Macroeconomics chapter 9

1. Chapter Eight 1
CHAPTER 9
Economic Growth II: Technology,
Empirics and Policy
Daw Chan Myae July
20.6.21

2. Chapter Eight 2
The Solow model does not explain technological progress but,
instead, takes it as given and shows how it interacts with other
variables in the process of economic growth.
Chapter 9

3. Chapter Eight 3
To examine how a nation’s public policies can influence the level
and growth of the citizens’ standard of living, we must ask five
questions.
1) Should our society save more or less?
2) How can policy influence the rate of saving?
3) Are there some types of investment that policy should encourage?
4) What institutions ensure that the economy’s resources are put
to their best use?
5) How can policy increase the rate of technological progress?
The Solow model provides the theoretical framework within which
we consider these issues.
Chapter 9

4. Chapter Eight 4
To incorporate technological progress,
the Production Function is now written as:
Y = F (K, L × E)
The term L × E measures the number of workers.
This takes into account the number of workers L and the efficiency
of each worker, E. It states that total output Y depends on capital K
and workers L × E. The essence of this model is that increases in E
(efficiency) are analogous to increases in L (number of workers). In
other words, a single worker (if twice as productive)
can be thought of as two workers. L × E doubles and the economy
benefits from the increased production of goods and services.
Chapter 9

5. Chapter Eight 5
Capital
per worker,
k
*
The Steady
State
Investment,
s
f
(k
)
(δ + n + g)k
Technological progress causes E to grow at the rate g, and L grows
at rate n so the number of workers L × E is growing at rate n + g.
Now, the change in the capital stock per worker is:
Δk = i –(δ+n +g)k, where i is equal to s f(k).
Note: k = K/LE and y=Y/(L × Ε).
So, y = f(k) is now different.
Also, when the g term is added,
gk is needed to provided capital
to new “effective workers”
created by technological progress.
s
f
(k
)
Chapter 9

6. Chapter Eight 6
Labor-augmenting technological progress at rate g affects the Solow
growth model in much the same way as did population growth at rate
n. Now that k is defined as the amount of capital per effective worker,
increases in the number of effective workers because of technological
progress tend to decrease k. In the steady state, investment sf(k)
exactly offsets the reductions in k because of depreciation, population
growth, and technological progress.
Important…
Chapter 9

7. Chapter Eight 7
Capital per effective worker is constant in the steady state.
Because y = f(k), output per effective worker is also constant. But
the efficiency of each actual worker is growing at rate g. So,
output per worker, (Y/L = y × E) also grows at rate g. Total output
Y = y × (E × L) grows at rate n + g.
Chapter 9

8. Chapter Eight 8
Steady-state consumption is maximized if
MPK = δ + n + g,
rearranging, MPK - δ = n + g.
That is, at the Golden Rule level of capital, the net marginal
product of capital, MPK - δ, equals the rate of growth of total
output, n + g. Because actual economies experience both
population growth and technological progress, we must use this
criterion to evaluate whether they have more or less capital than
they would at the Golden Rule steady state.
The introduction of technological progress also modifies the
criterion for the Golden Rule. The Golden Rule level of capital is
now defined as the steady state that maximizes consumption per
effective worker. So, we can show that steady-state consumption
per effective worker is:
c*= f (k*) - (δ + n + g) k*
Chapter 9

9. Chapter Eight 9
Capital per effective worker k = K/(E × L) 0
Output per effective worker y = Y/ (E × L) = f(k) 0
Output per worker Y/L = y × Ε g
Total output Y = y × (Ε × L) n + g
Chapter 9

10. Chapter Eight 10
So far we have introduced technological progress into the
Solow model to explain sustained growth in standards of living.
Let’s now discuss what happens when theory meets facts.
Chapter 9

11. Chapter Eight 11
According to the Solow model, technological progress causes
the values of many variables to rise together in the steady state
This property is called balanced growth.
In the steady state, output per worker, Y/L, and capital stock per
worker, K/L, both grow at rate g, which is the rate of technological
progress. This is consistent with U.S. data in that g has been
about 2 percent consistently over the past 50 years.
Technological progress also affects factor prices. The real wage
grows at the rate of technological progress, but the real rental
price of capital remains constant over time. Again, over the last
50 years, the real wage has increased by 2 percent and has increased by
about the same as real GDP. Yet, the real rental price of capital (real
capital income divided by the capital stock) has been about the same.
Chapter 9

12. Chapter Eight 12
The property of catch-up is called convergence. If there
is not convergence, countries that start off poor are
likely to remain poor.
The Solow model makes predictions about when
convergence should occur. According to the model,
whether two economies will converge depends on why
they differ in the first place (i.e., savings rates,
population growth rates, and human capital accumulation).
Chapter 9

13. Chapter Eight 13
Differences in income are a result of either:
1) Factors of production such as the quantities of physical and human
capital
2) Efficiency with which economies use their factors of production
Put simply, workers in a poor country either don’t have the tools
and skills, or they are not putting their tools and skills to the best use.
Chapter 9

14. Chapter Eight 14
In terms of the Solow model, the central question is whether
the large gap between the rich and poor is explained by
differences in capital accumulation, or differences in the
production function.
Chapter 9

