exercise 4

Exercise 4. Back to the pre-class activity due on Wednesday Sep 29. Suppose that the typical officer working for the Federal Reserve system has preferences over housing ()0 and other items (y) equal to U(x,y) = x1/4y3/4. a) Show that at any prices and with any budget, this officer wants to spend a fourth of her budget on housing, b) Find the expression of the officer's indirect utility function VCPx, Py, M). Suppose that the officer's pay in Atlanta is 240 and that in Atlanta the price of housing is PAx = I and the price of other items is Py = I (all variables are measured in thousands of dollars). c) In Atlanta, how much housing and how much other items does the officer consume? d) In Atlanta, what is this officer's level of maximized utility? In New York city, the price of housing is PNYx = 3 while the price of other items is Py =1. d) How much would the NY Fed need to pay the officer to convince her to move to New York city? e) How much housing would the officer consume in New York city if she decided to move? Page 2 f) In New York city, what is overall cost of the basket the officer used to consume in Atlanta? g) How much money would the Federal Reserve Bank save of it compensated the officer using a Hicksian compensation instead of a Slutsky compensation