Neoclassical Growth Model

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Michaelmas Term 2009
Part IIB. Paper 2
Economic Growth
Lecture 2 Neo-Classical Growth Model
Dr. Tiago Cavalcanti
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Readings and Refs
Texts ()Jones ch.2 BX chs.1,10 Romer ch.1.
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.
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The Neoclassical Growth modelSolow (1956) and
Swan (1956)

• simple dynamic general equilibrium model of
  growth

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Neoclassical Production Function
Output produced using aggregate production
function Y F (K , L ), satisfying A1.
positive, but diminishing returns FK gt0, FKKlt0
and FLgt0, FLLlt0 A2. constant returns to scale
(CRS)

• replication argument

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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 YL? f(k), show FK
f(k) and FKK f(k)/L .
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Competitive Economy

• representative firms maximise profits and take
  price as given (perfect competition)
• can show inputs paid their marginal products
• r FK and w FL
• inputs (factor payments) exhaust all output
• wL rK Y
• general property of CRS functions (Eulers THM)

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A3 The Production Function F(K,L) satisfies the
Inada Conditions
Note As f(k)FK have that
Production Functions satisfying A1, A2 and A3
often called Neo-Classical Production Functions
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Technological Progress
change in the production function Ft
Hicks-Neutral T.P.
Labour augmenting (Harrod-Neutral) T.P.
Capital augmenting (Solow-Neutral) T.P.
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A4 Technical progress is labour augmenting
Note For Cobb-Douglas case three forms of
technical progress equivalent
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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

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Model Dynamics
A5 Labour force grows at a constant rate n
A6 Dynamics of capital stock

• net investment gross investment - depreciation
• capital depreciates at constant rate ?

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closing the model

• 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

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Fundamental Equation of Solow-Swan model
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Steady State
Definition Variables of interest grow at
constant rate (balanced growth path or BGP)

• at steady state

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Solow Diagram
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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 d if

- satisfied from Inada Conditions (A3).
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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

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Transitional Dynamics
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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
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2. Changes in s, n, or d will 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 d increase
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.
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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 .

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Golden Rule and Dynamic Inefficiency
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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.

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Linear versus log scales
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Changes in the savings rate
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Next lecture

• Testing the neo-classical model
• Convergence
• Growth Regressions
• Evidence from factor prices