REVERSE MULTIPLIER

The multiplier can be used in the propagation of the income through the increase in the investment expenditure. The shifts in the opposite direction are also possible. In the case of the reverse operation of the multiplier, the initial reduction in the investment will cause a multiple contraction of the income via a reduction in the consumption. The magnitude of contraction due to the backward operation of the multiplier depends on the value of MPC. The higher is the MPC, the greater will be the cumulative decline in income and vice-versa. Thus, an economy with a high propensity to consume (or low propensity to save) will be hurt more by the reverse operation of the multiplier, as discussed below. The multiplier is, thus, symmetric and works both the ways. It is a double- edged weapon.

To illustrate, assume, that MPC is 0.80 and the investment declines from RS.200 lakhs to Rs. 100 lakhs. The drop in the income required to restore the equilibrium will be Rs. 500 lakhs. The reasoning is the same as before. The process of the decline of the income will be completed over a number of rounds. Initially, the fall in the income will be equal to the fall of the investment, that is Rs. 100 lakhs. Thereafter, the consumption level falls and results in the further fall of the level of the income to Rs.80 lakhs ( 80% of Rs.100 lakhs), then to Rs.64 lakhs and so on, till the planned investment again equals the planned saving. As the investment is reduced from Rs.200 lakhs to Rs.100  lakhs (by –Rs. 100 lakhs), the saving must also be reduced by Rs.100 lakhs. The new system reaches a new equilibrium with the income and the output get reduced by Rs. 500 lakhs.

The formula for the total decline in the income in the various rounds as a result of a given initial decline in the investment can be obtained in a similar manner

ΔY   =  - ΔI + b (- ΔI) + b² (-ΔI) +b³ (- ΔI) +b⁴ (-ΔI)

       = (-ΔI) (1+ b+b ²+b³ + b⁴ + ………)                       
       =     - Δ I     [ sum of the infinite terms of the geometric series         ]
              1-b            +b+b²+b³+b⁴+… is         1               ___         _  or     1                                              
                                                                       1-Common Ratio                 1-b                                                
       =       - ΔI       = -ΔI*K
             1-MPC             
  
In the present example, the decline in the initial investment (ΔI) is Rs. 100 lakhs and the marginal propensity to consume (MPC) is 0.8. The total decline in the income can be obtained from the formula

ΔY =  -100      = -100*4 = (-) Rs. 400 lakhs
         1-0.8
Thus, the total decline in the income of Rs.400 lakhs is obtained by multiplying the initial decline in the investment of Rs. 100 lakhs by the downward (reverse) investment multiplier of 4. It is important to note that had the MPC been higher than 0.8, the loss of income would have been much higher. No economy can afford to bear a permanent decline in the investment expenditure causing damage to the economy at such a scale.

For more help in Reverse Multiplier please click the button below to submit your homework assignment.