The investment multiplier and its round-by-round mechanism

Detail

Basic terms used in this section

• Autonomous spending (Ā): spending that does not depend on income. In this model it includes autonomous consumption (C̄) and planned investment (Ī), so Ā = C̄ + Ī.
• Marginal propensity to consume (MPC, c): the share of each extra rupee of income that people spend. c = ΔC/ΔY, and 0 ≤ c ≤ 1.
• Marginal propensity to save (MPS, s): the share of each extra rupee of income that people save. s = ΔS/ΔY = 1 − c.
• Aggregate demand (AD): total planned spending in the economy. In this model, AD = Ā + cY.
• Equilibrium output (Y*): the level of output at which AD equals output. It is found by solving Y = Ā + cY, which gives Y* = Ā/(1 − c).
• Multiplier: a number that shows how much total national income changes when total investment changes. It is the change in income divided by the change in investment [5].
• Keynes pushed the idea in the 1930s. He used it to work out how much government spending was needed to bring the economy to full employment when private investment was too low [5].

The shock: investment rises from 10 to 20

• Starting point: C = 40 + 0.8Y and Ī = 10.
• Ā = 40 + 10 = 50.

• Y₁* = 50/(1 − 0.8) = 50/0.2 = 250.

• After the shock: Ī rises to 20.

• Ā = 40 + 20 = 60.

• Y₂* = 60/0.2 = 300.

• Result: ΔY = 50 from ΔĪ = 10. Output rises 5 times as much as the extra spending.

Reading the graph

• AD₁ shifts up in parallel to AD₂.
• Only the intercept (Ā) changes. The slope (c = 0.8) stays the same.

• The upward shift equals ΔĀ = 10.

• Excess demand at the old output:

• At the old output Y₁*, demand is Y₁*F and output is Y₁*E₁.
• The gap E₁F is the excess demand: people want to buy more than firms are producing.

• Firms' stocks run down (unplanned inventories fall), so firms raise production.

• New equilibrium at E₂:

• Output keeps rising until AD₂ meets the 45° line at E₂.

• Key comparison on the graph:

• Rise in output = E₁G = E₂G (= 50).
• Rise in autonomous spending = E₁F = E₂J (= 10).
• E₁G is larger than E₁F. This gap shows the multiplier at work.

Mechanism: why output rises more than spending (Table 4.1)

• Output becomes income.
• Firms produce 10 more to meet the new investment demand.

• This 10 is paid out as wages, rent, interest and profit, so household income rises by 10.

• Income becomes spending.

• Households spend 0.8 of the new income, so demand rises by 8.

• Firms produce 8 more. That 8 becomes someone's income.

• The chain continues but gets smaller.

• From the 8, households spend 0.8 × 8 = 6.4. Then 5.12, then 4.096, and so on.
• Each round is smaller, because 0.2 of each round is saved and does not come back as demand.

Round	Consumption	Aggregate demand	Output/Income
1	0	10 (autonomous increment)	10
2	(0.8)10 = 8	8	8
3	(0.8)²10 = 6.4	6.4	6.4
4	(0.8)³10 = 5.12	5.12	5.12
…	…	…	…

• Sum of the geometric series:
• ΔY = 10{1 + 0.8 + 0.8² + 0.8³ + …}
• A geometric series 1 + c + c² + … adds up to 1/(1 − c) when c is less than 1.

• So ΔY = 10 × 1/(1 − 0.8) = 10 × 5 = 50.

• Running total: after 4 rounds, income has risen by 10 + 8 + 6.4 + 5.12 = 29.52. The remaining 20.48 comes from all the later, smaller rounds.

• Multiplier mechanism: the round-by-round process in which extra spending raises income, income raises consumption by MPC times as much, and the shrinking increments add up as a geometric series.
• The same logic, another example:
• Suppose investment rises by $1 million and people spend 3/5 of each extra income.
• Round 2 adds $600,000 of income to others. Round 3 adds 3/5 of that, and so on [5].

• Worked total: k = 1/(1 − 0.6) = 2.5, so income rises by $2.5 million.

• Where the leak happens: saving. When the total new saving equals the first rise in investment (0.2 × 50 = 10 = ΔĪ), the process stops. Planned saving again equals planned investment.

