Consumption, investment and the multiplier

Economics (BA) · Macroeconomics · free study notes for exams, placements and interviews

In short

This topic explains how households decide how much of their income to spend (the consumption function), how firms decide how much to invest (the marginal efficiency of investment), and how an initial injection of autonomous spending multiplies into a larger change in national income. The multiplier is the engine of the Keynesian income-determination model and the arithmetic behind every claim that capital expenditure "crowds in" growth. It is examined in BA/MA Macroeconomics papers, UGC-NET and Indian Economic Service, and in RBI Grade B, NABARD, SEBI and bank PO interviews. Analysts at the RBI, NITI Aayog, rating agencies and brokerages use the same ideas when they argue about the fiscal multiplier on the Union Budget's capital outlay or about why India's private capex cycle lags.

Explained

The consumption function and the propensities

Consumption function: Keynes's "fundamental psychological law" — as income rises, consumption rises but by less than the rise in income. Linear form C = a + bY, where a > 0 is autonomous consumption and 0 < b < 1.
MPC (b) = ΔC/ΔY — the fraction of an extra rupee of income spent on consumption. MPS = ΔS/ΔY. Since all income is consumed or saved, MPC + MPS = 1.
APC = C/Y and APS = S/Y; APC + APS = 1. With a > 0, APC falls as Y rises and APC > MPC at every income level.
At low income APC can exceed 1 (dissaving out of past wealth or borrowing); the break-even income is where C = Y, i.e. Y = a/(1 − b).
Determinants of consumption: income (objective, dominant), wealth and asset prices, expected future income, interest rates, credit availability, income distribution, taxation and transfers, demographics, and subjective factors (Keynes's motives for saving — precaution, foresight, improvement, independence, enterprise, pride, avarice).
Real versus nominal: the function is specified in real terms; money illusion is assumed away.
Keynes's version is the absolute income hypothesis — consumption depends on current absolute real income.

Rival theories of the consumption function

Kuznets's puzzle: long-run US time-series showed APC roughly constant (about 0.86-0.89), contradicting the falling APC of a short-run function with a > 0. This generated the alternatives below.
Duesenberry's relative income hypothesis: consumption depends on income relative to others (demonstration effect) and on the highest income previously attained (ratchet effect), so consumption falls less in a downturn than it rose in the upturn — the short-run function is a ratchet riding along a stable long-run function.
Friedman's permanent income hypothesis: C = k·Yp, where Yp is permanent (expected lifetime average) income; measured income = permanent + transitory, and transitory income is mostly saved. Implication: temporary tax cuts have small effects, permanent ones large.
Modigliani-Brumberg-Ando life-cycle hypothesis: households smooth consumption over the life span out of expected lifetime resources; C = αWR + βYL (wealth and labour income terms). Young dissave, middle-aged save, old dissave — so demographics drive the aggregate saving rate.
Pigou/real-balance effect: a rise in the real value of money balances (falling prices) raises consumption — a channel for self-correcting full employment that Keynes downplayed.
Indian relevance: a large informal sector, precautionary saving, physical-asset preference (gold, land) and credit constraints mean the simple current-income function fits Indian household data reasonably well; India's gross domestic saving rate has run broadly in the high-twenties to around 30% of GDP in recent years, with household saving the largest component — the latest figures come from MoSPI's National Accounts and the RBI's annual flow-of-funds release, and should be quoted from the current issue rather than from memory.

