Economic Modelling

1
Economic Modelling
Lecture 3 Steady State and Golden Rule of Saving
in Solow Model
2
Solow Growth Model
Production function with capital and labour as
its inputs (Close Economy without Government)
Firms Production Function
Market clearing

Households Saving
Investment requirement
Closure rule
Dynamics Capital accumulation
3
Per Capita Output and Per Capita Capital Stock in
the Steady State
SST
0.5ks
ks
4
Capital Stock and output in the Steady State in
the Solow Model
Per Capita Capital Stock
Take log both sides
Differentiate it with respect to time to get
growth rate of k
Fundamental equation of economic growth
5
Capital Stock and output in the Steady State in
the Solow Model
Fundamental equation of economic growth
Per Capita Capital Stock in the Steady State
Per Capita Output in the Steady State
6
Solow Growth Model
Production function with Labour augmenting
technology (Close Economy without Government)
Firms Production Function
Market clearing

Households Saving
Investment requirement
Closure rule
Dynamics Capital accumulation
7
Capital Stock and output in the Steady State in
the Solow Model with technical progress
Per Capita Effective Capital Stock
Take log both sides
Differentiate it with respect to time to get
growth rate of k
Fundamental equation of economic growth
8
Capital Stock and output in the Steady State in
the Solow Model with technical progress
Fundamental equation of economic growth
Per Capita Effective Capital Stock in the Steady
State
Per Capita Effective Output in the Steady State
9
Results from the steady state

1. Countries with higher saving rate have higher
   steady state level of output and countries with
   lower saving rate have lower level of output in
   the steady state.
2. Countries with higher level of technology have
   higher level of output and countries with lower
   level of technology have lower level of output in
   the steady state.
3. Countries with higher rate of population growth
   rate have lower level of output in the steady
   state.
4. Countries with higher capital share have higher
   output in the steady state.
5. Countries which differ in the initial capital
   stock eventually reach to the same output level
   in the steady state.
6. Growth of per capita income is zero in the steady
   state

10
Calculation of Steady State A Numerical Example
Output in the steady state
2-0.32(2) 1.36.
Consumption in the steady state
11
How does a higher saving rate affect the level of
output in the steady state?
High saving country
Low saving country
Note Saving rate affects level of income but not
the growth rates.
12
How does a higher rate of population growth
affect the level of output in the steady state?
High saving country
Higher population growth rate means lower output
and capital stock in the steady state
Low saving country
13
Golden Rule for Saving and Capital Accumulation
C-max
Kg
Kss
Golden rule
Steady State
14
How High Should be the Saving Rate? Saving Rate
that Maximises Consumption
C-max 1.25
y 0.5k0.5
y2.5
Consumption
k 25
C
s5
s4
s0.5
s1
s2
Saving rate
15
Golden Rule of Saving
Steady State
Golden Rule
16
Reading and References

• Text
• Blanchard Chapters 10, 11
• Mankiw 7
• Burda Wypslosz 3
• Miles and Scot 5-6
• Jones, Charles (CJ) Introduction to economic
  growth, 2002, 2nd Edition, Norton.
• Articles
• Freeman Richard
• Kaldor N. (1961) Capital Accumulation and
  Economic Growth in F.A. Lutz and D.C. Hague ed.
  The Theory of Capital, New York, St. Martin.
• Lucas R.E. (1988) "On the Mechanics of Economic
  Development", Journal of Monetary Economics, 22,
  3-42.
• Mankiw N.G., D. Romer and D. N. Weil (1992)
  Contribution to the Empirics of Economic Growth
  Quarterly Journal of Economics, 107 407-437.
• Parente S.L. and Prescott E. C. (1993) Changes in
  the Wealth of Nations, Federal Reserve Bank of
  Minneapolis, Quarterly Review, Spring, pp. 3-16.
• Romer, Paul (1989) Endogenous Technological
  Change, Journal of Political Economy, vol. 98,
  no. 5. Pt. 2, pp. S71-S102.
• Temple, Jonathan R. W. and Voth, Hans-Joachim
  (1998). Human capital, equipment investment, and
  industrialization. European Economic Review,
  42(7), July, 1343-1362.