Q.If the Marginal Propensity to Consume (MPC) in an economy is 0.8, calculate the investment multiplier. If autonomous investment increases by Rs. 200 crore, find the resulting total increase in national income.

The investment multiplier is a crucial concept in Keynesian economics that explains how an initial change in investment can lead to a much larger change in the economy's total income and output. This phenomenon occurs because spending by one person becomes income for another, who then spends a portion of that income, and so on, creating a chain reaction of expenditure.

The size of this multiplier effect depends directly on the Marginal Propensity to Consume (MPC), which is the fraction of additional income that households spend rather than save. If people spend a larger portion of any extra income they receive, the multiplier effect will be stronger, as more of the initial investment will circulate through the economy. Conversely, if people save a larger portion (meaning a lower MPC), the multiplier will be smaller.

To calculate the investment multiplier (K), we first need to identify the Marginal Propensity to Consume (MPC) from the given consumption function.

1. Identify the Marginal Propensity to Consume (MPC):

   The general form of a linear consumption function is $C = \bar{C} + cY$, where $C$ is consumption, $\bar{C}$ is autonomous consumption (consumption independent of income), $c$ is the Marginal Propensity to Consume (MPC), and $Y$ is income.

   Given the consumption function: $C = 100 + 0.75Y$.

   Comparing this with the general form, we can see that the MPC ($c$) is $0.75$.

2. Apply the Investment Multiplier Formula:

   The investment multiplier (K) is calculated using the MPC.

   The investment multiplier (K) is given by:

   $K = \frac{1}{1 - \text{MPC}}$

   Substitute the identified MPC into the formula:

   $K = \frac{1}{1 - 0.75}$

   $K = \frac{1}{0.25}$

   $K = 4$

   Note

   The autonomous investment $I_0 = 400$ is provided but is not required to calculate the value of the investment multiplier itself. It would be used if we were asked to find the total change in income resulting from this investment.

The value of the investment multiplier (K) is $4$. This means that for every rupee of investment, the national income will increase by four rupees.

Part (a)

The investment multiplier is $K = \dfrac{1}{\text{MPS}}$. Given $K = 5$:

"Dissavings are (−)100 crore" means that at zero income, saving is $-100$ — this is the autonomous saving (the intercept). The saving function is:

At $Y = 1400$:

Part (b)

The investment multiplier is:

Since MPC lies between 0 and 1 (strictly less than 1 in a closed economy without government), the denominator $(1-\text{MPC})$ lies between 1 and 0. Therefore:

• when $\text{MPC}=0$, $K = 1$;
• as $\text{MPC}\to 1$, $K \to \infty$.

The multiplier is always at least 1 and can rise without limit; it is never zero or negative.

The investment multiplier captures the Keynesian idea that an initial rise in investment sets off successive rounds of spending: one person's spending becomes another's income, part of which is re-spent, and so on. The total rise in income is therefore a multiple of the initial investment, and its size depends on how much of each extra rupee of income is spent (MPC) versus saved (MPS).

Part (a)

Given $\text{MPS} = 0.5$:

So the correct alternative is (b) 2.

Part (b)

Here the actual changes are given: $\Delta Y = ₹\,3{,}000$ crore and $\Delta I = ₹\,1{,}200$ crore.

So the correct alternative is (b) 2·5.