Question 2 Ruby is a sophisticated present-biased agent with 3 = 0.5 and 6 = 1. She has utility function u(x) = x. Ruby is deciding today (t = 0) whether she will either: work tomorrow (t 1) for $10 income to be received the day after she works (t = 2) or party tomorrow (t = 1) for immediate utility of 8 but no income. That is, she is deciding between (2, 10) and (1,8). a) What does Ruby decide? b) Ruby is able to commit to working at t = 1 by declining at t=0 the party invitation (at no cost). Will she decline the invitation? c) Suppose declining the party invitation comes at a cost to Ruby's reputation at t = 2. What is the largest utility cost that Ruby would be willing to incur such that she would still use the commitment device of declining the invitation? d) Victoria is a naive present-biased agent with = 0.5 and 8 = 1. She has utility function (): = x. Victoria faces the same choice as Ruby and also has the chance to decline at t=0 the party invitation at a cost to Victoria's reputation at t = 2. Will Victoria decline the invitation?