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Aggregate demand and supply, the consumption and saving functions, equilibrium by two routes, the investment multiplier, and the two gaps.
The theoretical core of the course. Every diagram on the following slides is plotted from the same economy: C = 100 + 0.8Y, I = 100.
S = I becomes the equilibrium condition. Unplanned inventory change becomes the mechanism that gets us there. And "fight inflation or a slump" becomes a precise statement about a measurable gap.
Under these assumptions, output is determined solely by aggregate demand. That sentence is the whole chapter.
Their components; ex ante vs ex post.
C = C̄ + cY, drawn and tabulated.
APC, APS, MPC, MPS and the two identities.
Derived from consumption, drawn beneath it.
AD = AS and S = I — same answer, drawn.
Why ₹50 crore of investment raises income by ₹250 crore.
And the kinds of unemployment.
Excess and deficient demand, measured vertically.
Fiscal and monetary — the payoff of Chapter 3.
Aggregate demand (AD) — the total planned expenditure on final goods and services that all the sectors of an economy intend to undertake at a given level of income during an accounting year.
AD = C + I + G + (X − M)
In a two-sector economy, AD = C + I.
Aggregate supply (AS) — the total value of final goods and services that all the producers in an economy plan to produce during an accounting year.
Whatever is produced is distributed as factor income, so AS = National income = Y. This is why AS is drawn as the 45° line.
Producing ₹1 crore of output requires paying out exactly ₹1 crore in factor incomes. So AS = Y identically. On a graph with income on the x-axis and value on the y-axis, the relation "y equals x" is a straight line through the origin at 45°. Aggregate supply is not a behavioural curve at all — it is an accounting identity, drawn.
Households do only two things with income: spend it or save it. So AS = Y = C + S. Keep both forms — the first gives the AD = AS route to equilibrium, the second gives the S = I route.
Ex ante — what is planned or intended at the beginning of the period. Ex ante consumption, ex ante investment, ex ante aggregate demand.
Ex post — what has actually happened, measured at the end of the period. This is what national income accounting records.
Ex post, saving always equals investment — it is an accounting identity, guaranteed by counting unsold goods as inventory investment. That identity is always true and therefore explains nothing.
Ex ante, planned saving need not equal planned investment. The economy is in equilibrium only when they do. That is a condition — and conditions determine things.
Firms plan to produce and sell ₹1,000 crore. Households plan to spend only ₹900 crore.
Ex ante: AD (900) < AS (1,000) — no equilibrium.
Ex post: ₹100 crore of goods go unsold and are recorded as unplanned inventory
investment. Measured investment rises by ₹100 crore, and the books balance perfectly.
"S = I always" (ex post, accounting identity) and "S = I only in equilibrium" (ex ante, behavioural condition) are both correct. Marks are lost by asserting one without naming which sense you mean.
Consumption function — the functional relationship between consumption expenditure and the level of income: as income rises, consumption rises, but by less than the rise in income.
The consumption that takes place even at zero income, financed by past savings or borrowing. It is the intercept of the consumption line.
A family with no income this month still eats.
The fraction of each additional rupee of income that is consumed. It is the slope of the consumption line. 0 < c < 1.
The part of consumption that depends on income. It is zero when income is zero and rises as income rises.
C = 100 + 0.8Y · I = 100 (₹ crore)
Autonomous consumption ₹100 crore; MPC = 0.8, so 80 paise of every extra rupee is spent. Investment is autonomous — it does not depend on income, so it is a horizontal line.
APC — Average Propensity to Consume: the ratio of total consumption to total income.
APS — Average Propensity to Save: the ratio of total saving to total income.
MPC — Marginal Propensity to Consume: the ratio of the change in consumption to the change in income.
MPS — Marginal Propensity to Save: the ratio of the change in saving to the change in income.
