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N. Gregory Mankiw
Macroeconomics
Sixth Edition
Chapter 3:
National Income:
Where it Comes From
and Where it Goes
CHAPTER 3
National Income
Econ 4020/Chatterjee
slide 0
In this chapter, you will learn…
 How an economy’s total output/income is
produced
 How the prices of the factors of production
are determined
 How total income is distributed
 What determines the demand for goods and
services (how is total income spent?)
 How equilibrium in the goods market is
achieved
CHAPTER 3
National Income
slide 1
Outline of model
A closed economy, market-clearing model
Economic Agents
 Households
 Firms
 Government
Markets where these agents interact
 Market for Goods and Services
 Factor Markets
 Financial Markets
The interaction between agents in the context of
markets determines an economy’s resource
allocation and progress
CHAPTER 3
National Income
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CHAPTER 3
National Income
slide 3
Who Produces Output?
Factors of production
K =
capital:
tools, machines, and structures used in
production
L =
labor:
the physical and mental efforts of workers
AND
TECHNOLOGY
CHAPTER 3
National Income
slide 4
The production function
 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
 exhibits “constant returns to scale”
CHAPTER 3
National Income
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Returns to scale: A review
Initially Y1 = F (K1 , L1 )
Suppose all inputs were to increase by the same factor z:
K2 = zK1 and L2 = zL1
(e.g., if z = 2, then all inputs are doubled)
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
CHAPTER 3
National Income
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Assumptions of the model
1. Technology is fixed.
2. The economy’s supplies of capital and labor
are fixed at
K K
and
LL
Why? Because we are looking at the “long run”
where all resources are fully utilized or
employed
CHAPTER 3
National Income
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Determining GDP
Output is determined by the fixed factor supplies
and the fixed state of technology:
Y  F (K , L)
CHAPTER 3
National Income
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The distribution of national
income
 determined by factor prices,
the prices per unit that firms pay for the
factors of production
 wage = price of L
 rental rate = price of K
CHAPTER 3
National Income
slide 15
Notation
W = nominal wage
R
= nominal rental rate
P
= price of output
W /P
= real wage
(measured in units of output)
R /P = real rental rate
CHAPTER 3
National Income
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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?
CHAPTER 3
National Income
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Demand for labor
 Assume markets are competitive:
each firm takes W, R, and P as given.
 Basic idea:
A firm hires each unit of labor
if the cost does not exceed the benefit.
 cost = real wage
 benefit = marginal product of labor
CHAPTER 3
National Income
slide 18
Marginal product of labor (MPL)
 definition:
The extra output the firm can produce
using an additional unit of labor
(holding all other inputs fixed):
MPL = F (K, L +1) – F (K, L)
CHAPTER 3
National Income
slide 19
MPL and the production function
Y
output
F (K , L )
1
1
MP
L
MP
L
As more labor is
added, MPL 
Slope of the production
function equals MPL
1
CHAPTER 3
MP
L
National Income
L
labor
slide 22
Diminishing marginal returns
 As a factor input is increased,
its marginal product falls (other things equal).
 Intuition:
Suppose L while holding K fixed
 fewer machines per worker
 lower worker productivity
CHAPTER 3
National Income
slide 23
MPL and the demand for labor
Units of
output
Each firm hires labor
up to the point where
MPL = W/P.
Real
wage
MPL,
Labor
demand
Units of labor, L
Quantity of labor
demanded
CHAPTER 3
National Income
slide 26
The equilibrium real wage
Units of
output
Labor
supply
equilibriu
m real
wage
L
CHAPTER 3
National Income
The real wage
adjusts to equate
labor demand
with supply.
MPL,
Labor
demand
Units of labor, L
slide 27
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 .
CHAPTER 3
National Income
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The equilibrium real rental rate
Units of
output
Supply of
capital
equilibriu
m R/P
K
CHAPTER 3
National Income
The real rental rate
adjusts to equate
demand for capital
with supply.
MPK,
demand for
capital
Units of capital, K
slide 29
The ratio of labor income to total
income in the U.S.
1
Labor’s
share of
total 0.8
income
0.6
Labor’s share of income
is approximately constant over time.
(Hence, capital’s share is, too.)
0.4
0.2
0
1960
CHAPTER 3
1970
National Income
1980
1990
2000
slide 30
The Cobb-Douglas Production
Function
 The Cobb-Douglas production function is:
 1
Y  AK L
where A represents the level of technology
 The Cobb-Douglas production function has
constant factor shares:
 = capital’s share of total income:
capital income = MPK x K =  Y
labor income = MPL x L = (1 –  )Y
.
