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CLASSICAL THEORY: THE ECONOMY IN THE LONG RUN National Income (Ch 3)

• What determines economy’s total output/income?

• How are the prices of the factors of production determined?

• How is total income distributed?

• What determines the demand for goods and services?

• How is the equilibrium in the goods market achieved?

Closed-Economy Market-Clearing Model

• Supply side

o factor markets (supply, demand, price)

o determination of output/income

• Demand side

o determinants of consumption, investment, and government purchases

• Equilibrium

• goods market

• loanable funds market

Factors of Production

K is capital: tools, machines, and structures used in production

L is labor: the physical and mental efforts of workers

The production function: Y = F(K,L)

• shows how much output Y the economy can produce from K units of capital and L units of labor

• reflects the economy’s level of technology

• often exhibits constant returns to scale (CRS)

Returns to Scale

• Consider Y1 = F (K1 , L1 )

• Scale all inputs by the same factor z

K2 = zK1 and L2 = zL1

For example, if z = 1.5, then all inputs are increased by 50%

• What happens to output, Y2 = F (K2, L2 )?

o If Y2 = zY1 for any z>0, then constant returns to scale

o If Y2 > zY1 for any z>1, then increasing returns to scale

o If Y2 < zY1 for any z>1, then decreasing returns to scale

Assumptions

• Technology is fixed

• The economy’s supplies of capital and labor are fixed at:

L= ̅

Determining Real GDP

Output is determined by the fixed factor supplies and the fixed state of technology: Y = F(K, L)

Distribution of National Income

• determined by factor prices, the prices per unit that firms pay for the factors of production

• wage is the price of labor

• rental rate is the price of capital

Notation

W is the nominal wage

R is the nominal rental rate

P is the price of output

w = W /P is the real wage (measured in units of output)

r = R /P is the real rental rate (measured in units of output)

Determining Factor Prices

• Factor prices are determined by supply and demand in factor markets

• Supply of each factor is fixed

• What about demand?

Demand for Labor

• Assume markets are competitive: each firm takes W, R, and P as given.

• A firm hires each unit of labor if the cost does not exceed the benefit.

o the cost is the real wage

o the benefit is the marginal product of labor

Marginal Product of Labor (MPL)

• The extra output the firm can produce using an additional unit of labor while holding other inputs fixed:

= ( , + ) − ( , )

• The slope of ( , ) equals MPL

MPL and the Production function

Output, Y ( , ) MPL

MPL

Labor, L

Diminishing Marginal Returns

• As one input is increased (holding other inputs constant), its marginal product falls.

• Intuition: If L increases while holding K fixed, the number of machines per worker falls and worker productivity decreases

MPL and the Production Function

Units of output

Real wage

MPL, Labor demand

Quantity of labor demanded Labor, L

Equilibrium Real Wage

Units of output

Labor Supply

Equilibrium real wage

MPL, Labor demand

Labor, L

Equilibrium in the Labor Market

• Each firm is hiring labor up to the point where the marginal product of labor equals the real wage. The MPL curve is the firm's demand curve for labor

• Supply of labor is fixed

• In equilibrium, the real wage adjusts to equate labor demand with labor supply.

Example: Assume output is given by = 9 / / and the supply of capital is 8 machines.

(a) What is the demand for labor if the real wage is 6? [Hint: Find MPL, use that MPL = w and plug in the supply of capital, i.e., 8, for K and 6 for w. Solve for L]

(b) If the supply of labor is 27 workers, what would be the equilibrium real wage? [Hint: Find MPL, plug in the supply of capital for K and the supply of labor for L, and use that MPL = w]

Determining the Real Rental Rate

• We have seen that MPL = w

• Analogously, the marginal product of capital, MPK, equals the real rental rate:

MPK = r

• Diminishing returns to capital: MPK falls as K rises

• The MPK curve is the firm’s demand curve for renting capital

• Firms maximize profits by choosing K so that MPK = r

Equilibrium Real Rental Rate

Units of output

Supply of capital

Equilibrium real rental rate

MPK, Demand for capital

Capital, K

Equilibrium in the Capital Market

• Each firm is demanding capital up to the point where the marginal product of capital equals the real rental rate. The MPK curve is the firm's demand curve for capital

• Supply of capital is fixed

• The real rental rate adjusts to equate capital demand with capital supply.

