NationMaster - Encyclopedia: Solow growth model

In economics, the Solow growth model is a dynamic model of economic growth. It was used in economic growth theory, mainly in the 1950s and 1960s, in order to explain the differences in productivity among countries, based on physical and human capital accumulation. It attempts to identify the reasons why different countries exhibit noticeably different life standards. The main idea behind the model is that changes in a country's rate of savings, population growth and technological progress will have an effect on its output's growth rate.

It is named for the American economist Robert Solow, who received the 1987 Bank of Sweden Prize in Economic Sciences in Memory of Alfred Nobel for his work on it.

Mathematical framework

The Solow growth model can be described by the interaction of five basic macroeconomic equations:

Macro-production function
GDP equation
Savings function
Change in capital
Change in workforce

Macro-production function

This is a Cobb-Douglas function where Y represents the total production in an economy. A represents multifactor productivity (often generalized as technology), K is capital and L is labour.

An important relation in the macro-production function:

Which is the macro-production function divided by L to give total production per capita y and the capital intensity k

GDP equation

Where C is private consumption, G is public consumption and I represents investments, or savings.

Savings function

This function depicts savings, I as a portion s of the total production Y.

Change in capital

The d is the rate of depreciation.

Change in workforce

gL is the growth function for L.

The model's solution

First we'll need to define some growth functions.

1. Growth in capital

2. Growth in the GDP

3. Growth function for capital intensity

If we then assume there is no growth in the multifactor productivity (a simplification often neccesary to comprehend the model's solution, it is also possible to include growth in multifactor productivity) we can do the following calculations:

When there is no growth in A then we can assume the following based on the first calculation:

Moving on:

Divide the fraction by L and you will see that

By subtracting gL from gK we end up with:

If k is known in the year t then this formula can be used to calculate k in any given year.

In the first segment on the right side of the equation we see that and

The golden rule of growth

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Results from FactBites:

NationMaster - Encyclopedia: Robert Solow (1095 words)
	Solow's model of economic growth, often known as the neo-classical growth model, allows the determinants of economic growth to be separated out into increases in inputs (labour and capital) and technical progress.
	Exogenous growth model, also known as the Neo-classical model or Solow growth model is a term used to sum up the contributions of various authors to a model of long-run economic growth within the framework of neoclassical economics.
	Solows essential argument is that the poorest members of society should not be guaranteed a dole, but instead be guaranteed a job that pays them enough for them to live on, including the cost of adequate job training, child care and health care.

Robert M. Solow - Prize Lecture (8246 words)
	Growth theory, like much else in macroeconomics, was a product of the depression of the 1930s and of the war that finally ended it.
	If the condition for steady growth is that the savings rate equal the product of the growth rate of employment and a technologically-determined capital-output ratio, then a recipe for doubling the rate of growth in a labor surplus economy was simply to double the savings rate, perhaps through the public budget.
	The growth of "capital" accounts for 12 percent of the growth of output; this is coincidentally almost exactly what I found for 1909-1949 using my original method, of which Denison's is in some ways a practical refinement.

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