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 II:
Technology, Empirics, and Policy
8

Chapter 7 had a single focus:  the in-depth development of the Solow model with population growth.
In contrast, Chapter 8 is a survey of many growth topics.
First, the Solow model is extended to incorporate labor-augmenting technological progress at an
exogenous rate.  This is followed by a discussion of growth empirics, including balanced growth,
convergence, and growth from factor accumulation vs. increases in efficiency.  Next, policy
implications are discussed.  Finally, the chapter presents two very simple endogenous growth
models.
New material has been added in the 6^th edition:  At the end of the “growth empirics” discussion,
there’s a case study on the effects of free trade on economic growth.  At the end of the chapter,
there’s a discussion of Schumpeter’s notion of “creative destruction.”
The models in this chapter are presented very concisely.  If you want your students to master these
models, you will need to have them do exercises and policy experiments with the models.  The
chapter includes some excellent Problems and Applications for this, which you can assign as
homework or use in class to break up your lecture.
If you are pressed for time and are considering skipping this chapter, I encourage you to at least
cover section 8-1, so that your students will have learned the full Solow model with technological
progress. One class period should be enough time to cover it, allowing for one or two in-class
exercises if you wish.   If you can spare a few more minutes, also consider section 8-3:  it
discusses policy implications, it’s not difficult or time-consuming, and students find it very
interesting - it gives additional real-world relevance to the material in Chap 7 and in Section
8-1.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
In this chapter, you will learn…
§how to incorporate technological progress in the Solow model
§about policies to promote growth
§about growth empirics:  confronting the theory with facts
§two simple models in which the rate of technological progress is endogenous

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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).

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Source:  data used to construct Figure 1-1, p.4, and some simple calculations.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Examples of technological progress
§From 1950 to 2000, U.S. farm sector productivity nearly tripled.
§The real price of computer power has fallen an average of 30% per year over the past three
decades.
§Percentage of U.S. households with ≥ 1 computers:
8% in 1984,  62% in 2003
§1981:  213 computers connected to the Internet
2000:  60 million computers connected to the Internet
§2001:  iPod capacity = 5gb, 1000 songs.  Not capable of playing episodes of Grey’s Anatomy.
§ 2006:  iPod capacity = 80gb, 20,000 songs.  Can play episodes of Grey’s Anatomy.

Students are certainly aware that rapid technological progress has occurred.  Yet, it’s fun to show
these figures, to take stock of some specific kinds of technological progress.
Sources:
U.S. Census Bureau
Wikipedia.org
The Economist, various issues
The Elusive Quest for Growth, by William Easterly
The 2001 Statistical Abstract of the United States  at
http://www.census.gov/prod/2002pubs/01statab/stat-ab01.html
USDA:  http://www.ers.usda.gov/Data/AgProductivity/

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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:

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Technological progress in the Solow model
§We now write the production function as:
§where L ´ E  = the number of effective workers.
§Increases in labor efficiency have the
same effect on output as increases in
the labor force.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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)

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If your students have trouble wrapping their heads around quantities in “per effective worker”
terms, tell them not to worry:  it’s not exactly intuitive, it’s merely a mathematical device to
make the model tractable.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Technological progress in the Solow model
§(d + n + g)k  = break-even investment:
the amount of investment necessary
to keep k constant.
§Consists of:
§d 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

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The only thing that’s new here, compared to Chapter 7, is that gk is part of break-even investment.
Remember:  k = K/LE, capital per effective worker.  Tech progress increases the number of effective
workers at rate g, which would cause capital per effective worker to fall at rate g (other things
equal).  Investment equal to gk would prevent this.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Technological progress in the Solow model
Investment, break-even investment
Capital per
worker, k
sf(k)
(d +n +g ) k
k*
Dk = s f(k) - (d +n +g)k

The equation that appears above the graph is the equation of motion modified to allow for
technological progress.
There are minor differences between this and the Solow model graph from Chapter 7:
•Here, k and y are in “per effective worker” units rather than “per worker” units.
•The break-even investment line is a little bit steeper:  at any given value of k, more investment
is needed to keep k from falling - in particular, gk is needed.  Otherwise, technological progress
will cause k = K/LE to fall at rate g (because E in the denominator is growing at rate g).
With this graph, we can do the same policy experiments as in Chapter 7.  We can examine the effects
of a change in the savings or population growth rates, and the analysis would be much the same.
The main difference is that in the steady state, income per worker/capita is growing at rate g
instead of being constant.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Steady-state growth rates in the
Solow model with tech. progress
n + g
Y  = y´E´L
Total output
g
(Y/ L) = y´E
Output per worker
0
y = Y/(L´E )
Output per effective worker
0
k = K/(L´E )
Capital per effective worker
Steady-state growth rate
Symbol
Variable

