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CHAPTER
8
Economic Growth II:
Technology, Empirics, and
Policy
MACROECONOMICS
Introduction
In the Solow model of Chapter 7,
 the production technology is held constant.
 income per capita is constant in the steady state.
Neither point is true in the real world:
 1904-2004: U.S. real GDP per person grew by a
factor of 7.6, or 2% per year.
 examples of technological progress abound
(see next slide).
CHAPTER 8
Economic Growth II
slide 1
Technological progress in the
Solow model
 A new variable: E = labor efficiency
 Assume:
Technological progress is labor-augmenting:
it increases labor efficiency at the exogenous
rate g:
g
CHAPTER 8
E
Economic Growth II
E
slide 2
Technological progress in the
Solow model
 We now write the production function as:
Y  F (K , L  E )
 where L  E = the number of effective
workers.
 Increases in labor efficiency have the
same effect on output as increases in
the labor force.
CHAPTER 8
Economic Growth II
slide 3
Technological progress in the
Solow model
 Notation:
y = Y/LE = output per effective worker
k = K/LE = capital per effective worker
 Production function per effective worker:
y = f(k)
 Saving and investment per effective worker:
s y = s f(k)
CHAPTER 8
Economic Growth II
slide 4
Technological progress in the
Solow model
( + n + g)k = break-even investment:
the amount of investment necessary
to keep k constant.
Consists of:
  k to replace depreciating capital
 n k to provide capital for new workers
 g k to provide capital for the new “effective”
workers created by technological progress
CHAPTER 8
Economic Growth II
slide 5
Technological progress in the
Solow model
Investment,
break-even
investment
k = s f(k)  ( +n +g)k
( +n +g ) k
sf(k)
k*
CHAPTER 8
Economic Growth II
Capital per
worker, k
slide 6
Steady-state growth rates in the
Solow model with tech. progress
Variable
Symbol
Steady-state
growth rate
Capital per
effective worker
k = K/(LE )
0
Output per
effective worker
y = Y/(LE )
0
Output per worker
(Y/ L) = yE
g
Total output
Y = yEL
n+g
CHAPTER 8
Economic Growth II
slide 7
The Golden Rule
To find the Golden Rule capital stock,
express c* in terms of k*:
In the Golden
*
*
*
c = y
 i
Rule steady state,
the marginal
= f (k* )
 ( + n + g) k*
product of capital
*
c is maximized when
net of depreciation
MPK =  + n + g
equals the
pop. growth rate
or equivalently,
plus the rate of
MPK   = n + g
tech progress.
CHAPTER 8
Economic Growth II
slide 8
Growth empirics:
Balanced growth
 Solow model’s steady state exhibits
balanced growth - many variables grow
at the same rate.
 Solow model predicts Y/L and K/L grow at the
same rate (g), so K/Y should be constant.
 This is true in the real world.
 Solow model predicts real wage grows at same
rate as Y/L, while real rental price is constant.
 This is also true in the real world.
CHAPTER 8
Economic Growth II
slide 9
Growth empirics: Convergence
 Solow model predicts that, other things equal,
“poor” countries (with lower Y/L and K/L) should
grow faster than “rich” ones.
 If true, then the income gap between rich & poor
countries would shrink over time, causing living
standards to “converge.”
 In real world, many poor countries do NOT grow
faster than rich ones. Does this mean the Solow
model fails?
CHAPTER 8
Economic Growth II
slide 10
Growth Empirics: Convergence
 Solow model predicts that, other things equal,
“poor” countries (with lower Y/L and K/L) should
grow faster than “rich” ones.
 No, because “other things” aren’t equal.
 In samples of countries with
similar savings & pop. growth rates,
income gaps shrink about 2% per year.
 In larger samples, after controlling for differences
in saving, pop. growth, and human capital,
incomes converge by about 2% per year.
CHAPTER 8
Economic Growth II
slide 11
Growth empirics: Convergence
 What the Solow model really predicts is
conditional convergence - countries converge
to their own steady states, which are determined by
saving, population growth, and education.
 This prediction comes true in the real world.
CHAPTER 8
Economic Growth II
slide 12
Growth empirics: Factor accumulation
vs. production efficiency
 Differences in income per capita among countries
can be due to differences in
1. capital – physical or human – per worker
2. the efficiency of production
(the height of the production function)
 Studies:
 both factors are important.
 the two factors are correlated: countries with
higher physical or human capital per worker also
tend to have higher production efficiency.
CHAPTER 8
Economic Growth II
slide 13
Growth empirics: Factor accumulation
vs. production efficiency
 Possible explanations for the correlation
between capital per worker and production
efficiency:
 Production efficiency encourages capital
accumulation.
 Capital accumulation has externalities that
raise efficiency.
 A third, unknown variable causes
capital accumulation and efficiency to be
higher in some countries than others.
CHAPTER 8
Economic Growth II
slide 14
Policy issues:
Evaluating the rate of saving
To estimate (MPK   ), use three facts about the
U.S. economy:
1. k = 2.5 y
The capital stock is about 2.5 times one year’s
GDP.
2.  k = 0.1 y
About 10% of GDP is used to replace depreciating
capital.
3. MPK  k = 0.3 y
Capital income is about 30% of GDP.
CHAPTER 8
Economic Growth II
slide 15
Policy issues:
Evaluating the rate of saving
1. k = 2.5 y
2.  k = 0.1 y
3. MPK  k = 0.3 y
To determine  , divide 2 by 1:
k
0.1y

