Question 3 Consider a consumer whose consumption set is given by X = {(x1,x2) E R2:x1 2 0,352 2 0} and whose preferences are represented by the utility function u(x) = max {ax1,ax2} where a > 0,19 > 0 and where x1- denotes the quantity of commodity i = 1,2. a) Is this consumer's preferences (i) Monotone? (ii) Strongly monotone? (iii) Convex? (10 points) b) Derive the consumer's Walrasian demand function x(p, w). (10 points) c) Derive the consumer's indirect utility function v(p, w). (10 points) d) Calculate the Slutsky matrix and verify the compensated law of demand. [10 Marks]