Download Answers to Midterm Test - November 1st, 2008

Midterm Test
ECMC54 (Economics of the Family, Women and Work)
November 1st, 2008.
2 hours
______________________________________
____________________
Your name (Print clearly and underline your last name)
Your student number
There are eight questions on this test, but you should only answer six of
them. Each question is worth 16 2/3 marks. Answer each question to the
best of your ability.
1.
In the small economy of Xanadu, there are 1000 people living.
Of these, 200 are aged 0-14 years of age. There are 80 people who
do not have jobs, but are actively looking for work. Another 300
people are currently working full-time and 240 are currently working
part-time. Another 50 women are on maternity leave from their jobs.
50 people are students attending university full-time, with no other
employment-related activities.
(a)
How is the participation rate defined, and what is the
participation rate in this economy;
The labour force participation rate is defined as the
number of persons in the labour force divided by the
working age population, expressed as a percentage. In
this case, there are 670 persons in the LF
(300+240+50+80), and the working age population is 800.
The participation rate is therefore 83.75%
(b)
How is the employment rate defined and what is the
employment rate in this economy;
The employment rate is defined as the number of
persons employed divided by the working age population,
expressed as a percentage. In this economy, there are
590 persons employed and 800 in the working age
population for an employment rate of 73.75%
(c)
what is the part-time rate in this economy;
The part-time rate is the number of persons working
part-time divided by the total working either full-time or
part-time, expressed as a percentage. The part-time
rate in this economy is 240/540 or 44.44%
(d)
How is the unemployment rate defined and what is the
unemployment rate in this economy?
The unemployment rate is the number of persons
unemployed (not employed but actively seeking work)
divided by the number of persons in the labour force,
expressed as a percentage. The unemployment rate in
this economy is 80/670 = 11.94%
2. Define the following terms:
(a)
the tax base
The tax base is the financial sum to which tax rates are applied in
order to calculate amount of tax owing. In the case of the income
tax, taxable income is the tax base. For a property tax, the assessed
value of real estate is the base to which property tax rates (mill
rates) are applied.
(b)
the tax unit
the tax unit is the entity that is responsible for paying taxes (i.e., the
taxpaying unit). For instance, with an income tax, it might be the
individual whose income is assessed and taxed or it could be the
household or family whose joint income is assessed and taxed.
(c)
the tax rates
The tax rates are the amounts (usually percentages) that are
multiplied by the tax base to produce the amounts of tax owing,
before tax credits are subtracted. In a progressive income tax
system, these tax rates are graduated, with higher rates being
charged the larger the taxable income of the individual.
(d)
Thinking of the personal income tax system, what things are
included in (i) the tax base and (ii) the tax unit in Canada?
In the Canadian income tax system, the definition of income is very
comprehensive, so that employment income, self-employed income,
business and professional income, income from rentals, income from
financial assets, and capital gains are all included in the tax base.
However, the value of unpaid household labour is not included in
taxable income.
The tax unit for personal income taxes is the individual, rather than
the household or family.
3. There are three different families in a small economy. All of them
earn $50,000. One is a single parent family. One is a single earner
(two-parent) family. One is a two-earner (two-parent) family, with
both parents having equal earnings ($25,000 each). Each family has
one child. All of the income comes from employment earnings.
The tax system taxes individuals, rather than families. Each employed
individual receives a personal tax credit of $5,000 (multiplied by the
lowest tax rate which is 20%). For families with a spouse with no
earnings, there is a spousal credit of $5,000 (multiplied by 20%). If
you are a single parent, your first child is eligible for an equivalent-tospouse credit of the same amount.
Tax rates are 20% on the first $20,000, 30% on the next $20,000
and 40% on any additional income. There is no child care expense
deduction; however families with all parents employed have child care
expenses of $5,000 per year.
(a)
How much tax will each family pay in total?
The single parent family will be assessed $14,000 in taxes minus
$2,000 of tax credits for a total of $12,000 in income tax.
The single earner family has only one earner who will be assessed
$14,000 in taxes minus $2,000 of tax credits for a total of $12,000
in income tax.
Each of the two earners in the two-earner family will be assessed
$5,500 in taxes minus $1,000 of tax credits for a total of $4,500
each in taxes or a total of $9,000 for the whole family.
(b)
What are the marginal tax rates on each adult?
There are five adults. The single parent pays 40% on her last dollar
of income, so her marginal tax rate is 40%. By the same logic, the
marginal tax rate of the earner in the single earner family is 40%.
The spouse in that same family has a marginal tax rate of 0%. Each of
the two earners in the two-earner family has a 30% marginal tax rate.
(c)
How much consumable income does each family have left after
taxes and child care expenses are paid?
The single parent family has ($50,000 - $12,000 - $5,000) $33,000
of consumable income.
The single earner family has ($50,000 - $12,000) $38,000 of
consumable income.
