Question

The function of the investment multiplier of the economy is denoted as:

• A. 1 - MPS
• B. 1/1-MPS
• C. MPC
• D. 1/1-MPC

Hint:

Key Multiplier formulas:
\(k = \frac{1}{1 - MPC} = \frac{1}{MPS}\).
Beware of options like \(1/(1 - MPS)\), which is mathematically incorrect because \(1 - MPS = MPC\).

Answer 1

The Correct Option is D

Concept:
The investment multiplier indicates the ratio of the total change in national income to the initiating change in investment spending.
It can be expressed mathematically in terms of the Marginal Propensity to Consume (\(MPC\)) or the Marginal Propensity to Save (\(MPS\)).

Step 1: Deriving the Multiplier Formula:
At macroeconomic equilibrium: \[ Y = C + I \] Assuming a linear consumption function \(C = \bar{C} + cY\), where \(c = MPC\): \[ Y = \bar{C} + cY + I \] Differentiating with respect to investment: \[ \Delta Y = c \Delta Y + \Delta I \] \[ \Delta Y (1 - c) = \Delta I \] \[ \frac{\Delta Y}{\Delta I} = \frac{1}{1 - c} \] Therefore, the multiplier \(k\) is given by: \[ k = \frac{1}{1 - MPC} \]

Step 2: Comparison with Other Expressions:
Since \(1 - MPC = MPS\), the formula can also be written as \(k = \frac{1}{MPS}\).
Among the given options, the correct mathematical formula is represented by \(1/(1 - MPC)\).
Final Answer:
The investment multiplier is denoted by \(1/(1 - MPC)\). Hence, option (D) is correct.