader in the market and going to act first. What will be the best response and output level of firm 2. What is difference between previous and new situation? Why? What is difference between Bertrand and previous competition? How would you like to find equilibrium price?
- Consider two firms that produce the same product and sell it in a market with the following demand function: d(p) = max{0, 12 − p}, where p ≥ 0 is the unit price of the good. Suppose that, for technological reasons, firm 1 can produce either 4 units of output at the total cost of 10, or 6 units at the total cost of 15. Similarly, firm 2 can produce either 3 units of output at the total cost of 8, or 4 units at the total cost of 10. Assume that the firms make their production decisions simultaneously. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game. Now assume that firm 1 makes its decision first. Firm 2 decides how much to produce after it observes firm 1’s output. Characterize the players’ strategy sets. Write down this game in the normal and extensive forms. Find all (if any) Nash equilibria of the game.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 there are in total 3 firms in the market. Firm 1 decides its output first, then Firm 2 and Firm 3 decide their outputs simultaneously. The inverse demand function is p = 14 – 3q, where q = q1 + q2 + 43, and each firm's cost function is c(q.) = 2q?. What is the quantity that Firm 1 produces? Round your answer to 2 decimal points. Answer: The correct answer is: 1.04
- Output is homogenous and the demand curve is P = 448 - Q. There are two firms with identical %3D costs given by C = q2 i where qi is the production of firm i. The marginal cost of firm i is Mci(qi) = 2qi . (a) Find the Cournot equilibrium firm outputs. (b)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.Suppose that two identical firms in a homogeneous-product market compete in prices. The capacity of each firm is 3. The firms have constant marginal cost equal to 0 up to the capacity constraint. The demand in the market is given by Q(p)=9- p . If the firms set the same price, they split the demand equally. If the firm set a different price, the demand of each one of the firms is calculated according to the efficient rationing rule. Show that p1=p2=3 can be sustained as an equilibrium. Calculate the equilibrium profits.
- Firm A and Firm B are the only two firms in a market where price is determined by the inverse demand function: P = 147 - Q. Q is the sum of Firm A and Firm B's output, so Q = 9A + 9B Firm A's total cost function is given by TCA(9A) = 39A Firm B's total cost function is given by TCB(9B) = 89B If these firms Cournot compete (simultaneously setting quantities), what will market price be when both firms are maximizing profits in equilibrium? (Note: The answer may not be a whole number, so round to the nearest hundredth)Here is a market with three firms: 1, 2, and 3. The demand curve is P=100-Q. There is no fixed cost but the marginal cost 10 for all firms. Firm 1 is a leader firm so that it decides the quantity Q1 first. Then two firms respectively decide their quantities Q2 and Q3 simultaneously. 1) At an equilibrium (SPE), Q1 is Q2=Q3= 2) At the equilibrium, (the market quantity) Q= and (the market price) P= 3) The profit of firm 1 is while the profit of firm 2 and 3 respectively isConsider two Cournot firms, Firm A and Firm B. Firm A has a marginal cost of 10 and Firm B has a marginal cost of 5. They face the market inverse demand function: P = 120 – Q How many units will Firm A produce?