Table 8-1, p.219.
Explanations:
•k is constant (has zero growth rate) by definition of the steady state
•y is constant because y = f(k) and k is constant
•To see why Y/L grows at rate g,
note that the definition of y implies (Y/L) = yE.
The growth rate of (Y/L) equals the growth rate of y plus that of E.
In the steady state, y is constant while E grows at rate g.
•Y grows at rate g + n.  To see this, note that Y = yEL = (yE)L.  The growth rate of Y equals the
growth rate of (yE) plus that of L.  We just saw that, in the steady state, the growth rate of (yE)
equals g.  And we assume that L grows at rate n.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
The Golden Rule
To find the Golden Rule capital stock,
express c* in terms of k*:
c*  =     y*  -     i*
=  f  (k* )    -   (d  + n + g) k*
c* is maximized when
MPK = d + n + g
or equivalently,
MPK - d = n + g
In the Golden
Rule steady state,
the marginal product of capital net of depreciation equals the
pop. growth rate plus the rate of tech progress.

Remember:  investment in the steady state, i*, equals break-even investment.
If your students are comfortable with basic calculus, have them derive the condition that must be
satisfied to be in the Golden Rule steady state.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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Check out the third paragraph on p.221:  It gives a nice contrast of the Solow model and Marxist
predictions for the behavior of factor prices, comparing both models’ predictions with the data.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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?

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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The two reasons on this slide are both implied by the Solow model.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Average annual growth rates, 1970-89
closed
open
Growth empirics:
Production efficiency and free trade
§Since Adam Smith, economists have argued that free trade can increase production efficiency and
living standards.
§Research by Sachs & Warner:
0.7%
4.5%
developing nations
0.7%
2.3%
developed nations

This slide and the following one present material from a new case study in the 6^th edition, on
pp.223-224.  See note 4 on p.224 for references.
Interpreting the numbers in this table:
Sachs and Warner classify countries as either “open” or “closed.”  Among the developed nations
classified as “open,” the average annual growth rate was 2.3%.  Among developed nations classified
as “closed,” the growth rate was only 0.7% per year.
The average growth rate for “open” developing nations was 4.5%.  The average growth rate for
“closed” developing countries was only 0.7%.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Growth empirics:
Production efficiency and free trade
§To determine causation, Frankel and Romer exploit geographic differences among countries:
§Some nations trade less because they are farther from other nations, or landlocked.
§Such geographical differences are correlated with trade but not with other determinants of income.
§Hence, they can be used to isolate the impact of trade on income.
§Findings:  increasing trade/GDP by 2% causes GDP per capita to rise 1%, other things equal.

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See note 4 on p.224 for references.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues
§Are we saving enough?  Too much?
§What policies might change the saving rate?
§How should we allocate our investment between privately owned physical capital, public
infrastructure, and “human capital”?
§How do a country’s institutions affect production efficiency and capital accumulation?
§What policies might encourage faster technological progress?

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Evaluating the rate of saving
§Use the Golden Rule to determine whether
the U.S. saving rate and capital stock are too high, too low, or about right.
§If (MPK - d ) > (n  + g ),
U.S. is below the Golden Rule steady state
and should increase s.
§If (MPK - d ) < (n  + g ),
U.S. economy is above the Golden Rule steady state and should reduce s.

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This section (this and the next couple of slides) presents a very clever and fairly simple analysis
of the U.S. economy.
When asked, students often have reasonable ideas of how to estimate MPK (e.g., look at stock market
returns), n and g, but very few offer suggestions on how to estimate the depreciation rate:  there
are lots of different kinds of capital out there.  Here, Mankiw presents a simple and elegant way
to estimate the aggregate depreciation rate (which appears a couple of slides below).
First, though, you should make sure your students know why the inequalities in the last two lines
tell us whether our current steady-state is above or below the Golden Rule steady state.
To see this, remember that the steady-state value of capital is inversely related to the steady
state value of MPK.  If we’re above the Golden Rule capital stock, then we have “too much” capital,
so MPK will be smaller than in the Golden Rule steady state.  If we’re below the GR capital stock,
then MPK is higher than in the Golden Rule.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Evaluating the rate of saving
§To estimate (MPK - d ), 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. d 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.

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The three equations appear in the top part of the next slide.   Therefore, if you wish, instead of
showing this slide, you could just explain verbally what appears on this slide when you show the
three equations on the next slide.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Evaluating the rate of saving
§1. k = 2.5 y
§2. d k = 0.1 y
§3. MPK ´ k  = 0.3 y
To determine d , divide 2 by 1:

The actual U.S. economy has tens of thousands of different types of capital goods, all with
different depreciation rates.  Estimating the aggregate depreciation rate therefore might seem
incomprehensibly complicated.
But on this slide, we see Mankiw’s simple, clever, and elegant method of estimating the aggregate
depreciation rate.
Pretty neat!

