Harrod-Domar model

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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.

1 Overview
2 Mathematical formalism
3 Conclusions
4 Criticisms of the model
5 See also
6 External links

[edit] Overview

According to the model there are three concepts of growth:

Warranted growth – the rate of output growth at which firms believe they have the correct amount of capital and therefore do not increase or decrease investment, given expectations of future demand.
Natural rate of growth – The rate at which the labour force expands, a larger labour force generally means a larger aggregate output.
Actual growth – The actual aggregate output change.

Two possible problems are observed in an economy according to the Harrod-Domar model. First, the relationship between the actual and natural (population) growth rates can cause disparities between the two, as factors that determine actual growth are separate from those that determine natural growth. Factors such as birth control, culture, and general tastes determine the natural growth rate. However, other effects such as the marginal propensities to save and consume influence actual output. There is no guarantee that an economy will achieve sufficient output growth to sustain full employment in a context of population growth.

The second problem identified in the model is the relationship between actual and warranted growth. If it is expected that output will grow, investment will increase to meet the extra demand. The problem arises when actual growth either exceeds or fails to meet warranted growth expectations. A vicious cycle can be created where the difference is exaggerated by attempts to meet the actual demand, causing economic instability.

[edit] 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 the capital stock
$\ \frac{dY}{dK}=c$	2: The marginal product of capital is constant; the production function exhibits constant returns to scale
$\ \frac{d^2 Y}{dK^2}=0 \Rightarrow \frac{dY}{dK}=\frac{Y}{K}$	3: Since the marginal product of capital is constant, it equals the constant ratio Y/K
$\ sY=S=I$	4: The product of the savings rate and output equals saving, which equals investment
$\ \Delta\ K=I- \delta\$	5: The change in the capital stock equals investment less the depreciation of the capital stock

Derivation of output growth rate:

$\ c= \frac{dY}{dK}=\frac{Y(t+1) - Y(t)}{K(t) + sY(t) - \delta\ K(t) - K(t)}$

$\ c= \frac{Y(t+1) - Y(t)}{sY(t) - \delta\ \frac{dK}{dY} Y(t)}$

$\ c(sY(t) - \delta\ \frac{dK}{dY} Y(t))=Y(t+1) - Y(t)$

$\ cY(t)(s - \delta\ \frac{dK}{dY})=Y(t+1) - Y(t)$

$\ cs - c \delta\ \frac{dK}{dY}=\frac{Y(t+1) - Y(t)}{Y(t)}$

$\ s \frac{dY}{dK} - \delta\ \frac{dY}{dK} \frac{dK}{dY}=\frac{Y(t+1) - Y(t)}{Y(t)}$

$\ s \frac{dY}{dK} - \delta\ = \frac{ \Delta\ Y}{Y}$

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.

[edit] Conclusions

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 also had implications for less economically developed countries; labour is in plentiful supply in these countries but physical capital is not, slowing economic progress. LDCs do not have sufficient average incomes to enable high rates of saving, and therefore accumulation of the capital stock through investment is low.

The model has been used to imply that economic growth depends on policies to increase saving (investment), and using that investment more efficiently through technological advances.

The model concludes that an economy does not find full employment and stable growth rates naturally, similar to the Keynesian beliefs.

[edit] 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 widely believed to be false.

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.