School of Economics | The Harrod-Domar Growth Model:
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## 21 Dec The Harrod-Domar Growth Model:

#### The Harrod-Domar Growth Model:

The aggregate production function—which is the main pillar of every growth theory—can take different forms, depending on the actual relationship between the factors of production (K and L) and aggregate output. The Harrod- Domar model is based on the simple fixed-coefficient pro­duction function of the Leontief type. In this case, the isoquants are L-shaped, in which case K and L are always used in fixed proportion to produce different levels of out­put, as is shown in Fig. 1. The production function is the ray OR which connects points like a, b, c, i.e., the elbow of each isoquant. With CRS the isoquants will be L-shaped and the production function will be a straight line through their minimum combination points. In this case, both capital-output ratio and labour-output ratio remain constant.

The Capital-Output Ratio:

The Harrod-Domar model was developed during the forties to explain the relationship between growth and unemployment in advanced capitalist societies. The central focus of the model is on the role of capital accumulation in the growth process. This is why the model has been extensively used in LDCs to examine the relationship between growth and capital re­quirements.

In this model, output is assumed to be linear function of capital as:

Q = 1/v.K or Q = K/v…..(7)

where v is a constant. In eqn. (1) the capital stock is simply multiplied by the fixed number 1/v to calculate aggregate production.

Eqn. (1) can be also be expressed as:

V = K/Q……(8)

so v is the capital-output ratio. It is essentially a measure of the productivity of capital or investment.

Two things get reflected in the capital-output ratio: capital intensity and efficiency.

It is the reciprocal of the average product of K: A high value of v implies more capital- intensive production activities. Therefore, those countries which have a large share of produc­tion in capital-intensive activities (such as steel, machinery, petrochemicals or automobiles) will show a larger aggregate capital-output ratio than a country that specialises in labour- inten­sive industries such as agriculture, textiles, food processing and footwear.

A high value of v can also imply less efficient production because it indicates how effi­ciently a society is able to utilise its present capital stock. In this model, since v is assumed to remain constant, the average capital-output ratio is the same as the incremental capital-output ratio (ICOR). The ICOR measures the productivity of additional capital.

It is often interpreted as the reciprocal of the marginal physical product of K:

The production function eqn. (1) can be converted into another equation to relate changes in output to changes in the capital stock

∆Y = ∆K/v

The growth rate of output, g, is simply the increment in output divided by total output . Dividing both sides of eqn. (3) by Y, we get

g = ∆Y/Y = ∆K/Yv ……(10)

Since the change in the capital stock AK is equal to saving minus the depreciation of capital (∆K = sY-dK) from eqn. (9), get, by substituting eqn. (6) into eqn. (4), following relationship between capital stock and growth

g = s/v ………(11)

This is the basic equation of the Harrod-Domar growth model, from which we can make the following two predictions:

1. The stock of capital crested by an act of investment in plant and equipment is the man determinant of growth.

2. Saving (both by households and companies) makes investment possible. Equation (10) brings into focus two key determinants of the growth rate — the saving rate and the efficiency with which capital is used in production or the productivity of investment (v).

So the central message of the Harrod-Domar model is that if a country saves more to make productive investments, its economy will continue to grow.

Application of the Harrod-Domar Model:

It is very easy for planners and policymakers to apply the Harrod-Domar model. They are left with two alternatives:

Alternative 1:

The first step is to estimate v and d for the country. Then a target rate of growth of the economy (g) can be fixed. Then the equation will tell the economic policymakers the level of saving and investment necessary to achieve that growth.

Alternative 2:

The policymakers can decide on the rate of saving and investment that is feasible or desirable. Then the equation will tell them the rate of growth in national product that can be expected.

The model can be applied to the economy as a whole, or to each sector or each industry. The value of v can be estimated separately for agriculture and industry. Once planners decide how much investment will be allocated to each sector, the model will enable them to determine the growth rates that can be expected in each of the two sectors.

