The Harrod-Domar Models of Economic Growth

Roy Harrod (1939) and Evsey Domar (1949) developed a Keynesian theory of economic growth which predicted that an economy would exist on a knife-edge determined by the level of investment and saving. Rather than verging towards equilibrium following a disturbance (a rise or fall in withdrawal or injection) the economy would diverge away from equilibrium, steady non-inflationary growth. There is, however, a full capacity growth of the economy which requires a correct level of investment – with investment growing continuously. It follows that one of the major tasks of public policy is to bring actual growth and full employment growth together in order to maintain long-run stability. One way of doing this is to ensure there is adequate Savings to achieve the equilibrium investment required.

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Introduction:

The Harrod-Domar models of economic growth are based on the experiences of advanced economies and attempt to analyse the requirements of steady growth in such economy.

Contents:

1. Requirements of Steady Growth
2. The Domar Model
3. The Harrod Model
4. Limitations of These Models

1. Requirements of Steady Growth:

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Both Harrod and Domar are interested in discovering the rate of income growth necessary for a smooth and uninterrupted working of the economy. Though their models differ in details, yet they arrive at similar conclusions.

Harrod and Domar assign a key role to investment (I) in the process of economic growth. But they lay emphasis on the dual character of investment.

1. Investment (I) creates income (Y) – a demand effect.
2. I raises the productive capacity of the economy by increasing its capital stock – the ‘supply effect’ of investment.

Hence so long as net investment is taking place, real income and output (Q) will continue to expand. However, for maintaining a full employment equilibrium level of income it is necessary that both real income and output should expand at the same rate at which the productive capacity of the capital stock is expanding.

Otherwise, any divergence between the two will lead to excess of idle capacity, forcing entrepreneurs to curtail their investment expenditure. Ultimately, it will adversely affect the economy by lowering incomes and employment in the subsequent periods and moving the economy off the equilibrium path of steady growth.

Thus, if full employment is to be maintained in the long run, net investment needs to expand continuously. This further requires continuous growth in real income at a rate sufficient enough to ensure full capacity use of a growing stock of capital. This required rate of income growth may be called the warranted rate of growth or “the full capacity growth rate.”

Assumptions:

The models constructed by Harrod and Domar are based on the following assumptions:

(1) There is an initial full employment equilibrium level of income.

(2) There is the absence of government interference.

(3) These models operate in a dosed economy which has no foreign trade.

(4) There are no lags in adjustments between investment and creation of productive capacity.

(5) The average propensity to save is equal to the marginal propensity to save.

(6) The marginal propensity to save remains constant.

(7) The capital coefficient, i.e., the ratio of capital stock to income is assumed to be fixed.

(8) The general price level is constant, i.e., the money income and real income are the same.

(9) There is a fixed proportion of capital and labour in the productive process.

All these assumptions are not necessary for the final solution of the problem, nevertheless they serve the purpose of simplifying the analysis.

A Numerical Example

Suppose the economy is currently operating at a capacity production level of 1000 per year and has a capital-output ratio of 3. This means the capital stock is 3000. Assume the marginal propensity to consume out of GDP is 0.7 so the marginal propensity to save is 0.3. This includes business and public saving as well as household saving.

The Harrod-Domar growth model tells that the equilibrium growth rate (g) is g = 0.3/3 = 0.1; i.e., the economy can grow at 10 percent per year. We can now check this result. At the current GDP of 1000 the level of saving is 0.3 x 1000=300. The growth in GDP is 0.1 x 1000 = 100 and with a capital-output ratio of 3 the additional capital required to produce the additional output is 3 x 100 = 300.

300 is the investment required in order to increase capacity by the right amount and, sure enough, this happens to be equal to the amount of saving available in the economy.

 

2. The Domar Model:

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Domar builds his model around the following question: since investment generates income on the one hand and increases productive capacity on the other at what rate investment should increase in order to make the increase in income equal to the increase in productive capacity, so that full employment is maintained?

He answers this question by forging a link between aggregate supply and aggregate demand through investment.

Increase in Productive Capacity:

Domar explains the supply side like this. If the annual rate of investment is I, and the annual productive capacity per dollar of newly created capital be equal on the average to s (which represents the ratio of increase in real income or output to an increase in capital or the reciprocal of the accelerator or the marginal capital-output ratio). Thus the productive capacity of I dollar invested will be I.s dollars per year.

But some new investment will be at the expense of the old. It will, therefore, compete with the latter for labour markets and other factors of production. As a result, the output of old plants will be curtailed and the increase in the annual output (productive capacity) of the economy will be somewhat less than I.s.

This can be indicated as 1Ϭ, where a (sigma) represents the net potential social average productivity of investment (= ∆Y/I). Accordingly la is less than I.s. 1Ϭ is the total net potential increase in output of the economy and is known as the sigma effect. In Domar’s words, this “is the increase in output which the economy can produce,” it is the “supply side of our system.”

Required Increase in Aggregate Demand

The demand side is explained by the Keynesian multiplier. Let the annual increase in income be denoted by AY and the increase in investment by ∆I and the propensity to save by a (alpha) (=∆S/∆Y).

