Economics 324: Labor Economics

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Economics 324 Labor Economics

• Any questions?
• Computer lab day on Tue.

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Labor-Leisure Choice for Salaried Workers

• Who are salaried workers?
• Lets assume same preferences
• Budget constraint
• When facing hourly wage?

Y (Income, )

• When facing a salary?

YHmax

• Hours of work decision
• When facing hourly wage?

z
YSmax

x

• When facing a salary?

• This suggests that salaried workers would work
  fewer than typical 40 hours/week of many hourly
  employees

T
l1
l2
0
Leisure
h1
h2
Hours of work
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Labor-Leisure Choice for Salaried Workers

• What does the data say?
• Empirically, just the opposite appears true.
  Salaried folks work gt 40 hours.
• 75 of executives work gt 50 hours
• Why? Possible explanations?
• Difference in Tastes for work
• Difference in Reward structures

Y (Income, )
YHmax
z
YSmax

x

• Difference in Tastes for work
• Psychic rewards of some jobs like advertising,
  doctors, etc. creates purple ICs (87 vs. 60)
• Will only work gt h2 hours if given more

T
0
Leisure
h1
h2
Hours of work
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Labor-Leisure Choice for Salaried Workers

• Difference in Reward structure
• Its not the love for work, but rather the
  expectation of future financial rewards (raise,
  promotion) that induces 60 hour work weeks
• Working gt h1 hours this year wont increase this
  years salary, but it can improve next years
  salary

Y (Income, year 1 dollars)
Yyr 2
(1r)
z
Yyr 1

x

• Salaried person earns Yyr 1, and would work h1
  hours if not for future gains
• Think of Y as total income over life of the
  job. BL rotates up indicating more Y tomorrow
  for more work now!

T
0
Leisure
h1
h2

• Which explanation is correct?
• No definitive answer. Likely some of both.

Hours of work
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Theory of Household Production
Main Issues (1) Much of household time is spent
working (child care, cooking, cleaning, repairs,
etc.) (2) If you live with a partner, assuming
income pooling, work/leisure/household work
decisions often are joint (3) Life cycle effects
work and leisure time are allocated over ones
life span (4) Fertility and retirement
decisions These changes wont affect our basic
results, but will facilitate analysis of certain
issues (child care and labor supply, e.g.)
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Theory of Household Production

• Household time is an input to the production of
  household commodities, which are the things that
  generate utility.
• Food Cooking ? Meals, Books/Toys Supervision
  ? smart kids
• Choice among Market work, Household work,
  Leisure
• In 1980-81 USA Norway
• Avg Hours per week Men Women Men Women
• Market work 44.0 23.9 34.2 17.6
• Household work 13.8 30.5 16.8 33.0
• Total work 57.8 54.4 51.0 50.6
• Leisure time 41.8 41.9 45.5 45.2
• Source Juster Stafford (1991), JEL,
  Allocation of Time
• Men spend much less time on household work, but
  Total Working hours and Leisure time are about
  the same!
• Although the levels differ, the gender
  differences are about the same in each country

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Magnitude of the Substitution Effect

• With 3 choices, we have another type of SE
• The usual SE between Consumption and Leisure, but
  now also a SE between Consumption (market work)
  and Household work
• Large SE between Market and Household work
• Smaller (relatively) SE between Market work and
  Leisure time
• What affects the shape of the IC?
• Flatter for the choice between market work and HH
  work
• Steeper for the choice between market work and
  leisure time
• Since women have traditionally been the primary
  household worker, this larger SE has been more
  important for women than men.
• Over time, women have likely moved to a steeper
  part of this curve, so substitution becomes
  harder.

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Life Cycle Time Allocation

• Consider time horizons When should I work?
• Expected vs. Unexpected wage increases
• Child Support Assurance program
• How would it be expected to affect mothers time
  at home hours worked?

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Labor Demand

• A firms demand for labor is a derived demand.
• Lets start with a Production function, which
  represents the technology a firm uses to produce
  their good/service.
• Q f(L,K)
• Assumptions about Labor
• 10 workers _at_ 8 hrs/day gives same output as 20 _at_
  4 hrs/day
• labor is labor but there are different types
  (skill, experience)
• This is important since many public policy
  issues are targeted at specific types of labor
  (min wage, tax credits, etc.)

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Marginal Product and Average Product

• Marginal Product of Labor (MPL) is the change in
  output resulting from hiring one more
  worker/hour, ceteris paribus
• MPL (?Q/ ?L ) gt 0 ? implies ceteris paribus
• MPK (?Q/ ?K ) gt 0
• Employment Output (Total Product) MPL APL
  MRPL
• 0 0
• 1 11
• 2 27
• 3 47
• 4 66
• 5 83
• 6 98
• 7 111
• 8 122
• 9 131

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Total, Marginal, and Average

• Average Product of Labor (APL) is the output per
  worker.
• APL Q/ L
• If the Average is rising, Marginal curve lies
  above Average curve, Marginal is below the
  Average, if the average is falling.
• Profit Maximization
• We assume the firm wants to maximize ? (profits)
• Profit Total Revenue - Total Cost
• PQ - (wL rK)
• P price of firms output Q amount of
  firms output
• P, w, r assumed constant for now ? perfect
  competition
• Decision variables for the firm are K and L ---
  right combination?

