THE CONCEPT OF MULTIPLIER

• The theory of multiplier is important in modern theory of income and employment.
• The concept was first developed by F.A. Kahn in the early 1930s, later refined by Keynes.
• Kahn’s multiplier is focused on the increase in employment due to an initial increase in investment.
• Keynes’s multiplier refers to the increase in total income as a result of initial investment.
• Kahn’s multiplier is called employment multiplier, while Keynes’s is known as investment or income multiplier.
• The essence of the multiplier is that the total increase in income, output, or employment is a multiple of the original increase in investment.
• For example, if an investment of ₹100 crore leads to a national income increase of ₹300 crore, the multiplier is 3.
• If ₹100 crore investment results in a ₹400 crore increase in income, the multiplier is 4.
• The multiplier is the ratio of increase in income (∆Y) to the increase in investment (∆I), expressed as k = ∆Y / ∆I.
• The increase in income is greater than the initial increase in investment due to a chain reaction of spending.
• For example, if the government invests ₹100 crore in public works like road construction, it will pay wages and prices for materials, increasing incomes by ₹100 crore.
• The people receiving the ₹100 crore will spend a portion on consumer goods. If the marginal propensity to consume(MPC) is 0.8, they will spend ₹80 crore on consumer goods.
• The recipients of the ₹80 crore will then spend ₹64 crore, continuing the chain of income increase.
• This cycle of spending continues, but each successive increase in income is smaller due to savings.
• As a result, total income increases by more than the initial ₹100 crore investment.

Derivation of Investment Multiplier

• The increase in national income as a result of an initial increase in investment can be expressed as:
  $\mathrm{\Delta }Y=100+100\times \frac{4}{5}+100{\left(\frac{4}{5}\right)}^2+100{\left(\frac{4}{5}\right)}^3+100{\left(\frac{4}{5}\right)}^4+\dots$
  
• The above series is a geometric progression with the common ratio 4/5.
• The sum of an infinite geometric series is given by the formula:
  $\mathrm{\Delta }Y=100[1+\left(\frac{4}{5}\right)+{\left(\frac{4}{5}\right)}^2+{\left(\frac{4}{5}\right)}^3+{\left(\frac{4}{5}\right)}^4+\dots ]$
  
• This is a geometric series with the first term 100 and the common ratio 4/5.
• The sum of an infinite geometric progression is calculated as:
  $\mathrm{\Delta }Y=\frac{100}{1-\frac{4}{5}}=\frac{100}{\frac{1}{5}}=100\times 5=500$
  
• Thus, if the marginal propensity to consume (MPC) is 4/5 (0.8), an investment of 100 crore results in an increase in national income by 500 crore.
• The multiplier in this case is 5.
• The formula for the multiplier is expressed as:
  $k=\frac{1}{1-\text{MPC}}$
  
• This shows that the size of the multiplier depends on the marginal propensity to consume (MPC).
• The multiplier is the reciprocal of 1 minus MPC.
• Saving (S) is equal to income minus consumption, so:
  $1-\text{MPC}=\text{MPS}$ (where MPS is the marginal propensity to save).
• Therefore, the multiplier can also be expressed as:
  $k=\frac{1}{\text{MPS}}$
  
• In summary, the multiplier is the reciprocal of the marginal propensity to save.