This chapter discusses macroeconomic concepts including national income, GDP, and the factors that determine and distribute total income in an economy. It presents models for how prices of labor and capital are determined by supply and demand in factor markets, and how total income is distributed to labor income and capital income based on marginal productivity. The chapter also examines the components of aggregate demand, including consumption, investment, and government spending, and how equilibrium is reached in the goods and loanable funds markets through price adjustments.

1. CHAPTER THREE
macro National Income:
Where it Comes From
and Where it Goes
macroeconomics
fifth edition
N. Gregory Mankiw
PowerPoint® Slides
by Ron Cronovich
© 2004 Worth Publishers, all rights reserved

2. In this chapter you will learn:
 what determines the economy’s total
output/income
 how the prices of the factors of production
are determined
 how total income is distributed
 what determines the demand for goods and
services
 how equilibrium in the goods market is
achieved
CHAPTER 3 National Income slide 2

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

4. Factors of production
K = capital,
tools, machines, and structures
used in production
L = labor,
the physical and mental efforts of
workers
CHAPTER 3 National Income slide 4

5. 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 slide 5

6. Returns to scale: a review
Initially Y 1 = F (K 1 , L 1 )
Scale all inputs by the same factor z:
K 2 = zK 1 and L 2 = zL 1
(If z = 1.25, then all inputs are increased by 25%)
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

7. Exercise: determine returns to scale
Determine whether each of the following
production functions has constant, increasing,
or decreasing returns to scale:
K2
(a) F ( K , L ) = K L (b) F ( K , L ) =
L
(c) F ( K , L ) = 2K + 15L
(d) F ( K , L ) = 2 K + 15 L
(e) F ( K , L ) = 2 K 2
+ 15 L
2
CHAPTER 3 National Income slide 7

8. 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
CHAPTER 3 National Income slide 8

9. Determining GDP
Output is determined by the fixed
factor supplies and the fixed state
of technology:
Y = F (K , L )
CHAPTER 3 National Income slide 9

10. 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 .
CHAPTER 3 National Income slide 10

11. Notation
WW ==nominal wage
nominal wage
RR ==nominal rental rate
nominal rental rate
P P ==price of output
price of output
W /P
W /P ==real wage
real wage
(measured in units of output)
(measured in units of output)
R /P ==real rental rate
R /P real rental rate
CHAPTER 3 National Income slide 11

12. 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 slide 12

13. 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 13

14. 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 )
CHAPTER 3 National Income slide 14

15. Exercise: compute & graph MPL
a. Determine MPL at each L Y MPL
value of L 0 0 n.a.
1 10 ?
b. Graph the production 2 19 ?
function 3 27 8
c. Graph the MPL curve 4 34 ?
with MPL on the 5 40 ?
vertical axis and 6 45 ?
L on the horizontal axis 7 49 ?
8 52 ?
9 54 ?
10 55 ?
CHAPTER 3 National Income slide 15

16. answers:
Production function Marginal Product of Labor
12
MPL (units of output)
60
Output (Y)
10
50
8
40
6
30
20 4
10 2
0 0
0 1 2 3 4 5 6 7 8 9 10 0 1 2 3 4 5 6 7 8 9 10
Labor (L) Labor (L)
CHAPTER 3 National Income slide 16

17. The MPL and the production
function
Y
output
F (K , L )
MP
1 L As more labor is
MP added, MPL ↓
1 L
MP Slope of the production
L function equals MPL
1
L
labor
CHAPTER 3 National Income slide 17

18. 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
CHAPTER 3 National Income slide 18

19. Check your understanding:
Which of these production functions have
diminishing marginal returns to labor?
a) F ( K , L ) = 2K + 15L
b) F ( K , L ) = KL
c) F ( K , L ) = 2 K + 15 L
CHAPTER 3 National Income slide 19

20. Exercise (part 2)
L Y MPL
Suppose W/P = 6. 0 0 n.a.
1 10 10
d. If L = 3, should firm hire 2 19 9
more or less labor? Why? 3 27 8
e. If L = 7, should firm hire 4 34 7
more or less labor? Why? 5 40 6
6 45 5
7 49 4
8 52 3
9 54 2
10 55 1
CHAPTER 3 National Income slide 20