Formula

• Investment multiplier (k): the rise in equilibrium output divided by the first rise in autonomous spending.
• k = ΔY/ΔĀ = 1/(1 − c) = 1/MPS

• Check: ΔY = k × ΔĀ = 5 × 10 = 50.

• NCERT printing error:

• Equation 4.5 prints "1/S".

• It should be 1/s, where s is the marginal propensity to save (a ratio), not S, the level of saving (an amount in rupees).

• Limits of the multiplier value:

• Because 0 ≤ c ≤ 1, k lies between 1 and infinity.

• k can never be less than 1 in this simple closed-economy model.

• A larger MPC gives a larger multiplier: when people spend more of each round, less leaks out as saving, so more rounds of income are created.

MPC	MPS	Multiplier
0.9	0.1	10
0.8	0.2	5
0.75	0.25	4
0.5	0.5	2
0	1	1 (limit)
1	0	∞ (limit)

• Reading the limits:
• c = 0: nobody spends extra income. Only the first 10 is added. k = 1.

• c = 1: nothing leaks out. The rounds never shrink. k = ∞. This is a theoretical limit only.

• It works in reverse too.

• Investment falls by 10 → income falls by 10 → consumption falls by 8 → income falls again …
• Output falls by 5 × 10 = 50.
• This is how a slump (a sharp fall in business activity) spreads through the economy. It is the Great Depression story behind Keynes's work (leec101).

Parametric shift

• Parametric shift: a line moves because one of its parameters (the fixed numbers that define the line) changes. It is different from a movement along the line, which happens when Y changes.
• A change in the intercept (Ā) shifts AD in parallel.

• Example: Ī from 10 to 20. AD moves up by 10 at every level of Y.

• A change in the slope (c) swings AD.

• A higher c makes AD steeper. A lower c makes it flatter. The intercept stays fixed.
• Worked example: Ā = 50. If c rises from 0.8 to 0.9, Y* rises from 50/0.2 = 250 to 50/0.1 = 500. The multiplier also rises from 5 to 10.

Leakages shrink the multiplier

• Leakage: any part of extra income that does not come back as demand for domestic output. Saving, imports and taxes are the three main leakages.
• Open economy multiplier (Class 12, Open Economy Macroeconomics):
• k = 1/(1 − c + m), where m = marginal propensity to import (the share of each extra rupee of income spent on foreign goods).
• Example: c = 0.8, m = 0.3 → 1/(1 − 0.8 + 0.3) = 1/0.5 = 2, compared with 5 in a closed economy.
• Why it is smaller:
  • Part of each round's spending buys imports.
  • That spending raises output in the foreign country, not at home.
  • So each domestic round shrinks faster.

• Balance-of-payments detail is in balance-of-payments-exchange-rate.

• Proportional taxes:

• Each round, the government takes a fixed share (t) of the extra income as tax. Households can spend only from what is left.
• Formula: k = 1/(1 − c(1 − t)).

• Worked example: c = 0.8, t = 0.25 → 1/(1 − 0.6) = 2.5, compared with 5 without tax.

• The G, tax, transfer and balanced-budget multipliers are in government-budget-fiscal-policy.

The multiplier in Indian fiscal policy

• Why it matters for policy: the multiplier links a change in autonomous spending to the change in national income that follows. This link is a key part of the Keynesian argument that fiscal policy works in a predictable way [5].
• Composition matters, not only size.
• An RBI study found that capital outlay (spending that creates assets, such as roads and power plants) raises growth more than revenue expenditure (day-to-day spending such as salaries, interest and subsidies) [2].
• Revenue expenditure makes up most of government spending at both the Centre and the States. So the impact multiplier (the first-year effect) of total government spending is less than one [2].

• Before COVID-19, government support to demand through heavy revenue spending over 6–7 quarters did not sustain the recovery. The study linked this to the low, short-lived multipliers of revenue spending (RBI Bulletin, June 2021) [2].

• Size of the capex multiplier:

• Studies cited by the government estimate that public spending on infrastructure raises GDP by about 2.5 to 3.5 times the amount spent over the medium term [4].

