Macroeconomics & The Global EconomyTerm III

Ace Institute of Management

Chapter 3: National income-where it comes and where it goes?

InstructorSandeep Basnyat

Sandeep_basnyat@yahoo.com9841 892281

What Macroeconomics study?• Some of the foremost important questions that

macroeconomics tries to investigate are:– What determines the total income in an economy?– What determines the level of production in an

economy?– Who gets the income from production?– How the income is distributed among the factors of

production?In general,How the economy works?Simple demonstration: Circular Flow of Income Model

Firms Households

Government

Financial Services

Market for goods and Services

Market for Factors of Production

Wages, Interest, Rent and Profit

National

Income (Y)

Foreign Sector

Imports (M)

Taxes (T)

Savings (S)

Consumption Expenditure

(C)

National Products

Government Purchase (G)

Investment (I)

Loans or

Investment Funds

Exports (X)International Capital Flows

Loans Repay

Transfer Payments

S + T + M = I + G + X Total Leakages = Total Injections

Equilibrium Level of National Equilibrium Level of National IncomeIncome

Aggregate Demand (AD) = Aggregate Supply (AS)

How do the interactions occur in an economy?

Our first theory:Our first theory:the Neo classical theory

(based on classical theory)

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P*P*

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The place where Classical-model mechanics are made easy!

The place where Classical-model mechanics are made easy!

Welcome to...Welcome to...Welcome to...Welcome to...

• Its roots go back to 1776—to Adam Smith’s Wealth of Nations.

• Economy was controlled by the “invisible hand”• Market system, instead of government mechanism• Buyers and sellers pursuing their own self-interest• Emphasis on competition and flexible wages/prices• Prices adjust to balance supply and demand in an

economy• Economy usually maintains Full employment of

resources and general equilibrium in economy

How will we proceed?• Sequence of Questions and Answers:1. What determines the level of output (or National

Income) in an economy?2. What determines the distribution of national income

among factors of production?3. What determines the factor prices?4. What determines the demand for factor of production?

An economy’s output of goods and services (GDP) depends on:

(1) Quantity of inputs : Factors of Production (Capital and Labour)

(2) Ability to turn inputs into output : Production Function

slide 9

Factors of productionK = capital,

tools, machines, and structures used in production

L = labor, the physical and mental efforts of workers

The production function• Usually denoted 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.

• Assumption: exhibits constant returns to scale

(Meaning: If we increase inputs by z, output will also increase by z.)

Returns to scale: a review

Initially Y1 = F (K1 , L1 )

Scale all inputs by the same factor z:

K2 = zK1 and L2 = zL1

(If z = 1.25, then all inputs are increased by 25%)

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

• If constant returns to scale, Y2 = zY1

• If increasing returns to scale, Y2 > zY1

• If decreasing returns to scale, Y2 < zY1

slide 12

Other assumptions of the model

1. Technology is fixed.2. The economy’s supplies of capital and labor

are fixed at

and K K L L

Determining Output: GDP•Factors of Production and Production Function

together determine the Total Output in the Economy.

•Since Technology (production function) and K and L are assumed to be fixed, the output (Y) is also assumed to be fixed in an economy.

Y = Y

, ( )Y F K L

How will we proceed?• Sequence of Questions and Answers:1. What determines the level of output (or National

Income) in an economy?– Factors of Production and the Production function

2. What determines the distribution of national income among factors of production?

3. What determines the demand for factors of production?

The distribution of national income

• Determined by factor prices: the prices per unit that firms pay for the factors of production.

• The wage is the price of L ,the rental rate is the price of K.

Notation

W = nominal wage R = nominal rental rate P = price of output W /P = real wage

(measured in units of output)[Note: P = i (inflation) reflects price level and Real Wage rate in %]

R /P = real rental rate

W = nominal wage R = nominal rental rate P = price of output W /P = real wage

(measured in units of output)[Note: P = i (inflation) reflects price level and Real Wage rate in %]

R /P = real rental rate

How factor prices are determined

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

• Recall: Supply of each factor is fixed.

• What about demand?

FactorFactorpriceprice(Wage or(Wage orrentalrentalrate)rate)

Quantity of factor

Factor demand

Factor supply

Equilibriumfactor price

This vertical supply curve is a result of thesupply being fixed.

