Question 1. (10 points) 1) The utility a consumer derives from the consumption of two goods X, and y is given by U { X; y} = Xaya The consumer has an income of l and the prices of the two goods x and y are px and py respectively. a) Set up the Lagrangean for the consumer's utility maximization problem, derive the rst order conditions, and solve for the utility maximizing levels ofx and y as a function of the consumer's income and the prices of the two goods. b) Derive the indirect utility function and consequently the expenditure function. Find the expenditure necessary to achieve a utility level of 2000, when the prices are px = 5 and py = 8 and when a = 6 = 0.5 c) Suppose you want to increase the consumer's utility from 2000 to 3000. You have two alternatives. An income subsidy and a price subsidy for the consumption of good x. Recommend one of the two alternatives by calculating the total size of the subsidy government has to spend. d) How would the costs of the two subsidy alternatives change if the relative importance of the two goods were a = 0.25 and 6 =0.75