Investment Multiplier Numericals: MPC, MPS and Income Changes

Investment rises by Rs 36 crore. People spend three-fourths of every extra rupee they earn. How much does national income rise?

If you answered Rs 27 crore, you have calculated the next round of consumption. The question asks for something bigger: the total change in income after the multiplier process.

Here, MPC is 0.75, MPS is 0.25, and the investment multiplier is 4. Income therefore rises by Rs 144 crore.

The arithmetic is short. The real skill is knowing which amount the question has given you and which amount it wants back. Let’s build that skill with a formula map, a spending-round illustration, and original solved questions that gradually become less obvious.

The investment multiplier formula

The investment multiplier, written as K, measures the change in equilibrium income caused by a change in autonomous investment:

K = Change in income / Change in investment

Using the symbol Delta to mean change:

K = Delta Y / Delta I = 1 / (1 - MPC) = 1 / MPS

MPC is the marginal propensity to consume. MPS is the marginal propensity to save. In the simple model, MPC + MPS = 1. These relationships and the successive-round mechanism appear in NCERT’s Determination of Income and Employment, Sections 4.1 and 4.3.3.

Throughout this guide, we assume a closed two-sector economy, constant MPC, unchanged autonomous consumption, fixed prices, and enough unused resources to expand production. Investment changes independently of income. Unless a question says otherwise, monetary figures refer to the same period and are in crore rupees.

Keep the words additional and change in view. They prevent most errors in this chapter.

Read the question before choosing the formula

What you need	What the question gives	Calculation
K	MPC	1 / (1 - MPC)
K	MPS	1 / MPS
Income change	K and investment change	Delta Y = K x Delta I
Investment change	K and income change	Delta I = Delta Y / K
MPC	K	MPC = 1 - 1/K
MPS	K	MPS = 1/K

For the opening question:

MPC = 3/4
MPS = 1 - 3/4 = 1/4
K = 1 / (1/4) = 4
Delta Y = 4 x 36 = Rs 144 crore

Do not write K as Rs 4 crore. It is a ratio, with no monetary unit. It tells you that the income change is four times the investment change under the stated assumptions.

Translate ordinary language into MPC or MPS

The question may hide the proportion in a sentence:

• “Households consume 80% of additional income” means MPC = 0.80.
• “Households save 20 paise out of each extra rupee” means MPS = 0.20.
• “Additional consumption and additional saving are in the ratio 4:1” means MPC = 4/5 and MPS = 1/5.
• “Consumption rises by Rs 72 crore when income rises by Rs 90 crore” means MPC = 72/90 = 0.80.

All four statements lead to K = 5.

But “households consume 80% of their income” describes an average unless the question clearly specifies a proportional consumption function. Do not silently turn an average into a marginal propensity.

Why one investment change creates several rounds

Imagine a town where a firm orders newly produced equipment. The extra production generates income for workers and other resource owners. They spend part of their additional income, creating demand and income elsewhere. The next recipients repeat the process.

That is the useful idea behind the ripple metaphor in the picture: the initial disturbance is only the beginning. Each further round is smaller, but the rounds add up. The OpenStax explanation of the expenditure multiplier describes this connection between one person’s spending and another person’s income.

Let’s use our own figures. Investment rises by Rs 32 crore and MPC is 0.75.

Round	Additional income	Consumption passed onward	Additional saving
Initial investment round	32.00	24.00	8.00
Second round	24.00	18.00	6.00
Third round	18.00	13.50	4.50
Fourth round	13.50	10.125	3.375
All rounds together	128.00	96.00	32.00

The last row includes every later round, not just the four displayed.

After four rounds, income has increased by:

32 + 24 + 18 + 13.50 = Rs 87.50 crore

The remaining rounds contribute another Rs 40.50 crore. Together they approach Rs 128 crore:

K = 1 / 0.25 = 4
Delta Y = 4 x 32 = Rs 128 crore

Why does a sequence of smaller amounts give a larger total? Because we are adding the rounds, not asking whether the last round exceeds the first.

