# Sources of Economic Growth in the United States

ECONOMIC GROWTH
& THE SOLOW GROWTH MODEL
CHAPTER 6
GOALS OF CHAPTER 6
Answer the following questions:
ï‚¡ What factors effect Economic Growth?
ï‚¡ Does the standard of living necessary rise over time?
ï‚¡ What policy can be used to alter economic growth?
ï‚¡ Do all countries converge or diverge in terms of economic
growth? Why?
We develop a growth model to answer these questions.
Table 6.3 Sources of Economic Growth in the United States (Percent per
Year) â€“ productivity slowdown
Productivity Slowdown
MOTIVATION
Labor Productivity (Y/N) Growth:
mid 70â€™s to mid 90â€™s: 1.5%
mid 97 to end 2003: 3.6%
2004 to 2015: 1.6%
ACROSS COUNTRY COMPARISONS OF GDP/N
As you look at the WORLD DATA at the link below, keep in mind:
ï‚¡ The higher the GDP per person, the higher the consumption per
person, and hence the higher the standard of living
ï‚¡ Economies that are growing over time, typically see their standard of living rise.
ï‚¡ Countries with high income per capita (like US, Canada, and other western
economies), continue to have rising income per capita over time & hence rising
standards of living.
LINK: Growth in Standard of Living across the World
SOLOW GROWTH MODEL
PART I
THE SOLOW GROWTH MODEL
ï‚¡ Basic questions about growth
ï‚¡ Whatâ€™s the relationship between the long-run standard of
living and the saving rate, rate of technical progress,
and population growth rate?
ï‚¡ How does economic growth change over time? Will it
speed up, slow down, or stabilize?
THE SOLOW GROWTH MODEL â€“ SET UP
ï‚¡ Basic assumptions and variables
ï‚¡ Economy is closed and G = 0
Ct
= Yt
â€“ I
t
(6.4)
This is because Yt=Ct +It
;
It is also the case that St = It over time
ï‚¡ Population and work force grow at same rate = n
ï‚¡ Rewrite all variables in per-worker terms:
y
t = Yt
/Nt
; c
t = Ct
/Nt
; kt = Kt
/Nt
c
t measures standard of living â€“ ct
is consumption per worker
ï‚¡ kt
is the capital-labor ratio
THE SOLOW GROWTH MODEL â€“ SET UP
ï‚¡ The per-worker production function
y
t = f(kt
) (6.5)
Same shape as
aggregate
production
function in ch.3!
NOTE: Assume no productivity growth for now (to be discussed later)
THE SOLOW GROWTH MODEL â€“ SET UP
ï‚¡ STEADY STATE (definition)
ï‚¡ Steady state: y, c, and k are constant over time
ïƒž BUT Yt
, Ct
, and Kt grow over time!!!
ï‚¡ Gross investment AT STEADY STATE (ss) is given by:
I
t = (n + d)Kt
(6.6)
ï‚¡ Replace worn out capital, dKt
ï‚¡ Expand so the capital stock grows as the population grows, nKt
ïƒž these two ensure that kt
remains constant over time
NOTE: steady state investment is not always equal to actual investment in
the economy!
INVESTMENT PER WORKER AT STEADY STATE
ï‚¡ Since I
t = (n + d)Kt
per worker steady state investment = (n + d)k
ï‚¡ PLOT:
(n + d)k
capital-labor ratio = k
state
investment
per
worker
(n+d)k
CONSUMPTION AT STEADY STATE
ï‚¡ Use the Yt=Ct +It
and the definition of ss I (6.6) to get:
Ct = Yt
â€“ I
t
Ct = Yt
â€“ (n + d)Kt
(6.7)
ï‚¡ Hence, steady state per-capita consumption:
c = f(k) – (n + d)k at steady state (6.8)
ï‚¡ Plot of c, f(k), and (n + d)k (Fig. 6.4)
FIGURE 6.4 THE RELATIONSHIP OF
CONSUMPTION PER WORKER TO THE CAPITALâ€“
LABOR RATIO
DISCUSSION FIGURE 6.4
ï‚¡ Difference between the production
function and the (n+d)k line is â€œcâ€
ï‚¡ Increasing k will increase c up to a
point
ï‚¡ kG
is the level of k that maximizes c:
ï‚¡ it is called â€œthe Golden Rule
capital-labor ratioâ€
ï‚¡ For k beyond this point, c will decline
ï‚¡ To simplify, we assume henceforth that
k is less than kG
ï‚¡ Hence c always rises as k rises
f(k)=(n+d)k
c=0!!!!
THE SOLOW GROWTH MODEL â€“ HOW DOES
THE ECONOMY GET TO SS?
ï‚¡ REACHING the steady state
ï‚¡ Suppose saving is proportional to current income:
St = sYt
, (6.9)
where s is the saving rate, which is between 0 and 1
Recall: savings always equals investment. However, it
may not always equal ss level of investment!
ï‚¡ Equating saving to ss investment gives
sYt = (n + d)Kt
(6.10)
THE SOLOW GROWTH MODEL â€“ STEADY STATE
ï‚¡ Putting this in per-worker terms gives
sf(k) = (n + d)k – this must hold in steady state
ï‚¡ Plot:
THE SOLOW GROWTH MODEL â€“ STEADY STATE
ï‚¡ The only possible steady-state capital-labor ratio is k*
ï‚¡ Hence at steady state, output at that point is y* = f(k*);
ï‚¡ consumption is c* = f(k*) â€“ (n + d)k*
ï‚¡ If k begins at some level other than k*, it will move toward
