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ECONOMIC GROWTH (Continued…):The Steady State

<< ECONOMIC GROWTH:THE SOLOW MODEL, Saving and investment
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Macroeconomics ECO 403
VU
LESSON 20
ECONOMIC GROWTH (Continued...)
Moving toward the steady state
Investment and
δk
depreciation
Δk = sf(k) - δk
sf(k)
Δk
Investment
depreciation
k1
k*
Capital per
worker, k
δk
Investment and
depreciation
sf(k)
Δk
k1
k*
Capital per
worker, k
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Macroeconomics ECO 403
VU
δk
Investment and
depreciation
sf(k)
Δk
k1
k2
k*
Capital per
worker, k
δk
Investment and
depreciation
sf(k)
Δk
investment
depreciation
k2
k*
Capital per
worker, k
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Macroeconomics ECO 403
VU
δk
Investment and
depreciation
sf(k)
Δk
k3
k2
k*
Capital per
worker, k
δk
Investment and
depreciation
sf(k)
As long as k < k*, investment will
exceed depreciation,
and k will continue to grow
toward k*.
k3 k*
Capital per
worker, k
Now you try:
Draw the Solow model diagram, labeling the steady state k*.
·
On the horizontal axis, pick a value greater than k* for the economy's initial capital
·
stock. Label it k1.
Show what happens to k over time.
·
Does k move toward the steady state or away from it?
·
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Macroeconomics ECO 403
VU
The Steady State
Investment
and
Depreciation
Depreciation,
k
At k*, investment equals depreciation and capital will
not change over time.
Investment, s f(k)
i* = δk*
k*
k1
k2
Capital
per worker, k
A numerical example
Production function (aggregate):
Y = F (K , L ) = K × L = K 1 / 2L1 / 2
To derive the per-worker production function, divide through by L:
1/2
Y  K 1 / 2L1 / 2   ⎛ K ⎞
=
=⎜  ⎟
L
L
⎝L ⎠
Then substitute y = Y/L and k = K/L to get
y = f (k ) = k  1 / 2
Assume:
·  s = 0.3
·  δ = 0.1
·  initial value of k = 4.0
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Macroeconomics ECO 403
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Approaching the Steady State
δk
Δk
Year
k
y
c
i
1
4.000
2.000
1.400
0.600 0.400
0.200
2
4.200
2.049
1.435
0.615 0.420
0.195
3
4.395
2.096
1.467
0.629 0.440
0.189
4
4.584
2.141
1.499
0.642 0.458
0.184
...
10  5.602
2.367 1.657 0.710 0.560 0.150
...
25  7.351
2.706 1.894 0.812 0.732 0.080
...
100  8.962
2.994 2.096 0.898 0.896 0.002
...
∞
9.000
3.000 2.100 0.900
0.900 0.000
Exercise: solve for the steady state
Continue to assume
s = 0.3, δ = 0.1, and y = k 1/2
Use the equation of motion
Δk = s f(k) - δk
to solve for the steady-state values of k, y, and c.
Solution:
Δk = 0
def. of steady state
s f (k *) = δ k *
eq'n of motion with Δk = 0
0.3 k * = 0.1k *
using assumed values
k*
= k*
3=
k*
Solve to get: k * = 9
and y * = k * = 3
Finally, c * = (1 - s )y * = 0.7 × 3 = 2.1
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Macroeconomics ECO 403
VU
An increase in the saving rate
δk
Investment
and
depreciation
s2 f(k)
s1 f(k)
k
K1 *
K2 *
An increase in the saving rate raises investment causing the capital stock to grow toward a
new steady state
Prediction:
Higher s ⇒ higher k*.
·
And since y = f(k) ,
·
higher k* ⇒ higher y* .
Thus, the Solow model predicts that countries with higher rates of saving and
·
investment will have higher levels of capital and income per worker in the long run.