The rounds are a teaching device, not a promise that adjustment takes exactly four weeks or four months. Also, this is extra production and income across the economy. It is not a fourfold return credited to the investing firm’s bank account.

The first-round trap

With investment of 32 and MPC of 0.75:

• The initial income increase is 32.
• Consumption generated from that income is 24.
• The total income increase is 128.
• The total induced consumption increase is 96.

Those are four different answers to four different questions. Write the requested label beside your answer before moving on.

Derive the formula without memorising a series

Start from equilibrium in the two-sector model:

Y = C + I

Compare two equilibria when only investment changes:

Delta Y = Delta C + Delta I

With unchanged autonomous consumption and constant MPC:

Delta C = MPC x Delta Y

Substitute and rearrange:

Delta Y = MPC x Delta Y + Delta I
Delta Y x (1 - MPC) = Delta I
Delta Y / Delta I = 1 / (1 - MPC)

Therefore K = 1 / MPS.

This also gives a handy answer check:

Delta S = MPS x Delta Y = Delta I

For the 32-crore example, additional saving is 0.25 x 128 = 32. Total induced consumption is 0.75 x 128 = 96. The two add to 128.

This equality concerns the change in saving between the old and new equilibria. It does not say that households save the entire initial income increase immediately.

Worked example 1: MPC is given as a percentage

Question: MPC is 80%. Investment rises by Rs 28 crore. Find K and the increase in income.

First convert the percentage:

MPC = 80/100 = 0.80
MPS = 1 - 0.80 = 0.20
K = 1/0.20 = 5

Now use the change equation:

Delta Y = 5 x 28 = Rs 140 crore

Check the result:

Delta C = 0.80 x 140 = 112
Delta S = 0.20 x 140 = 28
112 + 28 = 140

Answer: The multiplier is 5 and income increases by Rs 140 crore.

The denominator is 1 - 0.80, not 1 - 80. Converting percentages before substitution is a tiny habit that saves a surprising number of marks.

Worked example 2: MPS is given directly

Question: People save 40% of additional income. Investment increases by Rs 42 crore. Calculate the increase in income.

MPS = 0.40
K = 1/0.40 = 2.5
Delta Y = 2.5 x 42 = Rs 105 crore

A multiplier does not have to be a whole number. Here, every additional rupee of investment supports Rs 2.50 of additional equilibrium income in the model.

The check is 0.40 x 105 = 42.

A common wrong answer comes from calculating 1/(1 - 0.40). That treats the stated saving proportion as a consumption proportion. Circle the word “save” before you start.

Worked example 3: Find investment for a target income increase

Question: Equilibrium income must rise from Rs 1,800 crore to Rs 2,160 crore. MPC is 5/6. Find the required increase in investment.

The target is a change, so subtract first:

Delta Y = 2,160 - 1,800 = 360

Then calculate K:

MPS = 1 - 5/6 = 1/6
K = 6

Now divide:

Delta I = 360/6 = Rs 60 crore

Do not multiply 360 by 6. Multiplication answers the forward question, where investment is given. Here we are working backwards from the desired income effect.

Do not use 2,160 as Delta Y either. That is the new income level, not the increase.

Worked example 4: Recover MPC and MPS from two changes

Question: Investment rises from Rs 90 crore to Rs 135 crore. Equilibrium income rises from Rs 700 crore to Rs 925 crore. Assuming investment is the only autonomous change, find K, MPC, and MPS.

Delta I = 135 - 90 = 45
Delta Y = 925 - 700 = 225

K = 225/45 = 5
MPS = 1/5 = 0.20
MPC = 1 - 0.20 = 0.80

We can verify the answer through consumption:

Delta C = Delta Y - Delta I = 225 - 45 = 180
MPC = Delta C / Delta Y = 180/225 = 0.80

The tempting division 925/135 uses two levels. It does not measure the multiplier for this change.

Worked example 5: Use a consumption schedule

Question: A stable consumption relationship gives these observations. Find the multiplier, then calculate the income effect of an investment increase of Rs 30 crore.

