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 L Y 0 L1L1 Y1Y1 B Time at Work Leisure Time A 0B is the total time available 0L 1 is time at work L 1 B is time at leisure 0Y 1 measures output when Labor works 0L 1.

The Production Function Y = F(L) L Y 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

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.

The Marginal Product of Labor L L Y MP L Y=F(L) MP L /\Y 1 /\L 1 /\L 2 /\Y 2 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. 0 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 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 = Y S – (w/P)L –The equation shows that profit depends on the amount of commodities supplied, Y S, 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 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 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 = MP L –A profit-maximizing perfectly 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/P W L L MP L = L D P x MP L = L D (P) A profit maximizing firm employs labor to the point where the VMP is equal to the nominal or money wage. A profit maximizing firm employs labor to the point where the marginal product of labor is equal to the real wage. 0 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.

Demand for Labor: Math Production Possibilities Function Y S = L D – ( ½ )(L D ) 2 L <= 1 Max  = L D – ( ½ )(L D ) 2 – (w/P)L D Total Product Total Cost d  /dL D = 1 – L D – w/P = 0 1 – L D = 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 Y D <= (w/P)L S +  Deriving Labor Supply: Utility = Utility of Stuff – Disutility of Working Max U = (w/P)L S +  – (½ L S ) 2 Stuff Disutility of Working Take the first derivative, set to zero, solve for L S

Deriving Labor Supply dU/dL S = w/P – L S w/P – L S = 0 (w/P) = L S Labor supply equals the real wage. –As w/P rises, L S rises –As w/P falls, L S falls.

Labor Supply LSLS w/P 0 LSLS LSLS 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.

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. 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 w/P L LSLS At w/P labor demand just equals labor supply. The labor market clears. L 0 w/P LDLD

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 L Y Y Y P L w/P Y=F(L) LSLS Production Function Balancing Line Labor Market Aggregate Supply LDLD

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 Y Y Y L P w/P L1L1 Y1Y1 LSLS Y=F(L) P1P1 Y1Y1 L1L1 Y1Y1 L w/P 1. LDLD

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 is one point on the aggregate supply curve.

Y Y Y Y L P w/P Y1Y1 LSLS w/P 1 Y=F(L) P1P1 Y1Y1 LSLS Y1Y1 L P2P w/P 2 LDLD AS.. LDLD

Deriving Aggregate Supply Let the price level rise to P 2. –At the higher price level, the real wage falls to w/P 2. –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/P 2 = w/P 1.

Classical Aggregate Supply At the new equilibrium, the price level is P 2 and output is still Y 1. 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 - L D = (w/P)Labor Demand L S = (w/P)Labor Supply At equilibrium, L D = L S = L E, rewrite 1 – L E = L E Solve for L E : 1 = L E + L E 1 = 2L E ½ = L E

Aggregate Supply: Math Solve for the real wage: 1 – L E = w/P 1 – (½) = w/P ½ = w/P Solve for aggregate supply at equilibrium: Y E = L E – (½)(L E ) 2 = Production Function Y E = ½ – (½)(½) 2 = 3/8

Models Answer Questions 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?

Business Fluctuations 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 L Y Y Y P w/P Y 1 =F(L) LSLS L1L1 Y1Y1 Y1Y1 L w 1 /P Y 2 =F(L) Y2Y2 Y2Y2 AS 1 AS w 2 /P 1 LD1LD1 LD2LD2

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.

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 Y Y Y L P w/P Y1Y1 LS1LS1 Y=F(L) Y1Y1 L 1 L 2 Y 1 Y 2 L w 1 /P 1 LS2LS2 Y2Y2 w 2 /P 1 LDLD

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 L Y Y Y P L w/P Y=F(L) LSLS P1P1 L1L1 Y1Y1 Y1Y1 Y1Y1 AD 1 w/P LDLD