Economics 324: Labor Economics

1
Economics 324 Labor Economics

• Any questions?
• For next time, read Rizzo Blumenthal rest of
  Chapter 2.
• Presenter for Rizzo Blumenthal?
• Motivation
• Literature review (whats new in their paper)
• Theory/Conceptual framework
• Empirical specification
• Results
• Implications
• Problem presenters for 2.7 and 2.8?

2
Labor Supply Theory and Evidence
In order that people may be happy in their work,
they must not do too much of it. Herman
Melville

• Model of labor-leisure choice
• Goal is to identify factors that determine
  whether a person works and, if so, how much she
  works
• Representative individual has utility function, U
  f (C, L)
• C is composite consumption good, L is leisure
  hours
• Utility function transforms consumption of goods
  leisure into an index measuring the level of
  satisfaction ?
• We assume that more is better
• We assume the person endeavors to maximize
  utility
• Indifference curve is the locus of points (C,L)
  that yield the same level of utility

3
Properties of Indifference Curves

• ICs are downward-sloping
• Higher IC indicates higher utility
• ICs do not intersect
• ICs are convex to the origin
• Marginal utility of consumption the change in
  utility resulting from an additional 1 spent on
  goods, holding leisure constant
• Marginal utility of leisure the
  change in utility resulting from consuming an
  additional hour of leisure, holding consumption
  constant

C
U 750
U 500
Leisure (hours)
U XY U 10X ½Y ½ MUX and MUY?
4
Slope of an Indifference Curve

• Slope measures the rate at which a person is
  willing to give up leisure time for more
  consumption, holding U constant
• Total derivative of U U(C,L) is
• Solve for dC/dL
• In words, the absolute value of the slope of an
  IC is the ratio of the marginal utilities, and we
  call this the Marginal Rate of Substitution
• Slope is steep when lots of C, little L, but
  flatter when little C lots of L

5
Time and Budget Constraints

• Time constraint T L h
• Ignoring household sector for now
• V non-labor income
• w hourly wage rate
• Budget constraint is the boundary of the workers
  opportunity set.
• C ? wh V cant consume more than your
  income
• Assume w constant, but note that marginal wage
  rate (wage received for last hour worked) can
  depend on hours worked (OT premium is higher,
  part-time wage often lower)

C
(wTV)
E
V
Leisure (hours)
T
0
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Time and Budget Constraints

• Combine the budget and time constraints to get
• wT V C wL
• This says that full income (potential income if
  worked T hours) is spent on consumption and
  leisure
• Rewrite so its easier to graph
• C (wT V) - wL
• Point E is the endowment point. This person
  can consume V of goods services even if they
  use all their time for leisure.

7
To Work or Not to Work?

• Reservation wage is the wage at which a worker is
  indifferent between working and not working.
• In other words, it is the minimum increase in
  income that makes a worker indifferent between
  remaining at point E and working that first hour.
• A person will work if the market wage gt
  reservation wage
• Predictions
• a higher reservation wage makes a person less
  likely to enter LF
• the higher your market wage, the more likely you
  are to work (ceteris paribus, for given tastes
  and V)
• This positive correlation between offered wages
  and LFP rates helps explain the dramatic increase
  in female LFP
• What if you commute 30 minutes from Statesville?
  (time costs)
• How do monetary commuting costs affect the
  reservation wage?

8
Commuting Costs and Reservation Wage

• How do monetary commuting costs affect the
  reservation wage?
• Start with V non-labor income
• best utility level is U0
• Monetary commuting costs would be parking, tolls,
  car insurance, maintenance, gas, etc.
• Slope of line aE1 is the reservation wage in the
  presence of commuting costs
• Its greater than WRES without commuting costs
• Conclusion Commuting costs increase the
  reservation wage

C
(wTV)
a
E0
V
U0
V - Costs
E1
L
T
0
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Interior Solution to Labor-Leisure Choice

