suggested exercise set 02 solutions

suggested exercise set 02 solutions - Econ 110 / Pol Sci...

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Econ 110 / Pol Sci 135 Suggested Exercises Set 2 Solutions Fall 2009 Page 1 of 10 1. (a) Jack’s expected utility is 0.5* 250,000 + 0.5* 90,000 = 400. (b) Since Jack’s utility is the square root of his income, to achieve a utility of 400 Jack would need a certain income of 400 2 = $160,000. (c) The four possible luck outcome pairs for Jack and Janet are: (good, good) (good, bad) (bad, good) (bad, bad) Each of these outcomes happens with probability (0.5)(0.5) = 0.25. (d) Under the agreement, the expected utility for each participant is 0.25* 250,000 + 0.25* 170,000 + 0.25* 170,000 + 0.25* 90,000 406.1552. (e) For either Jack or Jill to achieve a utility of 406.1552, he or she would need a certain income of 406.1552 2 = $164,962.11. (f) The eight possible luck outcome triplets for Jack, Janet, and Chrissy are: (good, good, good) (good, good, bad) (good, bad, good) (bad, good, good) (good, bad, bad) (bad, good, bad) (bad, bad, good) (bad, bad, bad) Each of these outcomes occurs with probability (0.5)(0.5)(0.5) = 0.125. (g) Under the agreement, the expected utility for each participant is 0.125* 250,000 + 3*0.125* 196,666.667 +3*0.125* 143,333.333 + 0.125* 90,000 408.2744. (h) For Jack, Jill, or Chrissy to achieve a utility of 408.2744, he or she (or she) would need a certain income of 408.2744 2 = $166,687.99.
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Econ 110 / Pol Sci 135 Suggested Exercises Set 2 Solutions Fall 2009 Page 2 of 10 2. The table of certainty equivalents is as follows: (a) In order to plot the utility function, we need to show the relationship between a given input, the dollar value, which we can put on the x-axis, and the utility of that dollar value, which we put on the y-axis. Note that because the utility of $1000 is 10 and the probabilities above denote probabilities of winning $1000, we have, for example 0.8* u (1000)= u (512). u (1000)=10, so 8= u (512). We can graph this system: 0 1 2 3 4 5 6 7 8 9 10 0 100 200 300 400 500 600 700 800 900 1000 Dollar Payment Utility of Dollar Payment
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Econ 110 / Pol Sci 135 Suggested Exercises Set 2 Solutions Fall 2009 Page 3 of 10 Note that the utility relationship is the familiar cube-root utility that we have seen in lecture. So, the utility function is: 0 1 2 3 4 5 6 7 8 9 10 0 45 90 135 180 225 270 315 360 405 450 495 540 585 630 675 720 765 810 855 900 945 990 Dollar Payment Utility of Dollar Payment (b) The expected utility of the lottery is ( ) [ ] ) u(outcome2 * 2} Pr{outcome ) u(outcome1 * 1} Pr{outcome + = L U E . In this case, the expected utility is ( ) [ ] ( ) ( ) 2.0127 2.1544 4 3 1.5874 4 1 10 4 3 4 4 1 10 4 3 4 4 1 3 1 3 1 = + = + = + = u u L U E The certainty equivalent of the lottery is the dollar value that will yield a utility equal to the utility of the lottery. So, u(Certainty Equivalent) = 2.0127. So,
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This note was uploaded on 10/07/2009 for the course ECON 135 taught by Professor Zenou during the Fall '09 term at University of California, Berkeley.

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suggested exercise set 02 solutions - Econ 110 / Pol Sci...

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