Economics 207
Intermediate Microeconomics
Spring 2007
Dr. Léonie L. Stone
Homework 3—KEY
I will post graphs with this as soon as possible, but I’m having scanner problems at the moment!
(and we did the graphs in class today)
1.
Suppose the government wants to increase the ability of families to pay for college education.
Would a $500 income tax rebate differ from a $500 tax credit for tuition reimbursement?
Explain, using the concepts of income and substitution effects, and carefully using graphs to
support your answers. (Put education on the horizontal axis, and make the y axis a composite
commodity.)
Note: as written above, this problem is unclear, and it’s more like last week’s sock problem than
what I had in mind. If you’ve already done the problem, this is fine. However, the problem that
I had in mind should be written as follows:
Suppose the government wants to increase the ability of families to pay for college education.
Would an income tax credit differ from an equivalent tax credit for tuition reimbursement?
Explain, using the concepts of income and substitution effects, and carefully using graphs to
support your answers. (Put education on the horizontal axis, and make the y axis a composite
commodity.) Assume that the income tax credit is a flat amount, and that the tuition rebate
reduces the cost per hour of education by ½.
This is the answer to the second version of the question:
An income tax rebate would differ from a tuition rebate. Both programs increase the happiness
of recipients, but the results differ. There are TWO main points that should be made.
(1)Families will be happier with the tax rebate than with the tuition reimbursement. The rebate
is a gift of income, and thus has an income effect only; the tuition break is essentially a decrease
in the price of education, and thus has both an income and substitution effect. The substitution
effect induces families to substitute away from more-preferred goods, and thus they are worse off
than if they were able to freely allocate their income. (2) If the goal of the program is to induce
families to consume more education, then the tax credit is better, and again, that is because it
induces families to substitute toward education.
This is the answer to the first version of the question.
If you really think a lot (possibly too much!) about this question, there are other ways to answer
it. One is that a tax rebate is technically only relevant if you pay any taxes already, so very poor
families would not be affected by the rebate at all. Secondly, if you think of the tax credit as a
one-shot gift, like the socks in the previous homework, then you might answer the question
completely differently. In that case, families who spend more than $500 for tuition would be
indifferent; other families might prefer the rebate if they have a strong preference for other
goods. This is NOT the problem that I had in mind, though.
2. Helga currently receives $1000 in investment income and currently works 10 hours a week
for $50 per hour. Leisure is neither a normal nor an inferior good for her (that is, it is neutral
with respect to income). Suppose that she has a choice between receiving 10% more investment
income or 20% more wages. Which will she choose? Carefully graph her budget constraints
and current utility-maximizing point, and use your graphs to explain your answer.
The whole trick to this problem is that leisure is a neutral good for Helga. 10% more investment
income is equal to $100/week. Helga earns $500 in wages, so 20% more wages (if she does not
change her hours of work when wages rise) is also equal to $100. With any sort of convex
indifference curves (and her indifference curves should be convex; leisure is only neutral with
respect to income), she will be better off taking the wage increase.
Note that in general, workers would not be indifferent between these choices. Again, the
investment income increase is a pure income effect. Thus workers will want to purchase both
leisure and market goods. The wage increase has both income and substitution effects. There is
an incentive to substitute away from leisure and toward market goods, but also an income effect
that makes worker wish to purchase more of both.
Thus workers with a strong preference for market goods are likely to prefer the wage increase,
but workers who have a strong preference for leisure are likely to prefer the investment income
increase. Helga is difference because we know that she will not use her increased income to buy
more leisure, so the income effect makes her buy only more market goods. Thus she must be
even better off with the wage increase, since she has the potential to buy even more market
goods.