# Macro economics

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Macroeconomics ECO 403
VU
LESSON 22
ECONOMIC GROWTH (Continued...)
Issues under Consideration
·
Technological progress in the Solow model
·
Policies to promote growth
·
Growth empirics:
Confronting the theory with facts
·
Endogenous growth:
Two simple models in which the rate of technological progress is endogenous
Introduction
Previously, in the Solow model
·  The production technology was held constant
·  Income per capita was constant in the steady state.
Neither point is true in the real world
Tech. progress in the Solow model
·
A new variable: E = labor efficiency
·
Assume:
Technological progress is labor-augmenting: it increases labor efficiency at the exogenous
rate g:
ΔE
g=
E
·
We now write the production function as:
Y = F (K , L × E )
Where L × E = the number of effective workers.
·
­  Hence, increases in labor efficiency have the same effect on output as
increases in the labor force.
·
Notation:
y = Y/LE = output per effective worker
k = K/LE = capital per effective worker
·
Production function per effective worker:
y = f(k)
·
Saving and investment per effective worker:
s y = s f(k)
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(δ + n + g)k = break-even investment:
the amount of investment necessary to keep k constant.
Consists of:
δ k to replace depreciating capital
n k to provide capital for new workers
g k to provide capital for the new "effective" workers created by technological progress
Δk = s f(k) - (δ +n +g)k
Investment, break-even
investment
(δ +n +g ) k
sf(k)
k*
Capital per
worker, k
Steady-State Growth Rates in the Solow Model with Tech. Progress
Variable
Symbol
k = K/ (L ×E )
Capital per effective worker
0
y = Y/ (L ×E )
Output per effective worker
0
(Y/ L ) = y ×E
Output per worker
g
Y = y ×E ×L
Total output
n+g
The Golden Rule
To find the Golden Rule capital stock,
express c* in terms of k*:
=  y* -  i*
c*
= f(k* ) - (δ + n + g) k*
c* is maximized when
MPK = δ + n + g
or equivalently,
MPK - δ = n + g
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Macroeconomics ECO 403
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In the Golden Rule Steady State, the marginal product of capital net of depreciation equals the
population growth rate plus the rate of tech progress.
The Golden Rule Capital Stock
(δ +n+g) k*
output and
investment
f(k*)
C*gold
i*gold = (δ+ n+g)k*gold
k*gold
worker, k*
Policies to promote growth
Four policy questions:
·  Are we saving enough? Too much?
·  What policies might change the saving rate?
·  How should we allocate our investment between privately owned physical capital,
public infrastructure, and "human capital"?
·  What policies might encourage faster technological progress?
1. Evaluating the Rate of Saving
·
Use the Golden Rule to determine whether
our saving rate and capital stock are too high, too low, or about right.
·
To do this, we need to compare
(MPK - δ ) to (n + g).
· If (MPK - δ ) > (n + g), then we are below the Golden Rule steady state and should increase
s.
· If (MPK - δ ) < (n + g), then we are above the Golden Rule steady state and should reduce
s.
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To estimate (MPK - δ ), we use three facts about an economy;
1. k = 2.5 y
the capital stock is about 2.5 times one year's GDP.
2. δ k = 0.1 y
about 10% of GDP is used to replace depreciating capital.
3. MPK × k = 0.3 y
Capital income is about 30% of GDP
So
1. k = 2.5 y
2. δ k = 0.1 y
3. MPK × k = 0.3 y
To determine δ , divided 2 by 1:
0.1
δk
0.1 y
δ =
= 0.04
=
2.5
k
2.5 y
To determine MPK, divided 3 by 1:
MPK × k
0.3 y
0.3
=
MPK =
= 0.12
k
2.5 y
2.5
Hence, MPK - δ = 0.12 - 0.04 = 0.08
·
Real GDP grows an average of 3%/year,
so n + g = 0.03
·
Thus, in this economy,
MPK - δ = 0.08 > 0.03 = n + g
Conclusion:
The economy is below the Golden Rule steady state:
if we increase saving rate of this economy, the economy will have faster growth until it
reaches to a new steady state with higher consumption per capita.
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