k*
ï‚¡ For k below k*, saving > the amount of investment needed to keep k
constant, so k rises
ï‚¡ For k above k*, saving < the amount of investment needed to keep k
constant, so k falls
CONCLUSION: SOLOW GROWTH MODEL
With no productivity growth (i.e. unless there is productivity
growth), the economy reaches a steady state, with constant
capital-labor ratio, constant output per worker, and
constant consumption per worker
SOURCES OF GROWTH IN THE MODEL
ï‚¡ The fundamental determinants of long-run living
standards according to the Solow Growth Model are:
ï‚¡ The saving rate
ï‚¡ Productivity growth
ï‚¡ Population growth
THE SOLOW GROWTH MODEL
1. The saving rate
Higher saving rate
means higher capitallabor ratio, higher
output per worker, and
higher consumption
per worker
THE SOLOW GROWTH MODEL
2. Productivity growth
ï‚¡ The key factor in economic growth is productivity improvement
ï‚¡ Productivity improvement raises output per worker for a given level of the
capital-labor ratio – since savings depends on y, more is saved!
FIGURE 6.9 THE EFFECT OF A PRODUCTIVITY
IMPROVEMENT ON THE STEADY-STATE CAPITALâ€“
LABOR RATIO
Higher productivity means higher capital-labor ratio, higher output per
worker, and higher consumption per worker
The increase in
output per
worker
increases the
supply of saving,
causing the
long-run
capital-labor
ratio to rise
THE SOLOW MODEL
3. Population growth
Higher population growth means a lower capital-labor ratio, lower output per
worker, and lower consumption per worker
SOLOW GROWTH MODEL
PART II
POLICY IN THE SOLOW GROWTH MODEL
Should a policy goal be to raise the saving rate?
ï‚¡ Not necessarily, since the cost is lower consumption in the short
run
ï‚¡ If the private market is efficient, the government shouldnâ€™t try to
change the saving rate
ï‚¡ The private marketâ€™s saving rate represents its trade-off of
present for future consumption
ï‚¡ But if tax laws or myopia cause an inefficiently low level of
saving, government policy to raise the saving rate may be
justified
ï‚¡ One way is to raise the real interest rate to encourage saving;
but the response of saving to changes in the real interest rate
seems to be small
GOVERNMENT POLICIES TO RAISE LONG-RUN
LIVING STANDARDS
Policies to raise the rate of productivity growth
ï‚¡ Improving infrastructure
ï‚¡ Infrastructure examples: highways, bridges, utilities, dams, airports
ï‚¡ Empirical studies suggest a link between infrastructure and
productivity
ï‚¡ There might be reverse causation: Richer countries with higher
productivity spend more on infrastructure, rather than vice versa
ï‚¡ U.S. infrastructure spending has declined in the last two decades
ï‚¡ Would increased infrastructure spending increase productivity?
ï‚¡ Infrastructure investments by government may be inefficient, since
politics, not economic efficiency, is often the main determinant
GOVERNMENT POLICIES TO RAISE LONG-RUN
LIVING STANDARDS
Policies to raise the rate of productivity growth
ï‚¡ Building human capital
ï‚¡ Thereâ€™s a strong connection between productivity and human capital
ï‚¡ Government can encourage human capital formation through educational
policies, worker training and relocation programs, and health programs
ï‚¡ Another form of human capital is entrepreneurial skill
ï‚¡ Government could help by removing barriers like red tape
ï‚¡ Encouraging research and development
ï‚¡ Government can encourage R and D through direct aid to research
THE SOLOW MODEL
ï‚¡ Population growth
ï‚¡ Should a policy goal be to reduce population growth?
ï‚¡ Doing so will raise consumption per worker
ï‚¡ But it will reduce total output and consumption, affecting a nationâ€™s
ability to defend itself or influence world events
ï‚¡ The Solow model assumes that the proportion of the population
of working age is fixed
ï‚¡ But when population growth changes dramatically this may not be true
ï‚¡ Changes in cohort sizes may cause problems for social security
systems and areas like health care
THE SOLOW MODEL
Last question:
ï‚¡ Can consumption per worker grow indefinitely?
ï‚¡ The saving rate canâ€™t rise forever (it peaks at 100%) and the population
growth rate canâ€™t fall forever
ï‚¡ But productivity and innovation can always occur, so living standards
can rise continuously
ï‚¡ Summary: The rate of productivity improvement is
the dominant factor determining how quickly living
standards rise

