The preferences of two consumers are represented by the utility functions:

The consumers, face the standard budget constraint .

For each one of the utility functions above, derive the followings:

1) Confirm that preferences represented in by the utility function satisfy monotonicity and convexity: Derive the MRS and confirm that it is negative (monotonicity) and its absolute value is decreasing down the curve as and (convexity).

2) Derive the demand Functions. Will the solution for the consumers problem be always interior?

3) Derive the Indirect Utility Function and use Roys identity to confirm you got it right.

4) Derive the compensated demand functions, and confirm that is homogenous of degree zero in .

5) Derive the expenditure functions, and confirm that it is homogenous of degree one in .

u(x1,x2)=(x1+x2)2 p p x1 x2 u(x1,x2)=(x1+a)(x2),a>0 B(p,m)