question_answer

                                                What do you mean by Multiplier (K)? Explain the relationship between Marginal Propensity to Consume (MPC) and Multiplier (K).

Answer:

Ans.     Multiplier It means the ratio of change in income to change in investment. According to Keynes, "Investment multiplier tells us that when there is an increment of aggregate investment, income will increase by an amount, which is K times the increment of investment."        Relationship between MPC and Multiplier {K) The value of Multiplier is determined by the value of MPC. We know that,  \[K\frac{\Delta Y}{\Delta I}\]                \[\therefore \]\[K.\Delta I=\Delta Y\]or  \[\Delta I=\frac{\Delta Y}{K}\]or \[\frac{\Delta Y}{K}=\Delta I\]           ...(i) We also know that, \[Y=C+I\]or\[\Delta Y=\Delta C+\Delta I=\Delta Y-\Delta C\]           ...(ii) On putting the value of   from equation (ii) in the equation (i), \[\frac{\Delta Y}{K}=\Delta Y-\Delta C\] On dividing the above by \[\Delta Y\] \[\frac{\Delta Y}{K}\times \frac{1}{\Delta Y}=\frac{\Delta Y}{\Delta Y}-\frac{\Delta C}{\Delta Y}\]or\[\frac{1}{K}=1-\frac{\Delta C}{\Delta Y}\]or\[\frac{\Delta Y}{K}=\Delta Y-\Delta C\] Here,                 \[K=\frac{1}{1-MPC}\] \[\therefore \]                  \[\frac{\Delta C}{\Delta Y}=MPC\] This shows that there is a direct relationship between multiplier (K) and Marginal Propensity to Consume (MPC). As the value of MPC rises, the value of multiplier also rises and vice-versa.                           e.g. if    MPC=0.75 then, \[\frac{1}{1-0.75}=4\] and when the value of MPC = 0.80, then\[K\frac{1}{1-0.80}=5\] Thus, it is clear that the size of the Multiplier depends on the MPC. Higher the MPC, the larger the size of Multiplier and lower the MPC, the smaller is the size of Multiplier.