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Macroeconomics ECO 403
VU
International Evidence on Investment Rates and Income per Person
Income per
person in 1992
(logarithmic scale)
100,000
Canada
Denmark Germany
Japan
U.S.
Finland
10,000
Mexico
U.K.
Brazil
Singapore
Italy
France
Pakistan
Egypt
Ivory
Peru
Coast
Indonesia
1,000
Zimbabwe
India
Kenya
Uganda
Chad
Cameroon
100
25
30
35
0
5
10
40
15
20
Investment as percentage of output
(average 1960­1992)
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Table of Contents:
  1. INTRODUCTION:COURSE DESCRIPTION, TEN PRINCIPLES OF ECONOMICS
  2. PRINCIPLE OF MACROECONOMICS:People Face Tradeoffs
  3. IMPORTANCE OF MACROECONOMICS:Interest rates and rental payments
  4. THE DATA OF MACROECONOMICS:Rules for computing GDP
  5. THE DATA OF MACROECONOMICS (Continued…):Components of Expenditures
  6. THE DATA OF MACROECONOMICS (Continued…):How to construct the CPI
  7. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES
  8. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  9. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  10. NATIONAL INCOME: WHERE IT COMES FROM AND WHERE IT GOES (Continued…)
  11. MONEY AND INFLATION:The Quantity Equation, Inflation and interest rates
  12. MONEY AND INFLATION (Continued…):Money demand and the nominal interest rate
  13. MONEY AND INFLATION (Continued…):Costs of expected inflation:
  14. MONEY AND INFLATION (Continued…):The Classical Dichotomy
  15. OPEN ECONOMY:Three experiments, The nominal exchange rate
  16. OPEN ECONOMY (Continued…):The Determinants of the Nominal Exchange Rate
  17. OPEN ECONOMY (Continued…):A first model of the natural rate
  18. ISSUES IN UNEMPLOYMENT:Public Policy and Job Search
  19. ECONOMIC GROWTH:THE SOLOW MODEL, Saving and investment
  20. ECONOMIC GROWTH (Continued…):The Steady State
  21. ECONOMIC GROWTH (Continued…):The Golden Rule Capital Stock
  22. ECONOMIC GROWTH (Continued…):The Golden Rule, Policies to promote growth
  23. ECONOMIC GROWTH (Continued…):Possible problems with industrial policy
  24. AGGREGATE DEMAND AND AGGREGATE SUPPLY:When prices are sticky
  25. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…):
  26. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…):
  27. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  28. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  29. AGGREGATE DEMAND AND AGGREGATE SUPPLY (Continued…)
  30. AGGREGATE DEMAND IN THE OPEN ECONOMY:Lessons about fiscal policy
  31. AGGREGATE DEMAND IN THE OPEN ECONOMY(Continued…):Fixed exchange rates
  32. AGGREGATE DEMAND IN THE OPEN ECONOMY (Continued…):Why income might not rise
  33. AGGREGATE SUPPLY:The sticky-price model
  34. AGGREGATE SUPPLY (Continued…):Deriving the Phillips Curve from SRAS
  35. GOVERNMENT DEBT:Permanent Debt, Floating Debt, Unfunded Debts
  36. GOVERNMENT DEBT (Continued…):Starting with too little capital,
  37. CONSUMPTION:Secular Stagnation and Simon Kuznets
  38. CONSUMPTION (Continued…):Consumer Preferences, Constraints on Borrowings
  39. CONSUMPTION (Continued…):The Life-cycle Consumption Function
  40. INVESTMENT:The Rental Price of Capital, The Cost of Capital
  41. INVESTMENT (Continued…):The Determinants of Investment
  42. INVESTMENT (Continued…):Financing Constraints, Residential Investment
  43. INVESTMENT (Continued…):Inventories and the Real Interest Rate
  44. MONEY:Money Supply, Fractional Reserve Banking,
  45. MONEY (Continued…):Three Instruments of Money Supply, Money Demand