k
2.5 y
CHAPTER 8

Economic Growth II
0.1
 
 0.04
2.5
slide 16
Policy issues:
Evaluating the rate of saving
1. k = 2.5 y
2.  k = 0.1 y
3. MPK  k = 0.3 y
To determine MPK, divide 3 by 1:
MPK  k
k
0.3 y

2.5 y

0.3
MPK 
 0.12
2.5
Hence, MPK   = 0.12  0.04 = 0.08
CHAPTER 8
Economic Growth II
slide 17
Policy issues:
Evaluating the rate of saving
 From the last slide: MPK   = 0.08
 U.S. real GDP grows an average of 3% per year,
so n + g = 0.03
 Thus,
MPK   = 0.08 > 0.03 = n + g
 Conclusion:
The U.S. is below the Golden Rule steady state:
Increasing the U.S. saving rate would increase
consumption per capita in the long run.
CHAPTER 8
Economic Growth II
slide 18
Policy issues:
How to increase the saving rate
 Reduce the government budget deficit
(or increase the budget surplus).
 Increase incentives for private saving:
 reduce capital gains tax, corporate income tax,
estate tax as they discourage saving.
 replace federal income tax with a consumption
tax.
 expand tax incentives for IRAs (individual
retirement accounts) and other retirement
savings accounts.
CHAPTER 8
Economic Growth II
slide 19
Policy issues:
Allocating the economy’s investment
 In the Solow model, there’s one type of capital.
 In the real world, there are many types,
which we can divide into three categories:
 private capital stock
 public infrastructure
 human capital: the knowledge and skills that
workers acquire through education.
 How should we allocate investment among these
types?
CHAPTER 8
Economic Growth II
slide 20
Policy issues:
Allocating the economy’s investment
Two viewpoints:
1. Equalize tax treatment of all types of capital in all
industries, then let the market allocate investment
to the type with the highest marginal product.
2. Industrial policy:
Govt should actively encourage investment in
capital of certain types or in certain industries,
because they may have positive externalities
that private investors don’t consider.
CHAPTER 8
Economic Growth II
slide 21
Policy issues:
Establishing the right institutions
 Creating the right institutions is important for
ensuring that resources are allocated to their
best use. Examples:
 Legal institutions, to protect property rights.
 Capital markets, to help financial capital flow to
the best investment projects.
 A corruption-free government, to promote
competition, enforce contracts, etc.
CHAPTER 8
Economic Growth II
slide 22
CASE STUDY:
The productivity slowdown
Growth in output per person
(percent per year)
1948-72
1972-95
Canada
2.9
1.8
France
4.3
1.6
Germany
5.7
2.0
Italy
4.9
2.3
Japan
8.2
2.6
U.K.
2.4
1.8
U.S.
2.2
1.5
CHAPTER 8
Economic Growth II
slide 23
CASE STUDY:
I.T. and the “New Economy”
Growth in output per person
(percent per year)
1948-72
1972-95
1995-2004
Canada
2.9
1.8
2.4
France
4.3
1.6
1.7
Germany
5.7
2.0
1.2
Italy
4.9
2.3
1.5
Japan
8.2
2.6
1.2
U.K.
2.4
1.8
2.5
U.S.
2.2
1.5
2.2
CHAPTER 8
Economic Growth II
slide 24
CASE STUDY:
I.T. and the “New Economy”
Apparently, the computer revolution did not affect
aggregate productivity until the mid-1990s.
Two reasons:
1. Computer industry’s share of GDP much
bigger in late 1990s than earlier.
2. Takes time for firms to determine how to
utilize new technology most effectively.
The big, open question:
 How long will I.T. remain an engine of growth?
CHAPTER 8
Economic Growth II
slide 25
Endogenous growth theory
 Solow model:
 sustained growth in living standards is due to
tech progress.
 the rate of tech progress is exogenous.
 Endogenous growth theory:
 a set of models in which the growth rate of
productivity and living standards is endogenous.
CHAPTER 8
Economic Growth II
slide 26
A basic model
 Production function: Y = A K
where A is the amount of output for each
unit of capital (A is exogenous & constant)
 Key difference between this model & Solow:
MPK is constant here, diminishes in Solow
 Investment: s Y
 Depreciation:  K
 Equation of motion for total capital:
K = s Y   K
CHAPTER 8
Economic Growth II
slide 27
A basic model
K = s Y   K
 Divide through by K and use Y = A K to get:
Y
K

