Aggregate Demand, Income Determination and the Multiplier

1. From the classical presumption to the Keynesian revolution

Read the detailed note →

The classical presumption

• Before Keynes, the classical tradition held two beliefs:
• Every labourer who is ready to work finds a job.

• All factories work at full capacity.

• Output was therefore supply-determined. It was set by labour, capital and technology, not by demand.

• Two ideas supported this view:
• Say's law: supply creates its own demand.

• Flexible wages and prices: these clear every market automatically.

• The schools of thought are covered in detail in economic-thought.

The Great Depression broke the presumption

• Great Depression (1929 and after): output and employment fell sharply in Europe and North America, and the fall spread to other countries.
• USA, 1929–1933 (Class 12, Introduction):
• The unemployment rate rose from 3% to 25%.

• Aggregate output fell by about 33%.

• The picture on the ground:

• Demand for goods was low.
• Many factories lay idle.

• Workers were thrown out of jobs.

• Unemployment rate = people not working and looking for jobs ÷ people working or looking for jobs.

• The lesson was that an economy can stay in long-lasting unemployment. This needed a new theory.

Keynes and the birth of macroeconomics

• John Maynard Keynes:
• British economist, born 1883.
• Educated at King's College, Cambridge, and later its Dean.
• Took part in diplomacy after the First World War.

• A shrewd foreign-currency speculator.

• The Economic Consequences of the Peace (1919): predicted that the post-war peace settlement would break down.

• The General Theory of Employment, Interest and Money (1936): one of the most influential economics books of the 20th century.
• Keynesian economics: Keynes's 1936 approach.
• It studies the economy as a whole and how its sectors depend on each other.
• It explains persistent involuntary unemployment by deficient aggregate demand, meaning too little total spending.
• With it, macroeconomics was born as a separate subject in the 1930s.

	Classical	Keynesian
Normal state	Full employment	Can get stuck below full employment
What sets output	Supply (labour, capital)	Aggregate demand
Wages and prices	Flexible, so markets clear	Rigid in the short run
Unemployment	Voluntary or frictional only	Involuntary, from demand deficiency
Role of the State	Minimal	Active demand management

Method: ceteris paribus in two stages

• Ceteris paribus means "other things remaining equal". To solve for one variable, hold the others constant. It is like solving two equations by substitution.
• Class 12, Determination of Income and Employment works in two stages:
• Stage 1: the price level is fixed and the interest rate is constant, and national income is solved for. This whole note works at this stage.
• Stage 2: prices are allowed to vary, and the equilibrium is analysed again.

2. Ex ante vs ex post: plans, outcomes and unplanned inventories

Read the detailed note →

Two meanings of the same word

• Ex post: the actual or accounting value of a variable, measured after the period. This is how national-income accounting uses C, I and GDP.
• Ex ante: the planned or intended value, meaning what households meant to consume and firms meant to invest or produce.
• In short, ex ante is what was planned and ex post is what actually happened.

NCERT example: the producer's inventory

• A producer plans to add ₹100 of goods to her stock this year, so her planned (ex ante) investment = ₹100.
• An unforeseen upsurge in demand makes her sell ₹30 of goods out of stock.
• Her stock rises by only ₹100 − ₹30 = ₹70, so her actual (ex post) investment = ₹70.
• The gap of −₹30 is unplanned inventory investment.

Inventories reconcile plans and outcomes

• Inventory = output produced but not sold, which stays with the firm. Inventory investment = the change in inventory.
• Inventory investment can be:
• Positive, when stocks rise.

• Negative, when stocks are run down.

• There are two reasons for inventory investment:

• Planned: the firm chooses to keep stocks.

• Unplanned: sales differ from planned sales, so stocks pile up or run down by themselves.

• Unplanned inventory change is the balancing item that always makes actual output equal actual spending.

Identity vs equilibrium condition (a classic trap)

• Accounting identity (from national-income accounting): ex post output ≡ ex post C + ex post I.
• It always holds, even when the economy is out of equilibrium.

• Unintended inventory is counted inside ex post I.

• Equilibrium condition: Y = Ā + cY.

• The left side is ex ante supply (planned output).
• The right side is ex ante demand (planned C + I).

• It holds only in equilibrium.

• If ex ante demand < planned output:

• The equilibrium condition fails.
• Stocks pile up as unintended accumulation of inventories.
• The ex post identity still holds, because the unsold stock counts as (unplanned) investment.

	Ex ante	Ex post
Meaning	Planned or intended	Actual or realised
C + I = Y?	Only in equilibrium	Always (identity)
Role	Drives the adjustment of output	Records the outcome

3. Consumption, saving and the propensities

Read the detailed note →

The consumption function

• Consumption function: the relation between consumption and income. Household income is the most important determinant of consumption demand.

