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.
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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