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Increase in investment leads to an upward shift in the aggregate expenditure function and the AE curve, thereby leading to an increase in the level of national income. A decline in the investment, on the other hand, brings about a downward shift in the aggregate expenditure function and AE curve and thus causes a contraction in the level of income. Now, we interested to find out, what is the quantitative relationship between the change in investment and the resulting change in national income? In other words, we would like to know as to how much increase in income any given amount of increase in investment of $100 million, bring about an increase in national income equal to only dollars one hundred million, or will it be more than this?

The answer to this will depend upon the value of 'Multiplier'. Multiplier, is the numerical coefficient of the quantitative relationship between the change in income and change in investment. It is a number by which the given change in investment should be multiplied to find out the change in income resulting from this change in investment.

In we denote the multiplier by the word K the change in income by ΔY, and the change investment my ΔI, then

K = ΔY/ ΔI

or Δ Y = K.ΔI

This means that increase in income will be equal to the increase in investment multiplied by the multiplier. With the given increase in investment, ΔI, the increase in income ΔY will be large if the multiplier K has a higher value, and small when AKL has a lower value.

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