What is the range of values of investment multiplier? Clarify the relation of investment multiplier with MPC and MPS.

Dear Student

The range of investment multiplier is greater than 1 but less than infinity .
Let us do the algebric derivation of the investment multiplier to find out its relation with MPC and MPS , marginal propensity to consume and marginal propensity to save .

$$\begin{gathered} At equilibrium level of income : \\ Y= C+I \\ Writing in terms of changes in variables: \\ △Y=△C+△I \\ Consumption function: \\ C=a+bY \\ a=autonomous consumption (a cons\tan t term) \\ b=MPC \\ △C=b△Y \end{gathered}$$

$$\begin{gathered} △Y=b△Y+△I \\ Solving this we get: \\ (1-b)△Y=△I \\ or,\frac{△Y}{△I}=\frac{1}{1-b} \end{gathered}$$

$\frac{△Y}{△I}=\frac{1}{1-MPC}=\frac{1}{MPS}$
Note that the value of multiplier ∆Y/∆I will remain constant as long as marginal propensity to consume remains the same . Hence we obtain the relation of investment multiplier with MPC and MPS .

Regards .