Consider the CES utility function:

U(Qx, Qy)=(1/Qx+1/Qy)^-1

i. Plot indifferences curves for U = 0.5, U = 1, and U = 1.5. Based on your plot, would an individual with these preferences view X and Y as (imperfect) substitutes or complements?

ii. Using the Lagrangian method, find the optimal quantities of X and Y consumed, given pX, pY and I (income).

iii. Determine, mathematically, if X and Y are normal or inferior goods.

iv. Determine, mathematically, if X & Y are substitutes or complements. (Hint: how is the quantity of good X affected by a change in pY ? What about good Y and a change in pX?)