Then the increase in income will be equal to the multiplier (1/α) times the increase in investment:

∆Y = ∆I 1/α

Equilibrium:

To maintain full employment equilibrium level of income, aggregate demand should be equal to aggregate supply.

Thus we arrive at the fundamental equation of the model:

∆I 1/α = Iα

Solving this equation by dividing both sides by I and multiplying by a we get:

∆I/I = αϬ

This equation shows that to maintain full employment the growth rate of net autonomous investment must be equal to the MPS times the productivity of capital. This is the rate at which investment must grow to assure the use of potential capacity in order to maintain a steady growth rate of the economy at full employment.

3. The Harrod Model:

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R.F. Harrod tries to show in his model how steady (i.e., equilibrium) growth may occur in the economy. Once the steady growth rate is interrupted and the economy falls into disequilibrium, cumulative forces tend to perpetuate this divergence thereby leading to either secular deflation or secular inflation.

The Harrod Model is based upon three distinct rates of growth.

1. The actual growth rate represented by Q which is determined by the saving ratio and the capital-output ratio. It shows short-run cyclical variations in the rate of growth.
2. The warranted growth rate represented by Qw which is the full capacity growth rate of income of an economy.
3. The natural growth rate represented by Qn which is regarded as ‘the welfare optimum’ by Harrod. It may also be called the potential or the full employment rate of growth.

The Actual Growth Rate:

In the Harrodian model the first fundamental equation is:

I = S

The equation is simply a re-statement of the truism that ex-post (actual, realized) savings equal ex-post investment. The above relationship is disclosed by the behaviour of income. Whereas S depends on Y, I depends on the increment in income (∆Y), the latter is nothing but the accelerator principle.

The Warranted Rate of Growth:

The warranted rate of growth is, according to Harrod, the rate “at which producers will be content with what they are doing.” It is the “entrepreneurial equilibrium; it is the line of advance which, if achieved, will satisfy profit takers that they have done the right thing.”

Thus this growth rate is primarily related to the behaviour of businessmen. At the warranted rate of growth, demand is high enough for businessmen to sell what they have produced and they will continue to produce at the same percentage rate of growth. Thus, it is the path on which the supply and demand for goods and services will remain in equilibrium, given the propensity to save.

If income grows at the warranted rate, the capital stock of the economy will be fully utilised and entrepreneurs will be willing to continue to invest the amount of saving generated at full potential income. Qw is therefore a self-sustaining rate of growth and if the economy continues to grow at this rate, it will follow the equilibrium path.

Genesis of Long-run Disequilibria:

Full employment growth, the actual growth rate of Q must equal Qw, the warranted rate of growth that would give steady advance to the economy, and K (the actual capital goods) must equal Kr (the required capital goods for steady growth).

If Q and Qw are not equal, the economy will be in disequilibrium. For instance, if Q exceeds Qw, then K will be less than Kr. When Q>Qw, shortages result. There will be insufficient goods in the pipeline and/or insufficient equipment. Such a situation leads to inflation because actual income grows at a faster rate than that allowed by the growth in the productive capacity of the economy. It will further lead to a deficiency of capital goods, the actual amount of capital goods being less than the required capital goods (K<Kr).

Under the circumstances, desired investment would be greater than saving and aggregate production would fall short of aggregate demand. There would thus be chronic inflation.

Starting from the initial full employment level of income Y₀, the actual growth rate G follows the warranted growth path Gw up to point E through period t₂. But from t₂onward G deviates from Gw and is higher than the latter. In subsequent periods, the deviation between the two becomes larger and larger.

If Q < Qw, desired investment is less than saving and aggregate demand falls short of aggregate supply. The result is fall in output, employment, and income. There would thus be chronic depression.

Harrod  writes: “Around that line of advance which if adhered to would alone give satisfaction forces are at work, causing the system to depart further and further from the required line of advance.” Thus the equilibrium between Q and Qw is a knife-edge equilibrium.

For once it is disturbed, it is not self-correcting. It follows that one of the major tasks of public policy is to bring G and Gw together in order to maintain long-run stability. For this purpose, Harrod introduces his third concept of the natural rate of growth.

The Natural Rate of Growth:

The natural rate of growth is the rate of advance which the increase of population and technological improvements allow. It depends on population, technology, natural resources and capital equipment. In other words, it is the rate of increase in output at full employment as determined by a growing population and the rate of technological progress.

Now for full employment equilibrium growth Qn=Qw = Q. But this is a knife-edge balance. For once there is any divergence between natural, warranted and actual rates of growth conditions of secular stagnation or inflation would be generated in the economy.

If Q>Qw, investment increases faster than saving and income rises faster than Gw. If Q<Qw, saving increases faster than investment and rise of income is less than Qw. Thus Harrod points out that if Qw>Qn, secular stagnation will develop. In such a situation, Qw is also greater than Q because the upper limit to the actual rate is set by the natural rate.

When Qw exceeds Qn, K > Kr and there is an excess of capital goods due to a shortage of labour. The shortage of labour keeps the rate of increase in output to a level less than Gw. Machines become idle and there is excess capacity. This further dampens investment, output, employment and income. Thus the economy will be in the grip of chronic depression. Under such conditions saving is a vice.

