Zhou has a utility function given by U=X1X2X3 , where X1 is cups of soda consumed per month, X2 is pizza consumed per month and X3 is hamburgers consumed per month.
a) Derive Zhou’s Marshallian demand functions for soda, pizza and hamburger.
b) If Zhou’s monthly income is 300, the price of soda is 1 and the price of pizza is 1 and the price of hamburgers is 2 solve for the utility maximizing values of Zhou’s consumption of soda, pizza and hamburger. What is Zhou’s marginal utility of income? What is Zhou’s maximum utility?
c) Calculate the loss in Zhou’s consumer surplus if the price of if the price of soda were to increase to 2. Use the information in part (b) to answer this question.