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Macroeconomics & The Global Economy
Term III
Ace Institute of Management
Chapter 3: National income-where it comes
and where it goes?
Instructor
Sandeep Basnyat
[email protected]
9841 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
Equilibrium Level of National Income
Foreign Sector
International Capital Flows
Exports (X)
Market for goods
and Services
National
Products
Government Purchase (G)
Consumption
Expenditure
(C)
Imports (M)
Transfer Payments
Investment (I)
Government
Firms
Loans
Wages, Interest, Rent
and Profit
S+T+M=I+G+X
Total
Leakages = Total Injections
Households
Repay
Loans or
Investment Funds
Taxes (T)
Savings (S)
Financial
Services
National
Income (Y)
Market for Factors
of Production
Aggregate Demand (AD) = Aggregate Supply (AS)
How do the interactions occur in an
economy?
Our first theory:
the Neo classical theory
(based on classical theory)
Welcome to...
The place where
Classical-model
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are made easy!
P
S
P*
D
Q* Q
• 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
Factors of production
K = capital,
tools, machines, and structures used
in production
L =
slide 9
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
Other assumptions of the model
1. Technology is fixed.
2. The economy’s supplies of capital and labor
are fixed at
K K
slide 12
and
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
R
P
W /P
R /P
= nominal wage
= nominal rental rate
= price of output
= real wage
(measured in units of output)
[Note: P = i (inflation) reflects price
level and Real Wage rate in %]
= 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?
Determination of Factor Prices
Factor prices are determined by supply and demand in factor
markets.
Factor
price
(Wage or
rental
rate)
Factor supply
This vertical supply curve
is a result of the
supply being fixed.
What about demand?
Equilibrium
factor price
Factor demand
Quantity of factor
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)
The MPL and the production function
Y
output
F (K , L )
1
MPL
MPL
As more labor is
added, MPL 
1
MPL
1
Slope of the production
function equals MPL
L
labor
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
MPL and the demand for labor
Units of
output
Each firm hires labor
up to the point where
P × MPL (VMPL) = W
Real
wage
MPL = W/P
MPL, Labor
demand
Units of labor, L
Quantity of labor
demanded
slide 24
The equilibrium real wage
Units of
output
Labor
supply
equilibrium
real wage
MPL, Labor
demand
L
The real wage adjusts to equate
labor demand with supply.
Units of labor, 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
Units of
output
Supply of
capital
equilibrium
The real rental rate
adjusts to equate
demand for capital with
supply.
MPK, demand
for capital
R/P
K
Units of capital, K
How income is distributed:
total labor income =
W
L
P
R
K
total capital income =
P
 MPL  L
 MPK  K
If production function has constant returns to
scale, then
Y  MPL  L  MPK  K
national
income
labor
income
capital
income
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 observed that the division of
national income between capital and labor has been
roughly constant over time.
Paul Douglas
In other words, the total income of workers and the total
income of capital owners grew at almost exactly the
same 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 = αY
Labor Income = MPL × L = (1- α) Y
Cobb–Douglas Production Function
Capital Income = MPK × K = α Y
Labor Income = MPL × L = (1- α) Y
Production Function
Cobb-Douglas
α is a constant and measures capital and
labors’ share of income.
Cobb showed that the function with this property is:
α 1- α
F (K, L) = A K L
A is a parameter that measures the productivity
of the available technology. (Total Factor Productivity)
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,
α –α
α 1-α
MPL = (1- α) [A K L ] L / L = (1- α) [A K L
]/L
MPL = (1- α) Y / L
Average Labour
Productivity
Similarly, The Marginal product of capital is:
α-1 1–α
MPK = α A K L
or, MPK = α Y/K
Average Capital
Productivity
Properties of the Cobb–Douglas Production Function
(1) Consider the Cobb–Douglas production function:
MPL = (1- α)Y/L ………….(i)
MPK= α Y/ K ………………(ii)
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.
Properties of the Cobb–Douglas Production Functio
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) = zY
Therefore, Cobb-Douglas production function has constant
returns to scale.
Empirical Evidence of the Cobb–Douglas Production Fun
• According to C.D. Prod. Func. :
MPL α Y/L
• According to Neo Classical Theory, MPL = W /P
• So, MPL α W/P
Growth in Labour productivity and Real Wages in US
Period
Labour Productivity
Growth rate
Real Wages
Growth rate
1959-1973
1973-1995
1995-2003
2.9%
1.4%
3.0%
2.8%
1.2%
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.
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 & services
Components 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 = (YT ) / C = (Y  T ) / C
• Or, C
=
MPC  (Y  T )
The consumption function
C
C ( Y –T )
MPC
1
The slope of the
consumption function
is the MPC.
Y–T
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 function
r
Spending on
investment goods
is a downwardsloping function of
the real interest rate
I (r )
I
Government spending, G
• G includes government spending on goods
and services.
• G excludes transfer payments
• Assume government spending and total
taxes are exogenous:
G G
and
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
 Agg. demand:
 Agg. supply:
 Equilibrium:
C (Y  T )  I (r )  G
Y  F (K , L )
Y = C (Y  T )  I (r )  G
The real interest rate adjusts
to equate demand with supply.
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 curve
r
The investment
curve is also the
demand curve for
loanable funds.
I (r )
I
Supply of funds: Saving
The 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 curve
r
S  Y  C (Y  T )  G
National saving
does not
depend on r,
so the supply
curve is
vertical.
S, I
Loanable funds market equilibrium
r
S  Y  C (Y  T )  G
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:
If L.F. market in equilibrium, then
S=Y–C–G =I
Add (C +G ) to both sides to get
Y = C + I + G (goods market eq’m)
Thus,
Eq’m in
L.F. market

Eq’m in goods
market
Fiscal Policy Operations: Increase/Decrease in “G” or ‘T”
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
• Interest rate
• Investment level
Thus, government purchases are
said to crowd out investment
The Crowd-out effect
1. The increase in the
deficit reduces saving…
2. …which causes the real
interest rate to rise…
3. …which reduces the
level of investment.
r
S2
S1
r2
r1
I (r )
I2
I1
S, I
Fiscal Policy Operations: Increase/Decrease in “G” or ‘T”
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.
Two reasons: Technological changes and Tax Policy
Real
interest
rate, r
Saving, S
B
A
S
An increase in the demand for
investment goods shifts the investment
schedule to the right. At any given
interest rate, the amount of investment
is greater. The equilibrium moves
from A to B. Because the amount
of saving is fixed, the increase in
investment demand raises
the interest rate while leaving
I2
the equilibrium
I1
amount of investment
unchanged.
Investment, Saving, I, S
But, what if interest rates are even higher?
S(r)
Real
interest
rate, r
The higher
interest rate
induces people
to decrease
consumption
and increase
saving, which
in turn allows
investment to
increase.
Upward sloping savings
B
I2
A
I1
Investment, Saving, I, S
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).
Numerical Questions and Solutions for Practice
3) An economy's production function is cobb-douglas
with parameter α =0.3. (Macroeconomics, mankiw, Pg.
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) An economy's production function is cobb-douglas
with parameter α =0.3. (Macroeconomics, mankiw, Pg.
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) An economy's production function is cobb-douglas with
parameter α =0.3. (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) An economy's production function is cobb-douglas
with parameter α =0.3. (Macroeconomics, mankiw, Pg.
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