MACROECONOMICS
cover art ROW 1 (90)
C H A P T E R
© 2008 Worth Publishers, all rights reserved
SIXTH EDITION
PowerPoint® Slides by Ron Cronovich
N. GREGORY MANKIW
Economic Growth I:
Capital Accumulation and Population Growth
7

Chapters 7 and 8 cover one of the most important topics in macroeconomics.  The material in these
chapters is more challenging than average for the book, yet Mankiw explains it especially clearly.
New to the 6^th edition is a brief section at the end of the chapter on alternative perspectives on
population growth.
If you taught with the PowerPoint slides I prepared for the previous edition of this textbook, you
will find that I’ve streamlined the introduction a bit.
If you have not, you will find an introduction here, not appearing in the textbook, that provides
data to motivate the study of economic growth.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
In this chapter, you will learn…
§the closed economy Solow model
§how a country’s standard of living depends on its saving and population growth rates
§how to use the “Golden Rule” to find the optimal saving rate and capital stock

>

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Why growth matters
§Data on infant mortality rates:
§20% in the poorest 1/5 of all countries
§0.4% in the richest 1/5
§In Pakistan, 85% of people live on less than $2/day.
§One-fourth of the poorest countries have had famines during the past 3 decades.
§Poverty is associated with oppression of women and minorities.
§ Economic growth raises living standards and reduces poverty….

>

Income and poverty in the world
selected countries, 2000

This slide shows a negative relationship between income per capita and poverty.
Many economists believe that the causation runs from growth to poverty, i.e. increasing growth will
reduce poverty.
source:  The Elusive Quest for Growth, by William Easterly.  (MIT Press, 2001)
Note:   I have searched far and wide for updated poverty statistics, including the UN and World
Bank’s World Development Indicators.  At the time I write this (July 2007), the poverty rate data I
find are scattered – different years for different countries, and for most countries the latest
available is no more recent than 2000.  If you know of a source for more recent poverty statistics,
I would be most grateful if you could email me at roncron@unlv.nevada.edu.  Thank you!

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Why growth matters
§Anything that effects the long-run rate of economic growth – even by a tiny amount – will have
huge effects on living standards in the long run.
1,081.4%
243.7%
85.4%
624.5%
169.2%
64.0%
2.5%
2.0%
…100 years
…50 years
…25 years
percentage increase in
standard of living after…
annual growth rate of income per capita

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Why growth matters
§If the annual growth rate of U.S. real GDP per capita had been just one-tenth of one percent
higher during the 1990s, the U.S. would have generated an additional $496 billion of income
during that decade.

>

The $496 billion is in 2006 prices.
How I did this calculation:
1.  Computed actual quarterly growth rate of real income per capita from 1989:4 through 1999:4.
2.  Added one-fourth of one-tenth of one percent to each quarter’s actual growth rate.
3.  Computed what real income per capita in would have been with the new growth rates.
4.  Multiplied this hypothetical real income per capita by the population to get hypothetical real
GDP.
5.  Computed the difference between hypothetical and actual real GDP for each quarter.
6.  Cumulated these differences over the period 1990:1-1999:4.
Like the original real GDP data, the cumulative difference was in 1996 dollars.  I multiplied this
amount by 21%, the amount by which the GDP deflator rose between 1996 and 2006, so the final result
is expressed in 2006 dollars.
SOURCE of DATA:   Real GDP, GDP deflator - Dept of Commerce, Bureau of Economic Analysis.
Population -  Dept of Commerce, Census Bureau.
All obtained from “FRED” - the St. Louis Fed’s database, on the web at
http://research.stlouisfed.org/fred2/

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The lessons of growth theory
…can make a positive difference in the lives of hundreds of millions of people.
IND100
§These lessons help us
§understand why poor countries are poor
§design policies that
can help them grow
§learn how our own growth rate is affected by shocks and our government’s policies

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Solow model
§due to Robert Solow,
won Nobel Prize for contributions to
the study of economic growth
§a major paradigm:
§widely used in policy making
§benchmark against which most
recent growth theories are compared
§looks at the determinants of economic growth and the standard of living in the long run

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
How Solow model is different from Chapter 3’s model
§1. K  is no longer fixed:
investment causes it to grow,
depreciation causes it to shrink
§2. L  is no longer fixed:
population growth causes it to grow
§3. the consumption function is simpler

