1. Use the following twogood utility functions to answer parts a] through d). (1) 006.31) = 3x + y (2) U (x. y) = x231 (3) U (x. y) = NE (4) 006.31) = min {96, y} a) Graph indifference curves for U0 = 3 and U0 = 6 for each of the above utility functions. Label each indifference curve with the utility it provides. To avoid confusion, draw a new xyplane for each utility function. b) Starting at (x = 1, y = 1), nd the marginal utility of good x for each of the above utility functions. c) Find the marginal rate of substitution of utility function (1]. d] Which utility functions from (1] to [4) show a preference for variety? e) Suppose initially the price of both goods is equal, and then the price of x doubles. Assuming x and y are normal goods, nd the sign and briey explain the substitution and income effects on the optimal quantity of each good. f) Draw a graph of the new and old best affordable bundles using the price change in part e) and utility function (3). For good 31, did the income or substitution effect dominate in your graph