Step 1: Understanding the Concept:
The Investment Multiplier (\(k\)) measures the ratio of the change in national income (\(\Delta Y\)) to the initial change in investment (\(\Delta I\)).
It shows how many times the total income increases as a result of an initial injection of investment.
The Marginal Propensity to Consume (MPC) is the ratio of change in consumption to change in income. It represents the proportion of additional income that is spent on consumption.
Step 2: Key Formula or Approach:
The multiplier is mathematically related to the MPC and the MPS (Marginal Propensity to Save) by the following formulas:
\[ k = \frac{1}{1 - MPC} \]
Or, since \(MPC + MPS = 1\), then \(1 - MPC = MPS\), so:
\[ k = \frac{1}{MPS} \]
Step 3: Detailed Explanation:
Given: \(MPC = 0.8\)
Applying the formula:
\[ k = \frac{1}{1 - 0.8} \]
\[ k = \frac{1}{0.2} \]
To convert the decimal 0.2 into a fraction: \(0.2 = \frac{2}{10} = \frac{1}{5}\).
\[ k = \frac{1}{\frac{1}{5}} = 5 \]
This means that if there is an autonomous investment of \(\$100\) crore, the final increase in national income will be \(5 \times 100 = \$500\) crore.
The higher the MPC, the higher the multiplier, because a greater portion of income is re-spent in subsequent rounds of the circular flow of income.
Step 4: Final Answer:
The value of the investment multiplier is 5.