Heather Krull
Econ 190
Midterm 1 Solution
October 7, 2005
Name: _______________________________
Instructions:
1. Write your name above.
2. No baseball caps are allowed.
3. Write your answers in the space provided. If you need additional space, you may continue answers on the back
side of each page. Be sure to indicate that answers are continued and carefully identify any work that carries over.
4. After you have completed the exam, complete the last page of the exam and sign the Honor Code statement.
Multiple Choice (2 points each)
1. At the end of August, 225,400,000 non-institutionalized Americans were of working age, and the US population is
295,734,000. Of those, 142,449,000 were employed, and 7,391,000 were unemployed. Based on this information,
we can conclude that the August unemployment rate was (b) 4.93%, and the labor force participation rate was
66.48%.
Use the following information to answer questions 2-3. Suppose that for a sample for 10,000 individuals, the relationship
between annual hours supplied (H), the hourly wage rate in dollars (w), and the level of non-labor income in dollars (V)
was estimated by multiple regression to be:
H = 1200 + 0.5w – 0.04V
2. The coefficient of -0.04 associated with the independent variable V means that (b) on average, when a person’s
non-labor income increases by $1, he wishes to work 0.04 hours less, holding all else constant.
3. The coefficient on w suggests that (c) the substitution effect dominates when wages increase and V is held
constant, and the coefficient on V suggests that the income effect dominates when non-labor income increases,
holding constant the worker’s wages.
4. Suppose Sam's wage (w) is $15 an hour, consumption (C) is measured in
dollars, non-labor income (V) is $10 a day, and he has 12 hours in the day
to work or leisure. The slope of the budget constraint is (c) -15.
5. Consider the budget constraint, BC1, depicted to the right. Suppose this
individual is eligible for welfare benefits. The benefits are designed such
that the worker is now constrained by budget constraint, BC2. Hours
worked will (d) decrease for someone who initially maximized utility at
point A because the income and substitution effects work together.
6. The reservation wage (c) is the wage that yields the indifference curve
tangent to the budget constraint at L=T.
C
BC1
A
BC2
L
7. A non-worker who experiences a decrease in her non-labor income will be more likely to (b) enter the labor
market because her reservation wage decreases.
8. The intertemporal substitution hypothesis suggests that (b) labor force participation rates and hours worked
increase when wages are higher as people substitute time over the life cycle to take advantage of changes
in the price of leisure.
9. In the fertility model, an increase in income (a) has an income effect that increases the number of children
desired if children are a normal good.
Page 1 of 4
10. Suppose that Jack’s wage rate is $20 and that his marginal product of time in the household sector is $10 per hour.
Suppose also that Jill’s wage rate is $30 and that her marginal product of time in the household sector is $15 per
hour. We know that (b) it doesn’t matter who specializes in the tasks, because neither Jack nor Jill has a
comparative advantage in either activity.
Short Answer/Applications (30 total points): Show your work.
1. (4 points) The utility function of a worker is represented by U( C, L )  C 2 L 2 . The marginal utility of
1
1
leisure is then given by MUL  21 C 2 L
1
1
2,
1
and the marginal utility of consumption is given by
1
MUC  21 C 2 L 2 . Suppose that this person currently spends $81 on consumption and enjoys 16 hours of
leisure per day How many hours of leisure would a non-worker sacrifice to gain an additional $63 dollars
worth of income?
1
1
At the current consumption and leisure levels, this non-worker enjoys U1 = 81 2 16 2 = 9 * 4 = 36 units of utility.
In order to be equally happy, or to be willing to sacrifice one good for another, the utility level must remain
constant when the individual gains $63 in additional income. The new income level is $81 + $63 = $144, and
U2=36. Thus:
1
1
U 2 = 144 2 L 2 = 36
1
1
12 2 L 2 = 36
1
L 2 =3
∴L = 9
Therefore,is non-worker is willing to sacrifice 16 – 9 = 7 hours of leisure in order to enjoy $144 in total income.
2. (6 points) Suppose the government grants $2500 per child to households that have two or more children.
Do these child allowances influence the fertility behavior of households that had no children prior to the
government program? Graph and explain. You may assume for simplicity that initially V = 0.
Assume the original budget line of a family that wishes to have no children is given by ABC. The budget line will
become ABDE when the child subsidy program is enacted. If a
X
family is willing to have two children, the government provides them
with $5000, if they have three children, they will receive $7500, etc.
A
D
This system creates a new portion of the budget line (DE) which is
flatter than the original since the subsidy increases when the number
5000
of children increase.
7500
The result, there are two changes to consider. The
budget line is similar to a decrease in the cost of
Theoretically, when the price of children decreases,
incentive to substitute children for the commodity
prices have changed.
