Suppose that the utility function for two goods X and Y is given by U = xy2, and a consumer purchases 9 units of X and 6 units of Y.
(a) If the consumer purchases 9 units of Y, how many units of X must be purchased to retain the same level of utility?
(b) If the consumer purchases 81 units of X, how many units of Y must be purchased to retain the same level of utility?
(c) Graph the indifference curve for the utility level found in parts (a) and (b). Use the graph to confirm your answers to parts (a) and (b).