1) Consider the following choice problem for a consumer who spends her entire budget on purchasing two goods, X and Y, and derives utility as given by Table 1. (i) Suppose initially prices of the two goods are px = 3 , and py = 3 . The consumer's budget is M = 30 . Find the amount of X and Y in the optimal or utility-maximizing bundle for the consumer. (ii) Now suppose price of good X changes to px = 6 . Price of good Y remains unchanged at py = 3 , and the consumer's budget also remains unchanged at M = 30 . Find the amount of X and Y in the utility-maximizing bundle for the consumer. (iii) Using your answers to (i) and (ii) above, compute the price elasticity of demand for good X. Table 1: Good X Good Y Quantity Marginal Utility of the 1:"2 unit Quantity Marginal Utility of the )7\" unit consumed (x) consumed (M Ux) consumed ) consumed (MU ) 50 75 38 42 33 36 29 28 25 21 1 8 1 5 1 2 b.) L1] 19 18 17 16 15 14 13 12 14 1 14 11 5 11 13 (4 +4 + 2 = 10 points)