Prof. Erdinç. ECO 402 Fall 2013. Economic Growth. The Solow Model. The Neoclassical Growth model Solow (1956) and Swan (1956). Simple dynamic general equilibrium model of growth. Neoclassical Production Function.
The Solow Model
Output produced using aggregate production functionY = F (K , L ), satisfying:
A1. positive, but diminishing returns
FK >0, FKK<0and FL>0, FLL<0
A2. constant returns to scale (CRS)
Exercise: Given that Y=L f(k), show:
FK = f’(k) and FKK= f’’(k)/L .
r = FKand w = FL
wL + rK = Y
A3: The Production Function F(K,L) satisfies the Inada Conditions
Note: As f’(k)=FKhave that
Production Functions satisfying A1, A2 and A3 often called Neo-Classical Production Functions
= change in the production functionFt
Labour augmenting (Harrod-Neutral) T.P.
Capital augmenting (Solow-Neutral) T.P.
A4: Technical progress is labour augmenting
Note: For Cobb-Douglas case three forms of technical progress equivalent:
Under CRS, can rewrite production function in intensive form in terms of effective labour units
A5: Labour force grows at a constant rate n
A6: Dynamics of capital stock:
Definition: Variables of interest grow at constant rate (balanced growth pathor BGP)
Solow Diagram: Steady State
- satisfied from Inada Conditions (A3).
1. In steady state, per capita variables grow at the rate g, and aggregate variables grow at rate(g + n)
2. Changes in s, n, or dwill affect the levels of y* and k*, but not the growth rates of these variables.
- Specifically, y* and k* will increase as s increases, and decrease as either n or dincrease
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.
to find .
US real GDP grows on average at 3% per year, i.e.
Hence, US economy is under-saving because