 sA  
Y
K
 If s A > , then income will grow forever,
and investment is the “engine of growth.”
 Here, the permanent growth rate depends
on s. In Solow model, it does not.
CHAPTER 8
Economic Growth II
slide 28
Does capital have diminishing
returns or not?
 Depends on definition of “capital.”
 If “capital” is narrowly defined (only plant &
equipment), then yes.
 Advocates of endogenous growth theory
argue that knowledge is a type of capital.
 If so, then constant returns to capital is more
plausible, and this model may be a good
description of economic growth.
CHAPTER 8
Economic Growth II
slide 29
A two-sector model
 Two sectors:
 manufacturing firms produce goods.
 research universities produce knowledge that
increases labor efficiency in manufacturing.
 u = fraction of labor in research
(u is exogenous)
 Mfg prod func: Y = F [K, (1-u )E L]
 Res prod func: E = g (u )E
 Cap accumulation: K = s Y   K
CHAPTER 8
Economic Growth II
slide 30
A two-sector model
 In the steady state, mfg output per worker
and the standard of living grow at rate
E/E = g (u ).
 Key variables:
s: affects the level of income, but not its
growth rate (same as in Solow model)
u: affects level and growth rate of income
 Question: Would an increase in u be
unambiguously good for the economy?
CHAPTER 8
Economic Growth II
slide 31
Facts about R&D
1. Much research is done by firms seeking profits.
2. Firms profit from research:
 Patents create a stream of monopoly profits.
 Extra profit from being first on the market with a
new product.
3. Innovation produces externalities that reduce the
cost of subsequent innovation.
Much of the new endogenous growth theory
attempts to incorporate these facts into models
to better understand technological progress.
CHAPTER 8
Economic Growth II
slide 32
Chapter Summary
1. Key results from Solow model with tech progress
 steady state growth rate of income per person
depends solely on the exogenous rate of tech
progress
 the U.S. has much less capital than the Golden
Rule steady state
2. Ways to increase the saving rate
 increase public saving (reduce budget deficit)
 tax incentives for private saving
CHAPTER 8
Economic Growth II
slide 33
Chapter Summary
3. Productivity slowdown & “new economy”
 Early 1970s: productivity growth fell in the U.S.
and other countries.
 Mid 1990s: productivity growth increased,
probably because of advances in I.T.
4. Empirical studies
 Solow model explains balanced growth,
conditional convergence
 Cross-country variation in living standards is
due to differences in cap. accumulation and in
production efficiency
CHAPTER 8
Economic Growth II
slide 34
Chapter Summary
5. Endogenous growth theory: Models that
 examine the determinants of the rate of
tech. progress, which Solow takes as given.
 explain decisions that determine the creation of
knowledge through R&D.
CHAPTER 8
Economic Growth II
slide 35
CHAPTER
9
Introduction to Economic
Fluctuations
MACROECONOMICS
In this chapter, you will learn…




