1. Part IIB. Paper 2 Michaelmas Term 2009 Economic Growth Lecture 2: Neo-Classical Growth Model Dr. Tiago Cavalcanti

2. Readings and Refs Original Articles: Solow R. (1956) ‘A contribution to the theory of economic growth’ Quarterly Journal of Economics, 70, 65-94. Solow R. (1957) ‘Technical change and the aggregate production function’ Review of Economics and Statistics, 39, 312-320. Swan T. (1956) ‘Economic growth and capital accumulation’ Economic Record, 32, 334-361. Texts: (*)Jones ch.2; BX chs.1,10; Romer ch.1.

3. The Neoclassical Growth model Solow (1956) and Swan (1956) simple dynamic general equilibrium model of growth

4. Output produced using aggregate production function Y = F (K, L ), satisfying: A1. positive, but diminishing returns F K >0, F KK 0, F LL <0 A2. constant returns to scale (CRS) –replication argument Neoclassical Production Function

5. Production Function in Intensive Form Under CRS, can write production function Alternatively, can write in intensive form: y = f ( k ) - where per capita y = Y/L and k = K/L Exercise: Given that Y=L  f(k), show: F K = f’(k) and F KK = f’’(k)/L.

6. Competitive Economy representative firms maximise profits and take price as given (perfect competition) can show: inputs paid their marginal products : r = F K and w = F L –inputs (factor payments) exhaust all output: wL + rK = Y –general property of CRS functions (Euler’s THM)

7. A3: The Production Function F(K,L) satisfies the Inada Conditions Note: As f’(k)=F K have that Production Functions satisfying A1, A2 and A3 often called Neo-Classical Production Functions

8. Technological Progress = change in the production function F t Hicks-Neutral T.P. Labour augmenting (Harrod-Neutral) T.P. Capital augmenting (Solow-Neutral) T.P.

9. A4: Technical progress is labour augmenting Note: For Cobb-Douglas case three forms of technical progress equivalent:

10. Under CRS, can rewrite production function in intensive form in terms of effective labour units -note: drop time subscript to for notational ease - Exercise: Show that

11. A5: Labour force grows at a constant rate n A6: Dynamics of capital stock: net investment = gross investment - depreciation – capital depreciates at constant rate  Model Dynamics

12. National Income Identity Y = C + I + G + NX Assume no government (G = 0) and closed economy (NX = 0) Simplifying assumption: households save constant fraction of income with savings rate 0  s  1  I = S = sY Substitute in equation of motion of capital: … closing the model

13. Fundamental Equation of Solow-Swan model

14. Steady State Definition: Variables of interest grow at constant rate (balanced growth path or BGP) at steady state:

15. Solow Diagram

16. Existence of Steady State From previous diagram, existence of a (non- zero) steady state can only be guaranteed for all values of n,g and  if - satisfied from Inada Conditions (A3).

17. Transitional Dynamics If, then savings/investment exceeds “depreciation”, thus If, then savings/investment lower than “depreciation”, thus By continuity, concavity, and given that f(k) satisfies the INADA conditions, there must exists an unique

18. Transitional Dynamics

19. Properties of Steady State 1. In steady state, per capita variables grow at the rate g, and aggregate variables grow at rate (g + n) Proof:

20. 2. Changes in s, n, or  will affect the levels of y* and k*, but not the growth rates of these variables. Prediction: In Steady State, GDP per worker will be higher in countries where the rate of investment is high and where the population growth rate is low - but neither factor should explain differences in the growth rate of GDP per worker. - Specifically, y* and k* will increase as s increases, and decrease as either n or  increase

21. Golden Rule and Dynamic Inefficiency Definition: (Golden Rule) It is the saving rate that maximises consumption in the steady-state. Given we can use to find.

22. Golden Rule and Dynamic Inefficiency

23. Changes in the savings rate Suppose that initially the economy is in the steady state: If s increases, then Capital stock per efficiency unit of labour grows until it reaches a new steady-state Along the transition growth in output per capita is higher than g.

24. Linear versus log scales

25. Changes in the savings rate

26. Next lecture Testing the neo-classical model: 1.Convergence 2.Growth Regressions 3.Evidence from factor prices