Problem 5. Consider a consumer whose preferences can be described by the fol- lowing utility function: u(x, y) = 9xy Assume that there are only interior solutions to the optimization problem, so you do not have to impose the x > 0 and y > 0 restrictions in the optimization.

1. Write out the Lagrangian function to solve the consumer's expenditure min- imization problem (EMP). Use the first order conditions to derive the con- sumer's Hicksian demand functions for x and y, i.e. xh(px, py, u) and yh(px, py, u).

2. Use the Hicksian demand functions to derive the consumer's expenditure func- tion. Gather common terms to simplify. 3. Show that this expenditure function is increasing in u.

4. Show that this expenditure function is increasing in each of the prices.