Determination of Factor PricesFactor prices are determined by supply and demand in factor markets.

What about demand?

Factor Prices• Because the factor supply curve is vertical and fixed, it is the

demand curve for the factors of productions which determines the distribution of income among them.

• Big Question:

What determines the demand for factors of

production?

We know that the firm will hire labor and rent capital in the quantities that maximize profit.

But what are those maximizing quantities?

Answer: Depends upon Marginal Revenue earned from Marginal Product of Labour and Marginal Product of Capital.

Marginal product of labor (MPL)Def:

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

MPL = F (K, L +1) – F (K, L)

Youtput

The MPL and the production function

Llabor

F K L( , )

1

MPL

1

MPL

1MPL As more labor

is added, MPL

Slope of the production function equals MPL

Diminishing marginal returns

• As a factor input is increased, its marginal product falls (other things equal).

• Intuition:L while holding K fixed

fewer machines per worker

lower productivity

slide 24

MPL and the demand for labor

Each firm hires labor up to the point where

P × MPL (VMPL) = WMPL = W/P

Each firm hires labor up to the point where

P × MPL (VMPL) = WMPL = W/P

Units of output

Units of labor, L

MPL, Labor demand

Real wag

e

Quantity of labor

demanded

The equilibrium real wage

The real wage adjusts to equate labor demand with supply.

The real wage adjusts to equate labor demand with supply.

Units of output

Units of labor, L

MPL, Labor demand

equilibriuequilibrium real m real wagewage

Labor supply

L

Determining the rental rate

We have just seen that MPL = W/P

The same logic shows that MPK = R/P :• diminishing returns to capital: MPK as K • The MPK curve is the firm’s demand curve

for renting capital. • Firms maximize profits by choosing K

such that MPK = R/P .

The equilibrium real rental rate

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

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

Units of output

Units of capital, K

MPK, demand for capital

equilibriuequilibrium m R/PR/P

Supply of capital

K

How income is distributed:

total labor income =

If production function has constant returns to scale, then

total capital income =

WL

PMPL L

RK

PMPK K

Y MPL L MPK K

laborincome

capitalincome

nationalincome

The income that remains after firms have paid the factors of production is the economic profit of the firms’ owners.

Real economic profit is: Economic Profit = Y - (MPL × L) - (MPK × K) or to rearrange: Y = (MPL × L) + (MPK × K) + Economic Profit.

Usually we find (Lumping Y and MPL into Eco. Profit):Accounting Profit = Economic Profit + (MPK x K)

The Cobb-Douglas Production Function

Paul Douglas

Paul Douglas observed that the division of national income between capital and labor has beenroughly constant over time.

In other words, the total income of workers and the total income of capital owners grew at almost exactly thesame rate.

He then wondered what conditions might lead to constant factor shares. Cobb, a mathematician, said that the production function would need to have the property that:

Capital Income = MPK × K = αYLabor Income = MPL × L = (1- α) Y

Capital Income = MPK × K = α YLabor Income = MPL × L = (1- α) Y

Capital Income = MPK × K = α YLabor Income = MPL × L = (1- α) Y

α is a constant and measures capital and labors’ share of income.α is a constant and measures capital and labors’ share of income.

Cobb showed that the function with this property is:

F (K, L) = A Kα L1- α

Cobb showed that the function with this property is:

F (K, L) = A Kα L1- α

A is a parameter that measures the productivity of the available technology. (Total Factor Productivity)

A is a parameter that measures the productivity of the available technology. (Total Factor Productivity)

Cobb

-Dou

glas

Prod

uctio

n Fu

nctio

n

Cobb–Douglas Production Function

Cobb–Douglas Production Function:

Y = F (K, L) = A Kα L1- α

Differentiating, we get the Marginal product of labor:

MPL = (1- α) A Kα L–α

Multiply and Divide right hand side by L. Then,

MPL = (1- α) [A Kα L–α ] L / L = (1- α) [A Kα L1-α ] / L

MPL = (1- α) Y / L

Similarly, The Marginal product of capital is:

MPK = α A Kα-1L1–α or, MPK = α Y/K

Cobb–Douglas Production Function:

Y = F (K, L) = A Kα L1- α

Differentiating, we get the Marginal product of labor:

MPL = (1- α) A Kα L–α

Multiply and Divide right hand side by L. Then,

MPL = (1- α) [A Kα L–α ] L / L = (1- α) [A Kα L1-α ] / L

MPL = (1- α) Y / L

Similarly, The Marginal product of capital is:

MPK = α A Kα-1L1–α or, MPK = α Y/K

Average Labour Productivity

Average Capital Productivity

Cobb–Douglas Production Function

Properties of the Cobb–Douglas Production Function

Equation (i) tells us that marginal product of the labour is proportional to output per worker (average productivity of worker).