Income	Consumption
400	350
600	500

Calculate the changes:

Delta Y = 600 - 400 = 200
Delta C = 500 - 350 = 150
MPC = 150/200 = 0.75

Therefore:

MPS = 0.25
K = 4
Income increase = 4 x 30 = Rs 120 crore

Why not use 350/400 = 0.875? That is APC at the first income level. Why not use 500/600? That is APC at the second level. Neither is the slope between the observations.

These two rows lie on C = 50 + 0.75Y. The 50 makes the average consumption ratio differ from the marginal ratio. You can check the first row yourself: 50 + 0.75(400) = 350.

Worked example 6: Investment falls

Question: Investment decreases from Rs 150 crore to Rs 126 crore. MPS is 0.20. Find the change in equilibrium income.

Delta I = 126 - 150 = -24
K = 1/0.20 = 5
Delta Y = 5 x (-24) = -Rs 120 crore

Write the answer naturally: equilibrium income falls by Rs 120 crore.

K remains positive. The negative sign comes from the investment change. Lower investment reduces income, which reduces consumption and then income further. The multiplier can amplify a contraction as well as an expansion, as the OpenStax multiplier discussion explains.

Check: additional saving is 0.20 x (-120) = -24. Here “additional” means the change, which is negative.

Worked example 7: The units do not match

Question: Investment increases by Rs 75 lakh and income increases by Rs 3 crore. Find K and MPC.

Convert to one unit before division. Since one crore equals 100 lakh:

Rs 3 crore = Rs 300 lakh
K = 300/75 = 4
MPS = 1/4 = 0.25
MPC = 0.75

Alternatively, investment is Rs 0.75 crore, so K = 3/0.75 = 4.

The incorrect 3/75 = 0.04 divides crore by lakh as if they were the same unit. If the computed K looks unexpectedly tiny in a standard two-sector question, inspect the units before changing your formula.

Worked example 8: Additional consumption is given instead

Question: An investment increase of Rs 24 crore ultimately generates additional consumption of Rs 72 crore. Find the increase in income, K, and MPC.

Start with the accounting relationship between the changes:

Delta Y = Delta C + Delta I
Delta Y = 72 + 24 = 96

Then:

K = 96/24 = 4
MPC = 72/96 = 0.75
MPS = 0.25

Answer: Income rises by Rs 96 crore, K is 4, and MPC is 0.75.

Dividing 72/24 = 3 gives the ratio of induced consumption to investment. It is K - 1, not K. The missing one represents the initial investment contribution to income.

When the simple shortcut needs care

If MPC itself changes

Suppose C = 40 + 0.75Y and investment is 60. Initial equilibrium income is:

Y = (40 + 60)/0.25 = 400

Now investment rises to 80 and MPC rises to 0.80. New equilibrium income is:

Y = (40 + 80)/0.20 = 600

The income increase is 200. Multiplying the investment increase of 20 by the old K of 4 would give only 80. Using the new K of 5 would give 100. Neither captures both changes.

When the consumption slope changes too, calculate the two equilibria separately. Our guide to equilibrium income from a consumption function walks through that method.

If autonomous consumption changes too

With MPC fixed at 0.75, suppose investment rises by 20 and autonomous consumption rises by 10. The total autonomous spending change is 30. Income therefore rises by 4 x 30 = 120.

Calling 120/20 = 6 the investment multiplier would attribute both causes to investment alone. The model’s multiplier is still 4.

If taxes, imports, or capacity constraints matter

The basic 1/MPS result leaves out government and foreign trade. Taxes and imports can reduce the spending passed on to domestic producers; limited spare capacity can also limit the output response. CORE Econ’s multiplier model develops these extensions.

For a standard numerical, use the assumptions given. For an explanation of an actual economy, do not claim that MPC alone predicts the exact observed income response.

A compact revision check

Before you put down your pen, check these five things:

1. Changes: Have you subtracted old levels from new levels?
2. Propensity: Is the given number MPC, MPS, or an average ratio?
3. Units: Are both money amounts in the same unit?
4. Direction: Did you multiply to find income and divide to find investment?
5. Meaning: Does your final sentence say increase, decrease, or new level correctly?