Since Y = C + S, divide throughout by Y: 1 = C/Y + S/Y ⟹ APC + APS = 1
And since ΔY = ΔC + ΔS, divide throughout by ΔY: 1 = ΔC/ΔY + ΔS/ΔY ⟹ MPC + MPS = 1
Never memorise these. Derive them — it takes four seconds and it is a mark.
| Income Y | Consumption C | Saving S = Y − C | APC = C/Y | APS = S/Y | MPC | MPS |
|---|---|---|---|---|---|---|
| 0 | 100 | (−) 100 | ∞ | −∞ | — | — |
| 200 | 260 | (−) 60 | 1.30 | (−) 0.30 | 0.8 | 0.2 |
| 400 | 420 | (−) 20 | 1.05 | (−) 0.05 | 0.8 | 0.2 |
| 500 | 500 | 0 | 1.00 | 0.00 | 0.8 | 0.2 |
| 600 | 580 | 20 | 0.97 | 0.03 | 0.8 | 0.2 |
| 800 | 740 | 60 | 0.93 | 0.07 | 0.8 | 0.2 |
| 1000 | 900 | 100 | 0.90 | 0.10 | 0.8 | 0.2 |
Saving function — the relationship between saving and income, obtained by subtracting the consumption function from income.
Break-even point — the level of income at which consumption exactly equals income, so saving is zero. Here Y = 500: the point where the consumption line cuts the 45° line.
In an economy, when income rises from ₹400 crore to ₹500 crore, consumption rises from ₹350 crore to ₹430 crore.
Find (a) MPC, (b) MPS, (c) APC at ₹500 crore, (d) APS at ₹500 crore, (e) the consumption function, and (f) the break-even income.
MPC = 0.8 · MPS = 0.2 · APC = 0.86 · APS = 0.14 · C = 30 + 0.8Y · break-even Y = ₹150 crore.
Equilibrium level of income — the level of income and output at which aggregate demand equals aggregate supply, so that whatever producers plan to produce is exactly what all sectors plan to buy, and there is no tendency for output to change.
C = 100 + 0.8(1000) = 900 · I = 100 · AD = 900 + 100 = 1,000 = AS ✓ · S = 1000 − 900 = 100 = I ✓
The diagram shows where equilibrium is. This slide shows how the economy arrives there — and the mechanism is Chapter 2's unplanned inventory.
At Y = 1,000 and only there, unplanned inventory change is zero. Firms' expectations are exactly fulfilled, so no firm has any reason to change what it produces. Every other level of output generates a signal that pushes it back towards 1,000.
In microeconomics, disequilibrium is corrected by a change in price. Here — under the Keynesian fixed-price assumption — it is corrected by a change in quantity produced. That is why this model can explain unemployment, and the micro one cannot.
They are the same equation rearranged:
Y = C + I ⟺ Y − C = I ⟺ S = I
Route 1 says total spending equals total output. Route 2 says the leakage equals the injection — Chapter 1's condition, in a two-sector economy.
The saving curve is upward sloping (slope = MPS = 0.2) and the investment line is horizontal, because investment here is autonomous — it does not depend on income. This is the diagram examiners ask for when they say "explain equilibrium by the saving–investment approach".
Investment rises by ₹50 crore. By how much does equilibrium income rise?
₹250 crore — five times the initial rise. New equilibrium: Y = 250 ÷ 0.2 = ₹1,250 crore. This magnification is what the multiplier measures.
Investment multiplier (k) — the ratio of the total change in income to the initial change in investment (or in any autonomous expenditure) that caused it.
Because your spending is my income. The ₹50 crore spent on a new factory becomes income for construction workers, who spend 80% of it, which becomes income for shopkeepers, who spend 80% of that… The initial injection goes round the circular flow again and again, and each circuit adds to income.
| Round | Increase in income ΔY | Consumed (80%) | Saved (20%) | Cumulative ΔY |
|---|---|---|---|---|
| 1 | 50.00 | 40.00 | 10.00 | 50.00 |
| 2 | 40.00 | 32.00 | 8.00 | 90.00 |
| 3 | 32.00 | 25.60 | 6.40 | 122.00 |
| 4 | 25.60 | 20.48 | 5.12 | 147.60 |
| 5 | 20.48 | 16.38 | 4.10 | 168.08 |
| ⋮ | ⋮ | ⋮ | ⋮ | ⋮ |
| Total | 250.00 | 200.00 | 50.00 | 250.00 |
It comes to exactly ₹50 crore — the initial rise in investment. The process stops precisely when the extra income has generated enough extra saving to match the extra investment. S = I is restored, and that is what ends the process.
