Question

Calculate the multiplier for the following cases.

a.$MPS=0.25$

b. $\mathrm{MPC}=\frac{5}{6}$

c. $\mathrm{MPS}=0.125$

d. $\mathrm{MPC}=\frac{6}{7}$

Short answer

Calculation of Multiplier for the given values are found successfully.

a. The value of Multiplier for $MPS=0.25$is$4$.

b. The value of Multiplier for $MPC=5/6$is $6$.

c. The value of Multiplier for $MPS=0.125$is $8$.

d. The value of Multiplier for$MPC=6/7$is$7$.

Step-by-step solution

Calculation of Multiplier

Formula to calculate multiplier is

$Multiplier=1/1-MPC$

Where,

Marginal Propensity to Consume is represented by $MPC$

(Part a) Calculation of multiplier with MPS=0.25.

Calculate Multiplier when Marginal Propensity to save $MPS=0.25$

Multiplier$=\frac{1}{1-MPC}$

$=\frac{1}{1-MPC}\left(\begin{array}{l}\because MPC+MPS=1\\ MPC=1-MPS\end{array}\right)$

$=\frac{1}{1-(1-MPS)}$

$=\frac{1}{1-1+MPS}$

$=\frac{1}{MPS}$

$=\frac{1}{0.25}$

Multiplier$=4$

Therefore, the multiplier is $4$.

(Part b) Calculation of multiplier with MPC=5/6.

Calculation of Multiplier when the Marginal Propensity to Consume $MPC=5/6$

Multiplier $=\frac{1}{1-MPC}$

$=\frac{1}{1-\left(\frac{5}{6}\right)}$

$=\frac{1}{\left(\frac{6-5}{6}\right)}$

$=\frac{1}{\left(\frac{1}{6}\right)}$

$=\frac{1}{1}\times \frac{6}{1}$

$=\frac{6}{1}$

Multiplier=$6$

Therefore, The Multiplier is$6$.

(Part c) Calculation of Multiplier with MPS=0.125

Calculate Multiplier when The Marginal Propensity to save $MPS$$=0.125$$:$

Multiplier$=\frac{1}{1-MPC}$

$=\frac{1}{1-MPC}\left(\begin{array}{l}\because MPC+MPS=1\\ MPC=1-MPS\end{array}\right)$ localid="1651544551902" $=\frac{1}{1-(1-MPS)}$

localid="1651544570845" $=\frac{1}{1-1+MPS}$

$=\frac{1}{MPS}$

localid="1651544587536" $=\frac{1}{0.125}$

Multiplier =$8$

Therefore, The Multiplier =$8$

(Part d)Calculation of Multiplier with MPC =6/7

Calculate Multiplier when The Marginal Propensity to Consume $MPC=6/7$

Multiplier$=\frac{1}{1-MPC}$

$=\frac{1}{1-\left(\frac{6}{7}\right)}$

$=\frac{1}{\left(\frac{7-6}{7}\right)}$

$=\frac{1}{\left(\frac{1}{7}\right)}$

$=\frac{1}{1}\times \frac{7}{1}$

$=\frac{7}{1}$

Multiplier $=7$

Therefore ,The Multiplier =$7$.