15. Chapter Eight 15
The savings rate determines the steady-state levels of capital and
output. One particular saving rate produces the Golden Rule steady
state, which maximizes consumption per worker. Let’s use the
Golden Rule to analyze the U.S. saving rate.
Marginal product of capital
net of depreciation
(MPK – δ)
Growth rate of total output
(n + g)
Recall that at the Golden Rule steady state, (MPK – δ) = (n + g)
Chapter 9

16. Chapter Eight 16
Amount of capital in the Golden Rule steady state
If the economy is operating
with less capital than in the
Golden Rule steady state,
then (MPK – δ > n + g)
If the economy is operating
with more capital than in the
Golden Rule steady state,
then (MPK – δ < n + g)
Chapter 9

17. Chapter Eight 17
Marginal product of capital
net of depreciation
(MPK – δ)
Growth rate of total output
(n + g)
To make this comparison for the U.S. economy, we need to estimate
the growth rate of output (n + g) and an estimate of the net marginal
product of capital (MPK – δ). U.S. GDP grows at about 3 percent per
year, so, n + g = 0.03. We can estimate the net marginal product of
capital from the following facts:
Chapter 9

18. Chapter Eight 18
We solve for the rate of depreciation δ by
dividing equation 2 by equation 1:
δk/k = (0.1y)/(2.5y)
δ = 0.04
And we solve for the marginal product of capital (MPK)
by dividing equation 3 by equation 1:
(MPK × k)/k = (0.3y)/(2.5y)
MPK = 0.12
1) The capital stock is about 2.5 times one year’s GDP, or k = 2.5y
2) Depreciation of capital is about 10 percent of GDP, or dk = 0.1y
3) Capital income is about 30 percent of GDP, or MPK × k = 0.3y
Thus, about 4 percent of the capital stock depreciates each year, and
the marginal product of capital is about 12 percent per year. The net
marginal product of capital, MPK – d, is about 8 percent per year.
Chapter 9

19. Chapter Eight 19
We can now see that the returns to capital (MPK – δ = 8 percent per
year) is well in excess of the economy’s growth rate (n + g = 3 percent
per year).
This indicates that the capital stock in the U.S. economy is well
below the Golden Rule-level. In other words, if the United States saved
and invested a higher fraction of its income, it would grow faster and
eventually reach a steady state with higher consumption.
Chapter 9

20. Chapter Eight 20
Public saving is the difference between what the government receives
in tax revenue minus what it spends.
When spending > revenue, it is a budget deficit ☹
When spending < revenue, it is a budget surplus
☺
Private saving is the saving done by households and firms.
Chapter 9

21. Chapter Eight 21
• In 2009, one of President Barack Obama’s
first economic proposals was to increase
spending on public infrastructure such as
new roads, bridges, and transit systems.
• This policy was partly motivated by a desire
to increase short-run aggregate demand and
partly to provide public capital and enhance
long-run economic growth.
Chapter 9

22. Chapter Eight 22
Nations may have different levels of productivity in part because
they have different institutions that govern the allocation of their
scare resources.
For example, a nation’s legal tradition is an institution. Other
examples are the quality of the government itself and the level of
corruption that exists within the political infrastructure.
Chapter 9

23. Chapter Eight 23
The Solow model shows that sustained growth in income per worker
must come from technological progress. The Solow model, however,
takes technological progress as exogenous, and therefore does not
explain it.
Chapter 9

24. Chapter Eight 24
The Endogenous Growth Theory rejects
Solow’s basic assumption of exogenous technological change.
Chapter 9

25. Chapter Eight 25
Start with a simple production function: Y = AK, where Y is output,
K is the capital stock, and A is a constant measuring the amount of
output produced for each unit of capital (noticing this production
function does not have diminishing returns to capital). One extra unit
of capital produces A extra units of output regardless of how much
capital there is. This absence of diminishing returns to capital is
the key difference between this endogenous growth model and the
Solow model.
Let’s describe capital accumulation with an equation similar to those
we’ve been using: ΔK = sY - δK. This equation states that the
change
in the capital stock (ΔK) equals investment (sY) minus depreciation
(δK). We combine this equation with the production function, do
some rearranging, and we get: ΔY/Y = ΔK/K = sA – δ.
Chapter 9

26. Chapter Eight 26
ΔY/Y = ΔK/K = sA -
δ
This equation shows what determines the growth rate of output ΔY/Y.
Notice that as long as sA > δ, the economy’s income grows forever,
even without the assumption of exogenous technological progress.
In the Solow model, saving leads to growth temporarily, but diminishing
returns to capital eventually force the economy to approach a steady
state in which growth depends only on exogenous technological progress.
By contrast, in this endogenous growth model, saving and investment can
lead to persistent growth.
Chapter 9

27. Chapter Eight 27
Creative
Destruction
Schumpeter suggested that the economy’s progress come through
a process a creative destruction. According to Schumpeter, the
driving force behind progress is the entrepreneur with an idea
for a new product, a new way to produce an old product, or
some other innovation.
Chapter 9

28. Chapter Eight 28
• Efficiency of labor
• Labor-augmenting technological progress
• Endogenous growth theory
• Creative Destruction
Chapter 9