Question

Anne has been given a choice between two lotteries. In lottery A a fair coin is flipped. If it comes up heads, Anne wins $50, if it comes up tails, she wins $150. In lottery B a fair coin is also flipped. If it comes up heads, Anne wins nothing, if it comes up tails, she wins $200.

Problem 4 - Choice under uncertainty (20 points) Anne faces an uncertain World with two possible states, good and bad. In the good state she has money holding Mg and in the bad state, she has money holdings Mb. We will write the money bundle M = (MG, MB). The good state is realized with probability II and the bad state is realized with probability 1 - II. Anne's preferences are characterized by expected utility function, U (M) = II MG + (1 - II) MB. Let II = 3/4. 1. How does Anne rank the following three bundles My = (100, 100), M2 = (50, 250), M3 = (120,40)? 2. What is Anne's expected money holdings for the three bundles? (that is, weighted average money holdings over the two states). 3. Draw Anne's indifference curve for expected utility, U (M) = 10. 4. In the same graph, draw the constant expected money holdings line for expected money holding of 100 (that is, money bundles M that all have the same expected money holdings). 5. Is Anne risk loving, neutral, or averse? 6. Determine the certainty equivalent of each of the three bundles M1, M2, and M3. 7. In the same graph as above, draw Anne's indifference curve for U(M) = 10, but now set II = 1/2

Answer 1

Budget constratuta choices in front head of - Anne $50 lottery A - tail - $ 150 lottery head B - tails - $ 200 Probability (Mo, he good state bad state a - - R I-R M = U (M) = R VMG +(1-2) JMB Geinen R = 3/4 I 1. M = (100, 100) UC = 3100 + 1-2 21100 = 3x10 + xto - + uld a UCMI) = 10

M₂ = (so, 250) UCMa) - 3 (150) + + 1230 NO - 3x 7.071 + $x 15.311 + 3.95 = 5.3 = 9.25 M₂ = ( 120,40) u (H₂) = 3 x 120 + + 50 - 8.215 + 1.581 - 9.831 mce Anne will rank the bundles in descending order of utility (ie 1st breference will be given to highest utility ) Since 107 9.831 > 9.31 Bundle will be ordered in the following manner 1 M, > H₂> H₂ |

25 SO 2. ECHI) = 3 x 1 + 1 x 100 - 25 75 + 25 + 25 – 100 125 (M) + taxes - 206100 200 100 2 100 10 30 € (M₂) = 3 x 120 + x 40 - 90 + 10 - 100 100. eCM) € (42) 6 (H₂) = 100 Anne's expected money holdings for all the 3 bundles is a constant