#### Transcript Classical Macroeconomics

```The Theory of Aggregate Supply
Classical Model
Learning Objectives
• Understand the determinants of output.
• Understand how output is distributed.
• Learn how output is allocated between labor
and capital.
• Learn how to derive the aggregate supply
curve.
The Classical Model
• Assumptions:
– Workers, consumers, and entrepreneurs are
motivated by rational self-interest.
– People do not experience money illusion.
• People understand the difference between real and
nominal values.
– Perfect competition prevails in the markets for
both goods and services and for resources.
• Prices are determined by markets: Individuals and firms
are price takers.
Production: Definitions
• Production is the activity of transforming
resources into finished goods.
• Technology is a method for transforming
resources into finished goods.
• Factors of production are inputs used in the
production process such as labor and
capital.
Determining Total Output
• An economy’s output of goods and services,
GDP, depends on:
– The quantity and quality of inputs or factors
of production.
– The economy’s production function.
Factors of Production
• Factors of production are the inputs used to
produce goods and services.
• The two most important factors of
production are labor (L) and capital (K).
Production Function
• The production function is a relationship
between the quantities of factors of
production employed by all firms in the
economy and the total production of real
output by those firms, given the technology
available.
• Y = F(K, L)
Production Function
• Y = F(K, L)
– The supply of goods and services depends on
the quantities of labor and capital.
• Y = F(K, L)
– If K and L are fixed in supply, output also is
fixed in supply.
• The bars over the variables express the fact that they
are fixed.
Production Function
Y
Production Function
A
Y1
0B is the total time available
0L1 is time at work
L1B is time at leisure
0Y1 measures output when
Labor works 0L1.
B
0 Time at Work L1 Leisure Time
L
The Production Function
Y
Y = F(L)
Y = F(L) says that the total amount of
real output is a function of the amount
of labor employed by all firms in
the economy.
0
L
The Production Function
• The production function is concave.
– This means that the production function’s slope
rises at a decreasing rate.
• For every increase in labor, output increases by
smaller amounts.
– The production function is drawn this way
because we are assuming the law of
diminishing returns causes each additional unit
of labor to produce less output.
The Marginal Product of Labor
• The slope of the production function is /\Y//\L
or the additional amount of output produced
when one more worker is added.
• Another name for the change in output divided
by the change in labor is the marginal product
of labor (MPL).
• Since the production function increases at a
decreasing rate, MPL must slope down.
The Marginal Product of Labor
Y
/\L2
/\Y2
Y=F(L)
/\Y1
/\L1
0
MPL
0
L
Note that the change in L is the same but
the change in Y is smaller at the higher
level of L, reflecting the impact of the
Law of Diminishing Returns.
Note that the marginal product of labor
is drawn sloping down, reflecting the fact
that as more workers are added the
marginal product of the next worker
decreases.
MPL
L
Distribution of Income
• The distribution of national income is
determined by factor prices.
• Factor prices are the amounts paid to the
factors of production.
• How does a perfectly competitive firm
decide how much to pay its factors of
production?
Firm Decisions
• A profit-maximizing firm has two decisions to
make: How much output to produce and how
many workers to hire.
– A profit-maximizing perfectly competitive firm
produces output to the point at which its price just
equals its marginal cost.
– A profit-maximizing perfectly competitive firm
hires factors to the point where the factor’s value of
the marginal product just equals its marginal
resource cost.
Profits and the Competitive Firm
• A profit maximizing, competitive firm takes
the product price and the factor prices as
given and chooses the amounts of output,
labor and capital that maximize profits.
– How does the firm choose?
Profit Maximizing Math: Firm
• Profit = Commodities Supplied – Cost of Labor
• Profit =
YS
–
(w/P)L
– The equation shows that profit depends on the
amount of commodities supplied, YS, the product
price P, the factor price, w, and the quantity of the
factor L.
More Profit Maximizing Math
• Labor Demand
–
–
–
–
/\Profit = /\Revenue - /\Cost
/\Profit = (P x MPL) - w = 0
P x MPL = w
Labor Demand
MPL = w/P
Demand for Labor
• w = P x MPL
– A profit-maximizing perfectly competitive firm
hires labor up to the point where the nominal wage
just equals the value of the marginal product of
labor.
