Question 2 Consider the following utility functions for Axel and Imogen: UA = (xA) (yA) and UI = (x1) 0.7 (27 ) 0.3 Axel and Imogen's endowments of good r and good y are given by TA = 100, yA = 100, x1 = 100, y/ = 100. Assume everyone faces the same prices for a and y, given by Pr and Py respectively. (a) Write down Axel and Imogen's budget constraints. (2) (b) Using the Lagrangian approach, maximize Axel's utility subject to his budget con- straint in order to derive his demand equations x4 and yA. (Hint: these demand equations will depend on pr and Py) (5) (c) Using these demand equations, the demand equations you determined in part (b), the equilibrium conditions that total demand equals total supply for each commodity, and assuming that commodity a is the numeraire (p* = 1), determine the equilibrium relative price, Pz. (3)