Chapter 9 – Long-Run Economic Growth
• How do we measure long-run economic growth?
• Sources of long-run economic growth.
• The growth accounting equation.
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• Why growth rates differ among countries?
Comparing Economies Across Time and Space Some observations:
• Real GDP per capita varies across countries.
• Some countries grow faster while some countries grow slower.
• Real GDP per capita growth rate varies across time.
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Real GDP per Capita
• Real GDP per capita is a commonly used measure of long-run economic growth because:
It measures the value of the country’s final products and income.
It ignores the effects of a rising price level on output.
It isolates the effect of changes in population on output.
Growth Rates
• When looking at economic growth, we also look at the growth rate of real GDP per capita because it tells us how fast our income is changing over time.
• Rule of 70 – a simple rule that tells us how many years it takes a variable to
Note: the rule of 70 only applies to a positive growth rate.
Example: Suppose your salary is increasing at a rate of 3.5% per annum. How
long will it take for your salary to double?
# of years for a variable to double = 70
Annual growth rate of variable
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The Sources of Long-Run Growth
• We will look at factors that determine economic growth in the long run.
The Crucial Importance of Productivity
• In this chapter, to measure sustained economic growth, we will use output per worker, i.e., average product of labour (APL).
APL = real GDP # of workers
• In the long run, an increase in APL implies higher productivity.
Explaining Growth in Productivity
Increase in physical capital
• Holding all else constant, an in physical capital allows the economy to
produce more output real GDP APL
Increase in human capital
• Holding all else constant, a more educated and/or experienced work force
makes the workers to become more efficient real GDP APL .
Technological progress
• Holding all else constant, an improvement in production technology allows
the economy to produce more output for the same amount of inputs real GDPAPL .
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Accounting for Growth: The Aggregate and Per Worker Production Functions
• The aggregate production function summarizes the relationship among the
level of output, production technology, and productive inputs.
Y = A × F(K, L, H) + +++
where Y = aggregate real output (real GDP) A = total factor productivity (TFP) K = stock of (physical) capital
L = # of the labour used
H = stock of human capital
• Since the long-run economic growth is measured by output per worker (i.e.,
APL), we will focus on the per-worker production function:
Y = A×F(K, L, H) = A × f (K , H) y = A × f(k, h) = Af(k, h)
where Y = y = (real) output per worker L
K = k = (physical) capital per worker/capital-labour ratio L
H = h = human capital per worker L
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• The per-worker production function will take the following form: y = Akαh(1–α), where 1 > α > 0
The per-worker production function exhibits positive marginal product of physical capital (MPk) and marginal product of human capital (MPh).
MPk (= ∆𝑦)= 𝜕𝑦 ∆𝑘 𝜕𝑘
MPh (= ∆𝑦)= 𝜕𝑦 = ∆h 𝜕h
• By looking at history of economic growth, we observed one crucial fact about
the estimated per-worker production function is that it shows diminishing
marginal product of (physical) capital. 𝜕𝑀𝑃𝑘 =
• We will focus on the relationship between output per worker (y = 𝑌 = APL) 𝐿
and capital per worker (k = 𝐾). 𝐿
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Figure 9-4 – Physical Capital and Productivity
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y = Af(k, h)
Note: slope of y = ∆y = MPk ∆k
Growth Accounting Equation
• In the long run, all productive inputs (capital, labour, and human capital) and total factor productivity are increasing.
• To decompose the sources of economic growth, we use growth accounting. Growth accounting decomposes the sources of output growth into parts
attributable to growth of capital, labour, and total factor productivity.
It can be applied in both aggregate and per-worker production functions.
• The growth accounting equation using the per-worker production function:
∆y = ∆A +α(∆k)+(1−α)(∆h) yAkh
where ∆A = total factor productivity (TFP) growth A
α = capital share of income
(1 – α) = human capital share of income
α (∆k) = contribution of capital k
(1-α) (∆h) = contribution of human capital h
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Why Growth Rates Differ
• Earlier we showed that output growth rates differ across countries. What causes the differences?
• Recall, y = Y·= Af(k, h) any factors that affect A, k and h will affect y. L
Explaining Differences in Growth Rates
Savings and Investment Spending
• Holding all else constant, output when the stock of (physical) capital .
• The funds for investment can come from two sources:
1) Domestic savings – savings done by households and government.
2) Foreign savings – savings that come from foreigners (i.e., borrowing from
• Chapter 10 will examine the relationship between investment and savings.
• Holding all else constant, output when there is an in human capital.
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Research and Development (R&D)
• R&D refers to spending to create and implement new technologies.
• R&D is an important source of TFP growth.
The Role of Government in Promoting Economic Growth
• We will look at how government policies could promote or hinder economic growth.
Government Policies
• Government policies can foster economic growth in 4 different ways:
1) Lower the cost of building infrastructure through the provision of subsidies
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2) Make education less expensive by providing free or subsidized education
3) Lower the cost of undertaking research & development (R&D) by providing subsidies (or tax credit) to R&D
4) Maintain a well-functioning financial system
A healthy and well-functioning financial system helps to channel funds
from savers to borrowers so that those who have profitable investment opportunities will have the funds needed to finance their investment.
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Protection of Property Rights
• Property rights are the rights of owners of valuable items to dispose of those
items as they choose.
• The government needs to protect property rights, especially intellectual
property rights, in order for innovation to flourish.
• The government can solve the problem by granting patents to the inventors.
• In Canada, patents are granted and administered by the Canadian Intellectual
Property Office.
Political Stability and Good Governance
• Political stability provides a stable environment for firms and individuals to
undertake their investment projects and their R&D.
• Good governance is needed so that laws are enforced fairly and consistently
(people know that their properties are protected).
• Political stability and good governance are crucial in fostering long-run
economic growth.
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