Transcript Labor Supply and the Real Wage

Chapter 4
The Theory of
Aggregate Supply
The Theory of Production
• Representative Agent Economy:
all output is produced from labor and capital
and in which everyone has the same
preferences.
Economist often refer to the agent as Robinson
Crusoe.
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The Production Function
• Production is the activity of transforming
resources, such as labor and aw materials,
into finished goods.
• Technology
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The Production Function
Figure 4.1
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The Production Function
• Since the only factor used for producing Y is
Labor, we can express the production function
as
Y  F (L),
• We usually assume further that
F ( L)
 0,
L
 2 F ( L)
 0.
2
L
• Diminishing Returns: the extra output produced
when we input an extra unit of labor is smaller
as we add more and more labor to a fixed stock
of land or capital.
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Competitive Market
• Classical theory assumes that no one
individual can influence price.
• In our example, wage and price level.
• We assume there are so many individuals,
and so one can always buy the cheaper
goods and work for the higher wage if there
are.
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The Nominal and Real Wage
• In this chapter, we do not try to explain why
money is used or how money price are set.
• The nominal wage: The money paid to the
worker for each hour of work.
• The real wage: the amount of final
commodity that a firm must give up to
purchase an hour of labor time.
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Labor Demand and
the Production Function
• Firms choose how much labor to hire, given
the wage and price, trying to maximize profit:


Profit

Y
S

w / P L
D
Commodities
Supplied
Cost of Labor
demanded
F (L ) 
w / P L
D
D
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Labor Demand and
the Production Function

F ( L )
w


 0,
D
D
L
L
p
D
F ( L )
w


.
D
L
p
D
• The slope of the production function should be
equal to the real wage, w/p.
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Labor Demand and the
Production Function
Figure 4.2
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A Mathematical Example
• Production Function
Y  F ( L )  L  (1/ 2)( L ) , L  1
D
D
D 2
D
• Labor Demand Curve
1 L  w / P
D
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Household Decision
• Neoclassical economists assume that
households makes choices to make them
as happy as possible subject to
constraints.
• The happiness is measured by utility.
• Here, the utility function is a function of
demand for commodities and labor supply
(or leisure time):
U  U (Y , L ) or U (Y , Leisure )
D
S
D
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Household Decision
• Households’ choices are subjected to the
budget constraints.
Y
D

Demand for
commodities
S
(w / P)L
Income from
selling labor


Profit from the
family firm
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Household Decision
• Max
U (Y , L )  U w / P L   , L
D
S
S
S

U
dU Y
dU

 S
S
D
S
L
dY L
dL
dU w dU

 S  0,
D
dY P dL
dU S
D
dY
w
dL

 S  .
dU D dL
P
U
dY
• Slope of U(．) = w/P = Slope of Budge Constraint.
D
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A Mathematical Example
• Utility Function
U
 Y
D
 (1/ 2)( L )
S 2
• The Labor Supply
(w / P)  L
S
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Labor Supply and the Real Wage
• Given the real wage, w/P, household choose
the optimal labor supply. What will happen
to labor supply if real wage varies?
• Substitution Effect:
When w/P increases, leisure becomes
relatively more expensive than commodity,
and households tend to work more.
• Wealth Effect:
An increase in w/P makes the households
wealthier and households tend to consume
more and work less.
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Labor Supply and the Real Wage
• If Substitution Effect > Wealth Effect,
w/p ↑ → Labor supply ↑
• If Substitution Effect < Wealth Effect,
w/p ↑ → Labor supply ↓
• The neoclassical theorists assumed the S.E.
is bigger than the W.E. and the labor supply
curve slopes upward.
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Labor Supply and the Real Wage
Figure 4.3
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Factors that Shift Labor Supply
• Preference (Utility Function):
If leisure become more preferable (detestable)
than labor time (or commodity (Y) ), this will
lead to a shift of the labor supply.
Ex. Labor time becomes more detestable.
Necessary condition:
Slope of U(．) = w/P
Since U(Y,L) becomes steeper, labor supply
will decrease given the same w/p.
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Factors that Shift Labor Supply
• Income Taxes:
Taxes reduce the supply of labor by
lowering the wage received by
household.
Ex. Income Taxes= T (w/P) and
household receives (1-T)(w/P).
The budget of household is tightened:
YD
 (1  T )( w / P) LS


