Question Topics covered: Consumer theory.

04 Jun Question Topics covered: Consumer theory.

Question

Topics covered: Consumer theory.

NB: Where the question is multiple choice you still need (for the purposes of these

1001 classes, but not in the end of term assessments) to explain your answers.

1. Consider the utility function ? 2? .

a. Is the assumption that more is better satisfied for both goods (X and Y)?

b. Does the marginal utility of X diminish, remain constant or increase as the consumer buys more X? Explain.

c. What is the MRSX,Y?

d. Is the MRSX,Y diminishing, constant or increasing as the consumer substitutes more X for less Y along an

indifference curve?

e. On a graph with X on the horizontal axis and Y on the vertical, draw a typical indifference curve. Label it U1. Then draw another

indifference curve, labelled U2.

2. Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches

cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in

a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint, paying

attention to the slopes and intercepts. Is it possible that Carmela might have more than one utility-maximizing

solution?

3. In the field of financial management it has been observed that there is a trade-off between the rate of

return that one earns on investments and the amount of risk that one must bear to earn that return. Putting

risk on the horizontal axis and the rate of return on the vertical:

a. draw a set of indifference curves between risk and return for a person that is risk averse (a person that

does not like risk).

b. draw a set of indifference curves for a person that is risk neutral (a person that does not care about

risk one way or the other).

c. draw a set of indifference curves for a person that likes risk.

4. The above diagram refers to Max who has allocated £100 toward meats for his barbecue. His budget line and two

curves from his indifference map are shown. (You can assume his utility function is of the general form

where B is burger meat and C is chicken).

a. Which of the bundles labelled are in Max’s opportunity set?.

b. If the price of burger meat increases, which of the labelled bundles (a, b, c, d, e) are in Max’s opportunity set?

c. Which bundle will Max choose?

d. What is the price of chicken?

e. If Max is currently at point d

i. his MRS is larger than the trade-off offered by the market.

ii. Max is willing to give up more chicken than he has to given market prices.

iii. Max is not maximizing his utility.

iv. All of the above.

f. Suppose the price of burger meat increases:

i. Max will buy less burger and more chicken.

ii. Max will buy less burger and the same quantity of chicken.

iii. Max will buy less of both meats.

iv. More information is needed to answer the question.

g. Supposes Max’s mother gives him 10 pounds of burger meat. Would he prefer this gift to the monetary (£)

value of the burger meat or would he prefer the £ value of the meat or would he be indifferent between the

two?

h. Supposes Max’s mother gives him 30 pounds of burger meat. Would he prefer this gift to the monetary (£)

value of the burger meat or would he prefer the £ value of the meat or would he be indifferent between the

two?

i. If max is given £100 to spend on barbecue meats what how will his consumption of both meats change?

ECON1001/Problemset3/2012-13 3

5. Suppose a consumer has a utility function given by