B
flattening of the
having children.
families have an
good as relative
C
N1
2 N2 3
E
N
Additionally, the outward shift of the budget constraint serves as an increase in the opportunity set. The income
effect suggests that with a high level of income, families will demand higher quantities of all normal goods,
children included. Therefore, both the income and substitution effects suggest that some families will demand
more children. As drawn, the family will now have N2 children and take advantage of the child subsidy program.
Page 2 of 4
3. (20 points + 2 bonus points) Suppose Larry is offered an hourly wage of w, his non-labor income (V) is
$1,920, consumption (C) is measured in dollars, and he has 120 hours to work (H) or leisure (L). Suppose
also that Larry derives utility from consumption and leisure according to the utility function: U = LC 2 .
As such, his marginal utility functions are MU L = C 2 and MU C = 2LC.
a. (2 bonus points) Should Larry accept an $7/hour wage offer? For credit, explain. [Note: This is
a tricky problem, but solvable. I recommend working on this after you’ve done what you can on
the rest of the exam.]
This problem requires that you solve for Larry’s reservation wage, the wage offer that makes him
indifferent between working and not working. Thus, it is the slope of his indifference curve at the
endowment point, V. The slope of his indifference curve is given by:
MUL
C2
C
=
=
MUC 2LC 2L
At the endowment point, i.e. not working, Larry’s consumption level is made up of just his non-labor
income, and L = T. Therefore,
MUL ~ 1920
=w=
= $8
MUC
2(120 )
Larry should not accept a $7 wage offer, because his reservation wage is $8. Any offer in excess of $8 will
be enough to entice him to choose H* > 0.
b. (6 points) Suppose now that Larry is offered a wage of $10 per hour. Provide the equation of his
daily budget constraint and graph it in the space provided below. Carefully label the axes, and
indicate intercepts and the slope of the budget constraint.
Budget constraint: C = V + wH = 1920 + 10(120 – L)
C
P  Q: Income Effect (H↓)
Q  R: Substitution Effect (H↑)
3840
R
3120
slope = -w
= -10
Q
U2
P
U1
slope = -16
1920
120
Page 3 of 4
L
c. (7 points) Now, consider a wage increase from $10 per hour to $16 per hour. Assume
consumption simultaneously increases from $2080 to $2560. State, interpret, and use the utilitymaximization labor supply rule to determine how many hours Larry will work when his wages
change. Also, calculate and interpret Larry’s elasticity of labor supply when the wage rate
changes from $10 to $16 per hour. Is his responsiveness to wage changes elastic or inelastic?
The optimal level of consumption and leisure occurs at the tangency of the budget constraint and
indifference curve. At the tangency, the slopes of the two lines is equal, so
MUL
MU
= w ⇒ L = MUC
MUC
w
The condition can be interpreted as follows: at the tangency, the additional utility enjoyed from spending
an additional dollar on leisure is exactly equal to the additional utility enjoyed from spending an additional
dollar on consumption. In other words, the individual is indifferent between consuming more leisure or
consumption. Using this condition, we can solve for the optimal amount of leisure, and from that, hours
of work:
w = $10, C = $2080, H1* = T – L* = T – 104 = 16
MUL
C
2080
2080
= w⇒ = w⇒
= 10 ⇒
= L ⇒L* = 104
MUC
2L
2L
20
w = $16, C = $2560, H2* = T – L* = T – 80 = 40
MUL
C
2560
2560
= w⇒ = w⇒
= 16 ⇒
= L ⇒L* = 80
MUC
2L
2L
32
H
%H H 1 H w 1
The elasticity of labor supply is given by the formula:  
and is calculated here



%w w H 1 w
w1
ΔH w 1 40 - 16
10
as σ =
=
= 2.5. This suggests that when wages increase by 1%, hours of work
H 1 Δw
16
16 - 10
will increase by 2.5%. Because |σ| > 1, this is considered elastic labor supply, which means Larry is
relatively responsive in terms of hours worked to wage changes. A positive elasticity of labor supply
indicates that Larry’s substitution effect dominates in this example.
d. (7 Points) Finally, on the original graph, illustrate this wage change graphically (with appropriate
labels – slope, intercepts, etc). His hours worked will now increase.
Explain using
income/substitution effects. Decompose the graphical change in hours worked into income and
substitution effects. [Note: Your graph should correspond to your answer(s) in part (c).]
The substitution effect suggests that there exists a positive relationship between the wage rate and hours
worked. Because more can be earned by working an additional hour now that wages have increased, the
opportunity cost of consuming leisure has increased, thus reducing the demand for it.
The income effect states that this wage increase has caused total income/wealth to increase, and since
leisure is a normal good, more will be demanded when people have more money on which to spend it.
Thus, in this case, the demand for leisure will increase, and the income effect predicts fewer hours will be
spend working.
The income and substitution effects do not agree, but since H* did increase (from 16 - 104), the
substitution effect dominates Larry’s decision, as illustrated above.
Page 4 of 4