Growth and Accumulation
Session 1 & 2: Introduction to Macroeconomic growth and the Cobb
Douglas Production
Reading:
D, F & S Ch. 3: pp. 55-63 (13th ed)
D, F & S Ch. 3: pp.52-61 (12th ed)
Lecture objectives:
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•
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To explain the economic growth imperatives
To introduce the production function as the analytical tool for economic growth
To show how factors of production contribute to output expansion
Economic Growth questions
• Why are there vast differences in
growth rates between countries?
• Why have some developing
countries succeeded in catching up
to developed country income levels
and others not?
• These questions can be answered
by Growth Theory and Growth
Accounting Theory
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Growth accounting…
Explains what part of growth in total output is due to growth in
factors of production - capital, labour etc.
Growth theory…
Describes how economic decisions control the accumulation of
factors of production e.g. higher savings currently may affect future
capital stock
Growth Accounting
Output increases due to:
• Increases in inputs (K, L etc.)
• Increases in productivity - improved technology
• and a more able workforce
Production Function
• Provides a quantitative link between inputs and output e.g. how will increases in
capital stock, the labour force and technology affect output?
• Y = AF(K,N)
Y: output
A: technology
K: capital
N: labour
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• The increase in output generated by labour (marginal product of
labour) and the increase in output generated by capital (marginal
product of capital) are both positive.
• One example of a production function is the Cobb Douglas production
function: 𝑌 = 𝐴𝐾𝜃𝑁(1−𝜃)
• Assume MPK > 0, MPL > 0:
Translate production function into growth rates… (see end of notes for math)
Output Growth = (K Share X K Growth) + (N Share X N Growth) +(Technical
Progress)
•
How is technological progress (Total Factor Productivity) (TFP) measured?
TFP is also known as the Solow Residual- change in production that is not due to changes in factor inputs
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Example 1
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•
•
•
•
Consider the following information in calculating the growth rate in output.
θ=0.3
labour force growth = 2 percent
Growth in capital stock = 3 percent
Total factor productivity = 1.5 percent
• Ans: 3.8%
Note:
• Since labour’s share of income is higher than capital’s share, a 1% increase in labour raises output by more than a
1% increase in capital.
• Important implications for policy e.g. supply-side. In this case, a 6% increase in capital stock does not double output
growth rate.
Example 2
• If we assume a Cobb-Douglas production function, where the share of capital is 0.2 and the share of
labour is 0.8, then the marginal product of labour is equal to (let Y be output, K be capital and N be
labour):
A. 4Y/5N
B. 3Y/4N
C. 3N/4
D. 3K/4N
E. 3N/4Y
Ans: A
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Accounting for growth in per capita output
• Total values may be misleading if population is large:
Standards of living conventionally measured by output per capita.
• Per capita income:
𝑌 = 𝑦𝑁
Accounting for growth in per capita output
• To get this result:
𝑌 = 𝑦𝑁
∆𝑌 = ∆𝑦. 𝑁 + ∆𝑁. 𝑦
• i.e. the growth of Y is accounted for by the growth in y and N put together.
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Accounting for growth in per Capita Output
• Rearranging the equation we get:
• To translate the growth accounting equation into per capita terms, we subtract
population growth
• Similarly, to get the capital-labour ratio:
∆𝑘 ∆𝐾 ∆𝑁
=
−
𝑘
𝐾
𝑁
You should be able to solve this . . .
Solving for growth in per capita output
• Subtracting population growth from both sides of the growth
accounting equation
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Note that:
•
The number of machines per worker, k, is a key determinant of output
produced by a worker, but since θ<1, a 1% increase in capital per worker results
in a less than 1% increase in output per worker
Conclusion
• The important determinants of GDP growth
are technical progress, increased labour supply and capital accumulation.
• The important determinants of growth in GDP per capita
are technical progress and capital accumulation.
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Postwar convergence of the US and Japanese Economies
• Capital accumulation is not the only determinant of growth but very
• important.
• Savings to facilitate capital accumulation?
Empirical Estimates of Growth
Solow…
• Found that over 80% of the growth in output per labour hour in US is due
to technical progress
Important determinants of GDP growth
• Technical progress
• Capital growth
Increased population decreases GDP per capita although increasing GDP
(increased labour force).
Why?
• Diminishing marginal returns
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Factors other than N and K: Human Capital
The production functions shown omit a long list of inputs other than N and K
• While N and K are the most important factors of production, others matter
• Investment in human capital (H) through schooling, on-the-job training, and
health expenditure (consider HIV/AIDS pandemic) is an important determinant of
output in many economies
Adding human capital, H, the production function can be written as:
Y = AF(K, H, N)
• Mankiw, Romer and Weil (1992) suggest that H, K and N all contribute equally to
Y i.e. each contribute 1/3.
• According to D,F&S , approximately 80% of the variations in GDP per capita
between countries can be explained by differences in the growth rates of K, H
and N between countries.
Factors Other Than N and K: Human Capital
• Figure (a) illustrates a positive
relationship between the rate of
investment and per capita output
and income across many selected
nations
• Figure (b) illustrates a similarly
positive relationship between
human capital, using years of
schooling as a proxy for H, and per
capita output and income across
many selected nations
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Appendix: Deriving the growth accounting equation
• It is usually easier to work with growth rates than with levels.
𝑌 = 𝐴𝐹(𝐾𝑁)
Recall: 𝑑𝑌 =
𝑑𝑌
𝑑𝐾
(𝑑𝐾)in 𝑌 = 𝐹(𝐾)
∆𝑌 = 𝑀𝑃𝐾. ∆𝐾 + 𝑀𝑃𝐿. ∆𝑁 + ∆𝐴𝐹(K, N)
Appendix continued…
Let
Let (1-
= total payments to K as a share of all payments
= total payment to N as a share of all payments
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Appendix continued…
•
Output Growth = (K Share X K Growth) + (N Share X N Growth) +(Technical Progress)
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