Investment: types and the investment decision

Investment in economics means addition to the physical capital stock (plant, machinery, buildings, inventories) — not the purchase of shares, which is a financial transfer. In the national accounts this is gross capital formation; the fixed part is GFCF.
Gross versus net investment: net = gross − depreciation (consumption of fixed capital). Net investment raises the capital stock; replacement investment only maintains it.
Autonomous investment: independent of current income — infrastructure, public investment, long-gestation and innovation-driven projects; shown as a horizontal line against Y. Induced investment: rises with income or output, I = I₀ + vΔY-type behaviour.
Financial versus real; private versus public; domestic versus foreign (FDI/FPI); planned (ex-ante) versus realised (ex-post) — in equilibrium ex-ante S = ex-ante I; ex-post S = I always, by accounting, with unintended inventory change as the balancing item.
MEC (marginal efficiency of capital): the discount rate that equates the present value of expected net returns from an asset to its supply price. MEI (marginal efficiency of investment): the schedule of the same idea for the economy's rate of investment, allowing for rising supply price of capital goods.
Decision rule: invest while MEI > market rate of interest (i); equilibrium investment is where MEI = i. Hence the investment demand curve slopes downward against i.
Shifts in MEI come from business expectations ("animal spirits"), technology, demand growth, capacity utilisation, input and credit costs, taxes, and policy certainty — which is why investment is the most volatile component of demand.
Present-value / NPV criterion: NPV = Σ Rt/(1+i)^t − C₀; invest if NPV > 0. Equivalent to the MEC rule when cash flows are well behaved.
Investment in India: financed by retained earnings, bank credit, corporate bonds, equity, external commercial borrowings, and public capital outlay in the Union Budget; investment intentions are tracked through the RBI's order-books and capacity-utilisation surveys and the Centre's project monitoring.

Income determination and the simple multiplier

Two-sector equilibrium: Y = C + I, with C = a + bY and I = Ī autonomous. Solving: Y* = (a + Ī)/(1 − b).
Equivalent savings-investment condition: S = Y − C = −a + (1 − b)Y; setting S = I gives the same Y*.
Investment multiplier k = ΔY/ΔI = 1/(1 − b) = 1/MPS. It works because the first round of spending becomes someone's income, a fraction b of which is respent, and so on: ΔY = ΔI(1 + b + b² + …) = ΔI/(1 − b).
Assumptions of the simple multiplier: constant MPC, no leakages other than saving, unused capacity so output can rise, no supply bottlenecks, no induced price rise, closed economy with no tax, no time lag considered (instantaneous or "comparative-static" multiplier), and no change in investment as income rises.
Leakages that cut the multiplier: saving, taxes, imports, debt repayment, idle cash hoarding, undistributed corporate profits, and purchases from inventories rather than new output.
Dynamic (period) multiplier: the same result reached in rounds over time; the lag between income receipt and expenditure is the Robertsonian lag, which determines how fast the full effect appears.
Paradox of thrift: if everyone tries to save more (a fall in a, or a rise in MPS), income falls and realised saving may not rise at all — virtuous for a household, contractionary in aggregate when output is demand-constrained.
Limitations in a developing economy: supply-inelastic food and infrastructure, leakage into imports and gold, large informal sector, and already-full capacity convert much of the multiplier into inflation rather than output — the classic critique applied to India.

Multipliers in a four-sector economy

Government expenditure multiplier (lump-sum tax T): ΔY/ΔG = 1/(1 − b).
Tax multiplier: ΔY/ΔT = −b/(1 − b) — smaller in absolute size than the expenditure multiplier because the first round of a tax cut is partly saved.
Transfer-payment multiplier = b/(1 − b); the same logic as a negative tax.
Balanced-budget multiplier = 1/(1−b) − b/(1−b) = 1, when G and lump-sum T rise equally.
Proportional income tax (rate t): disposable income = (1 − t)Y, so k = 1/[1 − b(1 − t)] — the tax acts as an automatic stabiliser and flattens the multiplier.
Open economy with imports M = M₀ + mY (m = marginal propensity to import): k = 1/[1 − b(1 − t) + m]; the foreign trade multiplier for exports is the same expression applied to ΔX.
Super-multiplier (multiplier-accelerator interaction): the accelerator v = ΔI/ΔY (induced investment responds to output change); combining them gives k' = 1/[1 − b − v] where it converges, and generates the cyclical behaviour studied in business-cycle models.
Employment multiplier (Kahn): the ratio of total employment created to primary employment in the investment project — the forerunner of the income multiplier.
Money/credit multiplier is a different animal: 1/r (or (1+c)/(r+e+c) in fuller form) — a balance-sheet ratio, not a spending chain; do not mix the two.
Fiscal multipliers in India (orders of magnitude, not fixed constants): RBI and NIPFP studies repeatedly find the multiplier on capital expenditure well above 1 (often quoted in the range of roughly 2-3 over a few years) and on revenue expenditure well below 1. This is the published rationale for the Union Budget's shift towards capital outlay and the 50-year interest-free capex loans to states. Estimates differ by method and vintage — cite the specific study, not a single number.