Similarly, equation (ii) states that marginal product of the capital is proportional to the output per unit of capital (average productivity of capital).

In conclusion,Marginal productivity of a factor is proportional to its average productivity.

(1) Consider the Cobb–Douglas production function:MPL = (1- α)Y/L ………….(i)MPK= α Y/ K ………………(ii)

Properties of the Cobb–Douglas Production Function

2) The Cobb–Douglas production function has constant returns to scale. That is, if capital and labor are increased by the same proportion, then output increases by the same proportion as well.

Proof:Consider the Cobb-Douglas Production function:F (K, L) = A Kα L1- α

F(zK,zL) = A(zK)α (zL)1- α

F(zK,zL) = Az α Kαz1- αL1- α

F(zK,zL) = Az α z1- α KαL1- α

F(zK,zL) = Az α+1- α KαL1- α

F(zK,zL) = Az KαL1- α = zA KαL1- α = zF(K,L) = zYTherefore, Cobb-Douglas production function has constant returns to scale.

Empirical Evidence of the Cobb–Douglas Production Function

Growth in Labour productivity and Real Wages in US

Period Labour Productivity Real WagesGrowth rate Growth rate

1959-1973 2.9% 2.8%1973-1995 1.4% 1.2%1995-2003 3.0% 3.0%

1995-2003 2.1% 2.0%Source: US Economic Report of the President, 2005.

FYI: Prepare list of some of countries that support Cobb-Douglas production function with their growth rates.

• According to C.D. Prod. Func. : MPL α Y/L• According to Neo Classical Theory, MPL = W /P• So, MPL α W/P

How will we proceed?• Sequence of Questions and Answers:1. What determines the level of output (or National

Income) in an economy?– Factors of Production and the Production function

2. What determines the distribution of national income among factors of production?– Factor Prices

3. What determines the demand for factors of production?

Demand for goods & servicesComponents of aggregate demand:

C = consumer demand for g & s

I = demand for investment goods

G = government demand for g & s

(closed economy: no NX )

Consumption, C• def: disposable income is total income minus

total taxes: Y – T

• Consumption function: C = C (Y – T )Shows that (Y – T ) C

• def: The marginal propensity to consume is the increase in C caused by a one-unit increase in disposable income.

• MPC = (YT ) / C = (Y T ) / C

• Or, C = MPC (Y T )

The consumption functionC

Y – T

C (Y –T )

1

MPCThe slope of the consumption function is the MPC.

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 the cost of borrowing the opportunity cost of using one’s

own funds to finance investment spending.

So, r I

The investment functionr

I

I (r )

Spending on investment goods is a downward-sloping function of the real interest rate

Government spending, G• G includes government spending on goods

and services. • G excludes transfer payments • Assume government spending and total

taxes are exogenous:

and G G T T

Budget surpluses and deficits• When T > G ,

budget surplus = (T – G ) = public saving

• When T < G , budget deficit = (G –T )and public saving is negative.

• When T = G , budget is balanced and public saving = 0.

Equilibrium in The market for goods & services

The real interest rate adjusts to equate demand with supply.The real interest rate adjusts

to equate demand with supply.

Agg. demand: ( ) ( )C Y T I r G

Agg. supply: ( , )Y F K L

Equilibrium: = ( ) ( )Y C Y T I r G

Equilibrium in the Financial Market: The loanable funds market

A simple supply-demand model of the financial system.

One asset: “loanable funds” demand for funds: investment supply of funds: saving

“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 & equipment, new office buildings, etc. Consumers borrow to buy new houses.

• depends negatively on r , the “price” of loanable funds (the cost of borrowing).

Loanable funds demand curver

I

I (r )

The investment curve is also the demand curve for loanable funds.