Neoclassical Theory of Distribution

• states that each factor of production is paid its marginal product

• provides a good starting point for thinking about income distribution

The Distribution of Income to Labor and Capital

• total labor income = • total capital income =

If the production function exhibits constant returns to scale, then we have that = + Then, since MPL = w and MPK = r, we have: = + In other words,

national income = total labor income + total capital income

The Ratio of Labor Income to Total Income in the U.S., 1960-2010

Source: U.S. Bureau of Economic Analysis

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010

The Cobb-Douglas Production Function = • The Cobb-Douglas production function has constant factor shares:

α = capital’s share of total income 1-α = labor’s share of total income

Indeed we have seen that:

capital income = MPK × K = αY

labor income = MPL × L = (1 – α )Y

Each factor’s marginal product is proportional to its average product:

MPL = (1 − ) = (1 − ) MPK = =

• Theory: wages depend on labor productivity

• U.S. data:

period productivity growth real wage growth

1960–2013 2.1% 1.8%

1960–1973 2.9% 2.7%

1973–1995 1.5% 1.2%

1995-2013 2.3% 2.0%

Income Inequality as Measured by the Gini Coefficient

[If everybody has the same income, Gini coeff = 0. If one person has all the income, Gini coeff = 1.]

Explanations for the Rise in Income Inequality

• Rise in the capital’s share of income?

o Since capital income is more concentrated than labor income, a rise in the capital's share of income would increase income inequality.

• However, income inequality WITHIN labor income has also increased.

o Technological progress has increased the demand for skilled relative to unskilled workers

o Due to a slowdown in the expansion of education, the supply of skilled workers has not kept up

o This has resulted in a rising gap between wages of skilled and unskilled workers.

Demand for goods and services

• Components of aggregate demand:

o C is the consumer demand for goods and services

o I is the demand for investment goods

o G is the government demand for goods and services

o Note: since the economy is closed, there are no net exports (NX = 0)

Consumption, C

• depends on disposable income which is total income less total taxes: Y – T

• the consumption function is C (Y – T ),

i.e., consumption C is a function C of Y – T

• the marginal propensity to consume (MPC) is the change in consumption when disposable income increases by one unit of output (remember that C, Y and T are all in real terms, i.e., measured in units of output).

o MPC is the slope of the consumption function.

The Consumption Function

Consumption, C

( − )

MPC

Disposable Income, −

Investment, I

• The investment function is I = I (r ), where r denotes the real interest rate, the nominal interest rate corrected for inflation

• The real interest rate is

o the cost of borrowing

o the opportunity cost of using one’s own funds to finance investment spending

• I depends negatively on r

The Investment Function

I(r)

Government spending, G

• G is the government spending on goods and services

• G excludes transfer payments (e.g., social security benefits, unemployment insurance benefits)

• We assume government spending and total taxes are exogenous:

G = T =

The Market for Goods and Services

• Aggregate demand Y = ( − ) + ( ) +

• Aggregate supply Y = ( , ) =

• Equilibrium = ( − ) + ( ) +

o The real interest rate adjusts to equate demand with supply

The Loanable Funds Market

• A simple supply–demand model of the financial system

• One asset: “loanable funds”

o demand for funds: investment

o supply of funds: saving

o “price” of funds: real interest rate

Demand for Funds: Investment

• The demand for loanable funds comes from investment: firms borrow to

finance spending on plant and equipment, new office buildings, etc. Consumers borrow to buy new houses.

• The demand for loanable funds depends negatively on the real interest rate, the “price” of loanable funds (cost of borrowing).

Loanable Funds Demand Curve (The Investment Function Again)

I(r)

Supply of Funds: Saving

• The supply of loanable funds comes from saving:

o Households use their savings to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow in order to finance investment spending.

o The government may also contribute to saving if it does not spend all the

tax revenue it receives.

