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101A_finalsp

# 101A_finalsp - Econ 101A Final exam Th 15 December Do not...

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Econ 101A — Final exam Th 15 December. Do not turn the page until instructed to. 1

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Econ 101A — Final Exam Th 15 December. Please solve Problem 1, 2, and 3 in the f rst blue book and Problems 4 and 5 in the second Blue Book. Good luck! Problem 1. Shorter problems. (50 points) Solve the following shorter problems. 1. Compute the pure-strategy and mixed strategy equilibria of the following coordination game. Call u the probability that player 1 plays Up, 1 u the probability that player 1 plays Down, l the probability that Player 2 plays Left, and 1 l the probability that Player 2 plays Right. (20 points) 1 \ 2 Left Right Up 3 , 21 , 1 Down 1 , 12 , 3 2. For each of these cost functions, plot the marginal cost function and the supply function, and write out the supply function S ( p ) , with quantity as a function of price p (30 points): (a) C ( q )=2 q (8 points) (b) C ( q q 2 q +2 (12 points) (c) C ( q )= q 3 +10 q (10 points) 2
Problem 2. Monopoly and Duopoly. (40 points). Initially there is one f rm in a market for cars. The f rm has a linear cost function: C ( q )=2 q . The market inverse demand function is given by P ( Q )=9 Q . 1. What price will the f rm charge? What quantity of cars will the f rm sell? (8 points) 2. How much pro f t will the f rm make? (4 points) 3. Now, a second f rm enters the market. The second f rm has an identical cost function. What will the Cournot equilibrium output for each f rm be? (8 points) 4. What is the Stackelberg equilibrium output for each f rm if f rm 2 enters second? (7 points) 5. How much pro f t will each f rm make in the Cournot game? How much in Stackelberg? (5 points) 6. Which type of market do consumers prefer: monopoly, Cournot duopoly or Stackelberg duopoly? Why?

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101A_finalsp - Econ 101A Final exam Th 15 December Do not...

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