Harrod-Domar (H-D) Growth Model:

Any economy which wishes to grow it is in need of new investment, i.e., the net additions to capital stock. If for the output worth $1, the stock of capital worth $3 is required, then the ratio between capital and output will be 3 to 1. Such relationship is known as COR.

It means that to increase GNP worth $1, the new investment worth $3 will be required. The COR is represented by 'k', it is as:

Formula of COR:

k = K/Y or k = ΔK/ΔY

The saving ratio is shown by 's'. The saving ratio is shown by the equation:

S = sY

The investment (I) is defined as the change in capital stock (ΔK) then:

I = ΔK

As we told above that k = K/Y or k = ΔK/ΔY which means that there exists a direct relationship of total output and stock of capital. Solving for ΔK.

ΔK = k.ΔY

We know at equilibrium: I = S

As I = ΔK, and ΔK = k.ΔY, then:

I = ΔK = k.ΔY

While S = sY, then I = S.

S = sy= k.ΔY = ΔK = I or simply, it is:

sY = k.ΔY

Dividing the above equation by Y and k:

sY = k.ΔY or s = ΔY or ΔY = s = MPS

                                                     Y(k)   Y(k)      k     Y       Y     k    COR

The last equation shows that the rate of growth of GNP (ΔY/Y) is determined by saving ratio (s) and national COR (k).

In other words, it says that the growth rate of national income is directly or positively related to saving ratio     (i.e., the more an economy is able to save - and invest - out of given GNP, the greater will be the growth of GNP), and inversely or negatively related to the economy's COR (i.e., the higher is k, the lower will be the rate of GNP growth).

The economic logic of last equation is this that if the economies want to grow they must save and invest a certain proportion of their GNP. The more they save and invest, more will be their growth rate. The actual rate at which they can grow for any level of savings and investment depends upon on how productive that investment is.

The productivity of this investment, i.e., how much additional output can be produced from an additional unit of investment, can be measured by the inverse of the COR (k). It is as:

1/COR = 1/K which shows the output-capital ratio (or output investment ratio). As S = sY, by equating S and I, we get the following equation:

S = I or sY = I or s = 1/Y

This equation shows the rate of new investment. If we multiply it by its productivity we will get the rate at which GNP will increase.

(s) . 1 =  I x   1   = I x 1 x ΔY = ΔY

                                                              k     Y   I/ΔY   Y       I          Y

Now returning to the stages of growth theory and using final equation of H-D model (ΔY/Y = s/k), we come to know that the fundamental trick of economic growth is simply to increase the proportion of savings. If we raise 's' we can raise ΔY/Y (the rate of GNP growth). If the value of COR is 3 and the saving ratio is 6% in the country like Pakistan, then our economy can grow at the rate of 2% per year, as:

ΔY/Y = s/k = 6%/3 = 2%

If in the country like Pakistan the savings are increased to 15% through reducing the consumption and increasing the taxes, the growth rate can be increased from 2% to 5%. It is as:

ΔY/Y = s/k = 15%/3 = 5%

Rostow and his fellow stage theorists explained the take-off stage by this way. It means that those countries who were able to increase the savings rate by 15% to 20% grew at much faster rate than those which failed to boost their savings. Thus, the problem of economic growth and development is simply a matter of increasing saving and investment.

Constraints on Development of UDCs and the Remedy:

The main obstacle to or constraint on development in the most of UDCs is the low level of new capital formation or investment. Any country which wishes to grow at the rate of 6% per annum, if k = 3, then it will be in need of 18% of savings. If it manages for 15% domestic saving, then there would rise the "Saving Gap' of 3%. Such gap could be filled either through foreign aid or through the foreign private investment.

Thus the capital constraint stages approach to growth and development justifies "The Massive Transfers of Capital and Technical Assistance from DCs to UDCs".

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