It’s easier for students to learn the Solow model if they see that it’s just an extension of
something they already know, the classical model from Chapter 3.  So, this slide and the next point
out the differences.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
How Solow model is different from Chapter 3’s model
§4. no G or T
(only to simplify presentation;
we can still do fiscal policy experiments)
§5. cosmetic differences

The cosmetic differences include things like the notation (lowercase letters for per-worker
magnitudes instead of uppercase letters for aggregate magnitudes) and the variables that are
measured on the axes of the main graph.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The production function
§In aggregate terms:   Y  =  F (K, L)
§Define:   y = Y/L = output per worker
§ k = K/L = capital per worker
§Assume constant returns to scale:
zY  =  F (zK, zL ) for any z > 0
§Pick z = 1/L.  Then
§Y/L  =  F (K/L, 1)
§  y   =  F (k, 1)
§  y   =    f(k) where f(k) = F(k, 1)

When everything on the slide is showing on the screen, explain to students how to interpret f(k):
   f(k) is the “per worker production function,”  it shows how much output one worker could produce
using k units of capital.
You might want to point out that this is the same production function we worked with in chapter 3.
We’re just expressing it differently.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The production function
Output per
worker, y
Capital per
worker, k
f(k)
Note: this production function exhibits diminishing MPK.
1
MPK = f(k +1) – f(k)

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The national income identity
§Y = C + I  (remember, no G )
§In “per worker” terms:
        y = c + i
where c = C/L  and  i = I /L

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The consumption function
§s = the saving rate,
      the fraction of income that is saved
§            (s  is an exogenous parameter)
§ Note:  s  is the only lowercase variable
that is not equal to
its uppercase version divided by L
§Consumption function:   c = (1–s)y
(per worker)

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Saving and investment
§saving (per worker) =  y   –   c
§ =  y  –  (1–s)y
§ =     sy
§National income identity is  y = c + i
§ Rearrange to get:   i  = y  – c  = sy (investment = saving, like in chap. 3!)
§Using the results above,
 i  =  sy  = sf(k)

The real interest rate r does not appear explicitly in any of the Solow model’s equations.  This is
to simplify the presentation.  You can tell your students that investment still depends on r, which
adjusts behind the scenes to keep investment = saving at all times.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Output, consumption, and investment
Output per
worker, y
Capital per
worker, k
f(k)
sf(k)
k1
y1
i1
c1

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Depreciation
Depreciation per worker, dk
Capital per
worker, k
dk
d = the rate of depreciation
   = the fraction of the capital stock that wears out each period
1
d

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Capital accumulation
Change in capital stock =  investment – depreciation
Dk =        i  –      dk
Since i  =  sf(k) , this becomes:
Dk  =  s f(k)  – dk
§The basic idea:  Investment increases the capital stock, depreciation reduces it.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The equation of motion for k
§The Solow model’s central equation
§Determines behavior of capital over time…
§…which, in turn, determines behavior of
all of the other endogenous variables
because they all depend on k.     E.g.,
§ income per person:  y  =  f(k)
§ consumption per person: c  =  (1–s) f(k)
Dk  =  s f(k)  – dk

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The steady state
§If investment is just enough to cover depreciation
[sf(k)  = dk ],
§then capital per worker will remain constant:
Dk  = 0.
§
§This occurs at one value of k, denoted k*,
called the steady state capital stock.
Dk  =  s f(k)  – dk

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
Dk = sf(k) - dk
depreciation
Dk
k1
investment

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
k1
Dk = sf(k) - dk
Dk

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
k1
Dk = sf(k) - dk
Dk
k2

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
Dk = sf(k) - dk
k2
investment
depreciation
Dk

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
Dk = sf(k) - dk
Dk
k2

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
Dk = sf(k) - dk
k2
Dk
k3

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Moving toward the steady state
Investment and depreciation
Capital per
worker, k
sf(k)
dk
k*
Dk = sf(k) - dk
k3
Summary:
As long as k < k*, investment will exceed depreciation,
and k will continue to grow toward k*.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Now you try:
§Draw the Solow model diagram,
labeling the steady state k*.
§On the horizontal axis, pick a value greater than k*  for the economy’s initial capital stock.
Label it k1.
§Show what happens to k  over time.
Does k  move toward the steady state or
away from it?

