1. Steady State and Golden Rule of Saving in Solow Model
Economic Modelling
Lecture 3
Steady State and Golden Rule of Saving in Solow Model
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

3. Per Capita Output and Per Capita Capital Stock in the Steady State
SST
0.5ks ks
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

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:
@K.R.Bhattarai, Business School, University of Hull, UK.

9. Results from the steady state:
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.
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.
Countries with higher rate of population growth rate have lower level of output in the steady state.
Countries with higher capital share have higher output in the steady state.
Countries which differ in the initial capital stock eventually reach to the same output level in the steady state.
Growth of per capita income is zero in the steady state
@K.R.Bhattarai, Business School, University of Hull, UK.

10. Calculation of Steady State: A Numerical Example
Output in the steady state
Consumption in the steady state:
= (2) = 1.36.
@K.R.Bhattarai, Business School, University of Hull, UK.

11. Note: Saving rate affects level of income but not the growth rates.
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.
@K.R.Bhattarai, Business School, University of Hull, UK.

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
@K.R.Bhattarai, Business School, University of Hull, UK.

13. Golden Rule for Saving and Capital Accumulation
C-max Kg
Kss
Golden rule
Steady State
@K.R.Bhattarai, Business School, University of Hull, UK.

14. How High Should be the Saving Rate
How High Should be the Saving Rate? Saving Rate that Maximises Consumption
C-max = 1.25
y = 0.5*k0.5
y=2.5
Consumption
k = 25 C s5 s4 s1 s2
s*=0.5
Saving rate
@K.R.Bhattarai, Business School, University of Hull, UK.

15. Golden Rule of Saving Steady State Golden Rule
@K.R.Bhattarai, Business School, University of Hull, UK.

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,
Parente S.L. and Prescott E. C. (1993) Changes in the Wealth of Nations, Federal Reserve Bank of Minneapolis, Quarterly Review, Spring, pp
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,
@K.R.Bhattarai, Business School, University of Hull, UK.