This MCQ module is based on: Equilibrium Income, Multiplier & Paradox of Thrift
TOPIC 10 OF 17
Equilibrium Income, Multiplier & Paradox of Thrift
🎓 Class 12
Economics
CBSE
Theory
Chapter 4 — Determination of Income and Employment
⏱ ~25 min
🌐 Language: [gtranslate]
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Aggregate Supply, Equilibrium Output & the Investment Multiplier
Part 1 built the demand side: aggregate demand AD = C + I + G + (X − M) and the consumption and saving functions that drive it. Now we add the supply side and ask where the economy comes to rest. We will find the equilibrium two ways — through AD = AS and through Saving = Investment — work the famous NCERT numerical example, and discover the surprise of macroeconomics: a small change in autonomous spending produces a much bigger change in income. That magnification is the investment multiplier, and it is the single most important idea in Keynesian theory.
4.5 Aggregate Supply & the Production–Income Equality
In microeconomic theory the supply curve plots price on the vertical axis and the quantity supplied on the horizontal. In macroeconomics we are deliberately holding the price level fixed in this chapter, so the supply side cannot be plotted that way. Instead we use a different definition. Aggregate supply? in this fixed-price model is simply the total output (GDP) the economy produces. With unused labour, machines and buildings, producers can lift output without raising prices — so whatever quantity is demanded at the going price will be supplied. A 45° line through the origin captures this idea graphically: every point on a 45° line has equal horizontal and vertical coordinates, so if Y on the X-axis is 1000, the height on the Y-axis is also 1000 — exactly the supply that matches the income.
📐 In the Macro Fixed-Price Model
Aggregate Supply (AS) = YTotal output of final goods equals total income generated, because every rupee of output is paid out as wages, rent, interest or profit. So the AS line on the AD-Y diagram is the 45° line — it has slope 1, passes through the origin, and represents the rule "whatever income is generated equals the output supplied."
This identity — output = income — is itself worth pausing on. When firms produce ₹1,000 worth of final goods, every rupee of that ₹1,000 (in the absence of indirect taxes and subsidies) gets distributed to factors of production: wages to labour, rent to land, interest to capital, and any remainder as profit to the entrepreneur. So aggregate factor payments = aggregate value of output = National Income.
4.6 Equilibrium Output — Two Equivalent Approaches
The economy is in macroeconomic equilibrium? when the plans of suppliers match the plans of those who provide final demand. There are two equivalent ways to write this condition; both give the same equilibrium income.
4.6.1 Approach (a) — AD = AS (Income–Expenditure)
Setting ex-ante aggregate demand equal to ex-ante aggregate supply: AD must equal Y. Substituting AD = c̄ + Ī + bY:
📐 The AD = AS Equilibrium Condition
Y = c̄ + Ī + bYY(1 − b) = c̄ + ĪY* = (c̄ + Ī) / (1 − b) = Ā / (1 − b)Here Y* is the equilibrium income and Ā = c̄ + Ī is total autonomous expenditure. The factor 1/(1 − b) is the autonomous expenditure multiplier — see §4.7.
4.6.2 Approach (b) — Saving = Investment (Leakage = Injection)
An equivalent condition: at equilibrium, planned saving must equal planned investment. The intuition is that income not spent (saving) is a "leakage" out of the circular flow, while investment is an "injection" into it. Equilibrium requires the leakage to exactly match the injection.
📐 The S = I Equilibrium Condition
Saving function: S = −c̄ + (1 − b)YSetting S = Ī:
−c̄ + (1 − b)Y = ĪY(1 − b) = c̄ + ĪY* = (c̄ + Ī) / (1 − b) = Ā / (1 − b)Identical to approach (a) — as it must be, by the accounting truth Y ≡ C + S, which forces AD = C + I and S = I to be the same equation in disguise.
4.6.3 The NCERT Worked Example — C = 40 + 0.8Y, I = 10
NCERT works the equilibrium of an imaginary two-sector economy with consumption function C = 40 + 0.8Y and autonomous investment Ī = 10. Plugging into the equilibrium formula:
🧮 Step-by-Step
Ā = c̄ + Ī = 40 + 10 = 50.1 − b = 1 − 0.8 = 0.2.
Y* = Ā / (1 − b) = 50 / 0.2 = 250.