facts about the business cycle
how the short run differs from the long run
an introduction to aggregate demand
an introduction to aggregate supply in the short
run and long run
 how the model of aggregate demand and
aggregate supply can be used to analyze the
short-run and long-run effects of “shocks.”
CHAPTER 8
Economic Growth II
slide 37
Facts about the business cycle
 GDP growth averages 3–3.5 percent per year over
the long run with large fluctuations in the short run.
 Consumption and investment fluctuate with GDP,
but consumption tends to be less volatile and
investment more volatile than GDP.
 Unemployment rises during recessions and falls
during expansions.
 Okun’s Law: the negative relationship between
GDP and unemployment.
CHAPTER 8
Economic Growth II
slide 38
Growth rates of real GDP, consumption
Percent 10
change
from 4 8
quarters
earlier 6
Real GDP
growth rate
Consumption
growth rate
Average 4
growth
rate 2
0
-2
-4
1975 Growth
1980 1985
CHAPTER1970
8 Economic
II
1990
1995
2000
2005
slide 39
Growth rates of real GDP, consumption, investment
Percent 40
change
from 4 30
quarters
earlier 20
10
Investment
growth rate
Real GDP
growth rate
0
Consumption
growth rate
-10
-20
-30
1975 Growth
1980 1985
CHAPTER1970
8 Economic
II
1990
1995
2000
2005
slide 40
Unemployment
Percent 12
of labor
force
10
8
6
4
2
0
1975 Growth
1980 1985
CHAPTER1970
8 Economic
II
1990
1995
2000
2005
slide 41
Okun’s Law
Percentage 10
change in
real GDP 8
1951
Y
 3.5  2 u
Y
1966
1984
6
2003
4
1987
2
0
1975
2001
-2
1991 1982
-4
-3
CHAPTER 8
-2
-1
Economic Growth II
0
1
2
3
4
Change in unemploymentslide
rate42
Index of Leading Economic Indicators
 Published monthly by the Conference Board.
 Aims to forecast changes in economic activity
6-9 months into the future.
 Used in planning by businesses and govt,
despite not being a perfect predictor.
CHAPTER 8
Economic Growth II
slide 43
Components of the LEI index










