Harrod–Domar Model

# Harrod–Domar model

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Description:
The Harrod–Domar model is used in development economics to explain an economy's growth rate in terms of the level of saving and productivity of capital. It suggests that there is no natural reason for an economy to have balanced growth. The model was developed independently by Sir Roy F. Harrod in 1939 and Evsey Domar in 1946. The Harrod–Domar model was the precursor to the exogenous growth model.

## Mathematical formalism

Let Y represent output, which equals income, and let K equal the capital stock. S is total saving, s is the savings rate, and I is investment. δ stands for the rate of depreciation of the capital stock. The Harrod–Domar model makes the following a priori assumptions:

Derivation of output growth rate:

[itex]
begin& c= frac=frac \& c= frac \& c(sY(t) - delta frac Y(t))=Y(t+1) - Y(t) \& cY(t)left(s - delta fracright) = Y(t+1) - Y(t) \& cs - c delta frac=frac \& s frac - delta frac frac=frac \& s c - delta = fracend[/itex]

An alternative (and, perhaps, simpler) derivation is as follows, with dots (for example, [itex] dot [/itex]) denoting percentage growth rates.

First, assumptions (1)–(3) imply that output and capital are linearly related (for readers with an economics background, this proportionality implies a capital-elasticity of output equal to unity). These assumptions thus generate equal growth rates between the two variables. That is,

[itex] Y=cK......
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