Key points

Consumption function - C = a + bY; consumption rises with income but less than proportionately.
MPC - ΔC/ΔY, between 0 and 1; the single most important parameter in the model.
MPC + MPS = 1 and APC + APS = 1; with a > 0, APC > MPC and APC falls as income rises.
Break-even income - Y = a/(1 − b), where C = Y and saving is zero.
Absolute income hypothesis - Keynes: current real income governs consumption.
Relative income hypothesis - Duesenberry: demonstration and ratchet effects; consumption depends on relative and past peak income.
Permanent income hypothesis - Friedman: C = kYp; transitory income is largely saved.
Life-cycle hypothesis - Modigliani: consumption smoothed over lifetime wealth plus labour income.
Economic investment - addition to physical capital stock and inventories, not share purchase.
Autonomous vs induced investment - independent of income vs responding to income/output.
MEC/MEI - expected rate of return on capital; invest until MEI equals the interest rate.
Investment volatility - driven by expectations, so it is the swing factor in aggregate demand.
Simple multiplier - k = 1/(1 − MPC) = 1/MPS; higher MPC, bigger multiplier.
Leakages - saving, taxes, imports, hoarding and debt repayment all shrink k.
Tax multiplier - −b/(1 − b); weaker than the expenditure multiplier of 1/(1 − b).
Balanced-budget multiplier - exactly 1 with lump-sum taxes.
Open-economy multiplier - 1/[1 − b(1 − t) + m].
Paradox of thrift - a collective attempt to save more lowers income and may not raise aggregate saving.
Accelerator - v = ΔI/ΔY; with the multiplier it produces the super-multiplier and cycles.
Capex vs revex multipliers in India - capital expenditure multiplier > 1, revenue expenditure < 1 in RBI/NIPFP estimates.

Formulas and examples

C = a + bY — C: real consumption (₹ crore), a: autonomous consumption (₹ crore), b: MPC (dimensionless), Y: real national income (₹ crore)
S = Y − C = −a + (1 − b)Y — S: saving (₹ crore)
MPC b = ΔC/ΔY; MPS = ΔS/ΔY = 1 − b; APC = C/Y; APS = S/Y
Equilibrium income (two sector): Y* = (a + Ī)/(1 − b)
Simple investment multiplier: k = ΔY/ΔI = 1/(1 − b) = 1/MPS
Government expenditure multiplier = 1/(1 − b); Tax multiplier = −b/(1 − b); Transfer multiplier = b/(1 − b); Balanced-budget multiplier = 1
With proportional tax t: k = 1/[1 − b(1 − t)]
Open economy, imports M = M₀ + mY: k = 1/[1 − b(1 − t) + m]
Super-multiplier with accelerator v: k' = 1/(1 − b − v), valid while b + v < 1
Accelerator: It = v(Yt − Yt−1); v = capital-output ratio (dimensionless)
MEC rule: invest while MEI > i; NPV = Σ(t=1..n) Rt/(1 + i)^t − C₀ (₹), i as a decimal
Multiplier in rounds: ΔY = ΔI(1 + b + b² + … ) ; after n rounds ΔY = ΔI(1 − bⁿ)/(1 − b)

Example 1 - equilibrium income, multiplier and the round-by-round path. Given C = 200 + 0.8Y (₹ crore) and Ī = 300.

Y* = (200 + 300)/(1 − 0.8) = 500/0.2 = ₹2,500 crore.
Check: C = 200 + 0.8(2,500) = 2,200; S = 2,500 − 2,200 = 300 = Ī. ✔
k = 1/(1 − 0.8) = 5. If investment rises by ₹50 crore, ΔY = 5 × 50 = ₹250 crore, new Y = ₹2,750 crore.
Rounds: 50 + 40 + 32 + 25.6 + 20.48 = 168.08 after five rounds; (1 − 0.8⁵)/0.2 × 50 = (1 − 0.32768)/0.2 × 50 = ₹168.08 crore — about 67% of the final effect. ✔
Break-even income = 200/0.2 = ₹1,000 crore. At Y = ₹2,500 crore, APC = 2,200/2,500 = 0.88 > MPC = 0.80. ✔

Example 2 - APC, APS, MPC, MPS from a schedule.

