If MPC is $\frac{4}{5}$, then the value of multiplier will be equal to:

Question

Accepted Answer

The correct option is 2:
In Keynesian economics, the multiplier ($k$) measures the total change in equilibrium national income resulting from a change in autonomous expenditure, such as investment or government spending. It is fundamentally dependent on the Marginal Propensity to Consume (MPC), which is the fraction of additional income that households spend on consumption. The formula for the simple income multiplier is $k = \frac{1}{1 - \text{MPC}}$. In this problem, the MPC is given as $\frac{4}{5}$, which is equal to 0.8. Substituting this value into the formula: $k = \frac{1}{1 - 0.8} = \frac{1}{0.2}$. Calculating the final value, we find that the multiplier is equal to 5. This means that a one-unit change in autonomous spending will lead to a five-unit change in the national income.

The incorrect option is 1 (Value 4):
This answer may be arrived at by mistakenly using the reciprocal of the marginal propensity to save (MPS), but using the wrong MPS value, or by incorrectly multiplying the MPC. The MPS is calculated as $1 - \text{MPC} = 1 - 0.8 = 0.2$. The multiplier is $1 / \text{MPS} = 1 / 0.2 = 5$. Option 4 is simply the given value of MPC multiplied by 5.

The incorrect option is 3 (Value 2):
A multiplier value of 2 would imply an MPC of $0.5$ (since $1 / (1-0.5) = 2$). Since the given MPC is $0.8$, a value of 2 significantly underestimates the actual multiplier effect generated by an MPC of $\frac{4}{5}$, where a larger share of marginal income is consumed.

The incorrect option is 4 (Value 10):
A multiplier value of 10 would imply an MPC of $0.9$ (since $1 / (1-0.9) = 10$). A value of 10 overestimates the actual multiplier based on the provided MPC of 0.8. Furthermore, the multiplier must be positive and typically ranges from 1 to infinity (though usually a practical number) for positive MPC values.