Strengths and Weaknesses of the Harrod-Domar Model:

Over short periods of time (a few years) and in the absence of severe economic shocks (such as drought or large changes in export or import prices), the model can be used to estimate ex­pected growth rates easily and quickly. This is precisely the reason why this model has been extensively used in developing countries for economic planning.

However, the model has several limitations. The most serious is that in this model, the economy remains in equilibrium (with full employment of both labour force and capital stock) only in some special circumstances.

Since the production function is of fixed co efficiency type, capital stock and labour force must always grow at the same rate to main­tain equilibrium. But this is unlikely to happen. In order to keep v constant, K must grow at the rate g—which is the rate of growth of output. If K grew faster or slower than g, v would change.

Let us suppose that the labour force grows at rate n which is exactly the rate of population growth. Therefore, only if n = g = (s/v – d) then the capital stock and labour force will grow at the same rate. However, there is hardly any reason to suppose that the population will grow at the rate n.

On the one hand, if n > g, the labour force is growing faster than the capital stock. In this case, s is not high enough to support investment in new machinery sufficient to absorb all new additions to the labour force. So there will be the problem of unemployment (labour redun­dancy).

On the other hand, if g (or s/v -d)the capital stock is growing faster than the labour force. In this case, there will be shortage of manpower and some machines will remain idle. So actual growth rate will be n, which is less than g. The slowing down of the growth rate is due to non-availability of workers required to operate the machines fully.

In short, unless g = s/v – d, or exactly equal to n, either labour or capital will not be fully employed and the economy will not be in a stable equilibrium. This characteristic of the model is known as the knife-edge instability problem.

In short, as long as g = n, the economy remains in equilibrium. But as soon as either the capital stock or labour force grows faster than the other, the economy falls over the edge with growing unemployment or idle (machine) capacity.

The instability problem arises due to the assumptions of fixed capital-output and capital- labour ratios, which do not permit equalisation of g with n.

This lack of flexibility of the model is its most serious limitation. Moreover, the constancy of v is a reasonable assumption in short run but not in the long run. When the economy evolves and develops v may also rise or fall due to policy changes which affect efficiency with which capital is used.

Moreover, the capital-intensity of the production process may change over time. A low-income country with a low savings rate and surplus labour can achieve faster growth rates by making the maximum possible utilisation of its surplus labour and minimum amount of scarce capital.

With economic growth and rise in per capita income, there is less and less surplus labour in the economy and a gradual shift towards more capital-intensive production. Consequently, the ICOR increases. Thus, a rise in the value of v does not necessarily imply inefficiency or slower growth.

Fixity of ICOR:

Thus, the Harrod-Domar model tends to become more and more inaccurate over extended periods of time as the actual ICOR changes and with it the capital-labour ratio. These changes may occur to changes in wage rate and interest rates in response to changes in market forces (demand and supply conditions of labour and capital).

With economic growth the saving rate rises, and so the rate of interest or the price of financial capital falls while employment and wage rise. As a result, the production process becomes more capital-intensive since all producers increasingly economise on labour and use more capital and the ICOR tends to rise.

Lack of Factor Substitution:

Due to fixed coefficient type of production function, there is no scope for substitution of capital for labour or vice versa in the Harrod-Domar model. More output cannot be pro­duced by hiring one more worker without buying a machine or by purchasing one more machine without hiring some workers.

However, as the neoclassical growth theories, pre­sented by Solow and Meade, have convincingly demonstrated, the knife-edge instability problem can be solved by permitting factor substitution which is possible at least to some extent in the real world.

Technological Change:

Finally, there is no mention of any technological change in Harrod-Domar model. Technologi­cal progress plays a crucial role in the long-term growth and development by raising the pro­ductivity of existing resources. Technological progress can be shown by an inward shift of each isoquant towards the origin. The easiest way to capture technological progress in the Harrod- Domar framework is to introduce a smaller ICOR, but this would contradict the basic assump­tion of the model — constant ICOR.

#### Joan Robinson: The Accumulation of Capital:

Joan Robinson discussed the importance of capital accumulation to the growth process in 1956, the same year in which Solow’s Work on growth was published.