1. Use the following two-good utility functions to answer parts a) through d). (1] UOW) = 3x + J? (2] UOW) = 15231 (3] {106.30 = W5 (4] HOW) = min {my} a) Graph indifference curves for 110 = 3 and U',J = 6 for each of the above utility functions. Label each indifference curve with the utility it provides. To avoid confusion, draw a new ay-plane for each utility function. b) Starting at (x = 1, y = 1), nd the marginal utility of good It 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 inin'ally 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. 1) Draw a graph of the new and old best affordable bundles using the price change in part e] and utility function (3). For good y, did the income or substitution effect dominate in your graph? g] Draw a graph of the new and old best affordable bundles using the price change in part e) and utility function [4-]. For good y, did the income or substitution effect dominate in your graph