• C = C̄ + cY (equation 4.1)

• Autonomous consumption (C̄):

• Consumption that does not depend on income. It takes place even when income is zero.

• It is the subsistence level of spending, financed by dissaving (using past savings) or borrowing.

• Induced consumption (cY): the part of consumption that depends on income.

• Marginal propensity to consume (MPC):
• MPC = ΔC/ΔY = c, the change in consumption per unit change in income.
• It lies between 0 and 1, and NCERT includes both bounds:
  • MPC = 0: consumption does not change when income changes.
  • MPC = 1: the entire change in income is consumed.
  • 0 < MPC < 1: the usual case, where part of the extra income is consumed.

• It can never exceed 1, because ΔC cannot be larger than ΔY.

• Imagenia example: C = 100 + 0.8Y.

• Consumption is ₹100 even at zero income, so autonomous consumption = 100.
• MPC = 0.8, so a ₹100 rise in income raises consumption by ₹80.

Graph of the consumption function

• Recall the intercept form of a straight line: Y = a + bX, where a is the intercept and b = tan θ is the slope.
• For the consumption function:
• The intercept is C̄.
• The slope is c = tan α.

Saving and its propensities

• Savings: the part of income not consumed. S = Y − C.
• Marginal propensity to save (MPS):
• MPS = ΔS/ΔY = s.

• Since s = Δ(Y − C)/ΔY = 1 − c, it follows that s = 1 − c, and so MPC + MPS = 1.

• Average propensity to consume (APC) = C/Y, consumption per unit of income.

• Average propensity to save (APS) = S/Y, saving per unit of income.
• APC + APS = 1, because C + S = Y.

Average vs marginal (a standard extension)

• With a positive intercept, APC = C̄/Y + c. So APC > MPC, and APC falls as income rises.
• In Imagenia (C = 100 + 0.8Y):

Y	C	S	APC	APS	MPC
500	500	0	1.00	0	0.8
1,000	900	100	0.90	0.10	0.8
2,000	1,700	300	0.85	0.15	0.8

• At low income, APC can exceed 1. This is dissaving, and APS is then negative.

Policy angle

• Poorer households have a higher MPC, so each rupee transferred to them adds more to demand than a rupee given to the rich.
• With a government, consumption depends on disposable income:
• Yd = Y − T (+ transfers).
• So C = C̄ + c(Y − T).
• This links to personal disposable income in national-income-accounting.

4. Investment and aggregate demand

Read the detailed note →

Investment

• Investment has two parts:
• Additions to the stock of physical capital, such as machines, buildings and roads. This is anything that adds to future productive capacity.

• Changes in inventory.

• Investment goods are final goods, not intermediate goods. A machine is not used up in a year. It gives services over many years.

• Autonomous investment (Ī):
• Investment that does not depend on income.
• The model writes ex ante investment as I = Ī (equation 4.2), a positive constant.
• On a graph it is a horizontal line at height Ī.

• In reality, investment depends on:

  • The interest rate, which is the cost of investible funds. A higher rate means less investment.
  • The availability of credit. Easy credit encourages investment.

• The swing component: C̄ is subsistence spending and stays fairly stable, while Ī goes through periodic fluctuations. Changes in investment therefore drive most booms and slumps.

Aggregate demand in the two-sector model

• Two-sector model: an economy of households and firms only, with no government and no foreign trade.
• Aggregate demand (AD): the total ex ante demand for final goods.

• AD = C + I = C̄ + Ī + cY = Ā + cY

• Autonomous expenditure (Ā): spending that does not depend on income.

• Ā = C̄ + Ī.
• It grows to include G, transfers and exports when those sectors are added.

• A change in Ā shifts the AD line in parallel.

• Graph:

• AD is the vertical sum of the consumption line and the investment line.
• In NCERT's figure, OM = C̄, OJ = Ī and OL = C̄ + Ī.
• AD is parallel to the consumption function, with the same slope c.
• AD shows ex ante demand.

Adding government and trade

• With government:
• Y = C̄ + Ī + G + c(Y − T).
• The term G − cT simply adds to Ā.

• It does not change the analysis in any qualitative way.

• Without indirect taxes and subsidies, GDP ≡ National Income. NCERT therefore uses the two terms interchangeably in this model.

• With trade, net exports X − M join AD. Imports rise with income, and this is the root of the open-economy leakage in Section 6.

