A price-taking consumer consumes two goods X and Y. Let x and y denote the quantities of goods X andY respectively, and let P_x and P_y be the respective prices of the two goods. Assume that (i) the consumer's budget is given by M,  > M > 0; and (ii) P_x and P_y are finite and positive. 

(a) Let the consumer's utility function be given by . U(x, y) = min[x, y] Define Indirect Utility Function and derive this consumer's Indirect Utility Function.

(b) Suppose instead that his utility function is given by U(x, y) = xy. Define expenditure function and derive this consumer's compensated demand for good X using his expenditure function.   (200 words) (8+10=18 Marks)