| MPC | MPS | Multiplier k = 1/MPS | Meaning |
|---|---|---|---|
| 0 | 1 | 1 | Every extra rupee is saved. No further rounds — no multiplier at all. |
| 0.5 | 0.5 | 2 | Half leaks out each round. |
| 0.8 | 0.2 | 5 | Our economy. |
| 0.9 | 0.1 | 10 | Very little leaks out; the rounds continue for a long time. |
| 1 | 0 | ∞ | Nothing leaks out — the theoretical maximum. |
If investment falls by ₹50 crore, income falls by ₹250 crore. The multiplier is symmetric — which is precisely why a modest fall in investment can produce a deep recession. This is the arithmetic behind the Great Depression of Chapter 1.
In an economy, an increase in investment of ₹300 crore raises national income by ₹1,500 crore. Find (a) the multiplier, (b) MPS, (c) MPC. (d) If instead MPC had been 0.75, by how much would the same ₹300 crore have raised income?
k = 5 · MPS = 0.2 · MPC = 0.8 · and with MPC = 0.75 income would rise by only ₹1,200 crore.
A government wants to raise national income by ₹4,000 crore. MPC = 0.75. How much must it increase its own expenditure by? What assumption are you making?
k = 1 ÷ (1 − 0.75) = 4. So ΔG = ΔY ÷ k = 4,000 ÷ 4 = ₹1,000 crore.
The assumption: that the multiplier applies to government expenditure exactly as it does to investment. It does — the multiplier works on any autonomous expenditure, whoever spends it. The assumption that is being made is that the economy has spare capacity: if it were already at full employment, the extra spending would raise prices, not output.
Full employment — a situation in which all those who are able and willing to work at the prevailing wage rate get work. It does not mean zero unemployment; some frictional and voluntary unemployment always remains.
People who are able and willing to work at the existing wage rate but cannot find work. This is the unemployment Keynes was concerned with, and the kind the government can act on.
People who are not willing to work at the prevailing wage — perhaps holding out for a better job. No policy failure is involved.
Full-employment level of income (YF) — the level of income and output at which all the economy's resources, including labour, are fully employed. Output cannot rise above it in the short run.
The economy's equilibrium level of income is set by aggregate demand, and there is nothing that forces it to coincide with the full-employment level. It may settle below it (leaving people involuntarily unemployed) or the demand for it may exceed what can be produced (raising prices). Those two possibilities are the two gaps.
Excess demand — a situation in which aggregate demand exceeds aggregate supply at the full-employment level of income.
Inflationary gap — the amount by which aggregate demand exceeds the aggregate supply corresponding to full employment.
Deficient demand — a situation in which aggregate demand falls short of aggregate supply at the full-employment level of income.
Deflationary gap — the amount by which aggregate demand falls short of the aggregate supply required for full employment.
The deflationary gap is ₹100 crore, but equilibrium income is ₹500 crore short of full employment. Why the difference?
The multiplier. A demand shortfall of ₹100 crore costs the economy 100 × 5 = ₹500 crore of income. The gap is the cause; the income shortfall is the consequence, magnified k times. This also tells you the cure: closing a ₹100 crore gap is enough to recover the whole ₹500 crore.
| Measure | Excess demand — inflationary gap reduce AD | Deficient demand — deflationary gap raise AD |
|---|---|---|
| Fiscal · Government spending | Decrease G on public works, defence, subsidies | Increase G on roads, schools, employment programmes |
| Fiscal · Taxes | Raise taxes → less disposable income → less C | Cut taxes → more disposable income → more C |
| Fiscal · Public borrowing | Borrow more from the public → mops up purchasing power | Borrow less, or repay debt → releases purchasing power |
| Monetary · Repo / bank rate | Raise → costlier credit → less borrowing and spending | Lower → cheaper credit → more borrowing and spending |
| Monetary · CRR and SLR | Raise → banks can lend less; multiplier falls | Lower → banks can lend more; multiplier rises |
| Monetary · Open market operations | Sell securities → drains cash from the system | Buy securities → injects cash into the system |
| Monetary · Margin requirement | Raise → less credit against the same collateral | Lower → more credit against the same collateral |
The monetary rows are the instruments you learned last chapter, now with a reason attached. The fiscal rows are the government budget — the whole of Chapter 5.
