Fiscal policy and the multipliers

Detail

1. What fiscal policy is

• Fiscal policy: the government uses its expenditure and taxes to keep output and employment steady.
• Because of this, budgets often run a surplus (income more than spending) or a deficit (spending more than income), not an exact balance.

• The IMF defines it simply as "the use of government spending and taxation to influence the economy" [4].

• Keynes argued for fiscal policy in The General Theory of Employment, Interest and Money (1936). His point was that when private demand is weak, the government should fill the gap.

• The Indian link: the Union's fiscal policy stance is set out each year in the Annual Financial Statement (Art. 112). Since 2003 the FRBM Act limits how large the deficit can get.

2. The two ways the government changes income

• G (government purchases of goods and services) is part of aggregate demand (AD). So it raises AD directly, rupee for rupee.
• T (taxes) and TR (transfers), such as pensions, subsidies and scholarships, work indirectly. They change disposable income:
• YD = Y − T + TR
• Disposable income is the money households actually have left to spend or save.

• Households spend only part of any change in YD, namely c (the marginal propensity to consume, MPC: the share of each extra rupee of income that is spent).

• Lump-sum tax: a fixed tax amount T that does not change with income.

• Raising it lowers consumption by the same amount at every income level.
• So the consumption line, and with it the AD curve, shifts down in parallel. The slope does not change.

3. The model (Class 12, Box 5.1)

• Consumption: C = C̄ + c(Y − T + TR) (5.1)

• C̄ = autonomous consumption (spending that happens even at zero income).

• Aggregate demand: AD = C̄ + c(Y − T + TR) + I + G (5.2)

• Equilibrium: output equals planned demand, so set Y = AD:
• Y = C̄ + cY − cT + cTR + I + G
• Y(1 − c) = C̄ − cT + cTR + I + G

• Y* = (C̄ − cT + cTR + I + G) / (1 − c) (5.4)

• Reading the formula:

• G has a coefficient of 1/(1 − c).
• T and TR each carry an extra c, because they act only through consumption.
• This one fact explains every multiplier below.

4. The four multipliers (lump-sum taxes)

• Multiplier: the final change in equilibrium income (ΔY) that follows one change in a fiscal variable, divided by the size of that change.

Multiplier	Formula	c = 0.8	c = 0.75	Why
Government expenditure multiplier	ΔY/ΔG = 1/(1 − c)	5	4	G enters AD directly
Tax multiplier	ΔY/ΔT = −c/(1 − c)	−4	−3	Negative. The first-round effect is only cΔT
Transfer multiplier	ΔY/ΔTR = c/(1 − c)	4	3	Part of every transfer is saved
Balanced budget multiplier	1/(1 − c) − c/(1 − c) = 1	1	1	Equal ΔG and ΔT raise Y by exactly ΔG
G multiplier with proportional tax (T = tY)	1/[1 − c(1 − t)]	2.5 (t = 0.25)	2.5 (t = 0.2)	Less of each rupee of income is consumed

• Why the tax multiplier is negative: a tax rise lowers disposable income, so consumption falls and income falls.
• Why it is smaller in size:
• A ₹100 tax cut does not reach AD as ₹100.
• Households save (1 − c) of it, so the first round is only cΔT = ₹80 (c = 0.8).

• So |tax multiplier| is always exactly 1 less than the G multiplier: 5 vs 4, or 4 vs 3.

• Transfer multiplier = the tax multiplier with the sign flipped.

• A transfer is a "negative tax".

• It has the same size of effect (c/(1 − c)) but raises income.

• Policy lesson: rupee for rupee, spending by the government lifts output more than an equal tax cut or cash transfer.

5. Round-by-round working (c = 0.8)

• ΔG = ₹100:
• Round 1: output rises by ₹100 (this becomes someone's income).
• Round 2: 0.8 × 100 = ₹80 is spent.
• Round 3: ₹64. Round 4: ₹51.2. And so on.

• Total: 100 × (1 + 0.8 + 0.8² + …) = 100 × 1/(1 − 0.8) = ₹500.

• Tax cut of ₹100:

• Round 1: ₹80 is spent (₹20 saved). Round 2: ₹64. Round 3: ₹51.2. And so on.

• Total: 100 × (0.8 + 0.8² + …) = 100 × 0.8/0.2 = ₹400.