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Short-run Employment Decision
How many workers should the firm hire? A
competitive firm can hire all the workers they
want at going wage. Hire so that MRPL MCL For
a competitive firm, this is MRPL W NB This
does not say the firm should set W equal to
MRPL A competitive firm takes their W as given
or pre-determined. It does say A competitive
firm should hire until MRPL W Additional
conditions for short-run employment decision 1.
MRPL W 2. The MRPL curve must be
downward-sloping at the optimal workers 3. W
must be lt ARPL (PAPL), otherwise the per-worker
contribution to the firm is less than the wage, ?
lt 0 and the firm will EXIT the market. In other
words, we must also be on the downward portion of
the ARPL curve (after the intersection of MRPL
ARPL).
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Labor Demand

• Profit Maximization Derived Demands
• We assume the firm wants to maximize ? (profits)
• Profit Total Revenue - Total Cost
• PQ - (wL rK)
• P price of firms output Q amount of
  firms output
• Big Picture -- what does the profit maximization
  condition look like for various possibilities?
• Input Market Structure
• Output Mkt Structure Competition Monopsony
• Competition P MPL w P MPL MCL
• Monopoly MR MPL w MR MPL MCL

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Long-run Employment Decision

• Capital stock, K, is not fixed.
• Must choose both K and Labor.
• First, define an isoquant as the possible
  combinations of K and L which produce the same
  level of output.
• Properties of Isoquants
• (1) isoquants are downward sloping
• (2) isoquants do not intersect
• (3) higher isoquants are associated with higher
  levels of Q
• (4) isoquants are strictly convex to the
  origin

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Slope of an Isoquant

• Slope measures the rate at which a firm is
  willing to trade labor for capital and maintain
  the same level of output, Q
• Loss in output from X to Y ?L MPL
• Gain in output from X to Y ?K MPK
• Same isoquant ?
• ?L MPL ?K MPK 0
• A little algebra yields the slope
• ?K/ ?L - MPL/ MPK
• In words, the absolute value of the slope of an
  isoquant is the ratio of the marginal products,
  and we call this the Marginal Rate of Technical
  Substitution
• Slope is steep when lots of K, little L, but
  flatter when little K lots of L

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Iso-Cost Lines Optimal Inputs

• Total Cost wL rK
• K (-w/r)L (TC/r)
• Properties of Iso-Cost lines
• (1) it shows the different combinations of K and
  L which are equally costly
• (2) higher lines imply higher costs
• (3) slope of isocost line equals the negative of
  the ratio of the input prices
• A firm minimizes the costs of producing Q units
  of output at point Z where the isocost line is
  tangent to the isoquant ?
• MRTS ratio of the input prices
• MPL/MPK w/r

K
A
TC/r
Z
B
Q 100 widgets
Labor
TC/w
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Shocks to Input Prices

• Decrease in the price of labor (wage)
• A change in the price of an input generates scale
  and substitution effects.
• Substitution Effect (X to Y)
• lower wages ? L relatively less expensive ?
  shift toward L
• Scale Effect (Y to Z)
• lower wages ? lower costs ? expand production
  til MR MC again ? now whats cost-minimizing
  way to produce new Q ? more Labor needed

K
Q200
Q100
TC/r
Z
X
Y
Labor
TC/w
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Long-run Employment Decision

• Capital stock, K, is not fixed.
• Must choose both K and Labor.
• Lagrangian derivation
• For Labor we have derived MRPL MCL
• Same for capital MRPK MCK
• w/MPL r / MPK
• The firm adjusts L and K so that the marginal
  cost of producing an extra unit of output
  (widgets) using Labor is the same as the marginal
  cost of producing that extra widget using
  Capital.
• If theyre not equal, then you can produce the
  same output at lower cost!
• Alternatively, MPL / w MPK / r

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Firms Demand for Inputs

• Initially at point E

Capital (K)

• Shock ? Pcapital (? r)

TC1/r
Q1
Q2lt

• Slope of the dashed isocost line is flatter, but
  SAME Total Cost (TC1)

TC2/r
expansion path ?w,r

• TC2 is new least-cost way to produce Q1 units of
  output
• Movement E to E? is the Input Substitution
  Effect Capital is now more expensive? use less
  K, more L

E
TC1/r
expansion path?w,r
E?
E??
TC1/w
TC2/w
Labor

• This higher TC2 changes MC, AC
• Costs can vary in two ways
• (1) as output varies input prices (movement
  along MC, AC curves)
• (2) as input prices vary (shifting MC,AC)

per unit
MC?
AC?
MC
MR
AC

• E? to E?? is the Scale Effect
• MC higher ? MC gt MR ? lower Q

Q
Q1
Q2
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Firms Demand for Inputs

• Initially at point E

Capital (K)

• Profit maximization yields
• MRPL w
• MRPK r

TC1/r
Q1
Q2lt
TC2/r
expansion path
E
TC1/r

• With 2 inputs,
• ?L/?w ?L/?w?Q ?L/?w (from ?Q)
• ?L/?w?Q lt 0
• ?L/?w (from ?Q)
• (?L/?q) (?Q/?P) (?P/?MC) (?MC/?w)
• (/-) (-) (1)
  (/-)
• Thus, ?L/?w (from ?Q) lt 0

expansion path
E?
E??
TC1/w
TC2/w
Labor

per unit
MC?
AC?
MC
P
AC
Q
Q1
Q2