Types of Saving

• private saving = (Y – T) – C

• public saving = T – G

• national saving, S = private saving + public saving

= (Y – T) – C + T – G

= Y – C – G

Changes in Savings

Notation: Δ = change in a variable

Example: If ΔK = 0, then MPL = ΔY /ΔL

Note:

ΔS = ΔY– Δ C – Δ G, where

ΔC = MPC Δ(Y – T), and

ΔY = MPK ΔK + MPL ΔL

Budget Surpluses and Deficits

• If T > G, budget surplus = T – G = public saving.

• If T < G, budget deficit = G – T, and public saving is negative.

• If T = G, balanced budget, public saving = 0.

• Note: The U.S. government finances its deficit by issuing Treasury bonds, i.e., by borrowing.

U.S. Federal Government Surplus/Deficit, Percent of GDP, 1940–2016

-35 -30 -25 -20 -15 -10

-5 0 5

1940 1950 1960 1970 1980 1990 2000 2010

U.S. Federal Government Debt, Percent of GDP, 1940–2016

100

120

140

1940 1950 1960 1970 1980 1990 2000 2010

Loanable Funds Market Equilibrium

̅ = − ( − ) − ̅

Equilibrium real interest rate

I(r)

Equilibrium level of investment S, I

The Special Role of r

• r adjusts to equilibrate the goods market and the loanable funds market simultaneously:

o If loanable funds market is in equilibrium, then:

Y – C – G = I(r)

o If we add (C + G) to both sides, we obtain:

Y = C + I(r) + G

o So, the goods market is in equilibrium

o Thus, an equilibrium in the loanable funds market ⇔ equilibrium in the goods market

How to Master a Model?

1. Which of the variables are endogenous and which are exogenous?

2. For each curve in a diagram, you should know:

(a) the definition

(b) the intuition for slope

3. You should use the model to analyze the effects of each item in 2(c).

Mastering the Loanable Funds Model

Things that shift the saving curve:

• public saving

o fiscal policy: changes in G or T

• private saving

o preferences

o tax laws that affect saving

 401(k)

 IRA

 replacing an income tax with a consumption tax

Case Study: The Reagan deficits

• Reagan policies during early 1980s:

o increases in defense spending: ΔG > 0

o big tax cuts: ΔT < 0

• Both policies reduce national saving: ̅ = − ( − ) − ̅ ↑ ̅ ⇒↓ ̅ ↓ ⇒↑ ( − ) ⇒↓ ̅

̅ ̅

I(r)

I2 I1 S, I

Are the data consistent with these results?

1970s 1980s

T – G –2.2 –3.9

S 19.6 17.4

r 1.1 6.3

I 19.9 19.4

All variables in the table are expressed as % of GDP

Investment Curve Shifters

• some technological innovations

o to take advantage of some innovations, firms must buy new investment goods

• tax laws that affect investment

o investment tax credit

An Increase in Investment Demand

S, I

• We see that an increase in desired investment will raise the equilibrium interest rate, but the equilibrium level of investment would stay the same because the supply of loanable funds is fixed.

• So far, we have assumed that saving is fixed. However, saving may depend on the interest rate

o Can you think of some reasons why (and how) saving might depend on r?

o How would the results of an increase in investment demand be different then?

 Would r rise as much?

 Would the equilibrium level of investment change?

An Increase in Investment Demand When Saving Depends on r

S(r)

I1 I2 S, I

SUMMARY

• Total output is determined by:

o the economy’s quantities of labor and capital

o the level of technology

• Competitive firms hire each factor until its marginal product equals its price

• If the production function has constant returns to scale, then labor income plus capital income equals total income (output).

• A closed economy’s output is used for consumption, investment, and government spending

• The real interest rate adjusts to equate the demand and supply of:

o goods and services

o loanable funds • A decrease in national saving causes the interest rate to rise and investment

to fall

• An increase in investment demand causes the interest rate to rise, but does not affect the equilibrium level of investment if the supply of loanable funds is fixed.