1. Indifference curves and utility: Consider the utility function U (X, Y) = XY that describes Herb's preferences. For the following, think of X as the variable you would graph on the horizontal axis. a. Derive an expression for Herb's marginal utility of X (Ux). Also, find Uy. b. What is Herbs marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. What is Joe's MRS when X = 5 and Y = 10? c. Show that Joe's MRS is that same if we us monotonic transformations of his original utility function: U(X,Y) = XY - 12; U(X,Y) = XY3 + 503; U(X,Y) = InX + InY d. Calculate Joe's MRS when X = (2, 5, 10, 20, 25) and U (X,Y) = XY = 100. Show that Herb has a diminishing MRS