At Y = 250: C = 40 + 0.8 × 250 = 240; AD = C + I = 240 + 10 = 250 = Y, confirming equilibrium. Check leakage = injection: S = Y − C = 250 − 240 = 10 = Ī. Both conditions hold.
| Income (Y) | Consumption (C) | Saving (S) | Investment (I) | AD = C + I | AD vs Y |
|---|---|---|---|---|---|
| 0 | 40 | −40 | 10 | 50 | AD > Y (deficit) |
| 100 | 120 | −20 | 10 | 130 | AD > Y (excess demand) |
| 200 | 200 | 0 | 10 | 210 | AD > Y |
| 250 | 240 | 10 | 10 | 250 | EQUILIBRIUM (Y* = AD) |
| 300 | 280 | 20 | 10 | 290 | AD < Y (excess supply) |
| 400 | 360 | 40 | 10 | 370 | AD < Y |
Reading the Schedule — Where AD Crosses Y
Figure 4.B: AD line (C + I) and the 45° AS line (Y) cross at Y* = 250. Below 250, AD is above the 45° line — excess demand pulls output up. Above 250, AD is below — excess supply pulls output down.
A Shift in Autonomous Investment — The AD Line Jumps Up
Bloom: L4 Analyse4.7 The Investment Multiplier
In the worked example, autonomous investment rose by just 10 — yet equilibrium income rose by 50, five times the original push. This is no accident. The phenomenon is called the investment multiplier? — the ratio by which a change in autonomous spending finally changes the equilibrium level of income. It is the single most important practical insight of Keynesian theory.
4.7.1 The Multiplier Formula
📐 The Investment Multiplier Formula
k = ΔY / ΔĀ = 1 / (1 − b) = 1 / MPSIn words: an extra rupee of autonomous spending raises equilibrium income by 1/(1 − b) rupees. Because the marginal propensity to consume b is between 0 and 1, the multiplier 1/(1 − b) is greater than 1. The smaller MPS is — i.e. the larger MPC is — the bigger the multiplier.
4.7.2 Why It Works — Round-by-Round Spending
The intuition behind the multiplier is a chain reaction. When firms spend ₹100 cr extra on capital goods, that ₹100 cr is paid out as wages, rent, interest and profit to factors of production. Households therefore receive ₹100 cr of new income (round 1). They consume MPC × 100 = 80 cr of it (assuming MPC = 0.8). That 80 cr becomes someone else's income (round 2). They in turn consume 0.8 × 80 = 64 cr (round 3). And so on, in ever-shrinking rounds.
| Round | Δ Consumption | Δ Aggregate Demand | Δ Income (Output) | Cumulative ΔY |
|---|---|---|---|---|
| Round 1 — initial investment | 0 | 100 | 100 | 100 |
| Round 2 | (0.8)·100 = 80 | 80 | 80 | 180 |
| Round 3 | (0.8)²·100 = 64 | 64 | 64 | 244 |
| Round 4 | (0.8)³·100 = 51.2 | 51.2 | 51.2 | 295.2 |
| Round 5 | (0.8)⁴·100 = 40.96 | 40.96 | 40.96 | 336.16 |
| … continues … | … | … | … | … |
| Total (sum of infinite series) | 400 | 500 | 500 | 500 |
📐 Summing the Geometric Series
Total ΔY = 100 + (0.8)·100 + (0.8)²·100 + (0.8)³·100 + …= 100 · [1 + 0.8 + 0.8² + 0.8³ + …]
= 100 · 1/(1 − 0.8)
= 100 · 5 = ₹500 crore
So a ₹100 cr push to investment finally raises income by ₹500 cr — the multiplier k = 5.
Round-by-Round Income Increments — The Multiplier Cascade
Figure 4.C: Each successive round adds a smaller increment because MPC = 0.8 < 1. The series converges quickly: by round 8 over 80% of the total ΔY = 500 has been generated.