• w/P = MPL
– A profit-maximizing perfectly competitive firm
hires labor up to the point where the real wage just
equals the marginal product of labor.
W
Alternative Demand for Labor
Schedules
A profit maximizing firm employs labor
to the point where the VMP is equal to
the nominal or money wage.
P x MPL = LD(P)
0
L
w/P
A profit maximizing firm employs labor
to the point where the marginal product
of labor is equal to the real wage.
MPL = LD
0
L
Demand for Labor
• The value of the marginal product of labor
schedule for a perfectly competitive firm is
that firm’s labor demand schedule.
– It shows how many units of labor the firm
demands at any given nominal wage W.
• The marginal product of labor schedule for a
perfectly competitive firm is that firm’s labor
demand schedule.
– It shows how many units of labor the firm
demands at any given real wage W/P.
Nominal Wages and Real Wages?
• The nominal wage is the money wage paid.
• The real wage in the nominal wage adjusted by
the price level as measured by the average
price of goods and services.
– The real wage reflects the true purchasing power of
the worker’s income.
Demand for Labor: Math
• Production Possibilities Function
YS = LD – (½)(LD)2
L <= 1
• Max p = LD – (½)(LD)2 – (w/P)LD
Total Product
Total Cost
• dp/dLD = 1 – LD – w/P = 0
•
1 – LD
=
w/P
Marginal Product
Marginal Cost
The Supply of Labor
• When determining how much labor to
supply, individuals must make a trade off
between more consumption of goods and
services and more labor supplied in the
market.
– More goods and services means more work
and less leisure.
– Fewer goods and services means less work
and more leisure.
Deriving the Labor Supply
• Demand for Stuff <= Labor Income + Profits
YD
<= (w/P)LS
+ p
• Deriving Labor Supply:
• Utility = Utility of Stuff – Disutility of Working
Max U = (w/P)LS + p
–
(½ LS)2
Stuff
Disutility of Working
• Take the first derivative, set to zero, solve for LS
Deriving Labor Supply
• dU/dLS = w/P – LS
• w/P – LS = 0
• (w/P) = LS
• Labor supply equals the real wage.
– As w/P rises, LS rises
– As w/P falls, LS falls.
Labor Supply
w/P
Individuals choose how many hours
to work.
LS
As the real wage rises, leisure becomes
more expensive relative to the goods
and services available, so people choose
to work more.
w/P
0
LS
LS
As the real wage falls, leisure becomes
less expensive relative to the goods and
services available, so people choose to
work less.
Factors that Shift Labor Supply
• Taxes:
– Taxes reduce labor supply by lowering the
• An increase in the tax rate shifts the labor supply
curve to the left.
• A decrease in the tax rate shifts the labor supply
curve to the right.
Factors that Shift Labor Supply
• Wealth:
– An increase in wealth reduces labor supply by
decreasing the need to work.
• An increase in the wealth shifts the labor supply
curve to the left.
• A decrease in the wealth shifts the labor supply
curve to the right.
– However, as the USA has become wealthier,
labor supply has not decreased. Why?
Labor Supply and Wealth
• As people become wealthier, they have an
incentive to consume more leisure.
– This is known as the wealth effect.
• But, as the real wage rises, people have an
incentive to work more.
– This is known as the substitution effect.
• The employment rate has been roughly constant
because the substitution effect and wealth effects
balance out over time
Equilibrium: The Labor Market
LS
w/P
At w/P labor demand just
equals labor supply.
w/P
The labor market clears.
LD
0
L
L
Putting It All Together
Deriving Aggregate Supply
What Does All This Mean for
Aggregate Supply?
• Aggregate supply is the total quantity of
goods and services produced by an
economy.
• The aggregate supply curve is a schedule
relating the total supply of all goods and
services in the economy to the general price
level.
• What does the aggregate supply curve look
like in the classical model?
Y
Y=F(L)
Y
Production Function
0
w/P
Balancing Line
L 0
Y
P
LS
Labor Market
Aggregate Supply
LD
0
L 0
Y
The Model Components
• The production function relates output
produced to labor employed.
• Labor employed is determined by labor
demand and labor supplied.
