Consider the following utility functions for Axel and Imogen: UA = (xA) 0.6 0.6 (A)0.4 and U₁ = (x1)0.7 (1) 0.3 = 100, JA = 100, Axel and Imogen's endowments of good x and good y are given by TA TI = 100, y₁ = 100. Assume everyone faces the same prices for x and y, given by Pa 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 A and y₁. (Hint: these demand equations will depend on pa and py) (5) Using these demand equations, the demand tions you determined in part (b), the equilibrium conditions that total demand equals total supply for each commodity, and assuming that commodity is the numeraire (p = 1), determine the equilibrium relative price, P. (3) Py
