Question

• Keynes’ Multiplier

1. Explain the multipliers’ central point.

2. What is the formula to calculate the multiplier?

3. Calculate the corresponding changes in disposable income, consumption and saving on each round in the model used in class in order to demystify the multiplier.

Answer 1

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1) According to Keynes, Multiplier is a constant number that measures the change in income due to change in an exogenous variable say consumption, saving, investment, and government expenditure.

2) Formula to calculate multiplier = 1/ 1 - b

where b = marginal propensity to consume

or 1 - b = marginal propensity to save

3)

Suppose In round 1 when autonomous investment change by △I, sine investment is a part of aggregate demand

(AD) that's why AD also changes by △I, here income level also changes by △I.

change in consumption function => C = a + bY

  △C = b △Y

   since △Y = △I = △S

  △C = b △I

and we know that consumption is also part of AD that is why AD also changes by b△I.

so, the total change in income = △I + b△I

= (1+b) △I

here again when income increases, consumption also increases:

  △Y = (1+b) △I at the end of the second round.

The change in consumption will be  △C = b.b △I = b2 △I

that's why the AD will change by b2 △I. Income also changes by the same amount and total change in income at the end of the third round will be = (1+b+b2) △I

This process remains to continue until the economy reaches in the equilibrium.

There will be n rounds in the economy then the total change in income in all rounds is =

  △Y = (1+ b + b2 + b3 + ------------+ bn-1) △I

the sum of a geometric progression = a / 1 - r

a = 1

r = b2 / b = b

sum will be = 1 / 1-b

so △Y = [1 / 1- b ] △I

   △Y / △I = 1 / 1-b

multiplier will be = 1 / 1-b

Change in income equals to multiplier times change in autonomous change in investment.