課程名稱︰個體經濟學二 課程性質︰必修 課程教師︰江淳芳 開課學院：社會科學院 開課系所︰經濟系 考試日期（年月日）︰ 考試時限（分鐘）： 試題 : MICROECONOMICS FINAL EXAM 2009 選擇題 (10%) 1. Consider the goalie's anxiety at the penalty kick. Let the kicker's payoff below represent the kicker's probability of success and the goalie's payoffs the probability of failure. (a) .50 (b) .38 (c) .63 (d) .50 (e) 1. 2. Suppose that in Enigma, Ohio, klutzes have a productivity of $1,000 and kandos have a productivity of $ 5,000 per month. You can't tell klutzes from kandos by looking at them or asking them, and it is too expensive to monitor individual productivity. Kandos, however, have more patience than klutzes. Listening to an hour of dull lectures is as bad as losing $250 for a klutz and $100 for a kando. There will be a separating equilibium in which anybody who attends a course of H hours of lectures is paid $5,000 per month and anybody who does not is paid $1,000 per month (a) if 16 < H < 80 (b) if 16 < H < 40 (c) only in the limit as H approaches infinity (d) for all positive values of H (e) if 14 < H < 35. 問答題 (90%) 1. (10%) In a small isolated town, there are two types of people, saints and crooks. In business dealings between any two residents of this town, the payoffs are below. Saint Crook ┌───┬───┐ Saint │ 7, 7 │ 0, 10│ ├───┼───┤ Crook │10, 0 │-5, -5│ └───┴───┘ What percentage of this town's residents would be saints in an evolutionary stable strategy? 2. (15%) Alice's utility function is U(H-A,C_A) = H-AC_A. Bob's utility function is min{H_B,C_B}. Alice's initial endowment is no cheese and 8 units of herring and Bob's initial endowments are 7 units of cheese and no herring. (a) Draw an Edgeworth box for Alice and Bob. Put H on the horizontal axis and C on the vertical axis. Show the contract curve (all Paretp efficient allocations) in the box. (b) Let p be competitive equilibrium price of herring and cheese is the numeraire (the price of cheese is 1), please solve for p. 3. (15%) Tip can write 2 pages of term paper or solve 2 workbook problems in an hour, while Spot can write 2 pages of term paper or solve 6 workbook problems in an hour. They each decide to work a total of 8 hours and to share their output. (a) Draw a graoh showing the economy's production possibility set. Put numerical labels on your graphs. (b) How many pages of term paper can they produce if they have to finish 14 workbook problems in 8 hour? 4. (15%) Firm 1 produces output x with a cost function c_1(x) = x^2+10. Firm 2 produces output y with a cost function c_2(y,x) = y^2+x. Thus, the more that firm 1 produces, the greater are firm 2's costs. Both firms face competitive product markets. The competitive price of x is $20 and the competitive price of y is $40. (a) If both firms are operated independently, how many units of x will firm 1 produce? (b) What is the efficient Pigouvian tax on firm 1's output? (c) How much is the tax revenue (t˙x) the government can collect? 5. (10%) Ten workers work jointly on a project. All 10 workers are equally skilled. The total value of the output produced is $60 times the sum of the number of hours worked by all 10 workers. Each worker's utility is equal to his income minus the square of the number of hours he works. Each worker is selfish. (a) They decide to let each person work as long as he wants to and they divide the total value of the output equally among the workers. How much income will each worker get? (b) Now the project is owned by someone who can monitor all 10 workers' working hours. How many working hours per worker should the employer ask his workers to work? 6. (25%) Beth and Sarah live on an island but work on the maunland. They are considering building a bridge and are trying to decide between no bridge, a two-lane bridge, or a four-lane bridge. Their total benefits, or willingness to pay, for the two types of bridges are given below: ┌──────────┬──────────┬──────────┐ │ │Beth │Sarah │ ├──────────┼──────────┼──────────┤ │Two-lane bridge │$7 │$11 │ ├──────────┼──────────┼──────────┤ │Four-lane bridge │$13 │$19 │ └──────────┴──────────┴──────────┘ The total cost of building a two-lane bridge is $10, while the total cost of a four-lane bridge is $20. (a) Is it Pareto efficient to build the bridge? If so, what is the Pareto efficient number of lanes? (b) Suppose that Beth and Sarah each independently decide whether or not to contribute $10 towards a fund to build the bridge. If neither contributes, no bridge is built. If only one of the two contributes, a two-lane bridge will be built. If both contribute, a four-lane bridge will be built. Complete the payoff box below: Payoff Box (first number notes Beth's utility, second notes Sarah's utility) ┌────────────┬───────────┬────────────┐ │ │Sarah contributes$ 10 │Sarah doesn't contribute│ ├────────────┼───────────┼────────────┤ │Beth contributes $10 │ ( 3, 9) │ (-3,11) │ ├────────────┼───────────┼────────────┤ │Beth doesn't contribute │ _______ │ ( 0, 0) │ └────────────┴───────────┴────────────┘ (c) Using this payoff box, what do predict will happen (i.e. what is the Nash equilibrium)? Provide a complete justification for your prediction. Provide an interpretation for any differences between your answer here and your answer in part (a). (d) Suppose now that the government provides $10 in funding so that a two-lane bridge will be built for sure. In this case, it is possible to build a six-lane bridge, which costs $30(including the $10 provided by the government), and each is willing to pay the following amounts: ┌──────────┬──────────┬──────────┐ │ │Beth │Sarah │ ├──────────┼──────────┼──────────┤ │Two-lane bridge │$7 │$11 │ ├──────────┼──────────┼──────────┤ │Four-lane bridge │$13 │$19 │ ├──────────┼──────────┼──────────┤ │Six-lane bridge │$15 │$22 │ └──────────┴──────────┴──────────┘ Suppose that each independently decides whether or not to contribute $10 towards a fund to build the bridge. If neither contributs, a two-lane bridge is built. If only one of the two contributes, a four-lane bridge will be built. If both contribute, a six-lane bridge will be built. Complete the payoff box below: Payoff Box (first number notes Beth's utility, second notes Sarah's utility) ┌────────────┬───────────┬────────────┐ │ │Sarah contributes $10 │Sarah doesn't contribute│ ├────────────┼───────────┼────────────┤ │Beth contributes $10 │ ( 5,12) │ ( 3,19) │ ├────────────┼───────────┼────────────┤ │Beth doesn't contribute │ (13, 9) │ _______ │ └────────────┴───────────┴────────────┘ (e) Using this payoff box, what do predict will happen (i.e. what is the Nash equilibrium)? How many lanes will be built? Provide an interpretation for any differences between your answer here and your answer in part (a). --

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