question_answer

Derive the formula,                                                             \[K=\frac{1}{MPS}\] Where K = Investment multiplier MPS = Marginal Propensity to save Or Complete the following table:

Consumption Expenditure(Rs.)	Saving (Rs.)	Income (Rs.)	Marginal Propensity to Consume
100	50	150	\[-\]
175	75	\[-\]	\[-\]
250	100	\[-\]	\[-\]
325	125	\[-\]	\[-\]

Answer:

 We know that,             \[K=\frac{\Delta Y}{\Delta I}\] Where, K = Investment multiplier \[\Delta Y\]= Change in income \[\Delta I\] =Change in investment Also, \[\Delta Y=AC+\Delta /\] \[\Rightarrow \,\,\,\,\Delta I=\Delta Y-\Delta C\]      \[[\Delta C=\]Change in consumption\[]\] Now, \[K=\frac{\Delta Y}{\Delta Y-\Delta C}[\therefore \Delta /=\Delta Y-\Delta C]\] Dividing the numerator and denominator by\[\Delta Y\], we get \[\Delta Y\]     \[K=\frac{\Delta Y}{\frac{\Delta Y}{\Delta Y}-\frac{\Delta C}{\Delta Y}}\] \[K=\frac{1}{1-MPC}\]               \[\left[ \because \frac{\Delta C}{\Delta Y}=MPC \right]\] \[\Rightarrow \]   \[K=\frac{1}{MPS}\]      \[[\because MPC+MPS=1\Rightarrow 1-MPC=MPS]\] Hence,  \[K=\frac{1}{MPS}\]

Consumption Expenditure (Rs.)	Saving (S)(Rs.)	Income(Rs.) \[(Y=C+S)\]	Change in Consumptions Expenditure\[(\Delta Y)\]	Change in Income\[(\Delta Y)\]	Marginal Propensity to Consume(MPC)
100	50	150	\[-\]	\[-\]	\[-\]
175	75	250	75	100	0.75
250	100	350	75	100	0.75
325	125	450	75	100	0.75

Formulae used \[Y=C+S,MPC=\frac{\Delta C}{\Delta Y}\]