N. Gregory Mankiw
Sixth Edition
Chapter 3:
CHAPTER 3 National Income
Econ 4020/Chatterjee slide 0

 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

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 slide 2

CHAPTER 3 National Income slide 3

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

 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 slide 5

Initially Y
1
= F(K
1
,L
1
)
Suppose all inputs were to increase by the same factor z:
K
2
= zK
1 and L
2
= zL
1
(e.g., if z = 2, then all inputs are doubled)
What happens to output, Y
2
= F (K
2
,L
2
)?
 If constant returns to scale , Y
2
= zY
1
 If increasing returns to scale , Y
2
> zY
1
 If decreasing returns to scale , Y
2
< zY
1
CHAPTER 3 National Income slide 6

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 slide 13

Output is determined by the fixed factor supplies and the fixed state of technology:
Y

F K L )
CHAPTER 3 National Income slide 14

 determined by factor prices , the prices per unit that firms pay for the factors of production
 wage = price of L
 ren tal rate = price of K
CHAPTER 3 National Income slide 15

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 slide 16

 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 slide 17

 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

 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
1
MP
L
1
MP
L
1
MP
L
Slope of the production function equals MPL
As more labor is added, MPL 
L labor
CHAPTER 3 National Income slide 22

 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

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

Units of output
Labor supply
The real wage adjusts to equate labor demand with supply.
equilibriu m real wage
L
MPL,
Labor demand
Units of labor, L
CHAPTER 3 National Income slide 27

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 slide 28

The equilibrium real rental rate
Units of output
Supply of capital
The real rental rate adjusts to equate demand for capital with supply.
equilibriu m R/P
K
MPK, demand for capital
Units of capital, K
CHAPTER 3 National Income slide 29

Labor’s share of total income
1
0.8
0.6
The ratio of labor income to total income in the U.S.
0.4
0.2
Labor’s share of income is approximately constant over time.
(Hence, capital’s share is, too.)
0
1960
CHAPTER 3
1970
National Income
1980 1990 2000 slide 30

 The Cobb-Douglas production function is:
Y

AK L 1
  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

 Each factor’s marginal product is proportional to its average product:
MPK
 
AK
 
1 L 1
  

Y
K
MPL (1

) AK L
  
(1
 
) Y
L
CHAPTER 3 National Income slide 32

total labor income =
MPL L
( 1   )
Y total capital income =   
Y
If production function has constant returns to scale, then
Y
  
MPK

K national income labor income
CHAPTER 3 National Income capital income slide 33

Empirical estimates of the Cobb-
Douglas 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
1/ 3
L
2 / 3
CHAPTER 3 National Income slide 34

Labor’s share of total income
1
0.8
0.6
The ratio of labor income to total income in the U.S.
0.4
0.2
Labor’s share of income is approximately constant over time.
(Hence, capital’s share is, too.)
0
1960
CHAPTER 3
1970
National Income
1980 1990 2000 slide 35

 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

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 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

A closed economy, market-clearing model
Supply side
DONE
DONE factor markets (supply, demand, price) determination of output/income
Next
Demand side
  determinants of
C
,
I
, and
G
Equilibrium
 goods market
 loanable funds market
CHAPTER 3 National Income slide 40

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

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

C
C (Y –T)
1
MPC
The slope of the consumption function is the MPC.
Y – T
CHAPTER 3 National Income slide 44

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

r
Spending on investment goods depends negatively on the real interest rate.
I (r )
I
CHAPTER 3 National Income slide 46

 G = govt spending on goods and services.
 Assume government spending and total taxes are exogenous:
G

G and T

T
CHAPTER 3 National Income slide 47

 Aggregate demand: C Y T )  I r  G
 Aggregate supply: Y  F K L
 Equilibrium: Y C Y T )  I r  G
 The real interest rate adjusts to equate demand with supply.
CHAPTER 3 National Income slide 48

 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

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

r
The investment curve is also the demand curve for loanable funds.
I (r )
I
CHAPTER 3 National Income slide 51

 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

private saving = (Y – T) – C public saving = T – G national saving , S
= private saving + public saving
= (Y –T ) – C + T – G
= Y – C – G
CHAPTER 3 National Income slide 53

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

r
S Y C Y T )  G
Equilibrium real interest rate
Equilibrium level of investment
CHAPTER 3 National Income
I (r )
S, I slide 55

 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%
-5%
-10%
-15%
-20%
-25%
-30%
1940
CHAPTER 3
1950 1960
National Income
1970 1980 1990 2000 slide 60

120%
100%
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.)
80%
60%
40%
20%
0%
1940
CHAPTER 3
1950 1960
National Income
1970 1980 1990 2000 slide 61

Year
U.S. Budget Deficits
2002
2004
2006
2007
Actual or
Projected
(USD, billions)
157
412
248
158*
450
400
350
300
250
200
Series1
150
2008 244*
100
50
2011 400*
0
2002 2004 2006 2007 2008 2011
CHAPTER 3 National Income 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

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
 Eq’m in goods market
CHAPTER 3 National Income slide 64

CASE STUDY:
 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  T   C   S
CHAPTER 3 National Income slide 65

CASE STUDY:
1. The increase in the deficit reduces saving… r
S
2 r
2
2. …which causes the real interest rate to rise… r
1
S
1
3. …which reduces the level of investment.
CHAPTER 3 National Income
I
2
I
1
I (r )
S, I slide 66

Are the data consistent with these results?
variable
T – G
S r
I
1970s
–2.2
19.6
1.1
19.9
1980s
–3.9
17.4
6.3
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

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

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

, 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

r
S
…raises the interest rate.
r
2
An increase in desired
investment… r
1
But the equilibrium level of investment cannot increase because the supply of loanable funds is fixed.
CHAPTER 3 National Income
I
1
I
2
S, I slide 73

 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

r
An increase in investment demand raises r, which induces an increase in the quantity of saving, which allows I to increase.
r
2 r
1
I
1
I
2
2
I(r)
I(r)
S, I
CHAPTER 3 National Income 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