Question 2 (12 marks) Ruby is a sophisticated presentbiased agent with ,5 = 0.5 and 5 : 1. She has utility function (:1:) : :3. Ruby is deciding today it = 0] whether she will either: . work tomorrow [15 = 1] for $10 income to be received the day after she works it = 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? [3 marks] bl Ruby is able to commit to working at t = 1 by declining at t = U the party invitation l[at no cost). Will she decline the invitation? [3 marks] c} Suppose declining the party invitation comes at a cost to Ruby's reputation att : 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? [3 marks] d] Victoria is a naive present-biased agent with ,3 = 0.5 and 5 = 1. She has utility function 11(9)) = :12. Victoria faces the same choice as Ruby and also has the chance to decline at t = D the party invitation at a cost to Victoria's reputation at t = 2. Will Victoria decline the invitation? [3 marks]