Government expenditure multiplier

Topic: Government Budget, Fiscal Policy and FRBM · NCERT: Class 12, Ch 5 "Government Budget and the Economy"

Meaning

The government expenditure multiplier is the final change in equilibrium income (ΔY) caused by a change in government purchases of goods and services (ΔG), divided by the size of that change. In the simple Keynesian model with lump-sum taxes, it is ΔY/ΔG = 1/(1 − c), where c is the marginal propensity to consume (MPC), meaning the share of each extra rupee of income that people spend.

It shows how much output rises when the government spends one more rupee. This is the main case for using fiscal policy to fight a slowdown, an idea Keynes set out in The General Theory (1936).

Explanation

How it works: spending that repeats

• G is part of aggregate demand (AD). So ₹100 of new government purchases raises AD directly by ₹100 in the first round.
• The spending then keeps going, round after round:
• The ₹100 becomes someone's income.
• They spend c of it, and that spending becomes someone else's income.

• The chain goes on, getting smaller each round.

• Worked example (c = 0.8, ΔG = ₹100):

• Round 1: ₹100. Round 2: 0.8 × 100 = ₹80. Round 3: ₹64. Round 4: ₹51.2. And so on.
• Total: 100 × (1 + 0.8 + 0.8² + …) = 100 × 1/(1 − 0.8) = ₹500.
• So the multiplier = 1/0.2 = 5. With c = 0.75, it is 1/0.25 = 4.

Where the formula comes from (NCERT Class 12, Box 5.1)

• Aggregate demand: AD = C̄ + c(Y − T + TR) + I + G

• C̄ = autonomous consumption (spending that happens even at zero income). T = taxes. TR = transfers such as pensions and subsidies.

• Equilibrium: set Y = AD and solve:

• Y* = (C̄ − cT + cTR + I + G) / (1 − c)

• Reading the formula:

• G carries the coefficient 1/(1 − c), so ΔY/ΔG = 1/(1 − c).
• T and TR carry an extra c, because they work only through disposable income (YD = Y − T + TR, the money households have left to spend or save).
• This is why the G multiplier is larger than the tax and transfer multipliers.

Comparing the fiscal multipliers (lump-sum taxes)

Multiplier	Formula	c = 0.8	c = 0.75
Government expenditure	1/(1 − c)	5	4
Tax	−c/(1 − c)	−4	−3
Transfer	c/(1 − c)	4	3
Balanced budget	1	1	1

• Why G beats a tax cut of the same size:
• A ₹100 tax cut does not reach AD as ₹100.
• Households save part of it, so round 1 is only cΔT = ₹80 (c = 0.8).
• Total = 100 × 0.8/0.2 = ₹400, compared with ₹500 for ΔG.

• The gap is exactly the first round (₹100). So |tax multiplier| is always 1 less than the G multiplier.

• Balanced budget multiplier: if ΔG = ΔT, then ΔY = ΔG, so the multiplier is 1 for any c.

• NCERT Exercise 5: C = 100 + 0.75Y, I = 200, G = 150, net taxes = 100.
• Y = 1,500. G multiplier = 1/0.25 = 4.
• ΔG = 200 gives ΔY = 4 × 200 = +800.

What makes it rise or fall

• MPC (c): a higher c means a bigger multiplier, because more of each round is spent.
• Proportional tax (T = tY), a tax that takes a fixed share of income:
• The effective MPC falls to c(1 − t), so AD becomes flatter.
• Multiplier = 1/[1 − c(1 − t)], which is smaller than 1/(1 − c).
• Example 5.2 (c = 0.8, t = 0.25): c(1 − t) = 0.6. Multiplier = 1/0.4 = 2.5. So ΔG = 100 gives +250, half of the lump-sum case (500).

• Exercise 9 (c = 0.75, t = 0.2): multiplier = 2.5, so ΔG = +20 gives +50.

• Slack in the economy:

• The multiplier is bigger in a recession, when workers and machines sit idle.

• At full employment, extra G mostly pushes up prices.

• Import leakage: spending on imports helps foreign producers, not Indian ones. The IMF says multipliers are larger when "only a small part of the stimulus is saved or spent on imports" [4].

• Interest rates and crowding out:
• Government borrowing → interest rates rise → private investment falls. This is crowding out.

