Economics 2900 Chapter 6: Long Run Growth
Chapter 6
Long Run Economic Growth
The Sources of Economic Growth
The relationship between output and inputs is described by the production function:
For Y to grow, either quantities of K or N must grow or productivity (A) must improve, or both.
The Growth Accounting Equation
N
ΔN
α
K
ΔK
α
A
ΔA
Y
ΔY
NK
++=
∆Y/Y is the rate of output growth;
∆K/K is the rate of capital growth;
∆N/N is the rate of labour growth;
∆A/A is the rate of productivity growth
K
α
= elasticity of output with respect to capital (about 0.3 in Canada)
N
α
= elasticity of output with respect to labour (about 0.7 in Canada).
The elasticity of output with respect to capital/labour is the percentage increase in output
resulting from a one percent increase in the amount of capital stock/labour.
Growth Accounting
Growth accounting measures empirically the relative importance of capital stock, labour and
productivity for economic growth.
The impact of changes in capital and labour is estimated from historical data.
The impact of changes in total factor productivity is treated as a residual, that is, not otherwise
explained.
N
ΔN
α
K
ΔK
α
Y
ΔY
A
ΔA
NK
--=
Growth Accounting and the Productivity Slowdown
Rapid output growth during 1962-1973 has slowed in 1974-2009.
Much of the decline in output growth can be accounted for by a decline in productivity growth.
The slowdown in productivity since 1974 is widespread.
Explanations of the reduced growth in productivity are:
■ output measurement problem;
■ the growth in oil prices;
Growth Dynamics: The Neoclassical Growth Model
he neoclassical growth model:
-clarifies how capital accumulation and economic growth are interrelated;
N)AF(K,Y
=
-explains the factors affecting a nation’s long-run standard of living;
-demonstrates how a nation’s rate of economic growth evolves over time.
Assumptions of the model of economic growth
Let us assume that:
population (Nt) is growing;
at any point in time a share of the population of working age is fixed;
both the population and workforce grow at fixed rate n;
the economy is closed and there are no government purchases.
Setup of the model of economic growth
Part of the output produced each year is invested in new capital or in replacing of worn-out
capital (It).
The uninvested part of output is consumed by population (Ct).
ttt
IYC
-=
The per worker Production Function
By assuming no productivity growth we focus on the role of the capital stock in the growth
process.
The production function in per worker terms is:
)f(kAy
ttt
=
𝑦𝑡=Yt/Nt is output per worker in year t
𝑘𝑡=Kt/Nt is capital stock per worker in year t
𝐴𝑡=the level of total factor productivity in year t
Graph of the per worker production function
The production function slopes upward. With more capital each worker produces more output.
The slope gets flatter at higher levels of capital per worker. This reflects diminishing MPK.
Steady States
A steady state is a situation in which the economy’s output per worker (𝑦𝑡), consumption per
worker (𝑐𝑡), and capital stock per worker (𝑘𝑡) are constant, do not change over time.
In the absence of productivity growth the economy reaches a steady state in the long run.
Since 𝑦𝑡, 𝑐𝑡 and 𝑘𝑡 are constant in a steady-state, Yt, Ct and Kt all grow at rate n, the rate of
growth of the workforce.
Characteristics of a Steady State
The gross investment in year t is:
tt d)K(nI
+=
Kt grows by nKt in a steady state.
Kt depreciates by dKt, where d is the capital depreciation rate.
ttt
d)K(n-YC
+=
Put above in per-worker terms.
Replace Yt with Atf(kt)
d)kAf(k)-(nc
+=
Steady state Consumption per worker
An increase in the steady-state capital-labour ratio:
raises the amount of output a worker can produce, Af(k);
increases the amount of output per worker that must be devoted to investment, (n+d)k.
The Golden Rule level of the capital stock maximizes consumption per worker in the steady
state.
The model shows that economic policy focused solely on increasing capital per worker may do
little to increase consumption possibilities of the country citizens.
Empirical evidence shows that higher capital stock does not lead to less consumption in the
long run.
Thus, we will assume that an increase in the steady-state capital-labour ratio raises steady-state
consumption per worker.
Reaching the steady state
Assume that saving in this economy is proportional to current income:
tt
sYS
=
s is a number between 0 and 1.