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# Sources of economic growth in the United States

1. According to Table 6.3, the sources of economic growth in the United States (i.e. in the data) are the growth of inputs (labor and capital) and TFP growth. Between 1929 and 2008, what was the growth of output, labor, capital, and TFP in the US?

2. How does the US compare to other counties in the world in terms of income per person? See the LINK provided in slides (go to https://knoema.com/atlas/maps/GDP-per-capita). What are some of the countries that rank higher? (give 2 to 3 examples)

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3. Solow Growth model: SET UP:

a) How is the steady state defined? Refer to the per capital variables as well as to the aggregate variables.

b) How is investment per capital at steady state defined? How is this interpreted intuitively? I.e. discuss the equation.

c) We know that when the economy is at steady state the savings per worker equals the breakeven investment per worker. Express this as an equation (i.e. write down the equation that holds when the economy is at steady state – use per worker terms, not aggregate terms).

4. What is the golden level of capital per worker? Explain (no graph needed).

5. In the Solow Growth Model what are the 3 factors (sources) that determine economic growth and the standard of living of a country? Just list.

6. Solow Growth model: GRAPH of Steady State

a) Illustrate the steady state level of capital-labor ration on the diagram. LABEL ALL CURVES AND AXES.

b) Suppose the economy is not at steady state yet, and instead it is currently at �̃ which is below k*. Illustrate �̃ on the diagram above. In this case, is savings per worker higher than breakeven investment per worker or lower or are they equal?

c) Continue with b): Since �̃ is below k* the economy continues to move towards steady state (towards k*). Can you provide the economic reasoning for why/how the economy moves from �̃ to k*?

7. Numerical Example: Solow Growth model. Suppose that output per worker is given by y=10k0.5, n=0.02, d=0.08, and consumers save 10% of their income.

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