The Multiplier Cascade — Visualised
Bloom: L4 Analyse4.7.3 Why MPC Matters — Multiplier Sensitivity
The size of the multiplier depends very sensitively on MPC. The closer MPC is to 1, the more of every extra rupee gets re-spent in the next round, and the larger the cumulative effect. Conversely, if MPC is small (people save most of any extra income), the multiplier is small — close to 1.
| MPC | MPS = 1 − MPC | Multiplier k = 1/MPS | ΔY for ΔĪ = ₹100 cr |
|---|---|---|---|
| 0.50 | 0.50 | 2 | ₹200 cr |
| 0.60 | 0.40 | 2.5 | ₹250 cr |
| 0.75 | 0.25 | 4 | ₹400 cr |
| 0.80 | 0.20 | 5 | ₹500 cr |
| 0.90 | 0.10 | 10 | ₹1,000 cr |
| 0.95 | 0.05 | 20 | ₹2,000 cr |
⚠ The Multiplier Works Both Ways
An increase in autonomous spending raises income by k × ΔĀ. But a decrease works the same way in reverse: a fall of ΔĀ in autonomous spending shrinks income by k × ΔĀ. This is why a small drop in business confidence — leading firms to invest less — can plunge an economy into a recession many times deeper than the original shock. It is also the basis of Keynesian counter-cyclical policy: the government must inject autonomous spending in downturns to offset private declines.
4.7.4 Paradox of Thrift — A Surprise of the Multiplier
Here is one of NCERT's most striking results, called the paradox of thrift?. If everyone in the economy decides to save more — i.e. their MPC falls and MPS rises — the total amount of saving in the economy does not rise. Either it stays the same or it actually falls.
How is this possible? When MPC falls from 0.8 to 0.5, the AD line swings down (it gets flatter). The new equilibrium is at a much lower income. In the NCERT example, with Ā = 50: original equilibrium Y₁* = 50/(1 − 0.8) = 250; new equilibrium Y₂* = 50/(1 − 0.5) = 100 — income falls by 150. But aggregate saving: at the original equilibrium S = Y − C = 250 − (40 + 0.8×250) = 250 − 240 = 10. At the new equilibrium S = 100 − (40 + 0.5×100) = 100 − 90 = 10. Total savings remain at exactly 10. Trying to save more, the entire economy ended up saving the same — because lower spending shrank the income they were trying to save out of.
💡 The Lesson of the Paradox
What is true for one household is not always true for the economy as a whole. An individual can save more by cutting consumption. But if every household tries it at once, aggregate demand falls, output falls, incomes fall — and the larger savings ratio is applied to a smaller base. This is a classic fallacy of composition, and it is one of the central lessons Keynes drew from the Great Depression.
LET'S EXPLORE — Compute Equilibrium Two Ways
Bloom: L3 Apply
An economy has the consumption function C = 30 + 0.75Y and autonomous investment Ī = 20. Find the equilibrium level of income (i) using AD = AS, (ii) using S = I, and verify both give the same Y*. Also compute the multiplier and the change in Y if Ī rises by 5 to 25.
- Write AD = C + I in terms of Y.
- Set AD = Y and solve for Y*.
- Write S = Y − C and set S = Ī. Solve for Y*.
- Compute k = 1/(1 − b). Then ΔY = k × ΔĪ.
✅ Worked Solution
(i) AD = AS: AD = 30 + 0.75Y + 20 = 50 + 0.75Y. Set AD = Y: Y = 50 + 0.75Y → 0.25Y = 50 → Y* = 200.(ii) S = I: S = Y − C = Y − (30 + 0.75Y) = −30 + 0.25Y. Set S = 20: −30 + 0.25Y = 20 → 0.25Y = 50 → Y* = 200. Same answer.
Multiplier: k = 1/(1 − 0.75) = 1/0.25 = 4. If Ī rises by 5, ΔY = 4 × 5 = 20; new equilibrium income = 220.
THINK — Why Is the Multiplier Always Greater Than 1?
Bloom: L4 Analyse
In the simple Keynesian model, the multiplier k = 1/(1 − b) = 1/MPS. (a) Show algebraically that if 0 < MPC < 1, then k > 1. (b) Use a one-line round-by-round argument (no algebra) to explain why the final ΔY must exceed the initial ΔĀ. (c) Could the multiplier ever equal 1? Or be less than 1?
✅ Discussion
(a) If 0 < MPC < 1 then 0 < MPS = 1 − MPC < 1, so 1/MPS > 1 — the multiplier exceeds 1. (b) The initial spending raises somebody's income, which raises their consumption, which raises somebody else's income, and so on. The total ΔY is the original ΔĀ plus all those positive successor rounds. Since they are all positive, the total exceeds the initial. (c) k = 1 only if MPC = 0 (every extra rupee of income is fully saved — no further round happens). k < 1 would require MPC < 0, which is empirically impossible. In richer models with taxes and imports, "leakages" reduce the size of the multiplier but do not push it below 1 in normal conditions.
