^{optimal consumption. intertemporal decition with a discount factor, utilty function.}

Option A During the Easter Holiday, Daniela went on a vacation to the beach for three days, on a budget of W. Before leaving, Daniela considered that her utility of consuming cocktails is given by u1(c1,62, C3) = ln(c1) i dlna) + 62ln(c:3), where c represents the consumption of cocktails on day i = 1, 2, 3, 6 is the discount factor and 11.1 means that we are analyzing utility on day 1. a) (6 points) Assuming that the price of each cocktail is US $ 1, the budget constraint is c1 +cz+03 = W. Find the optimal consumption for each day when Daniela is planning her trip. 6) (6 points) The day Daniela arrives at the beach, she begins to consume cocktails and, due to the effect of cocktails, her utility is modied to u1(cl,c2, C3) = 7110.031) + 61n(c2) + 621n(63), with '7 > 1. What is her optimal consumption now? c) (6 points) Show that given the existence of 'y, Daniela is not able to fulll her initial consumption plan. Specically, analyze her optimal consumption once she has reached day 2, that is, when she wants to maximize u2(C2, C3) = 7531(62) + dln(C3), and show that 62 and C3 in this case are not equal to those derived in b) d) (6 points) From her previous experience, Daniela knows that when she begins to drink cocktails, her utility function changes. In particular, last year it happened to her that her cocktail consumption on day 3 had to be reduced because she was her budget was limited. Therefore, this year she decides to bring more money. How much additional money should she bring if she wants to consume C3 2 c1 given her utility in b) and c)