Question 9 In class, we developed a simple model with mug utility and money utility. and we derived implica tions for the reservation values of buyers, sellers. and choosers in endowment-effect experiments. This question asks you to think through several variants of that model. For all parts, assume that the person has wealth w : $15,000, and that (Total Utility) : (Mug Utility) + (Money Utility). (3) Let's begin with the case studied in class: Suppose that money utility is um(m) : m. and that mug utility is u(c.r) : pc+ v(c r) where 1]ng *x if x 2 0 v(x) : A'fuglknmugikx ifo 0. (i) Derive the reservation values for buyers, sellers, and choosers as a function of p, Tlmug- and 1mg. (ii) Discuss how and why the three types differ. If it helps. consider the special case when p! : 3. nmug : 0.5 and 1mm: : 5. (b) Now, let's introduce loss aversion over money: Suppose that mug utility is as in part (a), but now suppose that money utility is u,,,(m, rm) : m + v,,,(m r,,,} where r,,r : wand \"money *x if): 2 0 Wu\") Z 2vmoney * Ifmoney * I ifx S 0. (i) Derive the reservation values for buyers, sellers, and choosers as a function of p, nmug- Amugv \"money and Amount- (ii) Discuss how and why the three types differ. If it helps, consider the special case When i\" Z 3v 71ng Z 0-5 '1ng Z 5. 1rinioriey Z 0-3' and Amoney Z 4~ (c) Next, instead of assuming loss aversion over money. let's assume diminishing marginal utility from money: Suppose again that mug utility is as in part (a), but now suppose that money utility is um(m) : 15,000: lnm. To simplify things, assume that ,Lt : 3. Timur: : 0.5, )vmug : 5. 7 (i) Derive the reservation values for buyers, sellers, and choosers. (ii) Discuss how and why the three types differ. ((1) Finally, let's keep diminishing marginal utility from money, but now eliminate loss aversion over mugs: Suppose that mug utility is tr(c} : 3.5:; and that money utility is u,,,(m} : 15,0001'lnm. (i) Derive the reservation values for buyers, sellers, and choosers. (ii) Discuss how and why the three types differ. Note: For parts (c) & (d), report your answers to 4 decimal points