• The difference is just the first round (₹100). This is why the balanced budget multiplier is 1.

6. Why the balanced budget multiplier is 1

• Balanced budget multiplier: the effect on income when G and T rise by the same amount, so the deficit does not change.
• Series method:
• Spending side: ΔY = ΔG(1 + c + c² + …)
• Tax side: ΔY = −ΔT(c + c² + …)

• If ΔG = ΔT, every term cancels except the first. So ΔY = ΔG.

• Algebra method:

• ΔY = ΔG + c(ΔY − ΔT)

• Put ΔT = ΔG: ΔY(1 − c) = ΔG(1 − c), so ΔY/ΔG = 1.

• Meaning: even a budget that stays balanced is not neutral. Spending ₹100 more, fully paid for by ₹100 more tax, still raises output by ₹100.

• Check (c = 0.75): 4 − 3 = 1. The answer is 1 for any value of c, with lump-sum taxes.

7. Proportional taxes

• Proportional tax: a tax that is a fixed share of income, T = tY. An example is a flat income-tax rate t.
• Consumption becomes: C = C̄ + c(1 − t)Y + cTR
• Out of each extra rupee of income, only (1 − t) reaches the household, and c of that is spent.

• So the effective MPC falls to c(1 − t).

• Effect on AD: the slope of AD falls, so AD becomes flatter.

• Equilibrium: Y* = Ā / [1 − c(1 − t)], where Ā = C̄ + cTR + I + G (all autonomous spending).
• The multiplier is smaller than with lump-sum taxes (NCERT summary point 5). Each round of spending loses some income to tax.
• Cutting the tax rate t works like raising the propensity to consume:
• AD shifts up (the intercept rises through TR and autonomous items), and

• AD pivots, becoming steeper as the slope c(1 − t) rises.

• Automatic stabiliser: a proportional tax acts like a built-in shock absorber.

• In a boom, tax collections rise on their own and hold back spending.
• In a slump, collections fall on their own and support disposable income.

• The IMF describes automatic stabilisers as changes in tax revenue and spending that "do not depend on specific actions but operate in relation to the business cycle". They "tend to be larger in advanced economies" because they depend on the size of the government [4].

• Transfer multiplier with proportional tax: c / [1 − c(1 − t)].

8. NCERT worked examples

• Example 5.1 (c = 0.8):
• ΔG = 100 gives ΔY = 5 × 100 = +500.
• A tax cut of 100 gives ΔY = 4 × 100 = +400.

• ΔG = ΔT = 100 gives 500 − 400 = +100 (balanced budget multiplier = 1).

• Example 5.2 (c = 0.8, t = 0.25):

• c(1 − t) = 0.8 × 0.75 = 0.6.
• Multiplier = 1/(1 − 0.6) = 1/0.4 = 2.5.

• ΔG = 100 gives +250, half the lump-sum case (500).

• Example 5.3 (c = 0.75):

• ΔG = 20 gives 4 × 20 = +80.

• ΔTR = 20 gives 3 × 20 = +60.

• Exercise 5: C = 100 + 0.75Y, I = 200, G = 150, net taxes = 100.

• Y = 100 + 0.75(Y − 100) + 200 + 150
• Y = 375 + 0.75Y, so 0.25Y = 375 and Y = 1,500.
• G multiplier = 1/0.25 = 4. Tax multiplier = −0.75/0.25 = −3.

• ΔG = 200 gives ΔY = 4 × 200 = +800.

• Exercise 9 (c = 0.75, t = 0.2):

• c(1 − t) = 0.75 × 0.8 = 0.6.
• ΔG = +20 gives ΔY = 2.5 × 20 = +50.
• ΔTR = −20 gives ΔY = (0.75/0.4) × (−20) = 1.875 × (−20) = −37.5.

9. Real-world fiscal multipliers

• Fiscal multiplier (applied definition): the change in output caused by a one-unit change in government spending or taxes.
• The IMF calls it the measure of how effective a stimulus is, "its translation in terms of output" [4].
• Impact multiplier: the effect in the first year.

• Peak or cumulative multiplier: the largest or total effect over several years.

• Real multipliers are much smaller than the textbook 4 or 5. Taxes, imports, saving and interest-rate reactions all leak demand out of the circular flow.

