 # ECON 402 ECON402 Final Exam Answers (Penn State University)

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ECON 402 ECON402 Final Exam with Answer (Penn State University)

1. P1,P2,P3havetocollaborateonaprojectworth10toeachofthemifitiscompletedsuccessfully and 0, otherwise. However, it takes effort to complete the project and effort is costly. Some of the work can be done today, some of the work next week. P3 cannot do any work next week. Let x1; x2; x3 the amount of work done today by P1,P2,P3 respectively and y1; y2 the amount of work done by P1,P2 next week. Suppose that the cost of an hour of work today is 2 and the cost of an hour of work next week is 1. The project is completed if the total number of hours of work done by all students is no less than 10. Students cannot work a negative number of hours. For instance, if x1 D x2 D x3 D y1 D y2 D 2 then the project is completed and the payoff for P1 is 10 2 2 2 D 4 and for

2. Consider a repeated game with two periods without discounting for which the stage game is

represented below.

3. Consider the following game. There is \$90 to divide between P1 and P2. P1 first offers to split the money .m1; 90 m1/, which P2 can accept or reject. If P2 accepts then the game is over and the money is distributed. If P2 rejects then P2 offers to split the money .m2; 90 m2/, which P1 can accept or reject. If P1 accepts then the game is over and the money is distributed. If P1 rejects then P1 offers to split the money .m3; 90 m3/, which P2 can accept or reject. If P2 accepts then the money is distributed. If P2 rejects then neither player gets anything. In both cases the game is over. Suppose that both players use a discount factor of ı D 2=3. Please show your work throughout.

4. SupposethatP1,P2arefirmsproducinganidenticalgoodatzeromarginalcostanddemandfor the product is q D 4 p in each of infinitely many periods. Make the usual assumptions and consider a discount factor ı D 0:5. Assume Bertrand competition wherever firms compete, with consumers purchasing from the firm with the lowest posted price and with consumers distributing evenly across firms if their prices are equal. Assume prices can be set at any value on the real line.

5. Please consider the following two player (P1,P2) game. At t D 1, P1 and P2 simultaneously and independently choose whether to work (W) or to shirk (S) on a project, which only has value to P2. If P1 has shirked at t D 1 then P2 receives the value of the project minus the cost of his effort (working). If P1 has worked at t D 1 then P1 and P2 bargain over a price that P2 will pay to P1 for her work. If they don’t come to an agreement, then the value of the project is zero. If they do come to an agreement, then the value to P2 of the project is 0 if both players shirked, 4 if one player worked, and 12 if both players worked at t D 1. The cost of working to P1 is 3 and to P2 it is 5. For instance, if both players work and negotiate a price p then the payoffs are p 3 and 12 5 p D 7 p, respectively.

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