What is Harrod’s model of economic growth?

Harrod’s model of economic growth

Like Domar, Harrod also examines the possibility of steady growth. He points out the nature of possible paths along with the economy might progress. Since the progress is never smooth, Harrod also indicates the difficulties which an economy might encounter in the process of steady growth.

Harrod has developed his model on the basis of three distinct concepts of rates of growth. First, there is the actual rate of growth indicated by G. It is determined by the saving ratio indicated by s and the incremental capital-output ratio indicated by C.

The second concept is the warranted rate of growth indicated by G_w. The warranted rate of growth is taken to be the rate of growth required for the full utilisation of a growing stock of capital.

If warranted rate of growth occurs, it “will leave all parties satisfied that they have produced neither more nor less than the right amount.” A third concept is the natural rate of growth indicated by G_n.

Harrod defines it as the rate of growth that is determined by the current growth of the working population and the current potential for technical progress. Such a rate of growth is not determined by the wishes of people as regards saving.

Harrod begins his argument by stating the truism that saving and investment, if interpreted in ex post sense, are equal to each other. He uses the following equation to express this relationship between the two:

Where G indicates the actual rate of growth in a given period, and can be expressed as C indicates the ratio of investment to the increase in income, and can be expressed as and s is saving expressed as a c proportion of income. It can thus be written as y. Substituting for G, -Jy for C and y for s in the above equation we get

After stating this truism, Harrod postulates behaviour relations with regard to saving and investment. Like Keynes, he believes that saving depends on the level of income. But about the investment he thinks differently.

For him investment depends on the rate of increase in income. Obviously this involves acceleration principle which was something alien to the Keynesian system.

In the Keynesian system income and employment are said to be in equilibrium if ex ante (planned) saving is completely offset by ex ante (planned) investment. However, at the equilibrium level of employment presence of involuntary unemployment is not ruled out.

To maintain full employment, ex ante saving out of a full employment income should be necessarily offset by an equal amount of ex ante investment. According to Harrod, this much of investment would not be made in the natural course.

In order to induce it, it is necessary that income grows. He uses the following fundamental equation to indicate the equilibrium of steady growth.

Where G_w is the warranted rate of growth, C_r is the amount of capital required for maintaining the rate of growth given by G_w and s is the same as indicated earlier.

In Harrod’s system it has been assumed that saving intentions are always realised. Therefore, if there is any discrepancy between ex ante saving and ex ante investment, it will take the form of unintended investment.

However, Harrod’s fundamental equation assumes that ex ante investment is always equal to ex ante saving which implies that economy is constantly in the state of Keynesian equilibrium. In other words, Harrod’s fundamental equation tells us that there is only one path of economic advance – that of steady growth. In reality this may not happen.

Harrod has also considered the implications of deviations of G (the actual rate of growth) from G_w (the warranted rate of growth). Let us first consider the case when G is greater than G_w. In this case the value of C will be lower than C_r. There will then be an undue depletion of stock or shortage of equipment.

This situation will develop into a case of chronic inflationary gap implying that ex ante investment will be larger than ex ante saving. Looked from a different angle it will be a case of production falling short of aggregate demand.

If, on the contrary, G is less than G_w then C will be greater than C_r implying that there will be redundance of capital goods. This situation will lead to chronic deflationary gap in which ex ante investment will fall short of ex ante saving.

Harrod also states that any departure of G from G_w is unstable. It “instead of being self-righting will be self-aggravating.” Thus if G is greater than G_w then ex ante investment is greater than ex ante saving, and this stimulates further expansion.

If on the contrary, G is less than G_w then ex ante investment falls short of ex ante saving. This situation will result in unintended build up of inventories which in turn will depress investors so much that they will keep the rate of increase in output below G_w. Obviously this will have a still more depressing influence retarding economic growth even more.

If a departure from equilibrium as would happen in all cases of G deviating from G_w is self-aggravating rather than self-righting, then the question arises as to how income will stop from shooting up or down without limit.

Harrod has assumed that propensity to save and capital coefficient are constant, and thus he cannot look for an answer to the above problem in the variability of propensity to save or capital coefficient.

According to Harrod, the stimulus to expansion in case of G being greater than G_w will certainly not result in an unending process. In fact, there is an upper limit to the expansion process which is set by fundamental natural conditions such as increase in population, accumulation of capital, technological improvement and the work/leisure preference schedule.

This limit may be characterised as the “full- employment ceiling.” Obviously that is not a fixed limit, it will keep on changing as the basic resources grow and technological progress occurs.

Harrod calls the rise in the upper full employment ceiling the natural rate of growth and indicates it by G_n. There is no inherent reason for the natural rate of growth and the warranted rate of growth to coincide.

Harrod does not think that there is some unique warranted rate of growth. Its value depends upon the phase of the trade cycle and the level of economic activity. However, one can consider that warranted rate which would be obtained in conditions of full employment.

Harrod calls it “proper” warranted rate, but cautions that a “proper” warranted rate higher than the natural rate will not necessarily be something good for the economy. He asserts, “The system cannot advance more quickly than the natural rate allows. If the proper warranted rate below its proper level and so keep its average value over a term of years down to the natural rate.

But this reduction of the warranted rate is only achieved by having chronic unemployment. The warranted rate may be pushed upwards by rising prices and profits. If the proper warranted rate is lower than the natural rate the average value of the warranted rate can be sustained above its proper level for some time by a succession of profit booms.

Harrod thus concludes that “each state of affairs has its appropriates evils.” Harrod has used his model to explain trade cycles. In the recovery phase, because of the existence of unemployed resources, G > G_n. When full employment is reached G = G_n. If G_w exceeds G_n at the full employment, slump is inevitable.

Since G had to fall below G_w, it will, for the time being, be driven progressively downwards. Further, G itself fluctuated during the course of the business cycle. Savings as a fraction of income, though fairly steady in the long run, fluctuate in the short run.

In the short run, savings tend to be residual between the earning and normal consumption. Companies, also, are likely to save a large portion of their short-period increased in net receipts.

Thus, even it G_w is normally below G_n, it is likely to ride above G_n in the later stages of advance, and, if it so happens, a vicious spiral of depression is inevitable when full employment is reached.

If G_w does not ride above G_n in the course of advance, there would be continued pressure to advance when full employment is reached; this would lead to inflation and consequently, sooner or later, to a rise of G_w above G_n, resulting ultimately into a vicious spiral of depression.

Actually, G may be reduced before the employment is reached because of immobilities, frictions, and bottlenecks and, if it so happens, depression may come before full employment is reached. If G_w is far above G_n, G may never rise far above G_w during the revival and the depression may result long before full employment is reached.