Y (₹ '000)	C (₹ '000)	S	APC	APS	MPC	MPS
100	110	−10	1.10	−0.10	—	—
200	190	10	0.95	0.05	0.80	0.20
300	270	30	0.90	0.10	0.80	0.20
400	350	50	0.875	0.125	0.80	0.20

Fitted function: MPC = (190 − 110)/(200 − 100) = 0.80; a = 110 − 0.8(100) = 30, so C = 30 + 0.8Y.
APC falls steadily while MPC stays constant — the standard short-run Keynesian pattern. Break-even income = 30/0.2 = ₹150 thousand.

Example 3 - four-sector multipliers and a balanced-budget check. Economy: b = 0.75, proportional tax t = 0.20, marginal propensity to import m = 0.10.

Simple multiplier (no tax, no trade) = 1/0.25 = 4.00.
With tax only: 1/[1 − 0.75(0.80)] = 1/(1 − 0.60) = 2.50.
With tax and imports: 1/[1 − 0.60 + 0.10] = 1/0.50 = 2.00.
A ₹1,00,000 crore rise in capital outlay therefore raises Y by 2.00 × 1,00,000 = ₹2,00,000 crore in this open, taxed economy, against ₹4,00,000 crore in the textbook closed case — leakages halve it.
Lump-sum version (ignore t and m, b = 0.75): ΔG = +₹100 crore and ΔT = +₹100 crore → ΔY = 4(100) − 3(100) = +₹100 crore; balanced-budget multiplier = 1. (Tax multiplier = −0.75/0.25 = −3.)

Example 4 - paradox of thrift. Initially C = 100 + 0.8Y, Ī = 200 → Y* = 300/0.2 = ₹1,500 crore; S = 0.2(1,500) − 100 = ₹200 crore. Households become thriftier: autonomous consumption falls to 60 (autonomous saving rises by 40), MPC unchanged.

New Y* = (60 + 200)/0.2 = ₹1,300 crore; new S = 0.2(1,300) − 60 = 260 − 60 = ₹200 crore.
Saving is unchanged at ₹200 crore (it must equal autonomous investment), but income has fallen by ₹200 crore — the paradox of thrift in its sharpest form.

Example 5 - MEI/NPV investment decision. A plant costs ₹100 crore and yields net returns of ₹40 crore, ₹45 crore and ₹50 crore in years 1-3 (no scrap value).

At i = 10%: PV = 40/1.1 + 45/1.21 + 50/1.331 = 36.36 + 37.19 + 37.57 = ₹111.12 crore → NPV = +₹11.12 crore; MEI > 10%, so invest.
At i = 18%: PV = 40/1.18 + 45/1.3924 + 50/1.643032 = 33.90 + 32.32 + 30.44 = ₹96.66 crore → NPV = −₹3.34 crore; reject.
So the MEC of this project lies just under 16% (about 16.0%: at 15% NPV is about +₹1.69 crore, at 16% about −₹0.04 crore). A rise in the policy rate that lifts the firm's cost of funds past that point kills the project — the interest-rate channel of monetary transmission to investment.

Multiplier	Formula (b = 0.8)	Value
Investment / government expenditure	1/(1 − b)	5.0
Tax (lump-sum)	−b/(1 − b)	−4.0
Transfer payment	b/(1 − b)	4.0
Balanced budget	1	1.0
With t = 0.25	1/[1 − b(1 − t)]	2.5
With t = 0.25, m = 0.15	1/[1 − b(1−t) + m]	1.82

Where it is used

Public finance and budget analysis: the Ministry of Finance, NITI Aayog and NIPFP use fiscal multipliers to rank capital outlay against subsidies; the Budget's "effective capital expenditure" framing rests on this evidence.
Central banking: RBI's Monetary Policy Report and its DSGE/structural models embed consumption and investment functions; the interest-rate-to-investment link (MEI versus repo-driven lending rates) is the core transmission channel.
Equity and credit research: brokerage and rating-agency analysts (CRISIL, ICRA, CARE) forecast GFCF and private final consumption expenditure (PFCE) — the two largest GDP components on the expenditure side — to call the capex cycle and consumer-demand cycle.
Infrastructure and project appraisal: NPV/IRR screening of road, metro, power and warehousing projects, and the regional income/employment multipliers quoted in DPRs and PPP appraisals.
FMCG, auto and consumer-durable demand planning: MPC and income-distribution logic behind rural-versus-urban demand forecasting, festive-season planning and the effect of DBT transfers, rural employment guarantee wages (VB-G RAM G, formerly MGNREGA) and pay-commission awards.
Job roles: economist/research analyst (RBI Grade B DEPR, NABARD, SEBI, banks), policy associate at think tanks, macro analyst in AMCs, government statistical and IES posts, and consulting roles doing economic-impact assessments.

