Investment multiplier (K) is the relationship between the final change in income and the initial change in investment. It is estimated as the ratio of change in investment income due to' change investment. Marginal Propensity to Consume (MPC) is the ratio of change in consumption to the change in income, There is a direct relationship between investment multiplier and MPC.
We know that,
\(Y=C+I\)
Or; \(\Delta Y=\Delta C+\Delta I\)
Dividing both sides by \(\Delta I\), we get:
\(\frac { \Delta Y }{ \Delta Y } =\frac { \Delta C }{ \Delta Y } +\frac { \Delta I }{ \Delta Y } \)
\(\Rightarrow \) \(I=\frac { \Delta C }{ \Delta Y } +\frac { \Delta I }{ \Delta Y } \)
\(\Rightarrow \)  \(I-\frac { \Delta C }{ \Delta Y } =\frac { \Delta I }{ \Delta Y } \)
Or;\(\frac { I }{ I-\frac { \Delta C }{ \Delta Y } } =\frac { \Delta Y }{ \Delta I } \)
Since  \(\frac { \Delta C }{ \Delta Y } =\)Marginal Propensity to Consume
Thus,  \(\frac { \Delta Y }{ \Delta I } =\frac { I }{ I-MPC } \)
\(\therefore \)  \(K=\frac { I }{ I-MPC } \)
One man's expenditure is another man's income. Whenever there is an increment in investment expenditure, some individuals' income is increased by the amount of investment with which they buy goods and services. They spend a part of their increased income on consumption and keep some income for saving. The individuals' MPC determines the amount they spend or save. If MPC is greater than MPS, individuals will spend more on consumption; and if MPC is less than MPS, the individuals' expenditure on consumption will be less.The extent of the effect of multiplier depends upon the Marginal Propensity to consume. Higher the MPC, higher will be the value of multiplier.
If MPC\(=\frac { 1 }{ 2 } \),
\(K=\frac { 1 }{ 1-\frac { 1 }{ 2 } } =\frac { 1 }{ \frac { 1 }{ 2 } } =2\)
If MPC\(=\frac { 3 }{ 4 } \),
\(K=\frac { 1 }{ 1-\frac { 3 }{ 4 } } =\frac { 1 }{ \frac { 1 }{ 4 } } =4\)
At lower MPC, multiplier is 2 and at higher MPC, multiplier is 4.