Assume that u xy and that px 10 py5 and i100 use the

Question

1. Consider the CES utility function:   U = a(X^d/d) + b(Y^d /d) if d¹ 0 and  U= a lnX + b lnY if d=0.

a. Assuming d¹ 0,  derive the equation for MU_x and MU_y. Find MRS.

b.  What sort of preferences are exhibited when d = 1? ...when d = 0? ...when 0d?

2. Assume that U =xy and that P_x =$10, P_y=$5, and I=$100. Use the Lagrange method to find the first-order conditions and the optimal values (i.e., utility maximizing values) of  x and y.