• The balancing line transfers output from the
vertical axis to the horizontal.
• Aggregate supply will show the relationship
between output and the price level.
Y=F(L)
Y
Y
Y1
0
w/P
L1
L 0
P
Y1
P1
.
Y
LS
w/P1
LD
0
L1
L 0
Y1
Y
Deriving Aggregate Supply
• Let the price level be P1.
– At the price level P1, the real wage is w/P1.
– At the wage w/P1, firms are willing to hire L1
workers.
• Given L1 workers, the production function
shows that output equals Y1.
• The combination Y1, P1 is one point on the
aggregate supply curve.
Y=F(L)
Y
Y
Y1
L 0
P
0
w/P
Y1
AS
LS
P2
P1
w/P1
Y
.
.
w/P2
LD
0
LS
LD
L 0
Y1
Y
Deriving Aggregate Supply
• Let the price level rise to P2.
– At the higher price level, the real wage falls
to w/P2.
– Employers want to hire more workers.
• They move down the labor demand curve.
– The workers realize that the real wage has
fallen and wish to supply less labor.
– They move down the labor supply curve.
Deriving Aggregate Supply
– As a result, the labor market moves into a
disequilibrium position where labor demand
exceeds labor supply.
– Equilibrium is restored when the
competition for labor causes the nominal
wage, w, to rise.
• w rises such that w/P2 = w/P1.
Classical Aggregate Supply
• At the new equilibrium, the price level is P2 and
output is still Y1. This combination is another
point on the aggregate supply curve.
– The aggregate supply curve is vertical at the full
employment level of output because the level of
employment of labor does not change as the price
level changes.
Aggregate Supply: Math
•
•
•
•
•
1 - LD = (w/P) Labor Demand
LS
= (w/P) Labor Supply
At equilibrium, LD = LS = LE, rewrite
1 – LE = LE
Solve for LE:
1 = LE + LE
1 = 2LE
½ = LE
Aggregate Supply: Math
• Solve for the real wage:
1 – LE = w/P
1 – (½) = w/P
½ = w/P
• Solve for aggregate supply at equilibrium:
YE = LE – (½)(LE)2 = Production Function
YE = ½ – (½)(½)2 = 3/8
• What will happen to output in this model if
labor productivity increases or decreases?
• What will happen to output if labor
resources increase or decrease?
• According to the classical theory of
employment and GDP, the explanation of
business fluctuations lies with the factors
that determine equilibrium in the labor
market. They are:
– Preferences
– Endowments
– Technology
Preferences, Endowments,
Technology
• Factors that cause fluctuations in the level
of output are those that shift labor demand
and labor supply.
– Labor demand shifts with changes in
technology and resource endowment
– Labor supply shifts with changes in
preferences.
Y
Y2
Y2=F(L)
2
Y
Y1=F(L)
Y1
1
L 0
0
w/P
P
Y
AS1
AS2
Y1
Y2
LS
2
w2/P1
w1/P1
0
1
LD1
L1
LD2
L
0
Y
Change in Technology
• New technology increases productivity.
– The production function shifts up.
– The labor demand curve shifts to the right.
• The increase in demand for labor increases
the real wage, causing an increase in labor
supply along the labor supply curve.
• Aggregate supply increases.
– At the price level, P1, more output is produced.
Increase in Aggregate Supply
• Aggregate supply increases for two reasons:
– The higher real wage increased the number of
laborers in the labor supply.
– The new technology increased the productivity
of each worker.
Resource Endowment
• An increase in resource endowment has the
same impact as an improvement in
technology, if it caused an increase in labor
productivity.
Y=F(L)
Y
Y
Y2
Y1
L 0
P
0
w/P
Y1
Y
LS1
LS2
w1/P1
w2/P1
LD
0
L1 L2
L 0
Y
Y1 Y2
Preferences
• A change in worker preferences with respect to
labor supply shifts the labor supply curve.
– If workers decide to work more, the labor supply curve
shifts to the right.
– The increase in labor supply decreases the real wage,
causing firms to move down along the labor demand
curve and hire more workers.
– Equilibrium employment and aggregate supply
increases
Y=F(L)
Y
Y
Y1
L
0
w/P
0
P
Y
Y1
LS
w/P1
P1