The two-earner family has ($50,000 - $9,000 - $5,000) $36,000 of
consumable income.
(d)
Assume that families with a stay-at-home parent are able to produce
$30,000 worth of “home production value”, whereas families without a
stay-at-home parent produce $10,000 worth of “home production
value”. Comment on horizontal equity and efficiency in this tax
system, while explaining what you mean by these terms.
Including the value of home production, the total well-being of the
single parent family will be $43,000; the total well-being of the
single-earner family will be $68,000; and the total well-being of the
two-earner family will be $46,000. Horizontal equity says that
individuals (or perhaps families) with equal ability to pay (or equal
well-being) should pay equal amounts of tax. Efficiency means that
economic decisions of families (labour supply, but also marriage,
divorce, child-bearing etc) should be distorted or changed as little as
possible because of taxation.
This tax system is neither horizontally equitable nor efficient. It
treats the single parent family and the single earner family as if they
were equivalent for taxation purposes (same amount of tax), ignoring
the extra value of untaxed household production for the single-earner
family, and the extra child care costs (reducing consumable income)
for the single parent family. Therefore, the single parent family is
overtaxed. This would distort decisions to divorce, or to have
children outside of marriage.
In comparing the single-earner family to the two-earner family, we
can see that the two-earner family pays less tax, partially
compensating for differences in well-being/ability to pay. However,
once child care costs and differences in household production are
taken into account, it appears that the two-earner family is overtaxed
as well. This horizontal inequity distorts the decision of parents with
children to enter the labour market.
4. (a) Some people argue that the Child Care Expense Deduction is unfair
because this child care assistance is not available to a family unless all
parents in the family are employed (or unable to work). What is the
rationale for the current rules on the Child Care Expense Deduction in
Canada?
The Child Care Expense Deduction (CCED) allows the lower-earning
spouse in a two-earner family to deduct the cost of annual child care
expenses from her taxable income before applying tax rates to
calculate the amount of tax she owes. This deduction is only
available to families in which all parents are employed (i.e., also to
single parents who are employed) because child care is considered to
be a “work expense” – a cost of being able to work. Therefore, the
income that goes towards paying these child care expenses is not truly
extra ability-to-pay or extra well-being, and therefore this income
should not be taxed. Other families that provide their own child care
or purchase child care services for other reasons, do not have a
similar work expense, so the cost of child care cannot be deducted.
(b) The Child Care Expense Deduction is deducted from the income of
the lower-earning spouse before tax rates are used to calculate
amount of tax owed. Explain why it is reasonable to deduct child care
expenses from the income of the lower-earning spouse, rather than
from the income of the higher earning spouse.
Since the CCED is being considered as a cost of getting to work or
being able to work, it is the labour force decision of the second
earner that triggers this expense. It is presumed that the higher
earning spouse is the “first” earner, and the lower-earning spouse is
the “second” earner that triggers child care expenses. Therefore,
the deduction is subtracted from her taxable income.
We might also notice that the second earner is often the mother, and
the mother’s labour supply decision is quite sensitive to the net wage.
Therefore, it is important, on efficiency grounds, to try to make the
net wage (after taxation) of this spouse as close as possible to the
gross wage.
5. According to our model of completed fertility decisions, the price
of child goods, the price of adult goods and the level of family income
will all affect the demand for children (the “completed fertility”
decision). Explain how each of these is likely to affect decisions about
completed fertility, giving examples of each one to explain what
effect each will have on the decision of a family about how many
children to have.
The price of child goods includes things like the price of child care or
the price of a child’s education. The price of adult goods would
include things like the price of housing or transportation. Income
refers to the overall income of the family (typically what is called the
full income), but could be construed to include the mother’s wage rate
(the mother’s cost of time).
An increase in the price of child goods will lead to an increased price
of having children, and therefore a lower planned completed fertility.
An increase in the price of adult goods would lead to decreased
consumption of adult goods (substituting away from adult goods and
towards child goods, but also lower real purchasing power so lower
ability to purchase both adult and child goods). In other words, the
effect on planned completed fertility is uncertain.
An increase in income should ordinarily lead to increased desire to
consume more of all normal goods (and therefore plans to have more
children). However, empirical results do not show much positive
effect of income on fertility. It appears that increased income can
lead to both a plan for a higher quantity of children, but also a plan
for a higher quality of children (in other words, higher levels of
expenditure on the children that you have already planned). The
effects of income on the planned “quality” of children seem to
overwhelm any positive effects of income on the quantity of children.
(Obviously, increases in the price of mother’s time will make childrearing more expensive and will tend to decrease planned fertility).
6. (a) What is the “reservation wage, and how is it measured?
The reservation wage is the wage rate (W*) that just makes the
individual indifferent between not entering the labour market and
entering the labour market. It is usually measured as the slope of the
indifference curve that just passes through the point indicating the
amount of non-labour income the individual will get (i.e., without
employment – this could be asset income, or government transfer
income, or the income of a spouse).