In an economy the full-employment level of income is ₹2,000 crore. The consumption function is C = 200 + 0.75Y and planned investment is ₹150 crore.
Find (a) the equilibrium level of income, (b) whether there is excess or deficient demand, (c) the size of the gap, and (d) by how much the government must change its expenditure to restore full employment.
(a) ₹1,400 crore (b) deficient demand (c) deflationary gap of ₹150 crore (d) increase government expenditure by ₹150 crore.
Many answer (d) with "₹600 crore" — the income shortfall. But the government does not have to supply the whole shortfall: it supplies the ₹150 crore gap and the multiplier supplies the remaining ₹450 crore. ΔG = gap, not ΔG = income shortfall.
Chapter 1 promised we would prove this with numbers. Here it is.
Paradox of thrift — if all the people of an economy increase the proportion of their income they wish to save, the total saving of the economy does not increase — it either remains unchanged or falls, because aggregate income falls.
Start with our economy: C = 100 + 0.8Y, I = 100, equilibrium Y = 1,000, saving S = 100.
Now every household decides to save more: MPS rises from 0.2 to 0.25, so C = 100 + 0.75Y and S = −100 + 0.25Y.
In equilibrium S = I. Investment did not change, so saving cannot change — no matter how hard households try. All their extra thrift could do was reduce the income out of which they save. The attempt to save more succeeds only in making everyone poorer.
The paradox holds in a demand-constrained economy with unemployed resources — the Keynesian short run. At full employment, extra saving does finance extra investment and raises future output. The paradox is an argument about a slump, not a claim that thrift is always harmful.
What is marginal propensity to consume? How is it related to marginal propensity to save?
MPC is the ratio of the change in consumption expenditure to the change in income: MPC = ΔC / ΔY. It measures the fraction of an additional rupee of income that is spent.
Since all income is either consumed or saved, ΔY = ΔC + ΔS. Dividing throughout by ΔY gives 1 = MPC + MPS, so MPS = 1 − MPC. The two are complements: a higher MPC necessarily means a lower MPS.
What do you understand by a "parametric shift of a line"? How does a line shift when (i) its slope decreases, and (ii) its intercept increases?
A straight line y = a + bx is fixed by two parameters: the intercept a and the slope b. A parametric shift is the change in the position of the line caused by a change in one of these parameters.
Measure the level of ex-ante aggregate demand when autonomous investment and consumption expenditure (A) is ₹50 crore, MPS is 0.2, and the level of income (Y) is ₹4,000 crore. State whether the economy is in equilibrium or not, citing reasons.
Ex ante aggregate demand = ₹3,250 crore. The economy is not in equilibrium, because planned aggregate demand falls short of aggregate supply by ₹750 crore. Goods worth ₹750 crore will remain unsold, causing an unplanned accumulation of inventories. Firms will therefore cut production, and income will fall — continuing until it reaches the equilibrium level of ₹250 crore.
An economy is in equilibrium. Find national income given: autonomous consumption = 100, MPS = 0.25, investment expenditure = 200.
National income = ₹1,200 crore. Check by the S = I route: S = −100 + 0.25Y = 200 ⟹ 0.25Y = 300 ⟹ Y = 1,200 ✓
"An increase in the propensity to save always reduces national income." Examine this statement critically, using the multiplier.
True in the Keynesian short run with unemployed resources. A rise in MPS lowers MPC, which lowers the multiplier k = 1/MPS. With autonomous expenditure unchanged, equilibrium income Y = A/MPS falls. And because S = I in equilibrium and investment is unchanged, total saving does not even rise — the paradox of thrift.
But the statement is too strong. It assumes investment is autonomous and that the economy is demand-constrained. In an economy at full employment, or over the long run, higher saving supplies the funds for higher investment, which raises the capital stock and future output. So thrift is contractionary in a slump and growth-promoting at full capacity — the correct answer states both cases.
We know the government can close a gap. Now: with what, exactly?
The correction table said "increase government expenditure" and "cut taxes" as though these were free. They are not — they must be paid for, and how they are paid for changes the answer. Chapter 5 opens the government's own accounts: where its money comes from, where it goes, and what it means when the two do not match.