• Indian estimates:
• NIPFP (Bose and Bhanumurthy, 2015): capital expenditure multiplier about 2.45, against about 0.99 for revenue spending and transfers.
• RBI Working Paper 07/2013 (September 2013, Structural VAR study):
  • A 1% rise in combined Centre and State expenditure raises GDP by about 0.11%. This is an impact multiplier of 0.59 for total spending [2].
  • Capital outlay: impact multiplier 1.29, peak multiplier 3.56, reached in about the fourth year [2].
  • Revenue expenditure: impact multiplier only 0.37, with its peak in the first year [2].
  • Capital outlay was just 13% of combined expenditure at the time. The study advised raising this share step by step [2].
  • State government spending multipliers were higher than the Centre's. The study argued for more decentralisation of spending [2].

• RBI Bulletin (June 2021): the capital expenditure multiplier in India is "known to be higher than 2". Capital outlays have higher multipliers than other kinds of spending [3].

• Why capex has a bigger multiplier:

• It builds roads, railways and power, which raise the economy's productive capacity as well as demand.
• It crowds in private investment: better infrastructure makes private projects more profitable.

• Revenue spending (salaries, interest, subsidies) mostly adds to consumption. Part of that is saved or spent on imports.

• This is why the "quality" of the deficit matters. A deficit spent on capex does more for growth than the same deficit spent on revenue items. (NCERT scaffold note: verify current RBI estimates. The 2013 and 2021 RBI figures above do that.)

10. What decides the size of the multiplier

• Slack in the economy:
• Multipliers are bigger in recessions, when workers and machines sit idle.

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

• Import leakage: when part of the extra spending goes on imports, that demand helps foreign producers, not Indian ones.

• The IMF: multipliers are larger when "only a small part of the stimulus is saved or spent on imports" [4].

• Monetary accommodation: whether the central bank keeps interest rates low while the government spends.

• If rates rise, private investment falls. This is crowding out: government borrowing takes resources "from the local private sector", which delays recovery [4].

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

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

• This is the link to the FRBM Act. A believable deficit path keeps bond yields low, so the stimulus works better.

• Tax structure: a higher proportional tax rate t means a smaller multiplier (Section 7).

Prelims Hooks

• G multiplier = 1/(1 − c). Tax multiplier = −c/(1 − c). The tax multiplier is always one less in absolute value. With c = 0.8 they are 5 and −4.
• Balanced budget multiplier = 1 for any MPC, with lump-sum taxes. Trap: it is not zero, even though the deficit does not change.
• Transfer multiplier = c/(1 − c): the same size as the tax multiplier, with the opposite sign. It is smaller than the G multiplier.
• A lump-sum tax shifts AD down in parallel. A proportional tax makes AD flatter (it changes the slope).
• Proportional-tax multiplier = 1/[1 − c(1 − t)]. For c = 0.8 and t = 0.25 it is 2.5, not 5.
• A proportional income tax works as an automatic stabiliser: it needs no new decision by the government.
• Keynes's case for fiscal policy comes from The General Theory (1936).
• RBI WP 07/2013: capital outlay impact multiplier 1.29 (peak 3.56) vs revenue expenditure 0.37 [2].
• According to the IMF, multipliers are larger when there are few leakages (to saving and imports), monetary policy accommodates and public debt is sustainable [4].
• Trap: "Revenue expenditure has a higher multiplier than capital expenditure." False. In India, capex has the higher multiplier [2][3].

Mains Points

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

• This supports effective-capex targets and capex-linked loans to States. It also supports reading the FRBM targets together with revenue deficit limits.

• Why the balanced budget multiplier matters.

• Output can be raised without adding to debt, by pairing new spending with equal new taxes.

• This matters for a country with high public debt like India, where FRBM targets limit how much the government can borrow.

• Stimulus design depends on conditions.

• Multipliers are larger in a slump, when RBI policy is accommodative, and when imports are low [4].
• Counter-cyclical spending in bad years, like the 2020-21 COVID response, works best when paired with credible consolidation in good years.

• This is the case for a rules-based framework with escape clauses, as in the FRBM Act.

• Centre–State angle.

• The RBI study found State spending multipliers above the Centre's [2].
• This supports stronger State capex capacity through Finance Commission devolution and well-designed Centre-to-State transfers. It links GS-II (federalism) to GS-III (growth).