Economy	Aggregate demand
Two-sector	C̄ + Ī + cY
Three-sector	C̄ + Ī + G + c(Y − T)
Four-sector (open)	C̄ + Ī + G + c(Y − T) + X − M

5. Equilibrium income: the 45° line and the effective demand principle

Read the detailed note →

Why keep the price level fixed?

• Fixed price assumption: the economy has unused resources, meaning idle machinery, buildings and labour.
• So the law of diminishing returns does not apply.
• Extra output comes without any rise in marginal cost.
• So the price level does not change as output changes.
• It is also a simplifying assumption that is dropped at the second stage.

Aggregate supply: the 45° line

• Aggregate supply: total planned output.
• With fixed prices and idle resources, whatever GDP is demanded is supplied. Supply is perfectly elastic.
• It is drawn as the 45° line, where every point has equal horizontal and vertical coordinates.
• Example: if GDP is ₹1,000 (point A on the horizontal axis), ₹1,000 worth of goods is supplied (point B on the 45° line).

Equilibrium

• Equilibrium income: the income at which ex ante AD = ex ante AS. Graphically, this is where AD cuts the 45° line (point E, income OY₁).
• Algebra:
• C̄ + Ī + cY = Y
• Y(1 − c) = C̄ + Ī

• Y* = (C̄ + Ī)/(1 − c) (equation 4.4)

• Worked example (C = 40 + 0.8Y, I = 10):

• Y = 50 + 0.8Y
• Y* = 50/0.2 = 250
• At Y* = 250: C = 40 + 200 = 240 and S = 250 − 240 = 10 = I.
• So at equilibrium, planned saving = planned investment (a standard extension).

Adjustment through unplanned inventory

• If AD < Y (excess supply):
• Unsold stocks pile up, which is unplanned inventory accumulation.
• Firms cut output.

• Y falls towards Y*.

• If AD > Y (excess demand):

• Inventories run down.
• Firms raise output.

• Y rises towards Y*.

• NCERT exercise: Ā = ₹50 crore, MPS = 0.2 (so c = 0.8), Y = ₹4,000 crore.

• AD = 50 + 0.8 × 4,000 = ₹3,250 crore, which is less than Y = ₹4,000 crore.
• The economy is not in equilibrium. There is excess supply of ₹750 crore, stocks pile up, and output will fall.
• Equilibrium would be 50/0.2 = ₹250 crore.

Effective demand principle

• Effective demand principle: with a fixed price level and perfectly elastic supply, aggregate output is determined solely by aggregate demand.
• This is the core break from Say's law:
• In the classical view, supply leads and demand follows.
• In the Keynesian short run, demand leads and output follows.

6. The investment multiplier and its round-by-round mechanism

Read the detailed note →

The shock

• With C = 40 + 0.8Y, investment rises from Ī = 10 to 20.

• Y* rises from 250 to 300: ΔY = 50 from ΔĪ = 10.

• On the graph:

• AD₁ shifts up in parallel to AD₂.
• At the old output Y₁*, demand (Y₁*F) exceeds output (Y₁*E₁) by E₁F, the excess demand.
• The new equilibrium is E₂.
• The rise in output (E₁G = E₂G) exceeds the rise in autonomous spending (E₁F = E₂J).

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

• Output becomes income, and income becomes spending:
• Extra output of 10 is paid out as wages, rent, interest and profit, so income rises by 10.
• Consumers spend 0.8 of it, so demand rises by 8. Firms produce 8 more.
• That 8 becomes income. Consumers spend 6.4, and so on.

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: 10{1 + 0.8 + 0.8² + …} = 10/(1 − 0.8) = 50.
• 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.

Formula

• Investment multiplier = the rise in equilibrium output divided by the initial rise in autonomous spending.

• k = ΔY/ΔĀ = 1/(1 − c) = 1/MPS

• NCERT printing error: equation 4.5 prints "1/S". It should be 1/s, where s is the marginal propensity to save, not the saving level S.

• A larger MPC gives a larger multiplier:

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)

• It works in reverse too: a fall in investment causes a magnified fall in output. This is how a slump spreads.

Parametric shift

• Parametric shift: a line moves because one of its parameters changes.
• A change in the intercept (Ā) shifts AD in parallel.
• A change in the slope (c) swings AD up or down.

Leakages shrink the multiplier

• Open economy multiplier (Class 12, Open Economy Macroeconomics):
• k = 1/(1 − c + m), where m is the marginal propensity to import.
• Example: c = 0.8, m = 0.3 gives 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, which raises foreign output, not domestic output.

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

• Proportional taxes: each round, tax takes part of the extra income, so the multiplier falls further.

