FIN 605 Week 8 Homework | Assignment Help | Kogod School Of Business American University

FIN 605 Week 8 Homework | Assignment Help | Kogod School Of Business American University 


Homework 8 – Chapter 12 o Exercises 6, 8, & 11

6. Suppose that two identical firms produce widgets and that they are the only firms in the market. Their costs are given by C1 = 60Q1 and C2 = 60Q2, where Q1 is the output of Firm 1 and Q2 the output of Firm 2. Price is determined by the following demand curve: P = 300 - Q where Q = Q1 + Q2. a. Find the Cournot-Nash equilibrium. Calculate the profit of each firm at this equilibrium.

b. Suppose the two firms form a cartel to maximize joint profits. How many widgets will be produced? Calculate each firm’s profit.


c. Suppose Firm 1 were the only firm in the industry. How would the market output and Firm 1’s profit differ from that found in part (b) above?


d. Returning to the duopoly of part (b), suppose Firm 1 abides by the agreement, but Firm 2 cheats by increasing production. How many widgets will Firm 2 produce?


What will be each firm’s profits?


8. Suppose the airline industry consisted of only two firms: American and Texas Air Corp. Let the two firms have identical cost functions, C(q) = 40q. Assume the demand curve for

the industry is given by P = 100 - Q and that each firm expects the other to behave as a Cournot competitor.


a. Calculate the Cournot-Nash equilibrium for each firm, assuming that each chooses the output level that maximizes its profits when taking its rival’s output as given.

What are the profits of each firm?

b. What would be the equilibrium quantity if Texas Air had constant marginal and average costs of $25, and American had constant marginal and average costs of $40?

c. Assuming that both firms have the original cost function, C(q) = 40q, how much should Texas Air be willing to invest to lower its marginal cost from $40 to $25, assuming that American will not follow suit? How much should American be willing to spend to reduce its marginal cost to $25, assuming that Texas Air will have marginal costs of $25 regardless of American’s actions?

11. Two firms compete by choosing price. Their demand functions are

Q1 = 20 - P1 + P2 and Q2 = 20 + P1 - P2

where P1 and P2 are the prices charged by each firm respectively and Q1 and Q2 are the

resulting demands. Note that the demand for each good depends only on the difference in prices; if the two firms colluded and set the same price, they could make that price as high as they want, and earn infinite profits. Marginal costs are zero.

a. Suppose the two firms set their prices at the same time. Find the resulting Nash equilibrium. What price will each firm charge, how much will it sell, and what will its profit be? (Hint: Maximize the profit of each firm with respect to its price.)

b. Suppose Firm 1 sets its price first and then Firm 2 sets its price. What price will each firm charge, how much will it sell, and what will its profit be?

c. Suppose you are one of these firms, and there are three ways you could play the game: (i) Both firms set price at the same time. (ii) You set price first. (iii) Your competitor sets price first. If you could choose among these options, which would you prefer? Explain why.




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