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ARE 100B - Homework 2

# ARE 100B - Homework 2 - HOMEWORK 2 Due in class Thursday...

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ARE 100B M. Whitney HOMEWORK 2 Due in class Thursday, May 14th Spring 2009 You should make a copy of your answers to study from. If necessary, you can round your answers to two decimal places. 1. (17) Inverse demand for sulfur is P = 1000 - 2Q. There are two sulfur mines whose cost functions are: TC I = 50 + 55ql + .1 *qI2; and TC 2 = 100 + 139*~ + .05*~ 1 a. Suppose the two firms behave as Cournot oligopolists. Find their reaction functions. What is the optimal output for each firm? Now find total market output, price and the profit or loss for each firm. b. Now, suppose firm 1 is a Stackelberg leader, while firm 2 is a follower. Find optimal output for each firm; market output and price. and profit or loss for each firm. How did adopting Stackelberg behavior affect the output and profit of the leader. as compared with the Cournot outcome of part a? How was the follower's output and profit affected as compared with part a? c. Next, assume the two firms behave as Bertrand oligopolists. Find the market price, each finn's output and the market quantity. Also find each finn's profit or loss. d. Repeat part c, assuming the finns fonn a cartel.

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