The increase in income in an economy is four times more than the increase in investment. What is the value of marginal propensity to consume in this economy?

The correct value of the Marginal Propensity to Consume (MPC) in this scenario is 0.8.

To understand why, we need to look closely at the language used in the problem and how it applies to the Investment Multiplier formula.

1. Understanding the Investment Multiplier ($k$)

The investment multiplier ($k$) represents the ratio of the change in income ($\Delta Y$) to the change in investment ($\Delta I$):

$k = \frac{\Delta Y}{\Delta I}$

It is also expressed in terms of the Marginal Propensity to Consume ($MPC$):

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

2. The Calculation

The problem states: "The increase in income is four times more than the increase in investment."

In mathematical phrasing, "four times more than" means the original amount plus four times that amount.

• Let the increase in investment be $\Delta I$.
• The increase in income ($\Delta Y$) = $\Delta I + 4(\Delta I) = 5\Delta I$.

Now, we find the multiplier ($k$):

$k = \frac{\Delta Y}{\Delta I} = \frac{5 \Delta I}{\Delta I} = 5$

Using the multiplier formula to find $MPC$:

$5 = \frac{1}{1 - MPC}$

$1 - MPC = \frac{1}{5}$

$1 - MPC = 0.2$

$MPC = 1 - 0.2$

$MPC = 0.8$

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Why people mistake it for 0.75

The most common error is a linguistic one, where the reader interprets "four times more than" as simply "four times."

The Mistaken Logic:

If a student interprets the statement as $\Delta Y = 4\Delta I$, then the multiplier ($k$) becomes 4.

$4 = \frac{1}{1 - MPC}$

$1 - MPC = \frac{1}{4}$

$1 - MPC = 0.25$

$MPC = 0.75$

The Distinction:

• "Income is 4 times the investment": This implies $\Delta Y = 4\Delta I$ (Multiplier = 4).
• "Income is 4 times MORE than investment": This implies $\Delta Y = \Delta I + 4\Delta I$ (Multiplier = 5).

Because the phrasing "more than" indicates an additive increase over the base value, the multiplier is actually 5, leading to an MPC of 0.8.