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
A numerical example
§Production function (aggregate):
To derive the per-worker production function, divide through by L:
Then substitute y = Y/L  and k = K/L  to get

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
A numerical example, cont.
§Assume:
§s = 0.3
§d = 0.1
§initial value of k = 4.0

>

As each assumption appears on the screen, explain it’s interpretation.
I.e.,
“The economy saves three-tenths of income,”
“every year, 10% of the capital stock wears out,” and
“suppose the economy starts out with four units of capital for every worker.”

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Approaching the steady state:
A numerical example
§Year   k    y    c    i   dk Dk
§   1 4.000 2.000 1.400 0.600 0.400 0.200
§   2 4.200 2.049 1.435 0.615 0.420 0.195
§   3 4.395 2.096 1.467 0.629 0.440 0.189
Eqn1
   4 4.584 2.141 1.499 0.642 0.458 0.184
  …
  10 5.602 2.367 1.657 0.710 0.560 0.150
  …
  25 7.351 2.706 1.894 0.812 0.732 0.080
  …
 100 8.962 2.994 2.096 0.898 0.896 0.002
  …
 ¥ 9.000 3.000 2.100 0.900 0.900 0.000

Before revealing the numbers in the first row, ask your students to determine them and write them
in their notes.  Give them a moment, then reveal the first row and make sure everyone understands
where each number comes from.
Then, ask them to determine the numbers for the second row and write them in their notes.
After the second round of this, it’s probably fine to just show them the rest of the table.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Exercise:  Solve for the steady state
§Continue to assume
s = 0.3,   d = 0.1,  and  y = k 1/2
Use the equation of motion
Dk = s f(k) - dk
to solve for the steady-state values of k, y, and c.

Suggestion:  give your students 3-5 minutes to work on this exercise in pairs.  Working alone, a
few students might not know that they need to start by setting k = 0.  But working in pairs, they
are more likely to figure it out.
Also, this gives students a little psychological momentum to make it easier for them to start on
the end-of-chapter exercises (if you assign them as homework).
(If any need a hint, remind them that the steady state is defined by k = 0.
A further hint is that they answers they get should be the same as the last row of the big table on
the preceding slide, since we are still using all the same parameter values.)

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Solution to exercise:

The first few lines of this slide show the calculations and intermediate steps necessary to arrive
at the correct answers, which are given in the last 2 lines of the slide.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
An increase in the saving rate
Investment
and
depreciation
k
dk
s1 f(k)
An increase in the saving rate raises investment…
…causing k to grow toward a new steady state:
s2 f(k)

Next, we see what the model says about the relationship between a country’s saving rate and its
standard of living (income per capita) in the long run (or steady state).
An earlier slide said that the model’s omission of G and T was only to simplify the presentation.
We can still do policy analysis.  We know from Chapter 3 that changes in  G and/or T affect
national saving.  In the Solow model as presented here, we can simply change the exogenous saving
rate to analyze the impact of fiscal policy changes.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Prediction:
§Higher s   Þ  higher k*.
§And since y = f(k) ,
higher k*  Þ higher y* .
§Thus, the Solow model predicts that countries with higher rates of saving and investment
will have higher levels of capital and income per worker in the long run.

After showing this slide, you might also note that the converse is true, as well:  a fall in s
(caused, for example, by tax cuts or government spending increases) leads ultimately to a lower
standard of living.
In the static model of Chapter 3, we learned that a fiscal expansion crowds out investment.  The
Solow model allows us to see the long-run dynamic effects:  the fiscal expansion, by reducing the
saving rate, reduces investment.  If we were initially in a steady state (in which investment just
covers depreciation), then the fall in investment will cause capital per worker, labor
productivity, and income per capita to fall toward a new, lower steady state.  (If we were
initially below a steady state, then the fiscal expansion causes capital per worker and
productivity to grow more slowly, and reduces their steady-state values.)
This, of course, is relevant because actual U.S. public saving has fallen sharply since 2001.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
International evidence on investment rates and income per person
100
1,000
10,000
100,000
0
5
10
15
20
25
30
35
Investment as percentage of output
(average 1960-2000)
Income per
person in
2000
(log scale)

Figure 7-6, p.197.  Source:  Penn World Table version 6.1.
Number of countries = 97
High investment is associated with high income per person, as the Solow model predicts.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Golden Rule:  Introduction
§Different values of s lead to different steady states.
How do we know which is the “best” steady state?
§The “best” steady state has the highest possible
consumption per person:   c*  =  (1–s) f(k*).
§An increase in s
§leads to higher k* and y*, which raises c*
§reduces consumption’s share of income (1–s),
which lowers c*.
§So, how do we find the s and k* that maximize c*?

