Problem:

Suppose the person faces the budget constraint given by the following equation:

PA A + PB B = I

were A and B are the quantities of apples and bananas, respectively. PA and PB are the prices of apples and bananas. The price of an apple is $0.4, and the price of a banana is $0.1. The person has an income I=$8.

Part A - _Budget Constraint:

Write down the budget constraint using the above information. (2 points)

Part B - _Utility Function:

If this person's utility function is given by

=.

1. What is this utility function called? (See page 71 in the book.) (2 points)

2. If A = 5 and B = 80, what will utility be? (2 points)

3. If A = 10, how many units of B should he consume to obtain the same level of utility you obtained in 1 above? (2 points)

4. If A = 20, how many units of B should he consume to obtain the same level of utility you obtained in 1 above? (2 points)

Part C - _Marginal Rate of Substitution: Slope of Indifference Curve

If the marginal rate of substitution is given by the following expression

=_ _

5. Building on the Cobb-Douglas utility maximization (Page 71) sheet posted on Blackboard, write down the expressions for MUB and MUA. (2 points)

6. Calculate the MRS. (2 points)

Part D - _Price Ratio: Slope of Budget Constraint

7. What is the price ratio for the above budget constraint? Please note that Apples are on the y-axis and Bananas are on the x-axis. (2 points)

Part E - Utility Maximization: MRS=Price Ratio

8. Based on your answers to parts 5 and 6, does this person maximize utility? Explain. (2 points)

9. Should this person buy more apples (and less bananas) or less apples (and more bananas) to maximize utility? (2 points)