The Theory of Aggregate Supply

Short Run Aggregate Supply Curve

Learning Objectives

• Understand the determinants of output.

• Understand how output is distributed.

• Learn how to derive the short run aggregate supply curve.

• Learn how to shift the short run aggregate supply curve.

• Learn how macroeconomic policy affects the real goods market and the labor market.

Aggregate Supply

• Aggregate supply: The amount of output supplied by firms in the economy at any given price level.

• Aggregate supply curve: The relation between the price level and the total amount of output that firms supply.

Aggregate Supply: Short Run

• In the

long-run

, the aggregate supply curve is vertical.

– Prices are completely flexible: Output is fixed.

• In the

short-run

, the aggregate supply curve may be horizontal or upward sloping.

– Horizontal aggregate supply curves exist when prices are completely inflexible and output is totally flexible.

– Upward sloping aggregate supply curves imply both price and output flexibility.

The Short Run Aggregate Supply Curve: Derivation

• Assumptions: –

The nominal wage is fixed at a particular value.

–

The real wage changes as the price level changes, rising as the price level falls and falling as the price level rises.

–

Worker behavior is ignored for now.

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)

Y

The Production Function

Y = F(L,K) Y = F(L,K) says that the total amount of real output is a function of the amount of labor employed by all firms in the economy.

Capital is assumed to be fixed.

L 0

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 (MP L ).

• Since the production function increases at a decreasing rate, MP L must slope down .

Y

The Marginal Product of Labor

Y=F(L) /\L 2 /\Y 2 /\L 1 /\Y 1 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.

L 0 MP L MP L L 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.

0

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 competitive firm decide how much to pay its factors of production?

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

• Labor Demand  /\Profit = /\Revenue - /\Cost    /\Profit = (P x MP L ) - w = 0 P x MP L = w MP L = w/P

Labor Demand

Demand for Labor

• w = P x MP L – A profit-maximizing competitive firm hires labor up to the point where the

nominal wage

just equals the

value of the marginal product of labor.

• w/P = MP L – A profit-maximizing 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.

w/P 0 P x MP L = L D (P) L A profit maximizing firm employs labor to the point where the marginal product of labor is equal to the real wage.

MP L = L D L 0

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.

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?

The Model Components

• The production function relates output produced to labor employed.

• Labor employed is determined by labor demand.

• 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 Y=F(L) Y w/P 0 0 Production Function L P 0 Labor Market L D L 0 Balancing Line Y Aggregate Supply Y

Sticky Wage Model

• When the nominal wage is set, a rise in the price level lowers the real wage.

• The lower real wage encourages firms to hire more labor.

• The additional labor produces more output.

• Y = Y + a (P - P e ) a > 0 – Output deviates from its natural rate when the price level deviates from the expected price level.

Aggregate Supply Curve with Sticky Wages

• Assumptions: – Workers and firms bargain over and agree on the nominal wage before they know what the price level will be when the agreement takes effect.

– After the nominal wage is set and before workers are hired, firms learn the price level. Workers do not.

– Employment is determined by the labor demanded by firms.

Deriving Aggregate Supply

• Let the price level be P 1 .

– At the price level P 1 , the real wage is w/P 1 .

– At the wage w/P 1 , firms are willing to hire L 1 workers.

• Given L 1 workers, the production function shows that output equals Y 1 .

• The combination Y 1 , P 1 aggregate supply curve.

is one point on the

Y Y 1 Y=F(L) Y 0 w/P L

1

w/P 1 0 L

1

L D L P 0 P 1 L 0 Y

1

Y Y

1

.

Y

Deriving Aggregate Supply

• Let the price level be P 2 .

– At the price level P 2 , the real wage is w/P 2 .

– At the wage w/P 2 , firms are willing to hire L 2 workers.

• Given L 2 workers, the production function shows that output equals Y 2 .

• The combination Y 2 , P 2 aggregate supply curve.

is another point on the

Y Y 1 Y=F(L) Y w/P 0 w/P 1 w/P 2 0 L 1 L 2 L D L P 0 P

2

P

1

L 0 Y 1 Y 1 .

.

AS Y Y

Aggregate Supply Curve

•

The aggregate supply curve is upward sloping because as the real wage decreases firms are willing to employ more workers.

–

As more workers are employed, output increases.

Determination of the Equilibrium Real Wage

Equilibrium Real Wage

• The equilibrium real wage is the real wage rate for the point at which the labor supply and demand curves intersect, so there is no pressure for change.

w/P w/P 0 L S

Labor Supply

L S Individuals choose how many hours to work.

As the real wage rises, leisure becomes more expensive relative to the goods and services available, so people choose to work more.

L S As the real wage falls, leisure becomes less expensive relative to the goods and services available, so people choose to work less.

Equilibrium: The Labor Market

w/P w/P L S At w/P labor demand just equals labor supply.

The labor market clears.

L D 0 L L

Labor Market Changes and Aggregate Supply

• Factors that shift labor demand and labor supply also cause cause fluctuations in the level of output.

– Labor demand shifts with changes in technology/productivity.

– Labor supply shifts with changes in taxes, preferences, and wealth.

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, P 1 , more output is produced.

Y Y 2 Y 1 1 2 Y 2 Y =F(L) 1 Y =F(L) 0 w/P w 2 /P 1 w 1 /P 1 0 L S 2 1 L 1 L D 1 L D 2 L P P 1 0 L 0 AS 1 Y Y 1 Y 2 Y AS 2

Factors that Shift Labor Supply

• Taxes: – Taxes reduce labor supply by lowering the wage received by households.

•

An increase in the tax rate shifts the labor supply curve to the left.

•

The decrease in labor supply increases the nominal wage, causing firms to move up along the labor demand curve and hire fewer workers.

