1. Consider a preference represented by Ma}, y) = mam, y]. (a) Is this preference wellbehaved? (1)) Suppose the price of X is l and the price of y is 2. If a person, Whose utility function is specied above, has income of 20, how much of X and y will this person choose to maximize their utility? 2. Suppose Dion's preferences are represented by u(x1, 22) = 527203. (a) Find the marginal utilities of x1 and 22 (b) Show that Dion's utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (c) Find the MRS. (d) Write down Dion's budget constraint. (e) Write down the tangency condition needed to find an optimal con- sumption bundle for well-behaved preferences. (f) Using the equations you wrote in (c) and (d), find Dion's ordinary demand functions for goods 1 and 2 (in other words, find out how much Alex will consume of good 1 as a function of p1, P2, and m, and how much Alex will consume of good 2 as a function of p1, p2, and m) . (g) Suppose that m = 100, p1 = 2 and p2 = 3. How much of good 1 will Alex choose to consume? How much of good 2 will Alex choose to consume