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# Economic Modeling (Neo-classical)

last edited by 7 years, 2 months ago

# Harrod-Domar Model

Brief Description

The model describes economy’s growth rate in terms of the level of saving and productivity of capital.

Model

Set-up

Production Function:

Y = F(K) = K/ ɵ

Evolution of Capital Stock:

dk/dt = sY(t) – δK(t)

Economy’s Growth rate:

g = s/ɵ  -  δ

Assumption:

1.  A closed economy
2.  Fixed population
3.  A fixed amount of capital is required for each unit of output

Endogenous:

Y = output (and income)

K = capital stock (or K(t))

Exogenous:

s = savings rate

δ = depreciation

ɵ = fixed coefficient production

Implications

• ·         Accumulation of savings (s) à economic growth increases (g)
• ·         Higher capital required to produce each unit of output (ɵ) à economic growth decreases (g)
• ·         Higher depreciation (δ) à economic growth decreases (g)

Limitations/Criticisms

Example

• ·
• ·         Marginal product of capital is not diminishing, which means the model assumes that the capital can accumulate forever
• ·         Savings rate might not be exogenous given it depends on the overall income of the population
• Performance of early Soviety Union conformed to the Model, but later became stagnant
• Model inspired aid for large infrastructure projects; which seemed to have disappointingly little effect (But it depends on level of aid) as per some critics such as Easterly

# Solow Model

Brief Description

Solow Model is neoclassical growth model that tries to explain long run economic growth by looking at productivity, capital accumulation and population growth.

Model

Set-up

Production Function:

Y = F(K,P)

Because of constant returns to scale, per capita production function:

y = f(k)

Evolution of Inputs to production:

dk/dt = sf(k) – (n+ δ)k

Capital Stock’s Growth rate in steady state

gK = (dY/dt)/K

= n

(Capital stocks grows (gK) just to keep up with population growth rate (n)]

Economy’s Growth rate in steady state

Y = (dY/dt)/Y

= n

(Economy grows (gY) just to keep up with population growth rate (n)]

Assumption:

1)      A closed economy

2)      Constant exogenous population growth

3)      Production Function assumptions:

• ·         Marginal products positive

• ·         Marginal products diminishing

• ·         Constant returns to scale

Endogenous:

Y = output (and income)

K = capital stock (or K(t))

P = population

Exogenous:

s = savings rate

δ = depreciation

ɵ = fixed coefficient production

n = Population growth rate (constant)

Implications

• ·         Regardless of initial level of capita stock (k),  the economy converges to a steady state k*
• ·         Per-capita income will converge to y*
• ·         Growth of per-capita income at k* is 0:
• o    Here capital stock is growing just to keep up with population growth
• o    Here total income is growing just to keep up with population growth
• ·         Comparative statics
• o    s ↑ Þ k*↑, y*↑
• o    δ↑ Þ k*↓, y*↓
• o    n↑ Þ k*↓, y*↓

Limitations/Criticisms

Example

• ·         It is difficult to reconcile with key features of the data:
• o   Lack of absolute convergence
• o   Lack of investment flows from rich to poor countries
• o   Countries that initially appear to be very similar that subsequently experience very different growth paths

South Korea and The Philippines while appear to be similar, they grew differently.