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Evaluating the rate of saving
To determine MPK, divide 3 by 1:
Hence, MPK - d   =  0.12 - 0.04  =  0.08
§1. k = 2.5 y
§2. d k = 0.1 y
§3. MPK ´ k  = 0.3 y

Similarly, the method of estimating the aggregate MPK shown on this slide is far simpler and more
elegant than somehow measuring and aggregating the returns on all different kinds of capital.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Evaluating the rate of saving
§From the last slide:  MPK - d  = 0.08
§U.S. real GDP grows an average of 3% per year,
so  n + g  = 0.03
§Thus,
MPK - d  = 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.

When the second bullet point displays on the screen, it might be helpful to remind students that,
in the Solow model’s steady state, total output grows at rate n + g.   Thus, we can estimate n + g
for the U.S. simply by using the long-run average growth rate of real GDP.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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If you have time available in class, you might consider asking students to brainstorm a list of
policies or actions the government could take to increase the national saving rate.
If you’ve been reading these annotations in the “notes” area of these slides, you’ve seen my
suggestions on generating classroom discussion, and hopefully have tried them. If you haven’t, now
would be a great time to try, and it’s easy:
Get students into pairs (they need not change seats – students sitting together can work
together).  Ask them to take out a sheet of paper, and give them 3-4 minutes to see if they can
come up with 3 different policies to increase saving.  After the 3-4 minutes are up, ask for
volunteers.  Write down their responses on the board, and then compare the list that the class came
up with to those appearing on this slide.
Having students work in pairs BEFORE discussing in class takes class-time, but yields many
benefits.
•All students become involved (while they are working in pairs), as opposed to only a few being
involved if you immediately ask for responses w/o giving them time to think first.
•Many students don’t have the confidence to volunteer a response when their instructor asks for
responses immediately after posing the question.  However, if these students are given a few
moments to think of possible answers, and if they have the chance to run it by a classmate first,
then they will be FAR more likely to volunteer their responses.
•This leads to a higher quantity and quality of class participation.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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?

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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Before showing the next slide, ask your students which of the two views is closest to their own.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Possible problems with
industrial policy
§The govt may not have the ability to “pick winners” (choose industries with the highest return to
capital or biggest externalities).
§Politics (e.g., campaign contributions) rather than economics may influence which industries get
preferential treatment.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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This slide corresponds to new material for the 6^th edition of the textbook – see p. 229.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Policy issues:
Encouraging tech. progress
§Patent laws:
encourage innovation by granting temporary monopolies to inventors of new products.
§Tax incentives for R&D
§Grants to fund basic research at universities
§Industrial policy:
encourages specific industries that are key for rapid tech. progress
(subject to the preceding concerns).

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
CASE STUDY:
The productivity slowdown
1.5
1.8
2.6
2.3
2.0
1.6
1.8
2.2
2.4
8.2
4.9
5.7
4.3
2.9
1972-95
1948-72
 U.S.
 U.K.
 Japan
 Italy
 Germany
 France
 Canada
Growth in output per person
(percent per year)

(Part of) Table 8-2 on p.231.
“Germany” in this table means W. Germany

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Possible explanations for the productivity slowdown
§Measurement problems:
Productivity increases not fully measured.
§But:  Why would measurement problems
be worse after 1972 than before?
§Oil prices:
Oil shocks occurred about when productivity slowdown began.
§But:  Then why didn’t productivity speed up when oil prices fell in the mid-1980s?

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Possible explanations for the productivity slowdown
§Worker quality:
1970s - large influx of new entrants into labor force (baby boomers, women).
New workers tend to be less productive than experienced workers.
§The depletion of ideas:
Perhaps the slow growth of 1972-1995 is normal, and the rapid growth during 1948-1972 is the
anomaly.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Which of these suspects is the culprit?
§All of them are plausible,
but it’s difficult to prove
that any one of them is guilty.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
CASE STUDY:
I.T. and the “New Economy”
2.2
2.5
1.2
1.5
1.2
1.7
2.4
1.5
1.8
2.6
2.3
2.0
1.6
1.8
2.2
2.4
8.2
4.9
5.7
4.3
2.9
1995-2004
1972-95
1948-72
 U.S.
 U.K.
 Japan
 Italy
 Germany
 France
 Canada
Growth in output per person
(percent per year)

Table 8-2 on p.231
Prior to 1995, “Germany” here refers to W. Germany.
During the late 1990s into 2000, there was much talk in the business world of a “new economy” in
which rapid productivity growth and high technology somehow nullified the standard rules and
principles of economics (e.g., diminishing returns).