For an extra numerical check, calculate MPS x Delta Y. In these examples it should equal Delta I. If it does not, revisit the calculation or check whether something besides investment changed.

Try these eight questions

Use the same simple model as above. All amounts are in crore rupees unless another unit is stated.

1. MPC is 0.60. Investment rises by 44. Find K and the income increase.
2. MPS is 0.125. Income must increase by 320. Find the required investment increase.
3. Investment rises by 35 and income rises by 140. Find MPC and MPS.
4. People consume 90% of additional income. Investment falls by 12. Find the income change.
5. Income rises from 500 to 650 and consumption rises from 440 to 560 along an unchanged linear consumption function. Find K.
6. MPC is 2/3. Income rises from 900 to 1,080 because of an investment increase. Find that increase.
7. Investment rises by 50 lakh and income rises by 2.5 crore. Find K and MPC.
8. An investment increase of 18 ultimately generates additional consumption of 54. Find the income increase and K.

Answers with the key step

1. MPS = 0.40, so K = 2.5 and Delta Y = 2.5 x 44 = 110.
2. K = 8, so Delta I = 320/8 = 40.
3. K = 140/35 = 4. MPS = 0.25, MPC = 0.75.
4. K = 10. Delta Y = 10 x (-12) = -120, a fall of 120.
5. MPC = (560 - 440)/(650 - 500) = 120/150 = 0.80. K = 5.
6. K = 3. Delta Y = 180, so Delta I = 180/3 = 60.
7. Income rises by 250 lakh. K = 250/50 = 5, so MPC = 0.80.
8. Delta Y = 54 + 18 = 72. K = 72/18 = 4.

If you missed a question, label the mistake before redoing it: wrong change, wrong propensity, wrong unit, or wrong direction. That makes the next practice session much more useful than copying the answer five times.

Frequently asked questions

What is the formula for the investment multiplier?

In the simple two-sector model, K = Delta Y / Delta I = 1/(1 - MPC) = 1/MPS. Use consistent units and hold the consumption relationship unchanged when comparing the two equilibria.

How do I know whether to use MPC or MPS?

If the question gives MPC, subtract it from 1 first. If it gives MPS, take its reciprocal directly. Both routes give the same K because MPC + MPS = 1.

Can the investment multiplier be a decimal?

Yes. With MPS = 0.40, K = 2.5. Keep the exact value where possible; rounding K too early can change the final monetary answer.

Why is K not equal to 1/MPC?

The denominator in the derived equation is the fraction saved, 1 - MPC. For MPC = 0.75, K is 1/0.25 = 4. Taking 1/0.75 would use the wrong fraction.

Is total income generated the same as additional consumption?

No. With unchanged autonomous consumption, Delta Y = Delta C + Delta I. An investment rise of 24 and induced consumption rise of 72 produce an income rise of 96.

What happens when MPC is zero?

MPS is 1 and K is 1. There is no induced consumption increase, so the income increase equals the initial investment increase in this model.

What happens when MPC is one?

MPS is zero, so the formula has a zero denominator. Textbooks often describe the limiting multiplier as infinite. More precisely, the simple process has no finite multiplier result for a positive autonomous spending increase at MPC = 1; do not report an ordinary finite income answer.

Does falling investment make K negative?

No. For the usual range 0 < MPC < 1, K is positive. A negative investment change gives a negative income change when multiplied by K.

Can I use APC in place of MPC?

Generally, no. APC is C/Y; MPC is Delta C/Delta Y. They coincide for a proportional function such as C = 0.80Y, but differ when there is a nonzero autonomous consumption term.

Is the investment multiplier the same as the money multiplier?

No. The investment multiplier relates an autonomous investment change to equilibrium income. The simple money multiplier concerns deposit creation and a reserve ratio. Similar-looking reciprocal formulas do not make the two concepts interchangeable.