Supply of funds: SavingThe supply of loanable funds comes from saving:

• Households use their saving to make bank deposits, purchase bonds and other assets. These funds become available to firms to borrow to finance investment spending.

• The government may also contribute to saving if it does not spend all of 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

Loanable funds supply curver

S, I

( )S Y C Y T G

National saving does not depend on r, so the supply curve is vertical.

Loanable funds market equilibriumr

S, I

I (r )

( )S Y C Y T G

Equilibrium real interest rate

Equilibrium level of investment

The special role of r

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

If L.F. market in equilibrium, thenS = Y – C – G = I Add (C +G ) to both sides to getY = C + I + G (goods market eq’m)

Thus,

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

If L.F. market in equilibrium, thenS = Y – C – G = I Add (C +G ) to both sides to getY = C + I + G (goods market eq’m)

Thus,

Eq’m in L.F. market

Eq’m in goods market

An Increase in Government Purchases (G) by G :

•Total demand for goods and services

• General price level and demand for money (Since Total Output ( Supply) is fixed)

• Savings Savings

•Interest rate Interest rate

•Investment level Investment level

Fiscal Policy Operations: Increase/Decrease in “G” or ‘T”

Thus, government purchases are said to crowd out investment

The Crowd-out effectr

S, I

1S

I (r )

r1

I1

r22. …which causes the real

interest rate to rise…

I2

3. …which reduces the level of investment.

1. The increase in the deficit reduces saving… 2S

A Decrease in Taxes: •Disposable (Y-T) income

•Consumption (C)

•Saving decreases (Since Y is fixed and C increased: Note: S =Y-C-G)

•Interest rate (r)

Like an increase in government purchases, tax cuts crowd out investment and raise the interest rate.

Fiscal Policy Operations: Increase/Decrease in “G” or ‘T”

An increase in the demand for investment goods shifts the investmentschedule to the right. At any giveninterest rate, the amount of investmentis greater. The equilibrium movesfrom A to B. Because the amountof saving is fixed, the increase in

investment demand raisesthe interest rate while leaving

the equilibriumamount of investmentunchanged.

But, what if interest rates are even higher?

Investment, Saving, I, S

I1

Realinterestrate, r

Saving, S

S

I2A

B

Two reasons: Technological changes and Tax Policy

When saving is positively related to the interest rate, it results in the upward-sloping S(r) curve.

A rightward shift in the investment schedule I(r) increases the interest rate (r) and the amount of investment (I).

Investment, Saving, I, S

I1

Realinterestrate, r

S(r)

I2AB

Upward sloping savingsUpward sloping savingsThe higher The higher interest rate interest rate

induces people induces people to decrease to decrease

consumption consumption and increase and increase saving, which saving, which in turn allows in turn allows investment to investment to

increase.increase.

Numerical Questions and Solutions for Practice

3) 3) An economy's production function is cobb-douglas with parameter α =0.3. (Macroeconomics, mankiw, Pg. Macroeconomics, mankiw, Pg. 73. Q. 3)73. Q. 3)a. what fractions of income do capital and labor recieve?b. suppose that immigration increases the labor force by 10 percent. what happens to total output (in percent)? c. Suppose that a technological advance raises the value of the parameter A by 10 percent. what happens to total output (in percent)?

Solutions for Practice

3) 3) An economy's production function is cobb-douglas with parameter α =0.3. (Macroeconomics, mankiw, Pg. Macroeconomics, mankiw, Pg. 73. Q. 3)73. Q. 3)

a.What fractions of income do capital and labor receive?

0.3 is a fraction of labor income while 0.7 is a fraction of capital income

Numerical Questions and Solutions for Practice

3) 3) An economy's production function is cobb-douglas with parameter α =0.3. (Macroeconomics, mankiw, Pg. 73. Q. 3)Macroeconomics, mankiw, Pg. 73. Q. 3)

b. Suppose that immigration increases the labor force by 10 percent. what happens to total output (in percent)?

Out put will increase 10%.

Numerical Questions and Solutions for Practice

3) 3) An economy's production function is cobb-douglas with parameter α =0.3. (Macroeconomics, mankiw, Pg. Macroeconomics, mankiw, Pg. 73. Q. 3)73. Q. 3)c. suppose that a technological advance raises the value of the parameter A by 10 percent. what happens to total output (in percent)?

Output increases by 10%

Thank You