The Neoclassical Growth Model

Solow Growth Model

Output Supply: CRS production function

Output Demand: Equilibrium condition.

Solow Growth Model

Let the exogenous saving rate be designated s

so that per capita investment i

is a function of per capita capital stock.

Solow Growth Model

y

= f(k)

k

y

= f(k)

sf(k) = i

k0

y0

i0

savings

consumption

Solow Growth Model

Assume that the rate of depreciation of the capital stock is constant and equal to δ, then the change in the (per capita) capital stock is investment minus depreciation.

Solow Growth Modely

= f(k)

k

δk

Depreciation Schedule

Solow Growth Model

A steady state is defined as the condition where Δk

= 0, i.e. zero change in per capita capital stock.

Solow Growth Modely

= f(k)

k

δk

Steady State per capita Capital Stock

sf(k)

k*

Solow Growth Model

If we assume that the population increases at the rate of n per period, then per capita capital stock will decline by n

each period. This effect is analogous to depreciation and will affect the depreciation schedule

Solow Growth Modely

= f(k)

k

(n+δ)k

Steady State per capita Capital Stock

sf(k)

k*

Equilibrium in the Solow Growth Model

Equilibrium in the Solow Growth Model

The Long-Run Effect of Changing the Saving Rate in the Solow Model

Population Growth in the Solow Model

Technical Change in the Solow Growth Model

If we now allow for improvements in technology that are labor-augmenting such that increases in technology increase the effective labor per worker (per capita) then the steady state condition becomes:

Because increases in technical knowledge increase the effective labor or increase the effective number of workers (even though the actual

number of workers only changes by n

each period) the per capita (or per effective worker) capital stock declines with improvements in technology.

Technical Change in the Solow Model

Optimal Steady State and the Golden Rule

Given that the steady state is a function of the (exogenously determined) rate of depreciation, δ, the rate of population growth, n, the rate of technical progress, θ, and the rate of savings, s, which steady state outcome is best? That which maximizes steady state per capita consumption.

The first order condition for a maximum is that the change in c

is equal to zero, i.e. the slope of the consumption function is zero at the max.

Golden Rule in the Solow Growth Model

y

= f(k)

k

y

= f(k)

sf(k) = i

k*

y*

δk

Slopes are equal.

Evaluating the Solow Model: Strengths and Weaknesses

•

Strengths: Allows for labor/capital substitution; Provides good insights about the relationship between role of technology and innovation on growth; yields testable hypotheses.

•

Limitations: One sector approach, assumes factors that drive steady state, and treats saving rate, population growth , and technical change as exogenous.