Balanced budget multiplier

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

Meaning

The balanced budget multiplier measures how much equilibrium income changes when the government raises its spending (G) and lump-sum taxes (T, a fixed tax amount that does not change with income) by the same amount. Because the budget deficit stays the same, this multiplier is equal to 1. Income rises by exactly the rise in spending.

• Formula: Balanced budget multiplier = 1/(1 − c) − c/(1 − c) = (1 − c)/(1 − c) = 1
• c = marginal propensity to consume (MPC), the share of each extra rupee of income that people spend.
• 1/(1 − c) is the government expenditure multiplier. −c/(1 − c) is the tax multiplier.

Why it matters: it shows that a budget which stays balanced still affects the economy. If the government spends ₹100 more and collects ₹100 more in tax to pay for it, output still rises by ₹100. So a government can raise output without adding to its deficit or its debt.

Explanation

How it works: G and T enter demand differently

• G acts directly. Government purchases of goods and services are part of aggregate demand (AD, the total planned spending in the economy). So ₹100 of extra G raises AD by the full ₹100 in the first round.
• T acts indirectly. A tax works only through disposable income (YD = Y − T + TR), which is the money households actually have left to spend or save.
• When taxes rise by ₹100, disposable income falls by ₹100.
• Households cut spending by only c × ₹100. They cover the rest by saving less.

• So the first-round fall in AD is smaller than ₹100.

• Equilibrium income (NCERT Class 12, Box 5.1): Y* = (C̄ − cT + cTR + I + G) / (1 − c)

• C̄ is autonomous consumption (spending that happens even at zero income), I is investment and TR is transfers.
• G has a coefficient of 1/(1 − c). T has a coefficient of −c/(1 − c), which carries an extra c because tax acts only through consumption.
• That extra c is the full reason the balanced budget multiplier is 1.

Two ways to prove it equals 1

• Series method (round by round):
• Spending side: ΔY = ΔG(1 + c + c² + …)
• Tax side: ΔY = −ΔT(c + c² + …)

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

• Algebra method:

• ΔY = ΔG + c(ΔY − ΔT)
• Put ΔT = ΔG: ΔY − cΔY = ΔG − cΔG

• ΔY(1 − c) = ΔG(1 − c), so ΔY/ΔG = 1

• The answer does not depend on c. Whatever the MPC is, the result is 1, as long as the taxes are lump-sum.

Worked example (NCERT Example 5.1, c = 0.8)

• G multiplier = 1/(1 − 0.8) = 5. Tax multiplier = −0.8/0.2 = −4.
• ΔG = ₹100:
• Rounds: 100 + 80 + 64 + 51.2 + …

• Total rise in income = ₹500

• ΔT = ₹100 (tax rise):

• Rounds: −80 − 64 − 51.2 − …

• Total fall in income = ₹400

• Net effect: 500 − 400 = +₹100, which is exactly the ₹100 of new spending.

• The only difference between the two series is the first round (₹100). A tax never removes that first round from demand.

• Check with c = 0.75: G multiplier 4, tax multiplier −3, so 4 − 3 = 1.

Assumptions behind the result

• Lump-sum taxes only. With a proportional tax (T = tY, a fixed share of income), the effective MPC falls to c(1 − t). AD becomes flatter and the multipliers change, so the simple "= 1" result is taught only for the lump-sum case.
• It is a textbook (Keynesian) result. Keynes argued in The General Theory (1936) that the government should fill the gap when private demand is weak. The model assumes idle workers and machines, fixed prices, no imports and no change in interest rates.
• In real economies leakages to saving and imports, and interest-rate reactions, make multipliers smaller than the textbook values [4].

In India

• Where fiscal choices are set out: the Union's fiscal policy stance appears each year in the Annual Financial Statement (Art. 112). This is where spending and tax changes are announced together.
• The FRBM limit: since 2003 the FRBM Act limits how large the deficit can get.

• This makes the balanced budget idea useful. When borrowing is limited, the government can still support demand by pairing new spending with equal new taxes.

• Indian example:

• Suppose the Centre spends ₹10,000 crore more on rural roads and pays for it fully by raising ₹10,000 crore in lump-sum taxes.

• In the textbook model, the fiscal deficit does not change, but national income still rises by ₹10,000 crore.

• What real Indian estimates show:

• RBI Working Paper 07/2013 (September 2013): the impact multiplier (first-year effect) for total government spending was 0.59 [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 [2].
• NIPFP (Bose and Bhanumurthy, 2015): the capital expenditure multiplier was about 2.45, against about 0.99 for revenue spending and transfers.
• RBI Bulletin (June 2021): the capital expenditure multiplier in India is "known to be higher than 2" [3].
• Lesson: a balanced budget increase does the most for growth when the extra money goes to capital expenditure (spending on roads, railways and power).

Don't confuse with

• Government expenditure multiplier: = 1/(1 − c), which is 5 when c = 0.8. It measures a rise in G with no tax rise, so the deficit grows. The balanced budget multiplier is always 1.
• Tax multiplier: = −c/(1 − c), which is −4 when c = 0.8. It is negative and always exactly 1 smaller in size than the G multiplier. The balanced budget multiplier is the sum of the two multipliers: 5 + (−4) = 1.
• "Fiscal neutrality" (multiplier = 0): a common trap. A balanced budget does not leave income unchanged. The deficit stays the same, but income rises by ΔG.
• Transfer multiplier: = c/(1 − c), the same size as the tax multiplier but positive. Raising transfers and taxes by equal amounts gives a net effect of zero, not 1, because both work only through disposable income.

Prelims Hooks

• Balanced budget multiplier = 1 for any value of MPC, with lump-sum taxes. It is not 0 and it is not 1/(1 − c).
• Derivation: 1/(1 − c) − c/(1 − c) = 1. With c = 0.8, this is 5 − 4 = 1. With c = 0.75, it is 4 − 3 = 1.
• NCERT Example 5.1 (c = 0.8): ΔG = ΔT = 100 gives ΔY = 500 − 400 = +100.
• Why it is 1: G enters AD directly, but a tax cuts spending only by cΔT. The two effects differ only in the first round (ΔG).
• Trap: "An equal rise in government spending and taxes leaves national income unchanged." False. Income rises by the amount of extra spending.
• The "= 1" result assumes lump-sum taxes. A proportional tax makes AD flatter and lowers multipliers. For example, the G multiplier is 2.5 when c = 0.8 and t = 0.25.

Mains Points

• Growth without adding to debt. India has high public debt, and the FRBM Act (2003) limits deficits. The balanced budget multiplier shows that output can still be raised by pairing new spending with equal new taxes. This gives the government some room even when it must reduce its deficit (fiscal consolidation).
• What the money is spent on matters. Capital outlay has an impact multiplier of 1.29 (peak 3.56), against 0.37 for revenue expenditure [2]. So a balanced budget increase aimed at capex will lift growth much more than one spent on salaries or subsidies. This supports shifting spending from revenue to capital heads.
• Limits of the textbook result. Real multipliers are smaller when part of the extra income is saved or spent on imports, when interest rates rise, or when debt is not seen as sustainable [4]. At full employment, extra G mostly pushes up prices. So the value of 1 is a guide to how policy works, not an exact forecast.

Related concepts

• Fiscal policy
• Lump-sum tax
• Government expenditure multiplier
• Tax multiplier
• Transfer multiplier
• Fiscal multiplier

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• Fiscal policy and the multipliers