 # The Theory of Aggregate Supply

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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)

The Production Function
Y 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

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 Y=F(L) /\Y2 /\L2 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. /\Y1 /\L1 L MPL 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 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 MPL) - w = 0 P x MPL = w MPL = w/P Labor Demand

Demand for Labor w = P x MPL w/P = MPL
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 = MPL A profit-maximizing competitive firm hires labor up to the point where the real wage just equals the marginal product of labor.

Alternative Demand for Labor Schedules
W 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) 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 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.

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 Y=F(L) Production Function Balancing Line L Y w/P P Labor Market Aggregate Supply LD L 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 - Pe) 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 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 Y Y=F(L) Y1 L Y Y1 L1 w/P P . P1 w/P1 LD L Y L1 Y1

Deriving Aggregate Supply
Let the price level be P2. At the price level P2, the real wage is w/P2. At the wage w/P2, firms are willing to hire L2 workers. Given L2 workers, the production function shows that output equals Y2. The combination Y2, P2 is another point on the aggregate supply curve.

Y Y=F(L) Y Y1 L Y Y1 w/P P AS . P2 . P1 w/P1 w/P2 LD L Y L1 L2 Y1

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.

Labor Supply 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. As the real wage falls, leisure becomes less expensive relative to the goods and services available, so people choose to work less. w/P LS w/P LS LS

Equilibrium: The Labor Market
w/P LS At w/P labor demand just equals labor supply. The labor market clears. w/P LD 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, P1, more output is produced.

Y Y Y2=F(L) Y2 2 Y1=F(L) 1 Y1 L Y w/P P AS1 LS AS2 2 w2/P1 P1 w1/P1 1 LD2 LD1 L1 L Y1 Y2 Y

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=F(L) Y Y Y1 Y2 L Y Y2 Y1 w/P P AS2 LS2 AS1 LS1 w/P1 w/P1 P1 LD L2 L1 L Y2 Y1 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 Y=F(L) Y2 Y1 L Y Y1 Y2 w/P P LS1 AS1 AS2 LS2 P1 w1/P1 w2/P1 LD Y L L1 L2 Y1 Y2

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

Equilibrium At point B, the model is in long-
LRAS P SRAS0(W0,LD0) At point B, the model is in long- run equilibrium and short-run equilibrium. AD = SRAS = LRAS The equilibrium price level is P0 and the full employment equilibrium output is Yfemp P0 B AD0 Yfemp Y

Fiscal or Monetary Expansion
Higher planned spending by the government or increases in the money supply shift AD0 to AD1. Y3 is the level of output that would be reached if the price level did not rise. At point L, output increases by the full amount of the simple multiplier. P SRAS0(W0,LD0) P0 B L AD1 AD0 Yfemp Y1 Y3 Y

Fiscal or Monetary Expansion
SRAS0(W0,LD0) Equilibrium occurs at point C, where both the price level and output have risen. At point C, the real wage has fallen, so firms are willing to hire more workers. C P1 P0 L B AD1 AD0 Yfemp Y1 Y3 Y

Fiscal or Monetary Expansion
SRAS1(W1,LD0) P SRAS0(W0,LD0) As workers realize that the real wage has fallen, they demand a higher nominal wage. The increase in the nominal wage causes the SRAS to shift left. A new equilibrium is established at D. P2 D P1 P0 C L B AD1 AD0 Yfemp Y1 Y

Fiscal or Monetary Expansion
SRAS3(W3,LD0) SRAS1(W1,LD0) P SRAS0(W0,LD0) 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. P3 E P2 D P1 P0 C L B AD1 AD0 Yfemp Y1 Y

Fiscal or Monetary Expansion
SRAS3(W3,LD0) SRAS1(W1,LD0) P SRAS0(W0,LD0) Long-run equilibrium is restored at point E. At this point, the nominal wage has risen such that W3/P3 = W0/P0. P3 E P2 D P1 P0 C L B AD1 AD0 Yfemp Y1 Y

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.

IS/LM-AD/AS Model Expansionary Fiscal Policy LM3 r LM2 LM1 5 r4
If interest rates do not rise, Y increases from Y1 to Y4. If the expansion causes interest rates to rise from r1 to r2,, Y increases from Y1 to Y3. As the expansion causes the price level to rise from P1 to P2,, Y increases from Y1 to Y2. If workers anticipate the price level change, Y does not change, but the price level rises to P3. 4 r3 r2 3 IS/LM-AD/AS Model Expansionary Fiscal Policy 2 r1 1 IS2 IS1 Y1 Y2 Y3 Y4 Y P SRAS2 SRAS1 5 P3 P2 4 AD2 1 3 2 P1 AD1 Y1 Y2 Y3 Y Y

IS/LM-AD/AS Model Expansionary Monetary Policy r LM1 LM3 LM2 5 1 r3 2
If interest rates fall to r0, Y increases from Y1 to Y4. If interest rates to fall to r1, Y increases from Y1 to Y3. As the expansion causes the price level to rise from, P1 to P2, Y increases from Y1 to Y2. If workers anticipate the price level changes, Y does not change, but the price level rises to P3. 3 r1 r0 4 IS/LM-AD/AS Model Expansionary Monetary Policy IS1 Y Y2 Y3 Y4 Y P AD1 AD2 SRAS2 SRAS1 P3 5 2 P2 3 4 P1 1 Y1 Y2 Y3 Y 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.