Introductory Microeconomics: Problem Set 5

Individual (or "consumer") choice.
1. Draw indifference curves to illustrate each of the following statements, commenting on the nature of preferences and on the marginal rate of substitution in each case:

1. I like Coke and Pepsi, and I don't care which I drink - I can't tell them apart.
2. I love Coke but hate Pepsi.
3. I love Pepsi but have no feelings one way or the other about Coke.
4. I always have milk in my coffee, but I never drink milk alone.
5. I like tea and coffee, but too much of either stops me sleeping.

2. A household has a weekly disposable income of £100, and consumes only sausages and potatoes. Sausages cost £4 per kg, and potatoes cost £2 per kg. The government, which is concerned about the household's diet, provides a free weekly allocation of 5kg of potatoes, and taxes sausage consumption above 10kg per week at £1p per kg. Draw the household's budget set.

3. The US "food stamp" programme has been around for a long time. Its impact on consumers can be analysed using budget constraints and indifference curves, dividing expenditure into "Food" and "All other goods". The objective of the programme is to alleviate hunger among poor people, who are given coupons ("stamps") that retailers accept as payment for food, later being reimbursed by the government. The coupons cannot be used for cigarettes, alcohol and various other items (nappies, for example).

1. What would the consumer's budget line look like if s/he were receiving a grant of \$200 and could spend that additional income on any goods desired?
2. Using indifference curves, show that for many consumers, receiving \$200 in cash or \$200 in food stamps will have the same effect on their optimal choice.
3. Again using indifference curves, show that some consumers may be forced to choose differently under the two alternatives.
4. Can you see any advantages of simply giving cash to the poor? Why do you think such programmes exist?

4. Max is a utility maximizer. His income is £100, which he can spend on canteen meals, and on notebooks. Each meal costs £5, and each notebook costs £2. At these prices, Max chooses to buy 16 canteen meals, and 10 notebooks. Now the price of notebooks falls to £1, while the price of canteen meals remains the same. At the same time, his income falls to £90. Do these two changes combined allow him to get onto a higher indifference curve, the same indifference curve as before, or a lower indifference curve?

5. A student receives a bursary of £2000 per annum. £1000 of this is needed for essential expenditure. The rest can be spent on books, priced at £20 each (with no second-hand value) and luxuries, priced at £10 (which contribute only to current utility). The student's utility function is: U(B,L) = B2L3.

1. Find the marginal utilities of books and luxuries, and the MRS of luxuries for books, as a function of B and L. Is this a well-behaved utility function?
2. The student chooses her consumption of books and luxuries to maximize her utility. Will she spend all her income? Why?
3. Use the indifference curve - budget line tangency condition to find the student's optimal consumption of books and luxuries. (How do we know we are justified in using the tangency condition in this case?)
4. Now consider the more general problem when disposable income is M and the prices of books and luxuries are pB and pL. Repeat the analysis in (c) to find the demand function for books, as a function of prices and income. What special properties does this demand function have?
5. Are these "luxuries" in the economic sense?