Model of Solow

The model of Solow is one of the principal models of the theory of the Economic growth.

It was developed by Robert Solow and is a model of the neo-classic economy .

Presentation

Robert Solow was the first to propose a formal model of the growth (It was in fact an extension of the model of Harrod-Domar. v. english language version). Of neo-classic inspiration , this model is based on a Fonction of production to two factors: labor and capital. The production thus results exclusively from the setting in combination of a certain quantity of capital (means of production) and of work (labor).

The model of Solow is based on the assumption that the factors of production know decreasing outputs, i.e. an increase in those in a certain proportion generates an increase in a smaller proportion of the production. It also poses as assumption that the factors of production are used efficiently by all the countries. While posing that the population knows a growth rate that Solow describes as “naturalness” (not influenced by the economy), the model deduces three predictions:

Augmenter the quantity of Capital (i.e. to invest) increases the growth: with a more important capital, the labor increases its Productivité (known as apparent).
the poor countries will have a growth rate more raised than the rich countries. They accumulated indeed less capital, and thus know outputs more slightly decreasing, i.e. any capital growth generates there an increase in the production proportionally stronger than in the rich countries.
Because of the decreasing outputs of the factors of production, the economies will reach a point where any increase in the factors of production will not generate any more increase of the production per capita. This point corresponds to the stationary state. Solow notes however that this third prediction is unrealistic: in fact, the economies never reach this stage, because of the Technological advance which increases the productivity of the factors.

In other words, for Solow, on the long run, the growth comes from the technological advancement. However, this technological advancement is exogenic with the model, i.e. he does not explain it but regards it as given (such a “basket fallen from the sky”).

Mathematical expression

The model of Solow is based on five macroeconomic equations:

a function of production
a countable equation on GDP
an equation of saving
an equation of evolution of the capital
an equation of evolution of the labor force

Function of production

Y=AK^aL^ {1-a} \,

It is a Fonction Cobb-Douglas where $Y$ represents the total production of the economy, $A$ the total Productivité of the factors (also called technological level or level of Technological advance), $K$ the capital and $L$ work.

Equation of the GDP

Y=C+G+I \,

where $C$ is the household consumption, $G$ the public expenditure and $I$ the investment, equal to the saving.

Equation of saving

I=sY \,

The saving is proportional to $Y$ , with a proportionality factor equal to $s$ .

Equation of evolution of the capital

\ Delta K=sY- \,

\ delta K \,

The saving is completely invested, which increases the stock of capital of the economy, and in addition the capital places from there is depreciated, at the rate/rhythm of the rate of depreciation of the capitalt $\ delta \,$ (at each period, a share $\ delta \,$ of the capital are lost).

Evolution of the labor force

L_ {t+1} =L_t (1+g) \,

where $g$ is the growth rate of the labor force $L$ .

Evolution of the model

In the prolongation of the model of Solow, the models of endogenous Croissance were developed during the Années 1980 to answer the problem of the origin of the technological advancement, which will be endogénéisé in these models.

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