Harrod–Domar model
The Harrod–Domar model is a
Neoclassical economists claimed shortcomings in the Harrod–Domar model—in particular the instability of its solution[5]—and, by the late 1950s, started an academic dialogue that led to the development of the Solow–Swan model.[6][7]
According to the Harrod–Domar model there are three kinds of growth: warranted growth, actual growth and natural rate of growth.
Warranted growth rate is the rate of growth at which the economy does not expand indefinitely or go into recession. Actual growth is the real rate increase in a country's GDP per year. (See also:
Mathematical formalism
Definitions
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:
1: Output is a function of capital stock only (labor is irrelevant). | |
2: The marginal product of capital is constant; the production function exhibits constant returns to scale. This implies capital's marginal and average products are equal. | |
3: Capital is necessary for output. | |
4: The product of the savings rate and output equals saving, which equals investment | |
5: The change in the capital stock equals investment less the depreciation of the capital stock |
Derivations
Derivation of output growth rate:
A derivation with calculus is as follows, using dot notation (for example, ) for the derivative of a variable with respect to time.
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,
Since the marginal product of capital, c, is a constant, we have
Next, with assumptions (4) and (5), we can find capital's growth rate as,
In summation, the savings rate times the marginal product of capital minus the depreciation rate equals the output growth rate. Increasing the savings rate, increasing the marginal product of capital, or decreasing the depreciation rate will increase the growth rate of output; these are the means to achieve growth in the Harrod–Domar model.
Significance
Domar proposed the model in the aftermath of the great depression, intending to model economies in the short-run, during a period where there is high enough unemployment such that any additional machine may be fully utilized by labor. Consequently, production can be modelled as a function of capital only.[8]
Although the Harrod–Domar model was initially created to help analyse the
The model implies that economic growth depends on policies to increase investment, by increasing saving, and using that investment more efficiently through technological advances.
The model concludes that an economy does not "naturally" find full employment and stable growth rates.
Criticisms
The main criticism of the model is the level of assumption, one being that there is no reason for growth to be sufficient to maintain full employment; this is based on the belief that the relative price of labour and capital is fixed, and that they are used in equal proportions. The model also assumes that savings rates are constant, which may not be true, and assumes that the marginal returns to capital are constant. Furthermore, the model has been criticized for the assumption that productive capacity is proportional to capital stock, which Domar later stated was not a realistic assumption.[9]
See also
References
- JSTOR 2225181.
- JSTOR 1905364.
- ^ Cassel, Gustav (1967) [1924]. "Capital and Income in the Money Economy". The Theory of Social Economy (PDF). New York: Augustus M. Kelley. pp. 51–63.
- .
- ISBN 0-07-055039-5.
- JSTOR 2228485.
- JSTOR 2138150.
- S2CID 13515227.
- ^ Easterly, William (1997), Ghost of the Financing Gap: How the Harrod-Domar Model Still Haunts Development Economics (PDF), World Bank Development Research Group
Further reading
- Ackley, Gardner (1961). "Economic Growth: The Problem of Capital Accumulation". Macroeconomic Theory. New York: Macmillan. pp. 505–535.
- ISBN 0-02-306660-1.
- Brems, Hans (1967). "The One-Country Harrod–Domar Model of Growth". Quantitative Economic Theory: A Synthetic Approach. New York: Wiley. pp. 426–435.
- Cochrane, James L.; ISBN 0-673-07639-3.
- Gapinski, James H. (1982). "Celebrated Paradigms of Economic Growth". Macroeconomic Theory: Statics, Dynamics, and Policy. McGraw-Hill. pp. 251–285. ISBN 0-07-022765-9.
- Keiser, Norman F. (1975). "An Introduction to Growth Theory". Macroeconomics (Second ed.). New York: Random House. pp. 386–399. ISBN 0-394-31922-2.
- ISBN 0-471-53572-9.