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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?

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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In the Solow model, the long-run economic growth rate equals the rate of technological progress,
which is exogenous in the model.  Hence, the Solow model is basically saying “all I can tell you is
that growth in living standards depends on technological progress.  I have no idea what drives
technological progress.”
Endogenous growth theory tries to explain the behavior of the rates of technological progress
and/or productivity growth, rather than merely taking these rates as given.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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: d K
§Equation of motion for total capital: K  = s Y - d K

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This is an extremely simple model, yet has a powerful implication (to be developed below).

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
A basic model
§ K  = s Y - d K
§If s A > d,  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.
§Divide through by K  and use Y  = A K  to get:

Y and K grow at the same rate because A is constant.
Discussion:
The return to capital is the incentive to invest.  If capital exhibits diminishing returns, then
the incentive to invest decreases as the economy grows.  Hence, investment cannot be a source of
sustained growth.
However, in this model, MPK does not fall as K rises, so the incentive to invest never declines,
people will always find it worthwhile to save and invest over and above depreciation, so investment
becomes an engine of growth.
The $64,000 question:
Does capital exhibit diminishing or constant marginal returns?  The answer is critical, for it
determines whether investment explains sustained (i.e. steady-state) growth in productivity and
living standards.  See the next slide for discussion.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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  - d K

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Before presenting this model, it might be helpful to tell students that it is an extension of
something they already know - the Solow model with tech progress.  There are two differences:
•First, a fraction of the labor force does not produce goods & services, but rather produces
“knowledge” by doing research in universities.
•Second, the rate of tech progress is not exogenous, but rather depends on how fast the stock of
knowledge grows, which in turn depends on how much labor the economy has allocated to research.
If you have a few minutes of class time after presenting the model, you should consider having your
students work problem #6 on p.243.  Otherwise, assign it as a homework exercise.
In regards to the specific elements of the model,
•Manufacturing production function:  Just like in the Solow model with exogenous technological
progress, output of manufactures depends on capital and the effective labor force employed in the
mfg sector, (1-u)EL.
•Research production function:   The “output” is increases in knowledge and
labor efficiency.  The “inputs” are labor and current knowledge.  The function g() shows how
changes in the amount of labor devoted to research affect the creation of new knowledge.  All we
need is for g( ) to be an increasing function.  It does not matter whether a doubling of scientists
causes the creation of knowledge to double, more than double, or less than double.
•Capital accumulation:  Same as in the previous model -- net investment equals gross investment
(sY) minus depreciation.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
A two-sector model
§In the steady state, mfg output per worker and the standard of living grow at rate
DE/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?

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In this model, the steady state growth rate of the standard of living equals the growth rate of
labor efficiency, just like in the Solow model with tech progress, covered at the beginning of this
chapter.  The difference here is that the rate of tech progress, g, is not exogenous: it depends on
how much labor the economy has allocated to research.
Answer to the question posed on the bottom of this slide:
No.  On one hand, higher u means faster growth.  On the other hand, higher u means less labor is
devoted to the production of goods & services.
If we increase u, output of goods & services per capita will fall in the near term.  But, with
faster growth, output per capita will eventually be higher than it would have.  Of course, if we
increase u to its maximum possible value, 1, then no goods and services would be produced, and
you’d have a bunch of starving geniuses.  Which would be kind of odd, if you think about it.
This tradeoff suggests that there must be some kind of “golden rule” for u,
a value of u that maximizes well-being per capita in the steady state.
Well, I’m clearly babbling now.  Perhaps I should let you get back to your class preparations.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
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.

R&D = research and development
An excellent quote on p.238 is relevant to fact #3:
Isaac Newton once said “If I have seen farther than others, it is because I was standing on the
shoulders of giants.”

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Is the private sector doing enough R&D?
§The existence of positive externalities in the creation of knowledge suggests that the private
sector is not doing enough R&D.
§But, there is much duplication of R&D effort among competing firms.
§Estimates:
Social return to R&D ≥ 40% per year.
§Thus, many believe govt should encourage R&D.

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CHAPTER 8   Economic Growth II
CHAPTER 8   Economic Growth II
Economic growth as “creative destruction”
§Schumpeter (1942) coined term “creative destruction” to describe displacements resulting from
technological progress:
§the introduction of a new product is good for consumers, but often bad for incumbent producers,
who may be forced out of the market.
§Examples:
§Luddites (1811-12) destroyed machines that displaced skilled knitting workers in England.
§Walmart displaces many “mom and pop” stores.

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This slide contains material from a new case study (new to the 6^th edition) on p.239-40.  The text
provides a nice, brief summary of the story of the Luddites.

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 46
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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
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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 48
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