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

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

• In an underdeveloped economy like India, the real multiplier is weak for four reasons:
• Supply bottlenecks: infrastructure, power and capital are short, so capacity is not truly idle.
• A large non-monetised or informal sector: much output is produced for own use, not for the market.
• Inelastic farm output: extra demand, much of it for food, cannot quickly raise farm supply.

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

• The Keynesian model assumes idle resources and elastic supply. Where these assumptions fail, a stimulus causes inflation rather than growth.

7. The paradox of thrift

Read the detailed note →

Statement

• Paradox of thrift: if all people save a larger share of their income (MPS rises), total savings do not rise. They stay the same or fall, because output and income fall.

Trigger: economic shocks

• Economic shocks: sudden, unexpected events such as disasters, war, pandemics or sudden policy changes. They cause big changes in how people earn, spend and save.
• NCERT's trigger is news of an imminent war or impending disaster. People become cautious, and MPC falls from 0.8 to 0.5.
• The fall in MPC comes from an outside cause, so it acts like an autonomous cut in spending.

NCERT arithmetic

• The shock: start at Y₁* = 250 with C = 40 + 0.8Y and I = 10.
• Consumption, and so AD, falls by (0.8 − 0.5) × 250 = 75.

• This creates an excess supply of 75. Stocks pile up, and firms cut output by 75.

• The downward rounds:

• Income falls by 75, so consumption falls by (0.5)75 = 37.5.
• Output falls by 37.5, then by 18.75, and so on.

• Total fall = 75 + 37.5 + … = 75/(1 − 0.5) = 150.

• New equilibrium: Y₂* = 250 − 150 = 100. As a check, Y₂* = Ā/(1 − c) = 50/0.5 = 100.

	Before (c = 0.8)	After (c = 0.5)
Y*	250	100
C	40 + 0.8(250) = 240	40 + 0.5(100) = 90
S = Y − C	10	10
I	10	10

• Savings are unchanged at 10. Income has fallen by 150.
• The reason: in equilibrium S = I, and Ī is fixed at 10.
• If investment depended on income, the fall in Y would cut I, and savings would actually fall.
• Graph (Fig. 4.8): MPC falls, so AD's slope falls and the line swings down (a parametric shift in slope, not a parallel shift).

Meaning

• Fallacy of composition: what is prudent for one household (saving more) becomes a collective loss when everyone does it. One person's spending is another person's income.
• This holds in a demand-constrained economy with idle resources.
• Contrast with other views:
• Classical/loanable-funds view: extra saving lowers the interest rate and finances extra investment, so there is no paradox.
• Long run: saving is the source of capital accumulation and growth (the Harrod-Domar model, in growth-theories-business-cycles). Thrift is harmful only when demand is short.

Applications

• COVID-19 (2020–21): lockdowns and uncertainty caused precautionary saving. Household financial savings jumped in 2020–21 while consumption demand collapsed. Net household financial savings later fell sharply by 2022–23 (verify current RBI/MoSPI figures).
• Japan's "lost decades" (1990s onward): high household saving, weak demand and deflation.
• General lesson: shocks such as disasters, war, pandemics or a sudden policy change can make saving jump suddenly and deepen a slump.

8. Full employment, deficient and excess demand, and policy relevance

Read the detailed note →

Equilibrium is not full employment

• Equilibrium output also sets the level of employment, given the other factors (through an aggregate production function).
• Full employment: the level of income at which all factors of production are fully employed.
• Equilibrium income may lie above or below it.
• Equilibrium only means that income will not change on its own, even if there is unemployment.

Deficient demand and the deflationary gap

• Deficient demand:
• Equilibrium output is below full-employment output, because demand is not enough to employ all factors.
• It leaves involuntary unemployment, meaning people willing to work at the going wage cannot find jobs.

• It leads to falling prices in the long run.

• Deflationary gap: the amount by which AD falls short of the AD needed for full-employment output.

• Through the multiplier, a small gap causes a large output shortfall.

Excess demand and the inflationary gap

• Excess demand:
• In micro terms, demand exceeds supply at the prevailing price. The result is a shortage, which pushes the price up.

• In macro terms, AD exceeds output at full employment.

• Inflationary gap: the amount by which AD exceeds the level needed for full-employment output.

• Output cannot expand further, so the extra demand raises prices.
• This is demand-pull inflation (link to inflation-price-indices).