DISCUSS — Effective Demand Principle
Bloom: L4 Analyse
NCERT calls the rule "aggregate output is determined solely by the level of aggregate demand" the effective demand principle. (i) What two simplifying assumptions make this rule work in the chapter's model? (ii) Under what real-world conditions would the principle fail — i.e. when would the supply side bind even with extra demand?
✅ Discussion Notes
(i) Two assumptions: (a) constant price level — supply is perfectly elastic, so any extra demand is met without raising prices; (b) unused resources of all kinds — labour, capital and raw materials are all available, so the law of diminishing returns does not bite. Together these make the supply curve the 45° line. (ii) The principle would fail (a) at full employment — once all factors are fully employed, extra demand cannot draw out more output and instead produces inflation. (b) During capacity bottlenecks (e.g. semiconductor shortage 2021–22), even with idle labour, missing inputs cap output. (c) When prices are flexible upwards, even partial bottlenecks raise prices alongside output, mixing the AD effect with an AS effect.
4.8 Looking Ahead — Bridging Equilibrium to Policy
So far we have a complete picture of the Keynesian short-run equilibrium: AD = Ā + bY, AS = Y, Y* = Ā/(1 − b), and the multiplier k = 1/(1 − b). But equilibrium is not the same as full employment. The equilibrium level of output may turn out to be either more than the full-employment output (driving prices up — an inflationary gap) or less than it (leaving idle workers and machines — a deflationary gap). Part 3 turns to these two policy-relevant cases. It shows how excess demand and deficient demand can be measured, what fiscal and monetary tools can close them, and answers every NCERT exercise at the end of the chapter with full numerical model solutions.
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Competency-Based Questions — Part 2
Case Study: The state of Aksharpur reports the following figures for its closed two-sector economy: consumption function C = 80 + 0.6Y; autonomous investment Ī = ₹120 cr. The Finance Department wishes to raise national income to ₹600 cr through a fresh public-investment package, while keeping the consumption function unchanged. (All figures in ₹ crore.)
Q1. Aksharpur's current equilibrium income Y* equals:
L3 ApplyAnswer: (B) — Ā = c̄ + Ī = 80 + 120 = 200. 1 − b = 1 − 0.6 = 0.4. Y* = 200 / 0.4 = ₹500 cr.
Q2. The investment multiplier in Aksharpur is:
L3 ApplyAnswer: (C) — k = 1/(1 − b) = 1/(1 − 0.6) = 1/0.4 = 2.5. So every extra rupee of autonomous spending finally raises income by ₹2.50.
Q3. To raise Y* from ₹500 cr to ₹600 cr (an increase of ₹100 cr), how much extra autonomous investment must the government inject?
L5 EvaluateAnswer: (B) — Use ΔY = k · ΔĪ ⇒ ΔĪ = ΔY / k = 100 / 2.5 = ₹40 cr. The multiplier does the rest of the work: ₹40 cr of new investment generates ₹100 cr of new income through successive rounds of spending.
HOT Q. The Finance Department now considers two alternative policies, each costing ₹40 cr to the exchequer: Policy A — direct government investment of ₹40 cr; Policy B — a tax-free cash transfer of ₹40 cr to households (assume MPC out of disposable income remains 0.6). Which policy will produce a larger ΔY, and by exactly how much? Show your reasoning.
L6 CreateModel Answer: Policy A — direct investment ΔĪ = 40 acts as an autonomous expenditure of the full ₹40 cr; ΔY = k · 40 = 2.5 × 40 = ₹100 cr. Policy B — the transfer raises households' disposable income by ₹40 cr, but they spend only MPC × 40 = 0.6 × 40 = ₹24 cr of it (the rest is saved). The autonomous boost is only ₹24 cr; ΔY = k · 24 = 2.5 × 24 = ₹60 cr. Policy A produces ₹40 cr more income than Policy B for the same fiscal cost. This is the difference between the investment multiplier (1/(1 − b) = 2.5) and the transfer multiplier (b/(1 − b) = 1.5). It explains why public-works programmes are usually more powerful per rupee than tax cuts or cash transfers in deep recessions.
⚖️ Assertion–Reason Questions — Part 2
Options:
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
(A) Both A and R are true, and R is the correct explanation of A.
