Chp6: Long-Run Economic Growth
Focus:

Determinants of Long Run Growth Rate and
Standard of Living

Growth Accounting

Neo-Classical Growth Model

Endogenous Growth Model
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Growth Accounting



Growth Accounting: Decomposition of growth in
output in terms of its sources.
Growth Accounting Equation relates output growth
to growths in inputs including technical change.
If Y = AF(K,N), then growth accounting equation
is given by
(∆Y/Y) = (∆A/A) +ά_K (∆K/K) + ά_N (∆N/N)
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


ά_K = the Elasticity of Production Function with
respect to Capital (K)
ά_N = the Elasticity of Production Function with
respect to Labor (N)
Alternatively, we have
(∆A/A) = (∆Y/Y) - ά_K (∆K/K) - ά_N (∆N/N)
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Neo-Classical (Solow) Growth Model

The model relates long run per-capita consumption
and growth rate in output to saving rate,
population growth rate, and technical progress.
Assumptions:
1)
2)
3)
4)
Constant returns to scale
Diminishing Marginal Productivity of Capital
Rate of saving (s) , population growth rate (n),
depreciation rate (d) are fixed.
No technical progress (Temporary Assumption)
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Some Notations: Upper case letters denote aggregate
variables and the lower case letters denote
corresponding per-worker variables.
y=(Y/N)= (AF(K,N)/N); k = (K/N); c = (C/N) etc.
Constant Returns to Scale implies
y= (AF(K,N)/N) = AF(K/N, N/N)= AF(k,1) = Af(k)
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

Steady State: A steady state is a situation in which
y, k and c (per-worker variables) are constant over
time. It is an equilibrium situation in the sense that
once an economy reaches this state it has tendency
to continue in the same state.
Solow Model predicts that an economy ultimately
reaches the steady state. This steady state is given
by the condition:
sf(k) = (n+d )k
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

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Let k*>0 be the steady state per-worker capital
stock. Then, this steady state is also stable in the
sense that if for (temporary) reason the economy
moves away from steady state it has tendency to
come back to the original steady state.
In the steady state per worker variables (c, k, y)
are constant, but aggregate variables (C,K,Y) are
growing at the rate of population growth (n).
The level of capital stock that maximizes the steady
state per-worker consumption (c) is called the
Golden Rule level of capital stock.
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Implications of the Model:
Case 1: No Technical Progress:
1)
2)
Per-Worker Consumption (c) in the long run
depends on s, n, and d. There will be no growth in
c in the long run.
Ultimately, an economy will grow (growth in Y, C,K)
at the rate of population growth (n).
Case 2: Technical Progress:
1)
Per-Worker Consumption (c) in the long run will
grow at the rate of technical progress.
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Endogenous Growth Theory
These models emphasize the role of Human
Capital (knowledge, skills, and training of
workers).
Assumptions:
1)
No population growth rate
2)
Constant Marginal Productivity of Capital.
Aggregate Production Function: Y = AK
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
The long run growth rate of output is
given by the condition that
∆Y/Y = sA – d
Implication:
Higher saving rate (s) implies higher long run growth
rate of output unlike Solow model in which with no
population growth, the growth rate of output is zero.
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