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Econ 201 Fall 2011 Exam 3

# Econ 201 Fall 2011 Exam 3 - ECONOMICS 201 FALL 2011 EXAM 3...

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Unformatted text preview: ECONOMICS 201 FALL 2011 EXAM 3 Instructions: Please mark your answers clearly. No class notes or other materials are allowed. 100 points total, Each question is worth 5 points except where indicated otherwise. 1. It’s bedtime for 4 brothers. Brothers A and B prefer to sleep with the Window open, which they value at \$10 and \$4, respectively. Brothers C and D prefer not to sleep with the window open, which they value at -\$5 and \$7, respectively. (10 points) a. Assume that Brother B has the right to open or close the window, and bargaining is possible. Do they sleep with the window open or closed? If there is a transfer, who gives it to whom, and what are the lower and upper bounds? b. Assume that Brother C has the right to open or close the Window, bargaining is possible, and there is a transaction cost of \$3, which every brother making a transfer must pay. Do they sleep With the Window open or closed? If there is a transfer, who gives it to whom, and what are the lower and upper bounds? If there is a transfer, express the bounds in terms of money received, not money paid. 2. A competitive ﬁrm makes a product. The output price of the product is \$10 and the ﬁrm’s cost function is C (y) = 0.25 * yz. There is a negative externality; the external cost function is ac ( y) = 025* y2 . There is also a positive externality; the external beneﬁt function is eg (y) = 6 * y , where 0 > 0. (10 points) a. What is the socially optimal level of output? b. What per-unit tax would induce the ﬁrm to produce the socially optimal level of output? (Hint: Your answer should involve 6 .) c. For what value of 6 is the ﬁrm’s choice of output socially optimal in the case it ignores the externalities? 3. True or false. For a positive externality with a convex external beneﬁt function, e.g. e( y) = y2 , the size of the optimal per-unit subsidy decreases as the socially optimal level of output increases. Explain. 4. A monopolist faces a demand function of y = 40 — 49 * P , where 6 > 0 . Its cost function is C( y) = 10 y . What is the monopolist’s choice of output? (Hint: You’ll need the inverse demand function.) 5. Suppose that two ﬁrms produce the same product and compete by setting quantity simultaneously. Both cost functions are C( y) = k * y. The inverse demand function is P( yE + yz) =10 — (y1 + yz) . (10 points) a. What is Firm 1’s PMP? b. What is Firm 1’s reaction function? c. What is Firm 1’s optimal choice of output in equilibrium? 6. Multiple choice. Suppose that two ﬁrms produce the same product and compete by setting price simultaneously. Firm 1 sets price P1 , and Firm 2 sets price P2 . Both have a marginal cost of k. They face the following demand curve: Firm 1 obtains all market demand ifP1 < P2; each ﬁrm obtains half of market demand if P1 = P2 ; and Firm 2 obtains all market demand if R > P2. Which of the following is the Nash Equilibrium? (Please circle one response.) (10 points) a. P1 = P2 = F , where F is the highest possible price b. k < P1 = P2 < .79 ' 0. P1 = P2 = k d. P1 = P2 = 0 ,iwhere O is the lowest possible price 7. True or false. In the NE of the game, the goalie’s probability of playing “defend left”, q, rises as the kicker’s payoff for outcome “kick left”/“defend right” rises. Explain. (10 points) Goalie Defend Left Defend Right Kick Left Kicker Kick Right 8. Find all Nash Equilibria (pure and mixed strategy). (10 points) Player B Left Between Right 9. For what value of X is the mixed strategy NE of the following game p 2% and q = E , Where p is the 5 probability that Player A plays Top, and q is the probability that Player B plays Left? Player B L Right eft Top 2.1 Bottom 0,0 3,X Player A 10. True or false. Adding a to all of Player A’s payoffs and adding [7 to all of Player B’s payoffs does not change the mixed strategy NE of a simultaneous game if 51,!) > 0 and a i b . Explain. 11. Multiple choice‘ In the following game, which of the following sets of inequalities make it impossible for both (Middle, Left) and (Bottom, Right) to be pure strategy NE? (Please circle one response.) (MM) Top < 3 Middle ‘1 EL 7. Bottom a. d>5,e<2,f<12 b. b<5,d>7,f<12 c. a>5,d>7,f>12 d. a<5,e<9,f<12 12. Consider the following game. Suppose that we subtract X from each player’s payoffs when he or she plays “No way!” For what values of X will the outcome (Just do it!, Just do it!) become a pure strategy NE? (10 points) Player B Just do it! No way! Just do it! Player A No way! ...
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