(B) Both A and R are true, but R is NOT the correct explanation of A.
(C) A is true, but R is false.
(D) A is false, but R is true.
Assertion (A): In the simple Keynesian model, the equilibrium output is the same whether we use the AD = AS condition or the S = I condition.
Reason (R): The accounting identity Y ≡ C + S, applied to the equation AD = C + I, immediately rearranges into S = I.
Answer: (A) — Both true, and R is the correct explanation of A. AD = Y and AD = C + I together give Y = C + I; substituting Y = C + S yields C + S = C + I, hence S = I. The two conditions are algebraic equivalents.
Assertion (A): The investment multiplier is greater than 1 whenever the marginal propensity to consume is positive but less than 1.
Reason (R): The multiplier formula is k = 1/(1 − MPC), which is less than 1 when MPC is positive.
Answer: (C) — A is true; R is false. With 0 < MPC < 1, we have 0 < (1 − MPC) < 1, so 1/(1 − MPC) is greater than 1, not less. R has the inequality reversed.
Assertion (A): If the entire economy tries to save a higher fraction of its income, the total amount of saving may not rise — and the equilibrium income falls.
Reason (R): A rise in MPS lowers MPC, which flattens the AD line, lowers equilibrium income, and shrinks the very income base out of which households were trying to save more.
Answer: (A) — Both true, and R is the correct explanation. This is the paradox of thrift: an increase in desire to save reduces aggregate demand, output and income; the higher saving ratio is applied to a smaller pie, so total saving stays the same (or falls). It is the textbook example of a fallacy of composition in macroeconomics.
Frequently Asked Questions
What is aggregate supply in NCERT Class 12 Macroeconomics?
Aggregate supply is the total value of final goods and services that producers are willing and able to supply at a given level of national income. In the simple Keynesian model used in NCERT Class 12, aggregate supply is identical to total income because every rupee of output produced becomes a rupee of income to factor owners. The aggregate supply curve in the AD–Y diagram is therefore the 45-degree line, since at every point output equals income at the same scale.
How is equilibrium output determined in NCERT Class 12?
Equilibrium output is the level of income at which planned aggregate demand exactly equals planned aggregate supply. NCERT Class 12 finds it in two equivalent ways. The AD = AS approach intersects the C + I curve with the 45-degree line. The S = I approach intersects the saving function with planned investment. Both methods give the same equilibrium income because they are the same identity rearranged — saving is just income minus consumption, and demand is consumption plus investment.
What is the saving equals investment (S = I) approach?
The S = I approach finds equilibrium where planned saving by households equals planned investment by firms. Below this income, planned investment exceeds planned saving, so unsold inventories fall and firms expand output. Above this income, planned saving exceeds planned investment, so unsold inventories rise and firms cut output. Only at the S = I point are planned flows balanced and output stable. NCERT Class 12 prefers this approach because it directly reveals the role of saving and investment in determining national income.
What is the investment multiplier in NCERT Class 12?
The investment multiplier is the ratio of the change in equilibrium income to the change in autonomous investment that caused it. Its formula is k = 1 / (1 − MPC), which is the same as 1 / MPS. If MPC = 0.8, the multiplier is 1 / 0.2 = 5, so an autonomous rise of ₹1,000 in investment raises equilibrium income by ₹5,000. Every round of new spending creates further rounds of induced consumption that decay by the factor MPC, and the infinite sum equals 1/(1 − MPC).
Why is the multiplier larger when MPC is larger?
A higher marginal propensity to consume means a higher fraction of every additional rupee of income is re-spent on consumption. That re-spending becomes someone else's income, which is again partly re-spent, and so on. With a high MPC the leakage at each round (the saving fraction MPS) is small, so each round adds nearly as much as the previous one and the total expansion is large. With MPC = 0.5 the multiplier is 2; with MPC = 0.8 it is 5; with MPC = 0.9 it is 10.
What is the difference between autonomous and induced expenditure?
Autonomous expenditure does not depend on the current level of income — it includes autonomous consumption (c̄), investment (I), government spending (G) and exports (X) in the simple Keynesian model. Induced expenditure varies with income; the prime example is induced consumption b · Y. NCERT Class 12 emphasises this distinction because the multiplier multiplies any change in autonomous expenditure into a much larger change in equilibrium income through the chain of induced consumption.
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