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Therefore once the size of the income (Y) and propensity to consume (C/Y = b) are known, the amount of savings and propensity to save (S/Y = 1 b) can be determined automatically. The level of employment directly depends upon the size of the effective demand. Therefore a higher value of the propensity to save is always desirable. Propensity to save varies in its values (between 1 to 0). Hence closer the value of 'b' to 1, more will it be favorable to promote employment. But if the 'b' value is closer to zero it would be highly unfavorable in generating employment. Contrarily, the value of S/Y closer to zero is favorable, while S/Y closer to 1 will be unfavorable in promoting employment opportunities. With this in mind let’s proceed with multiplier derivation.
ii) Derivation of multiplier: Keynes has established that deficiency in the effective demand as a cause of unemployment, is a result of the typical nature of consumers who display the propensity to consume. However, like classical economists he does not argue that such deficient effective demand can be compensated by an equivalent increase in private investment expenditure. Such investment spending (I) is also known as induced investment since it is induced by the profit motives of the entrepreneurs. With a fall in the value of propensity to consume and depressed demand for consumption goods it is more likely that investment expenditure will either remain constant or may even decline, but it cannot rise to compensate for deficiency. It is obvious that falling demand and sluggish market conditions will result in lower profit expectations.
The producer therefore will certainly not create fresh investment demand under the conditions of declining consumption demand. Here an important question arises: how can one correct the employment condition? Keynes has suggested that public authority should undertake public expenditure or an investment program (G) to correct the level of effective demand and to restore the level of employment. Since public investment activity is not motivated by the profit consideration, it is called autonomous investment. With the inclusion of G the income equation can be rewritten as follows:
Y = C + I + G
However, the size of the autonomous investment G need not be as large as the original gap between income and consumption (Y - C) expenditure. Even the small size of the public expenditure can significantly raise the level of effective demand. This is because of the presence of the multiplier. Keynes has made an important use of the multiplier operation. Let’s illustrate a multiplier.
Given the two equations of income and consumption function the multiplier is present implicitly.
Y = C + I and C = by (on substitution),
Y = by + I
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