•

Equilibrium employment and aggregate supply decrease.

Y Y 1 Y 2 Y=F(L) Y 0 w/P L S 2 L S 1 L P 0 w/P 1 w/P 1 0 L

2

L

1

L D L P 1 0 Y

2

Y 1 Y AS

2

AS

1

Y

2

Y 1 Y

Factors that Shift Labor Supply

• Taxes: – Decreases in taxes increase the labor supply by raising the wage received by households.

•

A decrease in the tax rate shifts the labor supply curve to the right.

•

The increase in labor supply decreases the nominal wage, causing firms to move down along the labor demand curve and hire more workers.

•

Equilibrium employment and aggregate supply increase.

Factors that Shift Labor Supply

• 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 nominal wage, causing firms to move down along the labor demand curve and hire more workers.

•

Equilibrium employment and aggregate supply increase.

Y Y 2 Y 1 Y=F(L) Y 0 w/P w 1 /P 1 w 2 /P 1 0 L

1

L 2 L D L S 1 L S 2 L P 0 P 1 L 0 Y

1

Y 2 Y AS 1 AS 2 Y

1

Y 2 Y

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

Expansionary Government Policy

A Short-Run Analysis

P P 0 0

Equilibrium

LRAS B Y femp SRAS 0 (W 0 ,LD 0 ) At point B, the model is in long run equilibrium and short-run equilibrium.

AD = SRAS = LRAS The equilibrium price level is P 0 and the full employment equilibrium output is Y femp AD 0 Y

Fiscal or Monetary Expansion

P SRAS 0 (W 0 ,LD 0 ) Higher planned spending by the government or increases in the money supply shift AD 0 to AD 1 .

Y 3 is the level of output that would be reached if the price level did not rise.

P 0 0 B L Y femp Y 1 Y 3 At point L, output increases by the full amount of the simple multiplier.

AD 0 Y AD 1

Fiscal or Monetary Expansion

P P 1 P 0 0 B C SRAS 0 (W 0 ,LD 0 ) Equilibrium occurs at point C, where both the price level and output have risen.

L Y femp Y 1 Y 3 At point C, the real wage has fallen, so firms are willing to hire more workers.

AD 0 Y AD 1

Fiscal or Monetary Expansion

P P 2 P 1 P 0 0 B D SRAS 1 (W 1 ,LD 0 ) SRAS 0 (W 0 ,LD 0 ) As workers realize that the real wage has fallen, they demand a higher nominal wage.

C The increase in the nominal wage causes the SRAS to shift left.

L Y femp Y 1 A new equilibrium is established at D.

AD 0 Y AD 1

Fiscal or Monetary Expansion

SRAS 3 (W 3 ,LD 0 ) SRAS 1 (W 1 ,LD 0 ) P SRAS 0 (W 0 ,LD 0 ) P 3 P 2 P 1 P 0 0 B E D C L Y femp Y 1 At point D, the real wage has fallen again, causing workers to demand a higher nominal wage.

As nominal wages increase, the SRAS shifts left.

AD 0 Y AD 1

Fiscal or Monetary Expansion

SRAS 3 (W 3 ,LD 0 ) SRAS 1 (W 1 ,LD 0 ) P SRAS 0 (W 0 ,LD 0 ) P 3 P 2 P 1 P 0 B E D C L Long-run equilibrium is restored at point E.

At this point, the nominal wage has risen such that W 3 /P 3 = W 0 /P 0 .

0 Y femp Y 1 AD 0 Y AD 1

Long Run Aggregate Supply

• The long-run aggregate supply curve is a vertical line drawn at the natural level of real GDP.

– It shows that equilibrium in the labor market can be achieved at many different price levels but only a single level of output.

– Long-run equilibrium occurs when labor input is the amount voluntarily supplied and demanded at the equilibrium real wage.

r r 4 If interest rates do not rise, Y increases from Y 1 to Y 4 .

r 3 r 2 If the expansion causes interest rates to rise from r 1 to r 2 ,, Y increases from Y 1 to Y 3 .

r 1 0 As the expansion causes the price level to rise from P 1 to P 2 ,, Y increases from Y 1 to Y 2 .

P If workers anticipate the price level change, Y does not change, but the price level rises to P 3 .

P 3 P 2 P 1 0 5 LM 3 LM 2 LM 1 4 3 1 2 Y 1 IS 1 Y 2 Y 3 Y 4 IS 2 Y IS/LM-AD/AS Model Expansionary Fiscal Policy 5 1 4 3 SRAS 2 SRAS 2 AD 1 AD 2 1 Y 1 Y 2 Y 3 Y 4 Y

r If interest rates fall to r Y increases from Y 1 0 to Y , 4 .

If interest rates to fall to r 1 , Y increases from Y 1 to Y 3 .

r 3 r 1 r 0 5 1 2 3 LM 1 LM 3 LM 2 4 As the expansion causes the price level to rise from, P 1 to P 2 , Y increases from Y 1 to Y 2 .

If workers anticipate the price level changes, Y does not change, but the price level rises to P 3 .

P 3 P 2 P 1 P 0 Y Y AD 1 AD 2 2 Y 3 Y 4 1 5 2 3 4 SRAS 2 SRAS 1 IS/LM-AD/AS Model IS 1 Y Expansionary Monetary Policy 0 Y 1 Y 2 Y 3 Y 4 Y

Cycles and the Real Wage

• Given an unchanging labor demand curve, employment rises when the real wage falls.

• This suggests that the real wage should be

countercyclical

; ie., it should fluctuate in the opposite direction from employment.

• However, data indicates that the real wage tends to be slightly

procyclical

; ie., it rises when output rises.