Interview questions

Q: Why must the MPC lie between 0 and 1? A: A rise in income is divided between extra consumption and extra saving; if MPC were above 1 households would spend more than the increment and run down wealth indefinitely, and if negative they would cut spending as income rose.
Q: Why is APC greater than MPC in the Keynesian function? A: Because autonomous consumption a is positive — APC = a/Y + b, which exceeds b for all finite Y and falls as Y rises.
Q: Share purchase on the NSE — is that investment? A: Not in macroeconomics; it is a transfer of existing financial claims. Investment means addition to physical capital and inventories, i.e. capital formation.
Q: What determines the size of the multiplier, and what shrinks it? A: It is 1/(1 − MPC); leakages into saving, taxes, imports, debt repayment and idle balances all reduce the fraction respent and hence the multiplier.
Q: Why is the tax multiplier smaller in magnitude than the government-expenditure multiplier? A: Government spending enters the income stream in full in the first round, whereas a tax cut first raises disposable income, of which only the MPC fraction is spent.
Q: Prove that the balanced-budget multiplier is 1. A: With equal lump-sum changes, ΔY = ΔG/(1−b) − bΔT/(1−b) = ΔG(1 − b)/(1 − b) = ΔG, so the multiplier is unity.
Q: Explain the paradox of thrift. A: When output is demand-determined, a general attempt to save more cuts consumption, income and output; realised saving need not rise and may fall, so individually prudent behaviour is collectively contractionary.
Q: Why do multipliers tend to be smaller in a developing economy like India? A: Supply bottlenecks and inelastic food and infrastructure supply turn demand into prices rather than output, and leakages into imports, gold and informal-sector saving break the spending chain.
Q: Difference between MEC and MEI? A: MEC is the expected rate of return on an additional unit of capital at a given supply price; MEI is the economy-wide investment schedule that allows for the rising supply price of capital goods as investment expands, so it is steeper.
Q: Why does the Union Budget favour capital expenditure over revenue expenditure? A: Published RBI and NIPFP estimates put the capital-expenditure multiplier well above one and the revenue-expenditure multiplier below one, because capex creates assets and induces private investment; the exact figures vary by study.
Q: How does the permanent income hypothesis change the policy conclusion about tax cuts? A: A temporary tax cut raises only transitory income, which is largely saved, so its multiplier is small; a permanent cut raises permanent income and consumption, so it works.
Q: Distinguish the investment multiplier from the money multiplier. A: The investment multiplier is a flow of successive spending rounds, size 1/MPS; the money multiplier is a stock relationship between base money and broad money, size roughly 1/reserve ratio — different mechanisms entirely.
Q: What is the accelerator, and what does it add to the multiplier? A: v = ΔI/ΔY — induced investment reacting to output change; combined with the multiplier it feeds back on itself, producing the super-multiplier and the self-reinforcing upswings and downswings of the trade cycle.

Common mistakes

Treating the purchase of shares, bonds or land as "investment" in the national-income sense.
Confusing APC with MPC, or reporting APC from a single income level as if it were the slope of the function.
Using 1/(1 − MPC) in a question that specifies taxes or imports — the leakage-adjusted formula 1/[1 − b(1 − t) + m] is required.
Giving the tax multiplier as 1/(1 − b) with a minus sign; it is −b/(1 − b).
Mixing up the investment multiplier with the money (credit) multiplier because both are reciprocals.
Forgetting that the multiplier assumes idle capacity; applying it to a full-employment economy where the result is inflation, not extra output.
Saying the paradox of thrift means saving is always bad — it bites only when output is demand-constrained; in a supply-constrained developing economy saving finances investment.
Writing the ex-post identity S = I as proof of equilibrium; equilibrium requires planned saving to equal planned investment, with unintended inventory change otherwise.