Unit 3 – Sessions 3 & 4 Show all your working!

1. Murphy was consuming 100 units of X and 50 units of Y. The price of X rose from 2 to

3. The price of Y remained at 4. a. How much would Murphy's income have to rise so that he can still exactly

afford 100 units of X and 50 units of Y?

2. Suppose a consumer’s utility derived from consuming bananas is described by the function U = 3X 2 – (1/3)X 3. Compute marginal utility. a. Make a table showing marginal utility for X from 1 to 7 units. b. What is the largest number of units of X this individual would ever choose to

consume? Explain.

3. Larry and Teri allocate their consumption between two goods: hats and bats. The price of hats is $4 each and the price of bats is $8 each. For Larry, the marginal utility of the last hat consumed was 8 and the marginal utility of the last bat was 24. For Teri the marginal utility of the last hat was 6 and the marginal utility of the last bat was 12. Which consumer is not maximizing his/her utility? How can you tell? How should he/she change their allocation?

4. Given the utility function , , . Explain the significance of a utility

function. a. Calculate total utility when 3    4. b. List 3 additional points on the indifference curve that passes through the point

(3,4). c. Explain the significance of the marginal rate substitution (MRS). d. Calculate the MRS at the point (3,4). e. Given another Utility function  , 3 , 10. Is there a relationship

between , and , ? If so, explain it.

5. What do we mean by “consumer’s optimal choice” and where are likely to find it? 6. Suppose a consumer has the utility function , , The price of good 1 is

3, the price of good 2 is 1 and his income is $270. a. Solve for the consumer’s MRS. b. Write down the budget constraint. What is the slope of the budget line? c. . What is the consumer’s optimal choice of goods 1 and 2

7. The demand equation for a good is   . Solve for the inverse demand

function and explain it?