21. MPL and the demand for labor
Units of
output Each firm hires labor
Each firm hires labor
up to the point where
up to the point where
MPL = W/P
MPL = W/P
Real
wage
MPL,
Labor
demand
Units of labor, L
Quantity of labor
demanded
CHAPTER 3 National Income slide 21

22. The equilibrium real wage
Units of Labor
output supply
equilibrium
real wage MPL,
Labor
demand
L Units of labor, L
The real wage adjusts to equate
The real wage adjusts to equate
labor demand with supply.
labor demand with supply.
CHAPTER 3 National Income slide 22

23. 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 slide 23

24. The equilibrium real rental rate
Units of
output Supply of The real rental rate
The real rental rate
capital
adjusts to equate
adjusts to equate
demand for capital
demand for capital
with supply.
with supply.
equilibrium
R/P MPK,
demand for
capital
K Units of capital, K
CHAPTER 3 National Income slide 24

25. The Neoclassical Theory
The Neoclassical Theory
of Distribution
of Distribution
 states that each factor input is
 states that each factor input is
paid its marginal product
paid its marginal product
 accepted by most economists
 accepted by most economists
CHAPTER 3 National Income slide 25

26. How income is distributed:
W
total labor income = L = MPL × L
P
R
total capital income = K = MPK × K
P
If production function has constant returns to
scale, then
Y = MPL × L + MPK × K
national labor capital
income income income
CHAPTER 3 National Income slide 26

27. 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 27

28. 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 )
CHAPTER 3 National Income slide 28

29. 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.
CHAPTER 3 National Income slide 29

30. The consumption function
C
C (Y –
T )
The slope of the
MPC
consumption function
1 is the MPC.
Y – T
CHAPTER 3 National Income slide 30

31. 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 31

32. The investment function
r
Spending on
investment goods
is a downward-
sloping function of
the real interest rate
I (r )
I
CHAPTER 3 National Income slide 32

33. 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
CHAPTER 3 National Income slide 33

34. The market for goods & services
• Agg. demand: C (Y − T ) + I ( r ) + G
• Agg. supply: Y = F (K , L )
• Equilibrium: Y = C (Y − T ) + I ( r ) + G
The real interest rate adjusts
The real interest rate adjusts
to equate demand with supply.
to equate demand with supply.
CHAPTER 3 National Income slide 34

35. 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 35

36. 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).
CHAPTER 3 National Income slide 36

37. Loanable funds demand curve
r
The investment
curve is also the
demand curve for
loanable funds.
I (r )
I
CHAPTER 3 National Income slide 37

38. 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.
CHAPTER 3 National Income slide 38

39. 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
CHAPTER 3 National Income slide 39

40. Notation: ∆ = change in a variable
 For any variable X , ∆ X = “the change in X ”
∆ is the Greek (uppercase) letter Delta
Examples:
 If ∆ L = 1 and ∆ K = 0, then ∆ Y = MPL .
∆Y
More generally, if ∆ K = 0, then MPL = .
∆L
 ∆(Y −T ) = ∆ Y − ∆ T , so
∆C = MPC × (∆ Y − ∆ T )
= MPC ∆ Y − MPC ∆ T
CHAPTER 3 National Income slide 40

41. EXERCISE:
Calculate the change in saving
Suppose MPC = 0.8 and MPL = 20.
For each of the following, compute ∆ S :
a. ∆ G = 100
b. ∆ T = 100
c. ∆ Y = 100
d. ∆ L = 10
CHAPTER 3 National Income slide 41

42. Answers
∆S = ∆Y − ∆C − ∆G = ∆Y − 0.8 ( ∆Y − ∆T ) − ∆G
= 0.2 ∆Y + 0.8 ∆T − ∆G
a. ∆S = − 100
b. ∆S = 0.8 × 100 = 80
c. ∆S = 0.2 × 100 = 20
d. ∆Y = MPL × ∆L = 20 × 10 = 200,
∆S = 0.2 × ∆Y = 0.2 × 200 = 40.
CHAPTER 3 National Income slide 42