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Golden Rule capital stock
§the Golden Rule level of capital,
the steady state value of k
that maximizes consumption.
To find it, first express c* in terms of k*:
c*  =    y*  -  i*
=  f (k*)    -   i*
=  f (k*)    -  dk*
In the steady state: i*  =  dk* because Dk = 0.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Then, graph
f(k*) and dk*,
look for the
point where
the gap between them is biggest.
The Golden Rule capital stock
steady state output and depreciation
steady-state capital per
worker, k*
f(k*)
d k*

Students sometimes confuse this graph with the other Solow model diagram, as the curves look
similar.
Be sure to clarify the differences:
1.On this graph, the horizontal axis measures k*, not k.  Thus, once we have found k* using the
other graph, we plot that k* on this graph to see where the economy’s steady state is in relation
to the golden rule capital stock.
2.On this graph, the curve measures f(k*), not sf(k).
3.On the other diagram, the intersection of the two curves determines k*.  On this graph, the only
thing determined by the intersection of the two curves is the level of capital where c*=0, and we
certainly wouldn’t want to be there.
4.There are no dynamics in this graph, as we are in a steady state.  In the other graph, the gap
between the two curves determines the change in capital.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Golden Rule capital stock
§c* = f(k*) - dk*
is biggest where the slope of the production function
   equals
the slope of the depreciation line:
steady-state capital per
worker, k*
f(k*)
d k*
MPK = d

If your students have had a semester of calculus, you can show them that deriving the condition MPK
=  is straight-forward:
The problem is to find the value of k* that maximizes c^* = f(k^*)  k^*.
Just take the first derivative of that expression and set equal to zero:
    f(k^*)    =  0
where  f(k^*) =  MPK = slope of production function
and    =  slope of steady-state investment line.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The transition to the
Golden Rule steady state
§The economy does NOT have a tendency to move toward the Golden Rule steady state.
§Achieving the Golden Rule requires that policymakers adjust s.
§This adjustment leads to a new steady state with higher consumption.
§But what happens to consumption
during the transition to the Golden Rule?

>

Remember:  policymakers can affect the national saving rate:
   - changing G or T affects national saving
   - holding T constant overall, but changing the structure of the tax system to provide more
incentives for private saving (e.g., a revenue-neutral shift from the income tax to a consumption
tax)

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Starting with too much capital
§
§then increasing c*  requires a fall in s.
§In the transition to the Golden Rule, consumption is higher at all points in time.
time
t0
c
i
y

t[0]  is the time period in which the saving rate is reduced.  It would be helpful if you explained
the behavior of each variable before t[0], at t[0] , and in the transition period (after t[0] ).
Before t[0]:   in a steady state, where k, y, c, and i are all constant.
At t[0]:   The change in the saving rate doesn’t immediately change k, so y doesn’t change
immediately.    But the fall in s causes a fall in investment [because saving equals investment]
and a rise in consumption [because c = (1-s)y, s has fallen but y has not yet changed.].  Note that
c = -i, because y = c + i and y has not changed.
After t[0]:   In the previous steady state, saving and investment were just enough to cover
depreciation.  Then saving and investment were reduced, so depreciation is greater than investment,
which causes k to fall toward a new, lower steady state value.   As k falls and settles on its new,
lower steady state value, so will y, c, and i (because each of them is a function of k).  Even
though c is falling, it doesn’t fall all the way back to its initial value.
Policymakers would be happy to make this change, as it produces higher consumption at all points in
time (relative to what consumption would have been if the saving rate had not been reduced.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Starting with too little capital
§
§then increasing c*  requires an
increase in s.
§Future generations
enjoy higher consumption,
but the current
one experiences
an initial drop
in consumption.
time
t0
c
i
y

