Directions: Pleaseshow all of your work and fully annotate all graphs. Simplify your answers onlyto the extent that 1t wall help you answer the problems. I. (25 points) Rebecca derives utility from bananas and chocolate according to the utility function: u(b; ) =b?c The prices of bananas and chocolate are Pb=5%0.5 and Pc=$1.0. Assume her income 1s 510. a. Assuming that Rebecca has Y dollars of income, calculate her Marshallian (x(p; Y')) dem and for bananas and chocolate using the short cut method. Compare your results using the Lagrangian method. b. Calculate Rebecca's Hicksian (h(p: u)) demand for bananas and chocolate, as well as her expenditure function, e(p; u). . What in words 1s the difference between direct and indirect utility? What in words 1s the difference between Marshallian demand and Hicksian demand? d. Is Rebecca's Marshallian demand for bananas more or less elastic than her Hicksian demand? What does your answer for the elasticity of the Hicksian and Marshalhan demand for bananas imply about the income effect for bananas? e. Assume that the price of bananas increases to $1. Show in a graph the price change and then show on the same graph the compensated variation needed for Rebecca to remain atthe same utility level