l 1 Suppose that an individual has utility function U(x, y) = x2 y 2. (a) Find the marginal rate of substitution. Are preferences convex? Why or why not. Draw an indifference curve. (b) If the price ofx is 4, the price of y is 5, and income is 40, find the optimal bundle of x and y. (c) Now suppose that income rises to 80. Find the new optimal bundle of x and y. Are the goods normal or inferior? (d) Suppose that income returns to its original level, but that the price of y falls to 4. Find the new optimal bundle of x and y. Are the goods substitutes or complements