1. [9 + 4+ 7 = 20 pta] Pam's utility function over goods X1 and X2 is given by: 3 u(:c1, 1:3) = at:if + I?\" (i) Find Pam's Marshal-tau demands for goods 1 and 2 and show that her indirect utility function is given by: g)\"; m) = ries\" (ii) Use your answers from (i) to derive Pam's expenditure flmction and her fclcsiau demand for good 1. (iii) Pam is currently located in acity where the prices of the two goods are 331 = 1, p2 = 1. Her utility over money we is given by the indirect utility function vtpl = 1, p2 = 1; m} above. Pam goes to a gambling parlour with wealth $100. At the parlour, she is offered the opportunity to bet on a horse that has a probability E of winning. If she chooses a bet of $3, she will gain a: if the horse wins, and lose a: if it loses. How much will Pam bet