• University of Massachusetts, Amherst

• RES ECON 313

ResEc 313 - PS 5 – ANSWER KEY Chapters 10-11.3 v1 1. The Lamberts family have three children: Macy, Theodore, and Jane. Each of them has different attitude towards money. In particular, Macy’s utility function is U(x)=6+0.5x and Theodore’s utility function is U(x)=5x1/2 . Unfortunately, we don’t know Jane, the youngest kid’s utility function yet. a) Given their utility functions, what are Macy and Theodore’s u-values if they can get each of the following monetary payoffs for sure (fill your answers in the table)? Dollar Value (x) Macy's u-value U(x)=6+0.5x Theodore's u-value U(x)=5x1/2 0 6 0.00 10 11 15.81 20 16 22.36 30 21 27.39 40 26 31.62 50 31 35.36 60 36 38.73 70 41 41.83 80 46 44.72 90 51 47.43 100 56 50.00 b) Draw the utility curves for Macy and Theodore (you can either draw 2 curves separately or on the same graph). Label them carefully. 0 10 20 30 40 50 60 0 10 20 30 40 50 60 70 80 90 100 u-value Dollar Values ($) Macy's u-value curve Theodore's uvalue curve c) Now both are facing the following uncertain deal (Deal A). Find Macy’s and Theodore’s expected u-values of Deal A. • First find u-value for each payoff under each state of nature. Since we already calculated them from question a, we don’t need to repeat this step. • Then find expected u-value f