Question

2. The table below shows the relationship between income (Y) and total utility U(Y) for Mary. Use the information in the table to answer the following questions. 4 20 27.9 34 35.6 52 74 3.6 4 (a) Graph the utility function, with Y on the horizontal axis and U(Y) on the vertical. You do not need graph paper. (b) Suppose Mary is offered a bet where with probability 0.6 she will get 2 and with probability 0.4 she will get 6. What is the expected value of this bet (EY)? What is the expected utility associated with this bet (EU)? Show these on the graph (c) Is Mary risk averse, risk neutral or risk loving, explain your answer. (d) In general, what is the certainty equivalent level of income? Using either your graph or the table, find the certainty equivalent level of income for Mary for this bet. Comment on your results

Answer 1

Utility function Gets elementof 2 with prob = .6 & elementof 6, with prob = .4, so E(y) = (2 times .6) + 6 times .4 = 1.2 + 2.4 = 3.6 elementof Eu = .6 u (2) + .4 u(6) Eu = (.6 times 10) + (.4 times 74) = 6 + 29.6 = 35.6 Now since utility func^n is convex in shape, so Mary is risk Loving. Now CE, is defined as the Guaranted cash amount, some our would accept rather than taking a part is Gamble, so it is amount of Money, that will provide same expected utility, from the Gamble. so CE = 4.1 Now since CE > E(y), since EC = CE + RP expected cons^n thus RP rightarrow Risk premium is -ve, hence Individual is �Risk Lover