43. digression:
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.
CHAPTER 3 National Income slide 43

44. The U.S. Federal Government Budget
5%
0%
percent of GDP
-5%
-10%
(T-G) as a percent of GDP
(T-G) as a percent of GDP
-15%
1940 1950 1960 1970 1980 1990 2000
CHAPTER 3 National Income slide 44

45. The U.S. Federal Government Debt
Fact: In the early 1990s,
Fact: In the early 1990s,
120% about 18 cents of every tax
about 18 cents of every tax
dollar went to pay interest on
dollar went to pay interest on
100% the debt.
the debt.
(Today it’s about 9 cents.)
(Today it’s about 9 cents.)
percent of GDP
80%
60%
40%
20%
1940 1950 1960 1970 1980 1990 2000
CHAPTER 3 National Income slide 45

46. 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 46

47. Loanable funds market equilibrium
r S = Y − C (Y − T ) − G
Equilibrium real
interest rate
I (r )
Equilibrium level S, I
of investment
CHAPTER 3 National Income slide 47

48. The special role of r
rr adjusts to equilibrate the goods market and the
adjusts to equilibrate the goods market and the
loanable funds market simultaneously:
loanable funds market simultaneously:
If L.F. market in equilibrium, then
If L.F. market in equilibrium, then
Y – C – G = II
Y–C–G =
Add ((C +G )) to both sides to get
Add C +G to both sides to get
Y = C + II + G (goods market eq’m)
Y = C + + G (goods market eq’m)
Thus,
Thus, Eq’m in
L.F. market ⇔
Eq’m in goods
market
CHAPTER 3 National Income slide 48

49. Digression: mastering models
To learn a model well, 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 49

50. Mastering the loanable funds model
1. 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 50

51. CASE STUDY
The Reagan Deficits
 Reagan policies during early 1980s:
♦ increases in defense
spending: ∆ G > 0
♦ big tax cuts: ∆ T < 0
 According to our model, both policies reduce
national saving:
S = Y − C (Y −T ) − G
↑G ⇒ ↓ S ↓T ⇒ ↑ C ⇒ ↓ S
CHAPTER 3 National Income slide 51

52. 1. The Reagan deficits, cont.
1. The increase in r S1
S2
the deficit
reduces saving…
r2
2. …which causes
the real interest
r1
rate to rise…
3. …which reduces I (r )
the level of I2 I1 S, I
investment.
CHAPTER 3 National Income slide 52

53. Are the data consistent with these results?
variable
variable 1970s
1970s 1980s
1980s
T –G
T –G –2.2
–2.2 –3.9
–3.9
S
S 19.6
19.6 17.4
17.4
rr 1.1
1.1 6.3
6.3
II 19.9
19.9 19.4
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 53

54. Now you try…
 Draw the diagram for the loanable funds
model.
 Suppose the tax laws are altered to provide
more incentives for private saving.
 What happens to the interest rate and
investment?
 (Assume that T doesn’t change)
CHAPTER 3 National Income slide 54

55. Mastering the loanable funds model
2. Things that shift the investment curve
• certain 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 55

56. An increase in investment demand
r S
An increase
…raises the in desired
interest rate. r2 investment…
r1
But the equilibrium
level of investment I2
cannot increase I1
because the
supply of loanable
S, I
funds is fixed.
CHAPTER 3 National Income slide 56

57. Chapter summary
1. Total output is determined by
 how much capital and labor the economy has
 the level of technology
2. Competitive firms hire each factor until its
marginal product equals its price.
3. If the production function has constant returns to
scale, then labor income plus capital income
equals total income (output).
CHAPTER 3 National Income slide 59

58. Chapter summary
4. The economy’s output is used for
 consumption
(which depends on disposable income)
 investment
(depends on the real interest rate)
 government spending
(exogenous)
4. The real interest rate adjusts to equate
the demand for and supply of
 goods and services
 loanable funds
CHAPTER 3 National Income slide 60

59. Chapter summary
6. A decrease in national saving causes the
interest rate to rise and investment to fall.
7. 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 61

60. CHAPTER 3 National Income slide 62