	Deficient demand	Excess demand
Equilibrium output vs full employment	Below	AD exceeds full-employment output
Gap	Deflationary gap	Inflationary gap
Symptom	Involuntary unemployment, idle capacity	Rising prices
Long-run price effect	Falls	Rises
Fiscal remedy	Raise G, cut taxes, raise transfers	Cut G, raise taxes
Monetary remedy	Cheaper, easier credit; lower interest rates	Dearer credit; higher interest rates

Stimulus episodes

• The New Deal (USA, 1930s): public works to fight the Depression.
• 2008–09 global financial crisis: stimulus packages in many countries, including India's fiscal stimulus and RBI rate cuts.
• COVID-19 in India:
• Atmanirbhar Bharat packages (2020).

• Then a Union capital-expenditure push of over ₹11 lakh crore a year in recent Budgets (verify current).

• Capex vs revenue spending: RBI and Economic Survey estimates suggest the capex multiplier exceeds the revenue-spending multiplier. Capex also adds capacity and crowds in private investment (verify current).

Limits of demand management

• Crowding out: government borrowing raises interest rates and lowers private investment.
• Fiscal-deficit constraints: FRBM targets and debt sustainability.
• Supply bottlenecks: in India, extra demand can turn into inflation (Rao's caveat).
• Import leakage: this lowers the open-economy multiplier.
• Fiscal detail is in government-budget-fiscal-policy.

---

Exam angles

Prelims — high-yield facts and traps

• Identities:
• MPC + MPS = 1.
• APC + APS = 1.
• 0 ≤ MPC ≤ 1, and NCERT includes both bounds.

• Trap: "MPC can exceed 1" is FALSE. APC can exceed 1 at low income through dissaving.

• Multiplier = 1/(1 − MPC) = 1/MPS: MPC 0.9 → 10; 0.8 → 5; 0.75 → 4; 0.5 → 2. MPC = 0 gives 1; MPC = 1 gives infinity.

• Equilibrium: Y* = Ā/(1 − c). With C = 40 + 0.8Y and I = 10, Y* = 250. If I rises to 20, Y* = 300.
• Saving and investment: planned S = planned I only in equilibrium, but ex post S ≡ I always. Trap: "Ex ante investment always equals ex post investment" is FALSE; they differ by unplanned inventory change.
• Positive intercept: APC > MPC, and APC falls as income rises.
• What reduces the multiplier:
• A higher MPS.
• The marginal propensity to import (open-economy k = 1/(1 − c + m); c = 0.8, m = 0.3 gives 2).

• Proportional taxes.

• Paradox of thrift: "a general rise in the saving propensity raises total savings" is FALSE. Savings stay the same or fall. With c going from 0.8 to 0.5, Y goes from 250 to 100 while S stays at 10.

• Parametric shift: an intercept (Ā) change gives a parallel shift of AD; a slope (c) change swings AD.
• Effective demand principle: output is set solely by AD, under a fixed price level and perfectly elastic supply (the 45° line).
• Gaps: deflationary gap goes with deficient demand, unemployment and expansionary policy. Inflationary gap goes with excess demand, demand-pull inflation and contractionary policy.
• Classical vs Keynes:
• Classical: Say's law, full employment, flexible wages.

• Keynes: involuntary unemployment, deficient demand.

• Chronology:

• Economic Consequences of the Peace: 1919.
• Great Depression: 1929.
• US 1929–33: unemployment 3% → 25%, output about −33%.
• General Theory: 1936.

Mains — GS-III themes

1. Relevance of Keynesian demand management in India: using public capex to crowd in private investment after COVID, and the trade-off between fiscal stimulus and consolidation under FRBM.
2. Limits of the multiplier in a developing, supply-constrained economy (V.K.R.V. Rao, 1952): the informal and non-monetised sector, rigid farm supply, infrastructure gaps and import leakage. When does a stimulus create inflation rather than output?
3. The paradox of thrift and India's household savings: precautionary saving in the pandemic, the later fall in household net financial savings, and debates on the consumption slowdown (verify current).
4. Diagnosing a slowdown: is it demand-deficient (a deflationary gap, idle capacity) or structural and supply-side? Indicators include capacity utilisation, inventories and inflation.
5. Choosing a stimulus instrument (income-tax relief vs direct transfers vs capex), judged by MPC differences across income groups (link to poverty-inequality) and by capacity creation.

Current-affairs hooks

• Union Budget capex allocations, and the Economic Survey's reading of consumption and investment demand.
• RBI Monetary Policy Committee statements on demand conditions, and capacity utilisation in the OBICUS survey.
• MoSPI GDP releases: growth of PFCE (private final consumption expenditure) and GFCF (gross fixed capital formation).
• RBI/MoSPI data on household savings, and personal income-tax relief as a consumption stimulus (verify current).
• Global stimulus debates: post-2008 packages, COVID-era packages, and China's stimulus measures.