• The IMF says multipliers are larger when "interest rates do not rise as a consequence of the fiscal expansion" [4].

• Fiscal credibility: multipliers are larger when the fiscal position after the stimulus "is viewed as sustainable" [4].

In India

• Legal framework: the Union's fiscal stance is set out each year in the Annual Financial Statement (Art. 112). Since 2003, the FRBM Act has limited the size of the deficit, and so how much the government can borrow to spend.
• Real multipliers are far smaller than the textbook 4 or 5. Taxes, imports, saving and interest-rate reactions all take demand out of the economy.
• RBI Working Paper 07/2013 (September 2013, Structural VAR study):
• A 1% rise in combined Centre and State spending raises GDP by about 0.11%, which is an impact multiplier of 0.59 (effect in the first year) [2].
• Capital outlay: impact multiplier 1.29. Its peak multiplier (largest effect over several years) is 3.56, reached in about the fourth year [2].
• Revenue expenditure: impact multiplier only 0.37, peaking in the first year [2].
• Capital outlay was just 13% of combined spending then. The study advised raising this share step by step [2].

• State spending multipliers were higher than the Centre's [2].

• NIPFP (Bose and Bhanumurthy, 2015): capital expenditure multiplier about 2.45, compared with about 0.99 for revenue spending and transfers.

• RBI Bulletin (June 2021): India's capital expenditure multiplier is "known to be higher than 2" [3].
• Why capex (capital expenditure) does more:
• It builds roads, railways and power, so it raises productive capacity as well as demand.
• It crowds in private investment, because better infrastructure makes private projects more profitable.
• Revenue spending (salaries, interest, subsidies) mostly adds to consumption, and part of that is saved or spent on imports.

Don't confuse with

• Tax multiplier: it is negative (−c/(1 − c)) and 1 smaller in size, because a tax change works only through consumption. The G multiplier is positive and acts on AD directly.
• Transfer multiplier: it is c/(1 − c), the same size as the tax multiplier but positive. It is smaller than the G multiplier because part of every transfer is saved.
• Balanced budget multiplier: equal rises in G and T give a multiplier of 1, not zero and not 1/(1 − c).
• Impact vs peak multiplier: the textbook 1/(1 − c) is a final equilibrium value. In real estimates, the impact multiplier is the first-year effect and the peak multiplier is the largest effect over several years (capex: 1.29 impact, 3.56 peak [2]).

Prelims Hooks

• G multiplier = 1/(1 − c). With c = 0.8 it is 5, and with c = 0.75 it is 4. The tax multiplier is −4 and −3 for the same values of c.
• With a proportional tax, the G multiplier = 1/[1 − c(1 − t)]. For c = 0.8 and t = 0.25 it is 2.5, not 5.
• Balanced budget multiplier = 1 for any MPC, with lump-sum taxes. Trap: it is not zero, even though the deficit does not change.
• Rupee for rupee, government purchases raise output more than an equal tax cut or transfer.
• RBI WP 07/2013: capital outlay impact multiplier 1.29 (peak 3.56) compared with revenue expenditure 0.37 [2].
• Trap: "Revenue expenditure has a higher multiplier than capital expenditure in India." False [2][3].

Mains Points

• Quality of spending, not just its size:
• Capital outlay has an impact multiplier of 1.29 (peak 3.56), compared with 0.37 for revenue spending [2].
• So moving spending from revenue to capital can raise growth without raising the fiscal deficit.

• This supports capex targets, capex-linked loans to States, and reading FRBM targets together with revenue deficit limits.

• Stimulus design depends on conditions:

• Multipliers are larger in a slump, when monetary policy keeps rates low, and when import leakage is small [4].

• Credible debt plans keep bond interest rates low, so the stimulus works better [4]. This supports counter-cyclical spending (like the 2020-21 COVID response) paired with credible consolidation and FRBM-style escape clauses.

• Centre–State angle (GS-II + GS-III):

• State spending multipliers are higher than the Centre's [2].
• This supports more decentralised spending and stronger State capex capacity through Finance Commission devolution and well-designed Centre-to-State transfers.

Related concepts

• Fiscal policy
• Lump-sum tax
• Tax multiplier
• Transfer multiplier
• Balanced budget multiplier
• Fiscal multiplier

Read more

• Fiscal policy and the multipliers