CHAPTER 3
National Income
slide 31
The Cobb-Douglas Production
Function
 Each factor’s marginal product is proportional to
its average product:
MPK   AK
 1 1
L

Y
K
(1   )Y
 
MPL  (1   ) AK L 
L
CHAPTER 3
National Income
slide 32
How income is distributed:
total labor income = MPL  L  (1   )Y
total capital income = MPK  K  Y
If production function has constant returns to
scale, then
Y  MPL  L  MPK  K
national
income
CHAPTER 3
labor
income
National Income
capital
income
slide 33
Empirical estimates of the CobbDouglas Production Function
 Economists have estimated that the share of capital
income in U.S. GDP is approximately 33%, .i.e.  =
0.33
 Labor’s share in U.S. GDP is approximately 67%.
 These shares are roughly constant over long periods
of time: fits the Cobb-Douglas Specification.
Y  AK
CHAPTER 3
National Income
1/ 3
2/3
L
slide 34
The ratio of labor income to total
income in the U.S.
1
Labor’s
share of
total 0.8
income
0.6
Labor’s share of income
is approximately constant over time.
(Hence, capital’s share is, too.)
0.4
0.2
0
1960
CHAPTER 3
1970
National Income
1980
1990
2000
slide 35
The Neoclassical Theory
of Distribution
 Each factor of production is paid its marginal
product
 In equilibrium, MPL = W/P (real wage)
MPK = r/P (real rental rate)
 Characterized by the Law of Diminishing Returns
 Growth in factor productivity should be tracked by
the growth in real factor income.
CHAPTER 3
National Income
slide 36
The Neoclassical Theory in
Action…
Black Death and Factor Prices
 Outbreak of bubonic plague in Europe or The
Black Death in the year 1348
 The population of Europe was reduced by a third
 Real wages doubled and peasants enjoyed
economic prosperity
 Real rents on land fell by nearly 50 percent and
the landowner class suffered significant
reductions in their incomes
CHAPTER 3
National Income
slide 37
The Neoclassical Theory in
Action…
The Abolition of Slavery Act, U.K. (1833)
 Former slaves in the Caribbean colonies
demanded higher wages and compensation
 Plantations in the Caribbean Islands became less
profitable as labor costs rose
 British response: IMPORT labor from colonies
in Asia and Africa
 What happened to wage rates in the Caribbean?
CHAPTER 3
National Income
slide 38
CHAPTER 3
National Income
slide 39
Outline of model
A closed economy, market-clearing model
Supply side
DONE 
factor markets (supply, demand, price)
DONE 
determination of output/income
Demand side
Next   determinants of C, I, and G
Equilibrium
 goods market
 loanable funds market
CHAPTER 3
National Income
slide 40
Demand for goods & services
Components of aggregate demand:
C = consumer demand for goods & services
I = firms’ demand for investment goods
G = government demand for goods & services
(closed economy: no exports or imports )
CHAPTER 3
National Income
slide 41
Gross Domestic Product, USA
[Billions of dollars]
Seasonally adjusted at annual rates
Source: Bureau of Economic Analysis
CHAPTER 3
National Income
slide 42
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: Marginal propensity to consume
(MPC) is the increase in C caused by a one-unit
increase in disposable income.
CHAPTER 3
National Income
slide 43
The consumption function
C
C (Y –T)
MPC
1
The slope of the
consumption
function is the MPC.
Y–T
CHAPTER 3
National Income
slide 44
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
CHAPTER 3
National Income
slide 45
The investment function
r
Spending on
investment goods
depends negatively on
the real interest rate.
I (r )
I
CHAPTER 3
National Income
slide 46
Government spending, G
 G = govt spending on goods and services.
 Assume government spending and total taxes are
exogenous:
G G
CHAPTER 3
National Income
and
T T
slide 47
The market for goods & services
 Aggregate demand:
C (Y  T )  I (r )  G
 Aggregate supply:
 Equilibrium:
Y  F (K , L )
Y = C (Y  T )  I (r )  G
 The real interest rate adjusts
to equate demand with supply.
CHAPTER 3
National Income
slide 48
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
CHAPTER 3
National Income
slide 49
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
(cost of borrowing).
CHAPTER 3
National Income
slide 50
Loanable funds demand curve
r
The investment
curve is also the
demand curve for
loanable funds.
I (r )
I
CHAPTER 3
National Income
slide 51
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 the tax revenue it
receives.
CHAPTER 3
National Income
slide 52
Types of saving
private saving = (Y – T) – C
public saving = T – G
national saving, S
= private saving + public saving
= (Y –T ) – C + T – G
=
CHAPTER 3
Y – C – G
National Income
slide 53
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
CHAPTER 3
National Income
slide 54
Loanable funds market
equilibrium
r
S  Y  C (Y  T )  G
Equilibrium
real interest
rate
I (r )
Equilibrium level
of investment
CHAPTER 3
National Income
S, I
slide 55
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.
 The U.S. government finances its deficit by
issuing Treasury bonds – i.e., borrowing.
