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N. Gregory Mankiw
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3
National Income: Where it
Comes From and Where it Goes
© 2011 Worth Publishers, all rights reserved
2010 UPDATE
CHAPTER
SEVENTH EDITION
MACROECONOMICS
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
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
2
The production function: Y = F(K,L)
 Shows how much output (Y )
the economy can produce from
K units of capital and L units of labor
CHAPTER 3
National Income
3
Assumptions
1. The economy’s supplies of capital and labor
are fixed at
K K
CHAPTER 3
National Income
and
LL
4
Determining GDP
Output is determined by the fixed factor supplies
and the fixed state of technology:
Y  F (K , L)
CHAPTER 3
National Income
5
The distribution of national income
 Determined by factor prices,
the prices per unit firms pay for the factors of
production
 wage = price of L
 rental rate = price of K
CHAPTER 3
National Income
6
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
7
In 2011 January
 Nominal wage = $20 per hour
 Price of the good = $4 per unit produced
 Real wage = (Nominal Wage / Price )
= $20 / $4
= 5 units of goods.
CHAPTER 3
National Income
8
In 2012 January
 Nominal wage = $20 per hour
 Price of the good = $5 per unit produced
 Real wage = (Nominal Wage / Price )
= $20 / $5
= 4 units of goods.
CHAPTER 3
National Income
9
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
10
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
11
Marginal product of labor (MPL )
 definition:
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
12
NOW YOU TRY:
Compute & graph MPL
a. Determine MPL at each
value of L.
b. Graph the production
function.
c. Graph the MPL curve with
MPL on the vertical axis and
L on the horizontal axis.
L
0
1
2
3
4
5
6
7
8
9
10
Y
0
10
19
27
34
40
45
49
52
54
55
MPL
n.a.
?
?
8
?
?
?
?
?
?
?
NOW YOU TRY:
Answers
MPL (units of output)
Marginal Product of Labor
12
10
8
6
4
2
0
0
1
2
3
4
5
6
7
8
9
Labor (L)
10
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
CHAPTER 3
National Income
15
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
16
NOW YOU TRY:
Identifying Diminishing Marginal
Returns
 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
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
18
The equilibrium real wage
Units of
output
Labor
supply
equilibrium
real wage
L
CHAPTER 3
National Income
The real wage
adjusts to equate
labor demand
with supply.
MPL,
Labor
demand
Units of labor, L
19
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
20
The equilibrium real rental rate
Units of
output
Supply of
capital
equilibrium
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
21
How income is distributed to L and K
W
L  MPL  L
total labor income =
P
R
K  MPK  K
total capital income =
P
If production function has constant returns to
scale, then
Y  MPL  L  MPK  K
national
income
CHAPTER 3
National Income
labor
income
capital
income
22
The ratio of labor income to total income
in the U.S., 1960-2007
Labor’s 1.0
share of
total
0.8
income
0.6
Labor’s share of income
is approximately constant over time.
(Thus, capital’s share is, too.)
0.4
0.2
0.0
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005
CHAPTER 3
National Income
23
The Cobb-Douglas Production Function
 The Cobb-Douglas production function is:
where A represents the level of technology.

1
Y  AK L
CHAPTER 3
National Income
24
 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
25
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
26
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
27
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 change in C when disposable income
increases by one dollar.
CHAPTER 3
National Income
28
The consumption function
C
C (Y –T )
MPC
1
The slope of the
consumption function
is the MPC.
Y–T
CHAPTER 3
National Income
29
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
30
The investment function
r
Spending on
investment goods
depends negatively on
the real interest rate.
I (r )
I
CHAPTER 3
National Income
31
Government spending, G
 G = Gov’t spending on goods and services.
 Assume government spending and total taxes
are exogenous:
G G
CHAPTER 3
National Income
and
T T
32
The market for goods & services
 Aggregate demand:
 Aggregate supply:
 Equilibrium:
CHAPTER 3
National Income
C (Y  T )  I (r )  G
Y  F (K , L )
Y = C (Y  T )  I (r )  G
33
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
34
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
35
Loanable funds demand curve
r
The investment
curve is also the
demand curve for
loanable funds.
I (r )
I
CHAPTER 3
National Income
36
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
37
Types of saving
private saving = S = (Y – T ) – C
public saving
=
T – G
national saving, = private saving + public saving
= (Y –T ) – C +
=
CHAPTER 3
National Income
T–G
Y – C – G
38
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
39
U.S. Federal Government Surplus/Deficit,
1940-2009 and estimates for 2010-2015
10
5
percent of GDP
0
-5
-10
-15
-20
-25
-30
-35
National
Income
1940
1950
1960
CHAPTER 3
1970
1980
1990
2000
2010
40
U.S. Federal Government Debt,
1940-2009 and estimates for 2010-2015
140
percent of GDP
120
100
80
60
40
20
0
National
Income
1940
1950
1960
CHAPTER 3
1970
1980
1990
2000
2010
41
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
42
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
43
Read ……..
The Reagan deficits
 Reagan policies during early 1980s:
CHAPTER 3
National Income
44