Neoclassical%20Growth%20Model

1
Prof. Erdinç
ECO 402 Fall 2013
Economic Growth
The Solow Model
2
The Neoclassical Growth modelSolow (1956) and
Swan (1956)

• Simple dynamic general equilibrium model of
  growth

3
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)
4
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 .
5
Competitive Economy

• Representative firm maximises profits and take
  price as given (perfect competition)
• Inputs paid by their marginal products
• r FK and w FL
• inputs (factor payments) exhaust all output
• wL rK Y
• general property of CRS functions (Eulers THM)

6
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
7
Technological Progress
change in the production function Ft
Hicks-Neutral T.P.
Labour augmenting (Harrod-Neutral) T.P.
Capital augmenting (Solow-Neutral) T.P.
8
A4 Technical progress is labour augmenting
Note For Cobb-Douglas case three forms of
technical progress equivalent
9
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

10
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 ?

11
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

12
Fundamental Equation of Solow-Swan model
13
Steady State
Definition Variables of interest grow at
constant rate (balanced growth path or BGP)

• at steady state

14
Solow Diagram Steady State
15
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).
16
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

17
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
18
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.
19
Policies to Promote Growth

1. Are we saving enough? Too much or too little?
2. What policies may change the savings rate?
3. How should we allocate savings between physical
   and human capital?
4. What policies could generate faster technological
   progress?

20
Golden Rule

• Definition (Golden Rule) It is the saving rate
  that maximises consumption in the steady-state.
• We can use the rule to evaluate if we are saving
  too much, too little or about right.
• Given we can use
• to find .

21
Golden Rule and Dynamic Inefficiency

• If our savings rate is given by then our
  savings rate is optimal and
• If then we must
  be under-saving
• If then we must be over-saving
• Check why this is the case!

22
Is Golden Rule attained in the US? Is it
Dynamically Efficient?

• Let us check Three Facts about the US Economy
• a)
• The capital stock is about 2.5 times the GDP
• b)
• About 10 of GDP is used to replace depreciating
  capital
• c)
• OR
• Capital income is 30 of GDP Note alpha also
  measures the elasticity of output with respect to
  capital!

23
Is Golden Rule attained in the US? Is it
Dynamically Efficient?

Since US real GDP grows on average at 3
per year, i.e. Hence, US economy is under-saving
because
24
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.