2. 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) = 5vx. 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 ($) Macy's u-value Theodore's u-value 0.00 10 11 15.81 20 16 22.36 30 21 27.39 26 31.62 50 31 35.36 8 36 38.73 70 41 41.83 80 46 44.72 90 51 47.43 100 56 50.00h. Three of them is now facing another deal (Deal B). Deal B Dollar Value $50 0.3 f... $20 CE,\" 0.2 \\.. $10 0.5 Find the (range oi) certain equivalent for Macy, Theodore, and Jane for the new deal. i. Among the two deals (A and B), what is the best deal for Macy, _T_he_odo_re_ and Jane, respectively? up any deal they chose above (let's call it Deal C). Who among them should walk away with $23? k. Draw a decision tree which characterizes the decision situations Macy was facing (see Figure 10.15/pg. 208 in the textbook for reference). Instructions: Boxes represent decision alternatives (i.e., Deal A, Deal B, and Deal C) Ovals/circles represent each state of nature for each deal. Record probabilities, payoffs, and u-value for each branch of the tree. Record u-value and certain equivalents for each deal (note that CE for Deal C is $23)