Before t[0]:   in a steady state, where k, y, c, and i are all constant.
At t[0]:    The increase in s doesn’t immediately change k, so y doesn’t change immediately.    But
the increase in s causes investment to rise [because higher saving means higher investment] and
consumption to fall [because we are saving more of our income, and consuming less of it].
After t[0]:
Now, saving and investment exceed depreciation, so k starts rising toward a new, higher steady
state value.  The behavior of k causes the same behavior in y, c, and i (qualitatively the same,
that is).
Ultimately, consumption ends up at a higher steady state level.  But initially consumption falls.
Therefore, if policymakers value the current generation’s well-being more than that of future
generations, they might be reluctant to adjust the saving rate to achieve the Golden Rule.
Notice, though, that if they did increase s, an infinite number of future generations would
benefit, which makes the sacrifice of the current generation seem more acceptable.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Population growth
§Assume that the population (and labor force) grow at rate n.    (n  is exogenous.)
§
§EX:  Suppose L = 1,000 in year 1 and the population is growing at 2% per year (n = 0.02).
§Then  DL = n L = 0.02 ´ 1,000 = 20,
so L = 1,020 in year 2.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Break-even investment
§(d  + n)k = break-even investment,
the amount of investment necessary
to keep k constant.
§Break-even investment includes:
§d k  to replace capital as it wears out
§n k  to equip new workers with capital
§ (Otherwise, k would fall as the existing capital stock would be spread more thinly over a larger
population of workers.)

>

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The equation of motion for k
§With population growth,
the equation of motion for k  is
break-even investment
actual investment
Dk = s f(k) - (d   + n) k

Of course, “actual investment” and “break-even investment” here are in “per worker” magnitudes.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Solow model diagram
Investment, break-even investment
Capital per
worker, k
sf(k)
(d + n ) k
k*
Dk = s f(k) - (d +n)k

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The impact of population growth
Investment, break-even investment
Capital per
worker, k
sf(k)
(d +n1) k
k1*
(d +n2) k
k2*
An increase in n causes an increase in break-even investment,
leading to a lower steady-state level of k.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Prediction:
§Higher n   Þ  lower k*.
§And since y = f(k) ,
lower k*  Þ lower y*.
§Thus, the Solow model predicts that countries with higher population growth rates will have lower
levels of capital and income per worker in the long run.

This and the preceding slide establish an implication of the model.
The following slide confronts this implication with data.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
International evidence on population growth and income per person
100
1,000
10,000
100,000
0
1
2
3
4
5
Population Growth
(percent per year; average 1960-2000)
Income
per Person
in 2000
 (log scale)

Figure 7-13, p.210.  Number of countries = 96.  Source:  Penn World Table version 6.1.
The model predicts that faster population growth should be associated with a lower long-run income
per capital  The data is consistent with this prediction.
So far, we’ve now learned two things a poor country can do to raise its standard of living:
increase national saving (perhaps by reducing its budget deficit) and reduce population growth.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
The Golden Rule with population growth
To find the Golden Rule capital stock,
express c* in terms of k*:
c*  =     y*  -     i*
=  f (k* )   -   (d  + n) k*
c* is maximized when
MPK  =  d + n
or equivalently,
MPK - d   =  n
In the Golden
Rule steady state,
the marginal product
of capital net of depreciation equals the population
growth rate.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Alternative perspectives on population growth
§The Malthusian Model (1798)
§Predicts population growth will outstrip the Earth’s ability to produce food, leading to the
impoverishment of humanity.
§Since Malthus, world population has increased sixfold, yet living standards are higher than ever.
§Malthus omitted the effects of technological progress.

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This and the next slide cover new material in the 6^th edition.  They can be omitted without loss
of continuity.

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CHAPTER 7   Economic Growth I
CHAPTER 7   Economic Growth I
Alternative perspectives on population growth
§The Kremerian Model (1993)
§Posits that population growth contributes to economic growth.
§More people = more geniuses, scientists & engineers, so faster technological progress.
§Evidence, from very long historical periods:
§As world pop. growth rate increased, so did rate of growth in living standards
§Historically, regions with larger populations have enjoyed faster growth.

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Michael Kremer, “Population Growth and Technological Change:  One Million B.S. to 1990,” Quarterly
Journal of Economics 108 (August 1993):  681-716.

Chapter Summary
§1. The Solow growth model shows that, in the long run, a country’s standard of living depends
§positively on its saving rate
§negatively on its population growth rate
§2. An increase in the saving rate leads to
§higher output in the long run
§faster growth temporarily
§but not faster steady state growth.
CHAPTER 7   Economic Growth I
slide 54
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Chapter Summary
§3. If the economy has more capital than the Golden Rule level, then reducing saving will increase
consumption at all points in time, making all generations better off.
§ If the economy has less capital than the Golden Rule level, then increasing saving will increase
consumption for future generations, but reduce consumption for the present generation.
CHAPTER 7   Economic Growth I
slide 55
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