• Interior solution requires that the market wage gt
  reservation wage
• That is, the person must decide to work positive
  hours
• Optimality conditions
• (1) slope of budget line slope of IC a.k.a.
  Wage MRS
• (2) Must be on the budget line ? C -wL
  (wTV)
• Solving these 2 equations in 2 unknowns (C L),
  we get Demand functions which tell us how much
  (L,C) a worker wants to purchase given w, V, and
  T
• (1) L L(w,V, T) ? leads to labor supply
  function h h(w,V, T)
• (2) C C(w,V, T)

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Optimal Labor-Leisure Choice example

• Suppose Jacks utility function is given by U
  L?C?
• Find the demand function for leisure hours, L
  L (w, V, T)
• Assume the following
• ? ? 1
• 0 in non-labor income/month
• Wage 4/hour
• T 400 hours
• What is Jacks optimal level of consumption,
  leisure hours and work hours?

C
U ?
(wTV)
C ?
E0
V
Leisure
L ?
T
0
Work
h ?
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Optimal Labor-Leisure Choice example

• Suppose Jacks utility function is given by U
  L?C?
• Find the demand function for leisure hours, L
  L (w, V, T)
• Assume the following
• ? ? 1, V 400, w 4, T 400
• What is Jacks optimal level of consumption,
  leisure hours and work hours?
• Add 1 to V V 401, Unew ?

C
U ?
(wTV)
C ?
E0
V
Leisure
L ?
T
0
Work
h ?
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Changing Non-labor Income

• What happens to hours of work when we change V?
• Shock ? V due to bigger dividends, beneficiary
  in a will, bigger unemployment insurance check,
  etc.
• Wage is held constant
• Leisure could be normal or inferior good
• Income effect impact on the D for leisure of a
  change in non-labor income, holding the wage
  constant
• (?L/ ?V) w gt 0 or equivalently, (?h/ ?V) w
  lt 0 , if Leisure is a normal good (which we
  will assume)
• How does ? V affect the reservation wage?
• 2 effects of ? V (1) lowers the probability of
  working (?WRES) (2) decreases
  hours worked, if you work

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Changing the Wage Rate

• What happens to hours of work when we change w ?
• Shock ?w due to a raise at work, perhaps
• Non-labor income (V) is held constant
• Total effect is ambiguous
• Two competing effects
• (1) Income effect higher w ? greater purch power
  ? demand more L
• (2) Substitution effect higher w ? higher
  Pleisure ? demand less L
• Isolating the Substitution effect
• Draw the new budget line. Move this new budget
  line parallel to itself until it is tangent to
  the old IC (at point Y) SE (?L/ ?w) U,V
  lt 0
• Isolating the Income effect
• Draw a new IC tangent to the new budget line at
  some point.

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Individuals Labor Supply Curve

• Backward-bending Labor Supply curve
• (?h/ ?w) V gt 0 ? SE gt IE
• (?h/ ?w) V lt 0 ? SE lt IE
• SE dominates initially, but IE is stronger
  eventually
• Empirically, data shows that female labor supply
  is backward-bending, while men generally have a
  positive slope, with a short vertical range
  (10-20/hour)
• Commuting costs and labor supply curve
• Wont work 1 hour per week
• Enter LF at h hours (say 20)

IE gt SE
w
SE gt IE
Wreservation
h
0
Hours of work
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Which Effect Dominates?

• The size of the income effect depends on
  where you start
• bigger at point A than B
• Z is the extreme, IE 0
• Empirically
• Cross-sectional data reveals that IE and SE are
  small for men (estimates for women are
  complicated by child care and household work)

C
A
B
Z
0
Leisure
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Optimal Labor-Leisure Choice example

• Suppose Jacks utility function is given by U
  L? C?
• Find the demand function for leisure hours, L
  L (w, V, T)
• Assuming ? ¾, ? ¼, V 0, T 400 and w
  4 what are the initial optimal values?
• Now suppose welfare program passed giving 200 of
  income if you dont work at all. As you earn
  income benefits are scaled back 0.20 per dollar
  earned.
• What is the break-even point and what are the
  effects on labor supply?
• Decompose, graphically and numerically, the
  change in demand due to the subsidy and tax into
  the substitution and income effects.
• What if U L¼ C¾ ?