1
Labor Economics I
Assignment 1
Suggested Solutions
1.
Are the following statements True, False or Uncertain? Please justify your answer.
(a)
If your marginal utility of leisure is larger than your marginal utility of consumption, you
should work fewer hours in the market.
Answer:
False. To determine the optimal hours of work, one also requires information on the relative
prices of consumption and leisure (i.e. wages and prices). Recall that the optimal amount of hours
is determined by the tangency condition: MRS(C,L) =
W
/p.
(b)
Jane’s indifference curves between consumption and leisure are concave to the origin. At all
wage levels, she will work zero hours (i.e. spend all her time on leisure).
Answer:
False. Depending on the relative wages (W/p), Jane will either work zero hours or spend all her
time on work. If W/p is high enough, Jane will consume zero hours of leisure. For low levels of
W/p, Jane will spend all her time on leisure and have zero consumption. Note that with concave
indifference curves, there will be no wage levels at which she decides to have positive amounts of
both consumption and leisure (it’s either all leisure and zero consumption or all consumption and
zero leisure).
(c)
If leisure is an inferior good, an increase in wage rates will lead to an increase in hours
worked.
Answer:
True. An increase in wage rates generates an income and a substitution effect. The substitution
effect results in an increase in hours worked (since leisure is now relatively more expensive).
Since leisure is an inferior good, the higher income as a result of the increase in wage rates will
result in
less
leisure, therefore increasing the hours worked. Therefore, if leisure is an inferior
good, both the income and substitution effects move in the same direction. The statement is true.
Hours of Leisure
Goods
T
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2.
Mike’s utility for consumption and leisure is U(C, L) = ln C + ln L.
There are 168 hours in the
week and he earns $10 per hour.
(a)
What is Mike’s optimal amount of consumption and leisure?
Mike’s optimal mix of consumption and leisure is found by setting his MRS = w (assuming p=1)
and solving for hours of leisure given that the budget line is C=10(168L).
w=MRS => 10 = C/L
(Equation 1: Tangency condition)
C=10(168L)
(Equation 2: Budget constraint)
Solving the two equations for L* and C*, we get:
10L = 1680 – 10L
L*=84, C*=10(84)=840
Thus, Mike will choose 84 hours of leisure, 84 hours of work and consume 840 units of
consumptions goods each week.
(b)
If the government starts a welfare policy that pays B to all nonworkers and pays $0 to all
workers, at what value of B will Mike opt out of the labor force and go on welfare?
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 Spring '09
 comptonw
 Utility, Labor Supply

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