This instability in Harrod’s model is due to the rigidity of its basic assumptions. They are a fixed production function, a fixed saving ratio, and a fixed growth rate of labour force. Economists have attempted to relieve this rigidity by permitting capital and labour substitution in the production function, by making the saving ratio a function of the profit rate and the growth rate of labour force as a variable in the growth process.

The policy implications of the model are that saving is a virtue in any inflationary gap economy and vice in a deflationary gap economy. Thus in an advanced economy, s has to be moved up or down as the situation demands.

A Comparative Study of the Two Models:

Points of Similarity:

The following are the points of similarity in the two models.

Given the capital-output ratio, as long as the average propensity to save is equal to the marginal propensity to save, the equality of saving and investment fulfils the conditions of equilibrium rate of growth.

It is the lack of labour and other factors of production which reduces Domar’s growth rate. Since labour is involved in Domar’s potential growth rate resembles Horrod’s natural rate.

Points of Difference:

There are, however, important differences in the two models:

(1) Domar assigns a key role to investment in the process of growth and emphasises on its dual character. But Harrod regards the level of income as the most important factor in the growth process. Whereas Domar forges a link between demand and supply of investment, Harrod, on the other hand, equates demand and supply of saving.

(2) The Domar model is based on one growth rate. But Harrod uses three distinct rates of growth: the actual rate (Q), the warranted rate (Qw) and the natural rate (Qn).

(3) Domar gives expression to the multiplier but Harrod uses the accelerator about which Domar appears to say nothing.

(4) For Harrod the business cycle is an integral part of the path of growth and for Domar it is not so but is accommodated in his model by allowing the average productivity of investment to fluctuate.

In other words, Domar does not suggest any behaviour pattern for entrepreneurs and the proper change in investment comes exogenously, whereas Harrod assumes a behaviour pattern for entrepreneurs that induce the proper change in investment.

4. Limitations of These Models:

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Some of the conclusions depend on the crucial assumptions made by Harrod and Domar which make these models unrealistic:

(1) The propensity to save (α or s) and the capital-output ratio (σ) are assumed to be constant. In actuality, they are likely to change in the long run and thus modify the requirements for steady growth. A steady rate of growth can, however, be maintained without this assumption. As Domar himself writes, “This assumption is not necessary for the argument and that the whole problem can be easily reworked with variable α and σ.”

(2) The assumption that labour and capital are used in fixed proportions is untenable. Generally, labour can be substituted for capital and the economy can move more smoothly towards a path of steady growth. Infact, unlike Harrod’s, model, this path is not so unstable that the economy should experience chronic inflation or unemployment if G does not coincide with Gw.

(3) The two models also fail to consider changes in the general price level. Price changes always occur over time and may stabilize otherwise unstable situations. According to Meier and Baldwin, “If allowance is made for price changes and variable proportions in production, then the system may have much stronger stability than the Harrod model suggests.”

(4) The assumption that there are no changes in interest rates is irrelevant to the analysis. Interest rates change and affect investment. A reduction in interest rates during periods of overproduction can make capital- intensive processes more profitable by increasing the demand for capital and thereby reduce excess supplies of goods.

(5) The Harrod-Domar models ignore the effect of government programmes on economic growth. If, for instance, the government undertakes programmes of development, the Harrod-Domar analysis does not provide us with causal (functional) relationship.

(6) It also neglects the entrepreneurial behaviour which actually determines the warranted growth rate in the economy. This makes the concept of the warranted growth rate unrealistic.

(7) The Harrod-Domar models have been criticised for their failure to draw a distinction between capital goods and consumer goods.

(8) According to Professor Rose, the primary source of instability in Harrod’s system lies in the effect of excess demand or supply on production decisions and not in the effect of growing capital shortage or redundancy on investment decisions.

Despite these limitations, “Harrod-Domar growth models are purely laissez-faire ones based on the assumption of fiscal neutrality and designed to indicate conditions of progressive equilibrium for an advanced economy.” They are important “because they represent a stimulating attempt to dynamize and secularise Keynes’ static short-run saving and investment theory, according to Kurihara.

Applications to Development Economics

Limitations / problems of the Harrod-Domar Growth Model

• Increasing the savings ratio in lower-income countries is not easy. The majority of developing countries have low marginal propensities to save. Extra income gained is often spent on increased consumption rather than saved. Many countries suffer from a persistent domestic savings gap.
• Many developing countries lack a sound financial system. Increased saving by households does not necessarily mean there will be greater funds available for firms to borrow to invest.
• Efficiency gains that reduce the capital/output ratio are difficult to achieve in developing countries due to weaknesses in human capital, causing capital to be used inefficiently
• Research and development (R&D) needed to improve the capital/output ratio is often under-funded
• Borrowing from overseas to fill the savings gap causes external debt repayment problems later.
• The accumulation of capital will increase if the economy starts growing dynamically – a rise in capital spending is not necessarily a pre-condition for economic growth and development – as a country gets richer, incomes rise, so too does saving, and the higher income fuels rising demand which itself prompts a rise in capital investment spending.