1. Use the utility function: U = xy with the budget constraint: m = P_xX + P_yY to answer the following questions.

a. Determine the optimal consumer purchases.

b. Derive the ordinary demand functions.

c. Check the signs on prices and income.

d. Show that the demand function are homogeneous of degree zero in income and price.

2. Determine the optimal shopping for the consumer whose utility function is:

     u = x^1.5y and whose budget constraint is 100 = 3x +4y

a. What is the economic interpretation of the problem?

b. Show that the optimal purchases represent a maximization problem.

3. Use the utility function and the results of question No. 1 to answer the following questions:

a. Show the indirect utility function.

b. Show the expenditure function.

c. Check and show the signs of the expenditure function.

4. Demostrate and explain with equation corresponding to the principle of absolute quantity (Lump-sum).