Average workweek in manufacturing
Initial weekly claims for unemployment insurance
New orders for consumer goods and materials
New orders, nondefense capital goods
Vendor performance
New building permits issued
Index of stock prices
M2
Yield spread (10-year minus 3-month) on Treasuries
Index of consumer expectations
CHAPTER 8
Economic Growth II
slide 44
Index of Leading Economic Indicators
160
1996 = 100
140
120
100
80
60
40
20
0
Source:
1970 1975
Conference
CHAPTER 8 Economic
Board
1980
1985
Growth II
1990
1995
2000
2005
slide 45
Time horizons in macroeconomics
 Long run:
Prices are flexible, respond to changes in supply
or demand.
 Short run:
Many prices are “sticky” at some predetermined
level.
The economy behaves much
differently when prices are sticky.
CHAPTER 8
Economic Growth II
slide 46
Recap of classical macro theory
(Chaps. 3-8)
 Output is determined by the supply side:
 supplies of capital, labor
 technology.
 Changes in demand for goods & services
(C, I, G ) only affect prices, not quantities.
 Assumes complete price flexibility.
 Applies to the long run.
CHAPTER 8
Economic Growth II
slide 47
When prices are sticky…
…output and employment also depend on
demand, which is affected by
 fiscal policy (G and T )
 monetary policy (M )
 other factors, like exogenous changes in
C or I.
CHAPTER 8
Economic Growth II
slide 48
The Quantity Equation as
Aggregate Demand
 From Chapter 4, recall the quantity equation
MV = PY
 For given values of M and V,
this equation implies an inverse relationship
between P and Y :
CHAPTER 8
Economic Growth II
slide 49
The downward-sloping AD curve
An increase in
the price level
causes a fall in
real money
balances (M/P ),
P
(v is constant)
AD
Y
CHAPTER 8
Economic Growth II
slide 50
Shifting the AD curve
P
An increase in the
money supply shifts
the AD curve to the
right.
(since MV=PY, and
increase in M, increase
PY)
Every value of P has
associated higher Y.
CHAPTER 8
Economic Growth II
AD2
AD1
Y
slide 51
Aggregate supply in the long run
 Recall from Chapter 3:
In the long run, output is determined by
factor supplies and technology
Y  F (K , L )
Y is the full-employment or natural level of
output, the level of output at which the
economy’s resources are fully employed.
“Full employment” means that
unemployment equals its natural rate (not zero).
CHAPTER 8
Economic Growth II
slide 52
The long-run aggregate supply
curve
P
LRAS
Y does not
depend on P,
so LRAS is
vertical.
Y
 F (K , L )
CHAPTER 8
Economic Growth II
Y
slide 53
Long-run effects of an increase in M
P
In the long run,
this raises the
price level…
LRAS
An increase
in M shifts
AD to the
right.
P2
P1
AD2
AD1
…but leaves output
the same. (money
neutrality)
CHAPTER 8
Economic Growth II
Y
Y
slide 54
Aggregate supply in the short run
 Many prices are sticky in the short run.
 For now (and through Chap. 12), we assume
 all prices are stuck at a predetermined level in
the short run.
 firms are willing to sell as much at that price
level as their customers are willing to buy.
 Therefore, the short-run aggregate supply
(SRAS) curve is horizontal:
CHAPTER 8
Economic Growth II
slide 55
EXTREME SHORT RUN: The short-run
aggregate supply curve
P
The SRAS
curve is
horizontal:
The price level
is fixed at a
predetermined
level, and firms
sell as much as
buyers demand.
CHAPTER 8
P
Economic Growth II
SRAS
Y
slide 56
Short-run effects of an increase in M
In the short run
when prices are
sticky,…
P
…an increase
in aggregate
demand…
SRAS
AD2
AD1
P
…causes output to rise.
What about
Unemployment?
CHAPTER 8
Economic Growth II
Y1
Y2
Y
slide 57
From the short run to the long run
Over time, prices gradually become “unstuck.”
When they do, will they rise or fall?
In the short-run
equilibrium, if
then over time,
P will…
Y Y
rise
Y Y
fall
Y Y
remain constant
The adjustment of prices is what moves the
economy to its long-run equilibrium.
CHAPTER 8
Economic Growth II
slide 58
The SR & LR effects of M > 0
A = initial
equilibrium
B = new shortrun eq’m
after Fed
increases M
P
C
P2
P
C = long-run
equilibrium
CHAPTER 8
LRAS
Economic Growth II
B
A
Y
Y2
SRAS
AD2
AD1
Y
slide 59
How shocking!!!
 shocks: exogenous changes in agg. supply or
demand
 Shocks temporarily push the economy away from
full employment.
 Example: exogenous decrease in velocity
If the money supply is held constant, a decrease in
V means people will be using their money in fewer
transactions, causing a decrease in demand for
goods and services.
CHAPTER 8
Economic Growth II
slide 60
The effects of a negative demand shock
AD shifts left,
depressing output
and employment
in the short run.
Over time,
prices fall and
the economy
moves down its
demand curve
toward fullemployment.
CHAPTER 8
P
P
LRAS
B
P2
Economic Growth II
A
SRAS
C
AD1
AD2
Y2
Y
Y
slide 61
Supply shocks
 A supply shock alters production costs, affects the
prices that firms charge. (also called price shocks)
 Examples of adverse supply shocks:
 Bad weather reduces crop yields, pushing up
food prices.
 Workers unionize, negotiate wage increases.
 New environmental regulations require firms to
reduce emissions. Firms charge higher prices to
help cover the costs of compliance.
 Favorable supply shocks lower costs and prices.
CHAPTER 8
Economic Growth II
slide 62
CASE STUDY:
The 1970s oil shocks
 Early 1970s: OPEC coordinates a reduction in
the supply of oil.
 Oil prices rose
