### *If MPC is 0.2, Find Multiplier (k)? Complete Explanation for APPSC, UPSC, Class 12 Economics*

*Introduction*

In macroeconomics, one of the most asked questions in APPSC Group 2, UPSC, and Class 12 CBSE Economics is: *If Marginal Propensity to Consume (MPC) is 0.2, what is the value of Multiplier (k)?*

Many students get confused between MPC, MPS, and Multiplier. In this post, Unique Study Centre Kadapa will explain step-by-step formula, calculation, graph, and importance.

*What is MPC? (Marginal Propensity to Consume)*

MPC is the ratio of change in consumption to change in income.

*Formula: MPC = ΔC / ΔY*

It means, if income increases by Rs 100, how much extra is spent on consumption. MPC value always lies between 0 and 1.

If MPC = 0.2, it means:

Out of every additional Rs 1 of income, the consumer spends only 20 paise (0.20 Rs) and saves 80 paise.

This is typical of an economy where people save more, like during recession or high-interest rate period.

*What is Multiplier (k)?*

The investment multiplier was given by *J.M. Keynes*. It shows how many times income increases due to an initial increase in investment.

*Definition:* Multiplier is the ratio of change in income to change in investment.

*k = ΔY / ΔI*

Keynes said: An initial investment creates income, that income creates consumption, that consumption again creates income - this chain continues.

*Formula to Find k from MPC:*

There are two main formulas:

*1. k = 1 / (1 - MPC)*

*2. k = 1 / MPS* where MPS = Marginal Propensity to Save and MPS = 1 - MPC

*Calculation: If MPC = 0.2, Find k*

Given: MPC = 0.2

Step 1: Find MPS

MPS = 1 - MPC = 1 - 0.2 = 0.8

Step 2: Apply Multiplier Formula

k = 1 / MPS = 1 / 0.8 = 1.25

OR directly

k = 1 / (1 - MPC) = 1 / (1 - 0.2) = 1 / 0.8 = *1.25*

*Answer: Multiplier k = 1.25*

*What Does k = 1.25 Mean?*

It means if initial investment increases by Rs 100 crores, total national income will increase by:

ΔY = k x ΔI = 1.25 x 100 = Rs 125 crores.

Income rises only 1.25 times. This is a *small multiplier*. It indicates high savings, low consumption.

*Comparison Table for Better Understanding*

MPC MPS (1-MPC) Multiplier k = 1/MPS Meaning

0.2 0.8 1.25 Very Low - High Saving Economy

0.5 0.5 2 Medium

0.8 0.2 5 High - High Consumption Economy

0.9 0.1 10 Very High

*Conclusion: Relation Between MPC and k is Direct.*

When MPC increases, k also increases. When MPC is low like 0.2, k is also low (1.25).

*Why Low MPC (0.2) is Important for APPSC?*

1.  In exam, they may ask in reverse: If k = 1.25, find MPC? Answer is 0.2

2.  Graph: As MPC falls, Aggregate Demand curve becomes flatter.

3.  Policy: If government wants faster growth, it should try to increase MPC by reducing taxes, giving subsidies.

4.  Paradox of Thrift: If everyone saves 80% (MPS=0.8), multiplier is low, economy grows slowly.

*Practice Questions (Previous Year APPSC / CBSE)*

*Q1. If MPC = 0.75, find multiplier?*

Ans: k = 1/(1-0.75) = 1/0.25 = 4

*Q2. If MPS = 0.2, find MPC and k?*

Ans: MPC = 1 - 0.2 = 0.8, k = 1/0.2 = 5

*Q3. If k = 2.5, find MPC?*

Ans: 2.5 = 1/(1-MPC) => 1-MPC = 0.4 => MPC = 0.6

*Final Note from Unique Study Centre Kadapa*

We hope this concept is clear. Remember the golden formula: *k = 1/(1-MPC)*. For any value, just put it.

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