ECO101H1 Chapter Notes - Chapter 2: Negative Income Tax, Household Income, Earned Income Tax Credit

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Published on 1 Nov 2012
School
UTSG
Department
Economics
Course
ECO101H1
1
CHAPTER 2
2-1. How many hours will a person allocate to leisure activities if her indifference curves between
consumption and goods are concave to the origin?
A worker will either work all available time or will not work at all. As drawn in Figure A, point B is
preferred to points A and C. Thus, the worker chooses not to enter the labor market. As drawn in Figure
B, point C is preferred to both points A and B. Thus, the worker chooses not to consume any leisure and
work all available time.
Figure A Figure B
2-2. What is the effect of a rise in the price of market goods on a worker’s reservation wage,
probability of entering the labor force, and hours of work?
Suppose the price of market goods increases from p to p
and the person’s non-labor income is V. If she
chooses not to work, she can purchase V/p
units of consumption after the price change, whereas she
could have consumed V/p units of consumption prior to the price increase. Thus, her endowment point
has moved from E to E
in Figure A. As long as leisure is a normal good, the indifference curve is steeper
as we move up a vertical line, indicating that the slope of the indifference curve is steeper at E than at E
.
Thus, an increase in the price of goods lowers the reservation wage and makes the person more likely to
work.
Hours of Leisure Hours of Leisure
Goods Goods
B
C
A A
B
C
U1
U1
U0 U
0
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2
Figure A.
To simplify the illustration of the effect on hours of work, assume for simplicity that V = 0. The increase
in the price of goods shifts the budget line from FE to GE, moving the worker from P to point R. This
shift induces both an income effect and a substitution effect. The price increase in effect lowers the
person’s real wage rate, increasing the demand for leisure and leading to fewer hours of work. This
substitution effect is illustrated by the move from point P to point Q in Figure B. The price increase also
reduces the worker’s wealth, lowering the demand for leisure and leading to more hours of work. This
income effect is illustrated by the move from Q to R. As drawn the income effect dominates the
substitution effect and the price increase lowers the demand for leisure and increases hours of work. It is,
of course, possible for the substitution effect to dominate the income effect (not pictured), so that hours of
work decreases. Thus, without further restrictions on preferences, an increase in the price of market goods
has an ambiguous effect on hours worked.
Figure B.
Goods
V/p
V/p
Hours of
Leisure
T
0
E
E
E
F
Goods
Q
P
R
G
T
Hours of Leisure
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2-3. Sally can work up to 3,120 hours each year (a busy social life and sleep take up the remaining
time). She earns a fixed hourly wage of $25. Sally owes a 10 percent payroll tax on the first $40,000
of income. Above $40,000 of income, there is no payroll tax. Sally also faces a progressive income
tax rate. There is no income tax on the first $10,000 of income. From $10,000 up to $60,000, the
marginal income tax rate is 25 percent. Above $60,000, the marginal income tax rate is 50 percent.
Graph Sally’s budget line.
Sally’s budget line will have kinks at gross income levels of $10,000, $40,000, and $60,000. As her wage
is $25 per hour, these kinks occur after 400 hours, 1,600 hours, and 2,400 hours of work respectively, or,
similarly, at 2,720, 1,520, and 720 hours of leisure.
From 0 to 400 hours, Sally’s after-tax wage is $22.50 (90 percent of $25). If she works exactly
400 hours, her after-tax income is $9,000.
From 400 to 1,600 hours, Sally’s after-tax wage is $16.25 (65 percent of $25). If she works
exactly 1,600 hours, her after-tax income is $9,000 + $16.25 (1600-400) = $28,500.
From 1,600 to 2,400 hours, Sally’s after-tax wage is $18.75 (75 percent of $25). If she works
exactly 2,400 hours, her after-tax income is $28,500 + $18.75 (2400-1600) = $43,500.
From 2,400 to 3,120 hours, Sally’s after-tax wage is $12.50 (50 percent of $25). If she works
exactly 3,120 hours, her after-tax income is $43,500 + $12.50 (3120-2400) = $52,500.
Sally's Budget Line
0
10000
20000
30000
40000
50000
60000
3120
2920
2720
2520
2320
2120
1920
1720
1520
1320
1120
920
720
520
320
120
Hours of Leisure
Dollars of Consumption
2-4. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for
every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care
expenses for each hour he works. Tom receives $80 in child support payments each week. There are
168 hour in the week. Graph Tom’s weekly budget line.
If Tom does not work, he leisures for 168 hours and consumes $80.
For all hours Tom works up to his first 40, his after-tax and after-child care wage equals (80
percent of $15) – $4 = $8 per hour. Thus, if he works for 40 hours, he will be able to leisure for
128 hours and consume $80 + $8(40) = $400.
For all hours Tom works over 40, his after-tax and after-child care wage equals (80 percent of
$30) – $4 = $20. Thus, if he works for 168 hours (128 hours at the overtime wage), he will not
leisure at all, but he will consume $80 + $8(40) + $20(128) = $2,960.
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Document Summary

A worker will either work all available time or will not work at all. As drawn in figure a, point b is preferred to points a and c. thus, the worker chooses not to enter the labor market. B, point c is preferred to both points a and b. Thus, the worker chooses not to consume any leisure and work all available time. Thus, her endowment point has moved from e to e in figure a. As long as leisure is a normal good, the indifference curve is steeper as we move up a vertical line, indicating that the slope of the indifference curve is steeper at e than at e . Thus, an increase in the price of goods lowers the reservation wage and makes the person more likely to work. To simplify the illustration of the effect on hours of work, assume for simplicity that v = 0.