11% in 1973
68% in 1974
16% in 1975
 Such sharp oil price increases are supply shocks
because they significantly impact production
costs and prices.
CHAPTER 8
Economic Growth II
slide 63
CASE STUDY:
The 1970s oil shocks
The oil price shock
shifts SRAS up,
causing output and
employment to fall.
In absence of
further price
shocks, prices will
fall over time and
economy moves
back toward full
employment.
CHAPTER 8
P
P2
LRAS
B
SRAS2
A
P1
Economic Growth II
SRAS1
AD
Y2
Y
Y
slide 64
Stabilization policy
 def: policy actions aimed at reducing the
severity of short-run economic fluctuations.
 Example: Using monetary policy to combat the
effects of adverse supply shocks:
CHAPTER 8
Economic Growth II
slide 65
Stabilizing output with
monetary policy
P
The adverse
supply shock
moves the
economy to
point B.
P2
LRAS
B
A
P1
Economic Growth II
SRAS1
AD1
Y2
CHAPTER 8
SRAS2
Y
Y
slide 66
Stabilizing output with
monetary policy
But the Fed
accommodates
the shock by
raising agg.
demand.
results:
P is permanently
higher, but Y
remains at its fullemployment level.
CHAPTER 8
P
P2
LRAS
B
C
A
P1
Economic Growth II
SRAS2
AD1
Y2
Y
AD2
Y
slide 67
Chapter Summary
1. Long run: prices are flexible, output and employment
are always at their natural rates, and the classical
theory applies.
Short run: prices are sticky, shocks can push output
and employment away from their natural rates.
2. Aggregate demand and supply:
a framework to analyze economic fluctuations
CHAPTER 9
8
Economic Growth
Introduction
to Economic
II
Fluctuations
slide 68
Chapter Summary
3. The aggregate demand curve slopes downward.
4. The long-run aggregate supply curve is vertical,
because output depends on technology and factor
supplies, but not prices.
5. The short-run aggregate supply curve is horizontal,
because prices are sticky at predetermined levels.
CHAPTER 9
8
Economic Growth
Introduction
to Economic
II
Fluctuations
slide 69
Chapter Summary
6. Shocks to aggregate demand and supply cause
fluctuations in GDP and employment in the short run.
7. The Fed can attempt to stabilize the economy with
monetary policy.
CHAPTER 9
8
Economic Growth
Introduction
to Economic
II
Fluctuations
slide 70
CHAPTER
10
Aggregate Demand I:
Building the IS -LM Model
MACROECONOMICS
In this chapter, you will learn…
 the IS curve, and its relation to
 the Keynesian cross
 the loanable funds model
 the LM curve, and its relation to
 the theory of liquidity preference
 how the IS-LM model determines income and
the interest rate in the short run when P is fixed
CHAPTER 8
Economic Growth II
slide 72
Context
 Chapter 9 introduced the model of aggregate
demand and aggregate supply.
 Long run
 prices flexible
 output determined by factors of production &
technology
 unemployment equals its natural rate
 Short run
 prices fixed
 output determined by aggregate demand
 unemployment negatively related to output
CHAPTER 8
Economic Growth II
slide 73
Context
 This chapter develops the IS-LM model,
the basis of the aggregate demand curve.
 We focus on the short run and assume the price
level is fixed (so, SRAS curve is horizontal).
 This chapter (and chapter 11) focus on the
closed-economy case.
Chapter 12 presents the open-economy case.
CHAPTER 8
Economic Growth II
slide 74
The Keynesian Cross
 A simple closed economy model in which income
is determined by expenditure.
(due to J.M. Keynes)
 Notation:
I = planned investment
E = C + I + G = planned expenditure
Y = real GDP = actual expenditure
 Difference between actual & planned expenditure
= unplanned inventory investment
CHAPTER 8
Economic Growth II
slide 75
Elements of the Keynesian Cross
consumption function:
C  C (Y T )
govt policy variables:
G  G , T T
for now, planned
investment is exogenous:
planned expenditure:
I I
E  C (Y  T )  I  G
equilibrium condition:
actual expenditure = planned expenditure
Y  E
CHAPTER 8
Economic Growth II
slide 76
Graphing planned expenditure
E
planned
expenditure
E =C +I +G
MPC
1
income, output, Y
CHAPTER 8
Economic Growth II
slide 77
Graphing the equilibrium condition
E
E =Y
planned
expenditure
45º
income, output, Y
CHAPTER 8
Economic Growth II
slide 78
The equilibrium value of income
E
E =Y
planned
expenditure
E =C +I +G
income, output, Y
Equilibrium
income
CHAPTER 8
Economic Growth II
slide 79
An increase in government purchases
E
At Y1,
there is now an
unplanned drop
in inventory…
E =C +I +G2
E =C +I +G1
G
…so firms
increase output,
and income
rises toward a
new equilibrium.
CHAPTER 8
Y
E1 = Y1
Economic Growth II
Y
E2 = Y 2
slide 80
Solving for Y
Y  C  I  G
equilibrium condition
Y  C  I  G
in changes

C
 G
 MPC  Y  G
Collect terms with Y
on the left side of the
equals sign:
(1  MPC) Y  G
CHAPTER 8
Economic Growth II
because I exogenous
because C = MPC Y
Solve for Y :


1
Y  
  G
 1  MPC 
slide 81
The government purchases multiplier
Definition: the increase in income resulting from a
$1 increase in G.
In this model, the govt
purchases multiplier equals
Y
1

G
1  MPC
Example: If MPC = 0.8, then
Y
1

 5
G
1  0.8
CHAPTER 8
Economic Growth II
An increase in G
causes income to
increase 5 times
as much!
slide 82
Why the multiplier is greater than 1
 Initially, the increase in G causes an equal increase
in Y:
Y = G.
 But Y  C
 further Y
 further C
 further Y
 So the final impact on income is much bigger than
the initial G.
CHAPTER 8
Economic Growth II
slide 83