• Policy response:

• The Centre's capital outlay rose by about 89%, from ₹5.92 lakh crore (FY22) to ₹11.21 lakh crore budgeted for FY26. The stated reason is the strong multiplier effect of infrastructure (Economic Survey 2025-26) [3].
• After COVID, the Centre began giving States 50-year interest-free loans for capital spending. This is the Special Assistance to States for Capital Investment. The stated reasons are its higher multiplier and its role in crowding in private investment (drawing more private investment in) [3].

Developing-economy caveat: V.K.R.V. Rao (1952)

• Rao's argument: in an underdeveloped economy like India, the real multiplier (the rise in actual output, not just money income) is weak, for four reasons:
• Supply bottlenecks:
  • Infrastructure, power and capital are short.
  • So factories and workers are not truly "idle and ready". Extra demand cannot quickly become extra output.
• A large non-monetised or informal sector:
  • Much output is produced for own use (for example, a farm family eating its own grain), not sold in the market.
  • Extra money income does not easily pass through market rounds.
• Inelastic farm output:
  • Much of the extra demand in a poor economy is for food. The MPC is high, and most of the extra spending goes on food.
  • Farm supply cannot rise quickly within a season.

• As a result, extra demand leaks into prices rather than output.

  • Money income rises by the multiplier, but real output rises much less. The rest shows up as inflation.

• The core point:

• The Keynesian model assumes idle resources and elastic supply (supply that can rise easily when demand rises).

• Where these assumptions fail, a stimulus causes inflation rather than growth.

• Link to current policy: this is one reason Indian policy prefers capital spending. Capex creates capacity and eases the supply bottlenecks Rao pointed to. Revenue spending mostly adds to demand [2][3].

Prelims Hooks

• k = ΔY/ΔĀ = 1/(1 − MPC) = 1/MPS. With MPC = 0.8, k = 5, so an extra ₹10 of investment raises equilibrium income by ₹50.
• In the simple closed-economy model, the multiplier lies between 1 (MPC = 0) and ∞ (MPC = 1). It can never be below 1.
• Higher MPC → higher multiplier. Higher MPS → lower multiplier. Trap: "a higher saving rate raises the multiplier" is wrong.
• A change in investment (intercept Ā) shifts AD in parallel. A change in MPC (slope c) swings AD. Both are parametric shifts.
• Open economy multiplier = 1/(1 − c + m). With c = 0.8 and m = 0.3, k = 2, compared with 5 in a closed economy. Imports are a leakage.
• The multiplier works in both directions. A fall in investment causes a magnified fall in output.
• Saving, taxes and imports are leakages. Investment, government spending and exports are injections.
• NCERT's equation 4.5 misprints "1/S". The correct form is 1/s (MPS), not the saving level.
• V.K.R.V. Rao (1952): the multiplier is weak in underdeveloped economies because of supply bottlenecks, the non-monetised sector and inelastic farm output. Extra demand raises prices, not output.
• RBI (June 2021): capital outlay has higher growth multipliers than revenue expenditure. The first-year multiplier of total government spending is below 1 [2].

Mains Points

• Quality of spending over quantity (GS-III, fiscal policy):
• Revenue spending has low, short-lived multipliers. Capital outlay has higher ones: about 2.5–3.5 over the medium term by government-cited estimates [2][4].

• This supports India's shift to capex. Capital outlay rose from ₹5.92 lakh crore (FY22) to ₹11.21 lakh crore (FY26 BE), and States get 50-year interest-free capex loans [3].

• The Keynesian multiplier versus Indian conditions:

• Rao's 1952 critique still applies. Supply bottlenecks, informality and inelastic farm output turn demand stimulus into inflation.

• So stimulus should be paired with supply-side reforms: infrastructure, farm productivity and formalisation. Pure demand pumping is not enough.

• Open economy and import leakage:

• A high marginal propensity to import (for example, electronics and energy) weakens the domestic multiplier (from 5 to 2 in the NCERT example).

• This gives a macro argument for domestic capacity building. Schemes such as Make in India and PLI aim to keep more of each spending round at home.

• The multiplier in reverse (counter-cyclical policy):

• A fall in private investment spreads into a magnified slump.
• This justifies counter-cyclical public investment in downturns, like the post-COVID capex push. The trade-off is fiscal deficit and debt sustainability.