Consider a consumer whose preferences can be described by the following 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.

[Hint: Use your preferred method to solve either the Utility Maximization Problem or the Ex- penditure Minimization Problem. ]

1. (15)Derive the consumer's expenditure function.Gather common terms to simplify.

2. (5) Calculate the minimum expenditure required to achieve u = 100 if p x = 4 and p y = 25.

3. (5)Show that this expenditure function is increasing in u.

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