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Factors that Shift Labor Supply
• The Wealth Effect:
As households get richer, if all other thing
remain equal, they work fewer hours.
Empirical:
The effect of increasing wealth on labor
supply is offset by the rise in the real wage.
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20
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Time
1900
1920
1940
1960
1987 dollars per year
(in thousands)
Percentage of population
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1980
Number unemployed as a percentage of U.S. population
Real wage in thousands of 1987 dollars per year
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Labor Market Equilibrium and
Aggregate Supply
• Put together the labor demand and supply,
the intersection represents the labor market
e
equilibrium ,  w / P  , Le  .
• Production relative to the labor market
e
equilibrium w / P  , Le  is the aggregate
supply Y e .
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Labor Market Equilibrium
Figure 4.4
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Labor Market Equilibrium and
Aggregate Supply
•
•
•
•
A mathematical Example
D
1

L
 ( w / P ),
Labor Demand:
Labor Supply: ( w / P)  LS ,
Labor Market Equilibrium: LD  LS ,
E
E
D
S
1  L  L , L  1/ 2  ( w / P) ,
S
D
D 2
• Production Fun.: Y  L  (1/ 2)( L ) ,
• Aggregate Supply:
Y  L  (1/ 2)( L )  1/ 2  1/ 2(1/ 2)  3 / 8.
E
E
E 2
2
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Walras Law
• Walras law says that if demand equals supply
for all but one of the commodities and for
labor, then supply also equal demand for the
last commodity.
• In this cases, there are only two things being
traded: labor and commodities. Commodities
are used to pay wages.
If H.H. is happy with the amount of labor it
supplies, it must happy with the amount of
goods it is purchasing. (Max U)
It’s the same on the firm’s side. (Max Π)
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Walras Law
• In our case, firms have zero profit in equilibrium
due to the competitive market.
• If equilibrium is reached in the labor market,
LS  LD  LE , Y S  F ( LE ).
• By the H.H. budget constraint
Y D  ( w / P ) E LS  
 ( w / P ) E LS  F ( LD )  ( w / P ) E LD  F ( LE ).
• Hence, Y D  F ( LE )  Y S ,
Equilibrium is also reached in the commodity
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market.
Disaequilibrium in Labor and
Commodity Market
• For simplicity, we consider the case that S.E.
dominates the W.E., i.e. labor supply curve is upward.
L
E
(
w
/
p
)

(
w
/
p
)
• When
, firms produce Y H  Y E
but
households demand only Y L  Y E . There exists
excess supply in the commodity market and excess
demand in the labor market.
• Hence, firm will raise the real wage and produce less
and households will work more for higher wage and
consume more until the equilibrium is reached.
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Disaequilibriums
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Factors that Shift the Aggregate Supply
LE and
w / P E
• The equilibrium value
depend on the economy’s technology,
household’s preferences and etc which are
the factors that shift the labor demand or
supply curves.
• Factors Shift the Factor Demand:
Technology Changes
• Factors Shift the Factor Supply:
Preferences, Wealth, Income Tax
Y E,
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The Effect of a New Invention on the
Labor Market
The firm’s problem is to maximize:
 
YS
 w / P LD
 F ( LD ) 
w / P LD
And the necessary condition is:
F ( LD ) w
 .
D
L
p
If a new invention leads the production function F(．)
to G (．) , the condition becomes
G( LD ) w
 .
D
L
p
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The Effect of a New Invention on the
Labor Market
Figure 4.5
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The Effect of a Change in Tastes on
Employment and Output
Figure 4.6
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Real Business Cycles (RBC)
• The RBC economists believe that random
shocks to technology account for 70% of postWorld War II business cycle fluctuations. (See
Figure 4.7) and the classical revival is so
called the RBC school.
• In the RBC economy, fluctuations are the
unavoidable responses of optimizing agents to
changing productive opportunities, and there is
no role for policy because the agents react in
the most efficient way possible.
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Real Business Cycles (RBC)
• Many macroeconomists are hostile to the
revival of the classical model:
1. The RBC model provides a partial
explanation of economic fluctuations, but it
is not the whole story.
2. The RBC model pays little or no attention
to unemployment.
• Even though, the idea that demand equals
supply is now widely used by modern
researchers in macroeconomics.
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Homework
Question 2, 4, 6, 8, 9
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END