CHAPTER 3
National Income
slide 59
U.S. Federal Government
Surplus/Deficit, 1940-2004
5%
0%
(% of GDP)
-5%
-10%
-15%
-20%
-25%
-30%
1940
CHAPTER 3
1950
1960
National Income
1970
1980
1990
2000
slide 60
U.S. Federal Government Debt,
1940-2004
Fact: In the early 1990s,
about 18 cents of every tax
dollar went to pay interest on
the debt.
(Today it’s about 9 cents.)
120%
(% of GDP)
100%
80%
60%
40%
20%
0%
1940
CHAPTER 3
1950
1960
National Income
1970
1980
1990
2000
slide 61
The U.S. Budget Deficit: Where is
it Headed?
2002
Actual or
Projected
(USD,
billions)
U.S. Budget Deficits
450
400
350
157
2004
412
2006
248
2007
158*
300
USD,bn
Year
250
Series1
200
150
2008
244*
100
50
2011
400*
0
2002
CHAPTER 3
National Income
2004
2006
2007
2008
2011
slide 62
"Over the long term, the budget
remains on an unsustainable path"
-Congressional Budget Office Report, 2007
 Continued military operations in Iraq and
Afghanistan
 Extension of temporary tax cuts enacted in
President Bush's first term
 Rising health-care and social security costs and
the retirement of the “baby-boom” generation
 Longer-term outlook is bleak.
CHAPTER 3
National Income
slide 63
The special role of r
r adjusts to equilibrate the goods market and the
loanable funds market simultaneously:
If Loanable Funds market is in equilibrium, then
Y–C–G =I
Y = C + I + G (goods market eq’m)
Thus,
Eq’m in
L.F. market
CHAPTER 3
National Income

Eq’m in goods
market
slide 64
CASE STUDY:
The Reagan deficits
 Reagan policies during early 1980s:
 increases in defense spending: G > 0
 big tax cuts: T < 0
 Both policies reduce national saving:
S  Y  C (Y  T )  G
G   S
CHAPTER 3
National Income
T   C   S
slide 65
CASE STUDY:
The Reagan deficits
1. The increase in
the deficit reduces
saving…
2. …which causes the
real interest rate to
rise…
3. …which reduces
the level of
investment.
CHAPTER 3
National Income
r
S2
S1
r2
r1
I (r )
I2
I1
S, I
slide 66
Are the data consistent with these results?
variable
1970s
1980s
T–G
–2.2
–3.9
S
19.6
17.4
r
1.1
6.3
I
19.9
19.4
T–G, S, and I are expressed as a percent of GDP
All figures are averages over the decade shown.
CHAPTER 3
National Income
slide 67
Military Spending and the Interest Rate
in the United Kingdom: 1730-1920
CHAPTER 3
National Income
slide 68
Digression: Mastering models
To master a model, be sure to know:
1. Which of its variables are endogenous and
which are exogenous.
2. For each curve in the diagram, know
a. definition
b. intuition for slope
c. all the things that can shift the curve
3. Use the model to analyze the effects of each item
in 2c.
CHAPTER 3
National Income
slide 69
Mastering the loanable funds
model
Things that shift the saving curve
 public saving
 fiscal policy: changes in G or T
 private saving
 preferences
 tax laws that affect saving
–401(k)
–IRA
–replace income tax with consumption tax
CHAPTER 3
National Income
slide 70
Mastering the loanable funds
model, continued
Things that shift the investment curve
 some technological innovations
 to take advantage of the innovation,
firms must buy new investment goods
 tax laws that affect investment
 investment tax credit
CHAPTER 3
National Income
slide 72
An increase in investment demand
r
…raises the
interest rate.
r2
S
An increase
in desired
investment…
r1
But the equilibrium
level of investment
cannot increase
because the
supply of loanable
funds is fixed.
CHAPTER 3
National Income
I1
I2
S, I
slide 73
Saving and the interest rate
 Why might saving depend on r ?
 How would the results of an increase in
investment demand be different?
 Would r rise as much?
 Would the equilibrium value of I change?
CHAPTER 3
National Income
slide 74
An increase in investment demand
when saving depends on r
An increase in
investment demand
raises r,
which induces an
increase in the
quantity of saving,
which allows I
to increase.
r
S (r )
r2
r1
I(r)
I(r)
2
I1 I2
CHAPTER 3
National Income
S, I
slide 75
Chapter Summary
 Total output is determined by
 the economy’s quantities of capital and labor
 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).
CHAPTER 3
National Income
slide 76
Chapter Summary
 A closed economy’s output is used for
 consumption
 investment
 government spending
 The real interest rate adjusts to equate
the demand for and supply of
 goods and services
 loanable funds
CHAPTER 3
National Income
slide 77
Chapter Summary
 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.
CHAPTER 3
National Income
slide 78