Transcript PPT chapter 12 - McGraw Hill Higher Education

Chapter 12
Saving, capital
formation and
comparative economic
growth
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Learning objectives
1. Based on the national income accounting identity, what is the
relationship between investment and national saving?
2. How can a production function be written in per capita terms?
3. What does the graph of a per capita production function
look like?
4. What is a saving function?
5. What is the economy’s steady state?
6. In what sense do countries converge?
7. According to the Solow-Swan model, what is the economy’s
long-run rate of growth?
8. What role does total factor productivity play in promoting longrun growth?
9. What is the Solow paradox?
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Chapter organisation
12.1
Saving, investment and economic growth
12.2
The Solow-Swan model of economic growth
Summary
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Saving, investment and capital
• Many factors affect economic growth, though capital
formation is a factor that plays a key role.
– Consequently, saving and investment play an important role
in economic growth.
– There is a positive relationship between the long-run level of
GDP per capita and the investment rate, which is i as a
percentage of GDP; although this breaks down for very poor
countries.
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Saving, investment and the income
accounting identity
• Both saving and investment are resources held back
from current income and are used to generate future
benefits, i.e. s and i are closely linked.
• Assume a closed economy whose income is
given by:
y=c+i+g
• This income can be spent on current consumption,
saved and used to pay taxes:
y=c+s+t
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Saving, investment and the income
accounting identity (cont.)
• Therefore, c + s + t = c + g + i, so
s + (t – g) = i
• The LHS of this is national saving. Therefore, we can
see a fundamental link between an economy’s saving
and its level of investment.
• An open economy can draw on international
borrowing and lending and we will look at this
complication later.
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Chapter organisation
12.1
Saving, investment and economic growth
12.2
The Solow-Swan model of economic growth
Summary
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The Solow-Swan growth model
• This model, also referred to as the ‘neo-classical
growth model’, predicts a positive relationship
between the level of saving and investment and the
long-run level of per capita GDP.
• Suppose the production function is given by:
y = Af(k,l)
• We start with the production function we saw last
chapter: y = Af(k,l),where y = amount of real output, A
= an index of secondary factors available to the firm,
k = the capital stock, l = amount of labour.
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The production function again
• We are interested in the amount of capital available
per worker and its implications for the level of per
capita GDP.
• We therefore rewrite this function in ‘per worker’
terms by dividing both sides by l where l = the labour
force. We start with a standard production function:
y = Af(k, l) = (Af
k l
k
, ) = Af ( , 1 )
l l
l
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The production function again (cont.)
• We can rewrite the previous expression with lowercase letters denoting per capita terms:
y
k
= Af ( )
l
l
• The level of per capita GDP therefore depends on the
level of total factor productivity and the amount of
capital relative to the size of the labour force.
• This means that the higher the capital stock relative
to the labour force, the higher the per capita GDP.
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Diminishing returns to the
capital– labour ratio
• We still assume diminishing marginal productivity.
This means the higher the existing capital–labour
ratio (k), the smaller is the increase in GDP per
worker (y) when there is an increase in k.
•
Note that, due to the circular flow of income, per
capita GDP is equivalent to per capita income.
• Therefore our production function can be regarded as
showing the level of per capita income earned in the
economy at each level of the capital–labour ratio.
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Diminishing return to the
capital–labour ratio (cont.)
Figure 12.1 The diminishing marginal productivity of the capital–labour ratio
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Are there limits to growth?
•
Given that the increase in the capital stock leads to
progressively smaller increases in output, will growth
stop at some level of capital?
–
•
This is also known as the steady state.
Yes, because there are actually two types of
investment:
1. Replacement investment
2. Net investment
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Total investment
•
Total investment equals replacement investment
plus net investment. We write this as follows:
i
l
•
=
ri ni
+
l
l
Since only net investment actually changes the
capital–labour ratio, we can write the above
equation as:
i
l
=
ri
k
+( )
l
l
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Replacement investment
• Before there can be net investment, investment must
be sufficient to meet the replacement investment
because:
1. new workers have to be equipped with enough capital that
the capital–worker ratio does not fall
2. a fraction of the capital stock which wears out (depreciates)
each year must be replaced.
• When these two claims are just met, the stock of
capital per worker, k, remains constant.
–
Net investment is said to be zero and output per worker, y,
remains constant.
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Replacement investment (cont.)
• Assume the stock depreciates at a rate of depreciation
d = 5% = 0.05, and the population n is increasing by 2%
per annum (0.02). Therefore, the year’s capital stock
would have to increase by 7% per annum just to satisfy
the economy’s need for replacement. In symbols, this
can be written as follows:
ri
l
k
= (d + n)
l
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Net investment
• When investment exceeds the replacement
investment, k can increase: net investment is positive
and y rises.