(b)What factors affect the reservation wage? Explain.
Two main types of factors will affect the reservation wage. First, and
most important are the tastes or preferences of the individual. An
individual who must be highly compensated before being willing to
enter the labour force will have a high reservation wage. Normally,
these preferences are associated with family responsibilities (e.g.,
number of young children at home), or the difficulty of accessing
employment (transportation difficulties, physical disability, etc.), but
will also be related to religious beliefs, attitudes to having young
children raised by non-family adults, levels of education, etc.
The second factor is the non-labour income of the individual. Because
leisure/household work is considered (usually) to be a normal good,
individuals will want to consume more of it as income rises. The
implication is that as we move vertically up the typical incomehousehold time model, indifference curves must get steeper
(reflecting the increased value of household time). In other words,
the reservation wage rises as non-labour income rises.
An additional factor that could be mentioned is the effect of fixed
costs of working (e.g., a fixed charge for child care). The higher the
fixed costs of child care, the higher will be the reservation wage.
(c) How does the reservation wage help explain the decision of
individuals to participate in the labour force?
Individuals compare their offered wage or actual wage (W) to the
reservation wage (W*). If W>W*, they will participate. If W<=W*,
they will not participate in the labour force.
(d) What effect would a pure increase in income ( a lump-sum increase
in income) have on the participation decision? How do you know this?
A pure increase in income (in other words, an increase in non-labour
income) will reduce the probability of participating in the labour force.
As described above, W* rises (indifference curves get steeper) as
income rises, reducing the probability that W>W*.
7. Assume an individual’s utility function is U = U(Y, H), where Y is income
(or consumption) and H is household time.
(a) Given that U = U(Y, H) is the utility function, what is the formula
for the Marginal Rate of Substitution? Explain how to interpret the
MRS (what information does it contain?).
MRS = MUH/MUY = (∂U/∂H)/(∂U/∂Y).
The marginal rate of substitution is the negative of the slope of an
indifference curve at a particular point. It indicates the willingness
of the individual to trade off leisure (household) time for employment
income at that point. The higher the marginal utility of household
time relative to income, the steeper the indifference curve will be.
(b) Why is it called the Marginal Rate of Substitution (what is the
meaning of this name)?
It is called MRS because it measures the rate of willingness to
substitute income for household time while staying at the same level
of utility, so it measures the full amount of the compensation
necessary to encourage an alternative usage of available time. It is
called marginal to reflect the fact that this willingness to substitute
one time use for another changes at each point along the indifference
curve (in other words, the willingness to give up household time
depends upon how much household time the individual still has).
(c) How can we derive the MRS from the utility function?
We can take the total differential of the utility function:
dU = ∂U/∂H  dH + ∂U/∂Y  dY
Since we are considering movement along an indifference curve dU =
0, so we can write ∂U/∂H  dH + ∂U/∂Y  dY = 0
Or, (∂U/∂H)∂U/∂Y = -dY/dH
-dY/dH is the (negative of) the slope of the indifference curve which
gives us our formula for MRS.
(d) Identify at least three factors that are likely to affect the steepness of
an individual’s indifference curves and explain why (briefly).
There are many factors that can affect steepness of indifference
curves. Anything that affects preferences/tastes for household time
(i.e., the value of household time to the individual) will affect the
steepness of indifference curves. The more valuable household time,
the steeper the indifference curves.
Normally, these preferences are associated with family
responsibilities (e.g., number of young children at home), or the
difficulty of accessing employment (transportation difficulties,
physical disability, etc.), but will also be related to religious beliefs,
attitudes to having young children raised by non-family adults, levels
of education, etc. In addition, holding the hours of household time
constant, the level of income will affect the steepness of indifference
curves. Because leisure/household work is considered (usually) to be a
normal good, individuals will want to consume more of it as income
rises. The implication is that as we move vertically up the typical
income-household time model, indifference curves must get steeper
(reflecting the increased value of household time.
8. The graph on the next page shows an income/leisure (or market
work/nonmarket work) diagram, for Claudia. Claudia is shown as deciding
to work for T – H0 hours in the labour market. (If you make a mistake on
the diagram, ask the invigilator for a replacement copy of the diagram).
(a)
You are to imagine that Claudia’s wage decreases, so that she
moves to a new equilibrium with T – H1 hours of work. Draw on the
new potential income constraint and new indifference curves that
are consistent with this new decision for Claudia. Label these lines
clearly
(b)
Also on this same diagram, draw the lines necessary to show how
this gross effect of the lower wage (i.e., the movement from H0 to
H1) can be broken down into an income effect and a substitution
effect. Identify clearly on your graph which is the income effect
and which is the substitution effect, and the size of each of these
effects.
Market
Goods (or
Consumption,
or Income)
$320
C
$160
B
A
H0
H1
T
Hours of nonmarket
time (or leisure)