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Problem Set 1 Solution Key
ECN 131
Public Finance
Prof. Farshid Mojaver
1. There are only two goods in the world: apples (A) and bananas (B). Your old budget constraint was
5A+10B=240. Your new budget constraint is 5A+12B=240.
a) What has changed? Be as specific as possible.
b) Sketch the old budget constraint, with A on the horizontal axis and B on the vertical. Label point
X as the consumer’s consumption choice. (Make sure it is an interior point.
c) Sketch the new budget constraint. Assuming A and B are substitutes, label point Z as the
consumer’s new choice.
d) Using a different color pen or pencil, sketch a third budget constraint to illustrate the substitution
effect separate from the income effect. Label one point on the graph Y such that the movement
from X to Y represents a substitution effect, and Y to Z represents the income effect.
a) The price of B has increased from $10 to $12.
b) See BC1 and point X on graph.
c) See BC3 and point Z on graph. Z must be below X, representing less consumption of good B
than before.
d) See BC2 (red dotted line) and point Y. This represents the new price ratio (hence its slope is
the same as BC3) but “gives back” enough income for the consumer to stay at his/her original
utility level. In this way, point Y on BC2 represents the consumer’s response to the change in
relative prices only (substitution effect), without the income effect. The income effect is
represented by the move from Y to Z, because this is a parallel shift of the budget constraint.
Note that as the consumer moves from X to Y (substitution effect), the demand for B decreases
but A increases. The income effect from Y to Z has demand for both goods decreasing. So
overall, demand for B must decrease, but demand for A could increase or decrease, depending on
which effect is stronger.
2. Assume Fifi has 2000 hours to allocate each year between leisure and work. Her wage is $8/hour.
a) Sketch Fifi’s budget constraint.
b) Suppose an income support program provides an income guarantee of $4000 and a benefit
reduction rate of 50%. Sketch Fifi’s budget constraint under this program. Label this budget
constraint BC2 and give coordinates for any endpoints or kink points.
c) Suppose a revised program provides $3000 and a benefit reduction rate of 25%. Using a different
color pen or pencil, sketch Fifi’s budget constraint under this program. Label this budget
constraint BC3 and give coordinates for any endpoints or kink points.
d) Does the reduced income guarantee in part (c) necessarily imply that Fifi will increase her labor
supply compared to her choice in part (b)? Use your graph to support your answer.
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a) See BC1 on the graph.
b) See BC2 (the heavy black line) on the graph.
c) See BC3 (red line) on the graph.
d) The change from BC2 to BC3 will NOT necessarily imply that someone will increase labor
supply. Consider someone who was choosing point d on BC2.
The new budget constraint BC3 represents a higher income level (BC3 is above BC2 around
point d), which tends to increase demand for leisure and market goods.
But BC3 is steeper than BC2, indicating a higher price of leisure (relative to market goods) and
thus the substitution effect tends to make Fifi choose less leisure – and more labor. So if the
substitution effect dominates the income effect, Fifi chooses more labor supply rather than less.
3. Using examples and graphs
a) Show that a cut in TANF benefit can increase labor supply.
b) Show that a cut in TANF benefit does not necessarily increase labor supply
c) Show that a cut in benefit reduction rate can decrease labor supply (carefully illustrate substitution
and income effects).
Ans.a)
Wage
Income
Leisure
b)
3
Wage
Income
Leisure
c)
Wage
Income
SE
IE
TE
Leisure
4
4. Consider the case of a single mother with two children, who is trying to decide how many hours to work
each month. Suppose, due to constraints such as child care, she is limited to working a maximum of 40
hours per week, for a total labor supply endowment of 160 hours per month. This mother has no other
source of labor income, and if she works, would receive a wage of $6 for each hour worked.
Assume that the mother’s utility function is defined over money (C) and leisure (L), and takes the
following form:
U = 3 log C + 5 log L
a) Solve for the mother’s optimal choice of labor supply. How much money does the mother have for
consumption?
a) L = leisure
C = 6(wage) × hours of work = 6(160–L) = 960–6L
U = 3 log C + 5 log L = 3 log(960–6L) + 5 logL
U/L = 0  (–18)/(960–6L) + 5/L = 0  –18L + 4800 – 30L = 0
 4800 = 48L
 100 = L
So leisure = 100
hours of work = 60
C = 6 × 60 = 360