A SIMULATION OF A COST-
BENEFIT ANALYSIS OF THE
CHILD CARE TAX CREDIT
A household cares about child care and
expenditures on goods other than child
care.
PCM Is the MARKET PRICE of child care.
Is the tax credit percentage (the proportion
s of annual expenditures on child care that
results in a tax credit).
.
M BT Is the household’s annual before-tax
income.
t Is the tax rate on taxable income.
Find an expression for the
household’s budget constraint
between child care and
expenditures on goods other
than child care.
Before-tax income can be spent on (1) child care; (2) goods
other than child care; or (3) taxes.
M BT PCM C E T
Taxes (in this simplified model) equal a constant tax rate
applied to taxable income, minus the tax credit.
T t M BT tax credit
The tax credit is a percentage of annual expenditures
on child care.
tax credit s PCM C
So,
T t M BT s P C C
M
Algebra…
1 t M BT 1 s PCM C E
E 1 t M BT 1 s P C
C
M
Define…
E Max 1 t M BT
PC 1 s PCM
So,
E EMax PC C
Derive the household’s
indifference map.
Assume a demand for child care that takes
on the following functional form (one that is
conducive to econometric estimation).
ln C ln a 1 ln E Max 2 ln PC
From observed values we estimate…
ln C ln 1 1 ln E Max 1 ln PC
5
So, the household’s demand for child care is…
1 E Max
C
5 PC
This allows us to derive
1 4
U C E 5 5
Let’s get specific…
The MARKET PRICE of child care is PCM $5
The household’s annual before-tax M BT $37 ,500
income is
The tax rate on taxable income is t 12%
.
The tax credit percentage is s 20%
Find the minimum amount of
(after-tax) money the household
must be given to make them
indifferent between the tax credit
and the additional cash.
Draw a diagram to provide a plan…
Now, apply the plan…
Start by finding the consumer
equilibrium with the tax credit.
Things we know…
(1) The budget constraint. E 33,000 4 C
1 33,000
(2) The quantity of child care demanded. C
*
1,650
5 4
(3) The quantity of other goods demanded E * 26,400
E
33000
(1650 , 26400)
Hours of Child Care
Find the substitution effect of
going from a subsidized price to
an unsubsidized price.
U1 1650 26,400 0.8 15,162 .818
0.2
Current utility equals
The equation for the current indifference curve is
E U1 4 C
5 1
4
The slope of the current indifference curve is
dE
dC
1
U1 4 C 4
4
5 5
Setting the slope of the current indifference equal to
the unsubsidized price gives the substitution effect.
1
U1 4 C 4 5
4
5 5
U C
1
5
4 54
20
C 54
20 U1 54
45
C 20 U1
C 1,380.24
E 27,604.88
E
(1380 , 27605)
33000
(1650 , 26400)
Hours of Child Care
Find the vertical intercept of the
“budget constraint” that gives
rise to the substitution effect.
Use the point-slope formula for a line E 27 ,604 .88 5 C 1,380 .24
When C equals 0… M 2 34 ,506 .08
E
Vertical intercept of the
“budget constraint” used
34506 to find the substitution
effect.
(1380 , 27605)
33000
(1650 , 26400)
Hours of Child Care
Find the benefit to the
household from the child care
tax credit.
The benefit of the child care tax credit to the recipient
is the minimum amount of (after-tax) money the
household must be given to make them indifferent
between the tax credit and the additional cash.
B $34,506.08 $33,000 $1,506.08
Find the cost of the child
care tax credit.
The tax credit results in a reduction of tax liability for
the household. The magnitude of the reduction is the
subsidy per hour of child care (in this case $1) times
the number of hours of child care (1650). This is called
a tax expenditure.
TE $11,650 $1,650
Find the welfare loss from
the child care tax credit.
The difference between the costs of the tax credit (the
tax expenditure) and the benefit of the tax credit is
sometimes called a welfare loss.
WL $1506.08 $1650 $143.92
34650 Benefit = $34506 - $33000 = $1506
34506
Tax Expenditure = $1650
Welfare Loss = $1650 - $1506 = $143
33000
(1380 , 27605)
(1650 , 26400)
Hours of Child Care
Find a tax rate that generates the
same tax revenue as that which the
current system produces.
Current taxes are T 0.12 37 ,500 0.2 5 1650 $2,850
A tax rate that collects the same revenue
without the tax credit requires that we 2,850 t2 37500
solve this.
t2 0.076 7.6%
Find the consumption bundle
that would be chosen under
these conditions.
If…
t .076 and s 0
Then…
E 1 0.076 37 ,500 5 C
E 34,650 5 C
C * 1,386
E * 27 ,720
E
34650
34506
(1386 , 27720)
33000
(1380 , 27605)
(1650 , 26400)
Hours of Child Care
The household is better off
replacing the tax credit with a
reduction in tax rates. The
treasury is just as well off
either way.