World Library  
Flag as Inappropriate
Email this Article

Harrod–Domar model

Article Id: WHEBN0001920997
Reproduction Date:

Title: Harrod–Domar model  
Author: World Heritage Encyclopedia
Language: English
Subject: Endogenous growth theory, Roy Harrod, Solow–Swan model, Feldman–Mahalanobis model, AK model
Collection: Economic Growth, Economics Models
Publisher: World Heritage Encyclopedia
Publication
Date:
 

Harrod–Domar model

The Harrod–Domar model is an early post-Keynesian model of economic growth. It 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 Roy F. Harrod in 1939,[1] and Evsey Domar in 1946,[2] although a similar model had been proposed by Gustav Cassel in 1924.[3] The Harrod–Domar model was the precursor to the exogenous growth model.[4]

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: Gross domestic product and Natural gross domestic product)

Contents

  • Mathematical formalism 1
  • Significance 2
  • Criticisms of the model 3
  • See also 4
  • References 5
  • Further reading 6

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:

\ Y=f(K) 1: Output is a function of capital stock
\ \frac{dY}{dK}=c \Rightarrow \frac{dY}{dK}=\frac{Y}{K} 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.
\ f(0)=0 3: Capital is necessary for output.
\ sY=S=I 4: The product of the savings rate and output equals saving, which equals investment
\ \Delta\ K=I- \delta\ K 5: The change in the capital stock equals investment less the depreciation of the capital stock

Derivation of output growth rate:

\begin{align} & c= \frac{dY}{dK}=\frac{Y(t+1) - Y(t)}{K(t) + sY(t) - \delta\ K(t) - K(t)} \\[8pt] & c= \frac{Y(t+1) - Y(t)}{sY(t) - \delta\ \frac{dK}{dY} Y(t)} \\[8pt] & c(sY(t) - \delta\ \frac{dK}{dY} Y(t))=Y(t+1) - Y(t) \\[8pt] & cY(t)\left(s - \delta\ \frac{dK}{dY}\right) = Y(t+1) - Y(t) \\[8pt] & cs - c \delta\ \frac{dK}{dY}=\frac{Y(t+1) - Y(t)}{Y(t)} \\[8pt] & s \frac{dY}{dK} - \delta\ \frac{dY}{dK} \frac{dK}{dY}=\frac{Y(t+1) - Y(t)}{Y(t)} \\[8pt] & s c - \delta\ = \frac{ \Delta Y}{Y} \end{align}

A derivation with calculus is as follows, using dot notation (for example, \ \dot{Y} ) 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,

\ Y=cK \Rightarrow log(Y)=log(c)+log(K).

Since the marginal product of capital, c, is a constant, we have

\ \frac{d\log(Y)}{dt}=\frac{d\log(K)}{dt} \Rightarrow \frac{\dot{Y}}{Y}=\frac{\dot{K}}{K}.

Next, with assumptions (4) and (5), we can find capital's growth rate as,

\ \frac{\dot{K}}{K}=\frac{I}{K}-\delta\ = s \frac{Y}{K}-\delta\
\ \Rightarrow \frac{\dot{Y}}{Y} = s c - \delta\

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

Although the Harrod–Domar model was initially created to help analyse the business cycle, it was later adapted to explain economic growth. Its implications were that growth depends on the quantity of labour and capital; more investment leads to capital accumulation, which generates economic growth. The model carries implications for less economically developed countries, where labour is in plentiful supply in these countries but physical capital is not, slowing down economic progress. LDCs do not have sufficiently high incomes to enable sufficient rates of saving; therefore, accumulation of physical-capital stock through investment is low.

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 of the model

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 explains economic boom and bust by the assumption that investors are only influenced by output (known as the accelerator principle); this is now believed to be correct.

In terms of development, critics claim that the model sees economic growth and development as the same; in reality, economic growth is only a subset of development. Another criticism is that the model implies poor countries should borrow to finance investment in capital to trigger economic growth; however, history has shown that this often causes repayment problems later.

The endogeneity of savings: Perhaps the most important parameter in the Harrod–Domar model is the rate of savings. Can it be treated as a parameter that can be manipulated easily by policy? That depends on how much control the policy maker has over the economy. In fact, there are several reasons to believe that the rate of savings may itself be influenced by the overall level of per capita income in the society, not to mention the distribution of that income among the population.

See also

References

  1. ^ Harrod, Roy F. (1939). "An Essay in Dynamic Theory". The Economic Journal 49 (193): 14–33.  
  2. ^ Domar, Evsey (1946). "Capital Expansion, Rate of Growth, and Employment". Econometrica 14 (2): 137–147.  
  3. ^ Cassel, Gustav (1967) [1924]. "Capital and Income in the Money Economy". The Theory of Social Economy (PDF). New York:  
  4. ^ Hagemann, Harald (2009). "Solow's 1956 Contribution in the Context of the Harrod-Domar Model". History of Political Economy 41 (Suppl 1): 67–87.  
  5. ^ Scarfe, Brian L. (1977). "The Harrod Model and the ‘Knife Edge’ Problem". Cycles, Growth, and Inflation: A Survey of Contemporary Macrodynamics. New York: McGraw-Hill. pp. 63–66.  
  6. ^  
  7. ^ Solow, Robert M. (1994). "Perspectives on Growth Theory".  

Further reading

  •  
  •  
  •  
  • Cochrane, James L.; Gubins, Samuel; Kiker, B. F. (1974). "Economic Growth (I)". Macroeconomics: Analysis and Policy. Glenview: Scott, Foresman and Co. pp. 328–353.  
  • Gapinski, James H. (1982). "Celebrated Paradigms of Economic Growth". Macroeconomic Theory: Statics, Dynamics, and Policy. McGraw-Hill. pp. 251–285.  
  • Keiser, Norman F. (1975). "An Introduction to Growth Theory". Macroeconomics (Second ed.). New York: Random House. pp. 386–399.  
  •  
This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.
 
Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.
 
By using this site, you agree to the Terms of Use and Privacy Policy. World Heritage Encyclopedia™ is a registered trademark of the World Public Library Association, a non-profit organization.
 


Copyright © World Library Foundation. All rights reserved. eBooks from Project Gutenberg are sponsored by the World Library Foundation,
a 501c(4) Member's Support Non-Profit Organization, and is NOT affiliated with any governmental agency or department.