• When replacement investment exceeds investment, k
can decrease: net investment is negative and y falls.
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Saving and investment
• As we have seen previously, saving finances
investment.
• Let us assume the saving in the economy occurs at a
constant fraction of the economy’s income = θ. Then
we know that:
i
= θ
y
l
l
due to the equality between national saving and
investment.
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Saving and investment (cont.)
• Therefore, combining the equations from slides
12.14, 12.16 and 12.18, we get the following relation
between investment (saving), replacement
investment and net investment:
y
k
k
θ ( ) = (d + n)
+( )
l
l
l
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Saving and investment (cont.)
• This means that the amount of investment in the
economy—which is equivalent to savings—can be
divided between the amounts of replacement and net
investment.
• We can re-arrange this equation:
k
y
k
 ( ) = θ ( ) – (d + n) ( )
l
l
l
This states that the capital–labour ratio in the economy
will grow (that is, (k/l) be a positive number) only if
the total savings in the economy, θ(y/l) exceeds the
replacement investment.
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Requirements for growth
• And further, the economy will stop growing—that is,
reach steady state—when all investment is
replacement investment, i.e. when (k/l) = 0.
– Growth continues when the capital–labour ratio increases:
when θ(y/l) > (d + n)(k/l)
– Growth ceases whenever the capital–labour ratio is equal to
or less than replacement: when θ(y/l) ≤ (d + n)(k/l)
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A diagrammatic treatment
• We can draw our production function on a graph, with
the capital–labour ratio on the x-axis and the GDP
per capita data on the y-axis. GDP per capita is
equivalent to income per capita.
• The Solow-Swan model assumes that saving is a
constant proportion of income, and we can draw the
savings function at each capital–labour ratio value
below it.
• Further, we can draw the replacement investment
line, which is a straight line with the slope (d + n).
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Production and saving functions
Figure 12.2 Production and saving functions
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Production, saving and replacement
investment functions
Figure 12.3 Production, saving and replacement investment functions
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Tendency towards steady state
Figure 12.4 Will the economy be at its steady state?
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Implications of the steady state
• All else being equal, the Solow-Swan model
predicts an end to growth as countries reach
their steady-state.
• A second implication is that poor countries will
grow at a faster rate than rich countries, as long as
both countries have the same long-run steady
state. This is the convergence hypothesis.
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Background to convergence
Figure12.5 Background to convergence
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Evidence of convergence
• How would we investigate whether there has been
convergence, as the Solow-Swan model predicts?
• We could select a base year and measure per capita
income for a cross-section of countries for that year.
Then calculate the average annual growth rates
in per capita income for all the years since the
base year.
• If the convergence hypothesis is correct we should
see a trend line with a negative slope.
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Stylised representation of convergence
Figure 12.7 Stylised representation of convergence
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Convergence in high-income OECD
Countries 1970–2007
Figure 12.8 Convergence in high-income OECD Countries 1970–2007
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Convergence for the world?
Figure 12.9 Convergence for the world?
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Convergence in the world’s open
economies
Figure 12.10 Convergence in the world’s open economies
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The Solow-Swan model and
convergence
• Therefore, our investigations show us that
convergence is present in the data, but only if we
restrict the analysis to broadly economically similar
countries.
• We should not expect convergence across the
complete spectrum of the world’s countries.
• Therefore, we talk of conditional convergence. For
countries that are similar, convergence is a definite
possibility.
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Long-run economic growth: The case
of the UK
Figure 12.11 The United Kingdom economy in the long run
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Technological change in the SolowSwan model
Figure 12.12 Technological change in the Solow-Swan model
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The Solow paradox
• The Solow paradox refers to the fact that relative to
the magnitude of the investment in information,
technology and communications (ITC) the
productivity gains seemed modest. Why?
1. It takes time for the productivity effects of new inventions to
become apparent.
2. Once depreciation is taken account of, ITC equipment is
actually a relatively small part of the total capital stock.
3. The productivity gains from ITC may well be illusory.
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Chapter organisation
12.1
Saving, investment and economic growth
12.2
The Solow-Swan model of economic growth
Summary
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Summary
• The Solow-Swan model is based on a production
function expressed in per capita terms, so that the
level of per capita output (or income) depends on
total factor productivity and the ratio of capital to
labour.
• The Solow-Swan model predicts that there will be no
further growth in per capita income once the
economy has reached its steady state.
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Summary (cont.)
• The law of diminishing marginal productivity of capital
means that countries with relatively low per capita
capital stocks will grow at a faster rate than countries
with high per capita capital stock.
• Countries with similar characteristics tend to
converge to the same steady-state capital–
labour ratio.
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