Keynesian income determination: consumption…

Core facts

Keynes (1936): output and employment depend on effective (aggregate) demand. The economy can settle below full employment.
Consumption function: C = C̄ + cY, where C̄ is autonomous consumption and c is the MPC.
MPC (marginal propensity to consume) = ΔC / ΔY. MPS = ΔS / ΔY.
MPC + MPS = 1.
APC (average propensity to consume) = C / Y. APC + APS = 1.
Investment multiplier (k) = 1 / (1 − MPC) = 1 / MPS.
Higher MPC → higher multiplier. If MPC = 0.8, k = 5.
Equilibrium income: where planned aggregate demand equals output, or planned saving equals planned investment.
Paradox of thrift: if everyone tries to save more, total saving in the economy does not rise (and income falls).

Explained

Aggregate demand

In an open economy with government: AD = C + I + G + (X − M).
Equilibrium: Y = AD. In the two-sector model: Y = C̄ + cY + I̅, so *Y\ = (C̄ + I̅) / (1 − c)**.
Assumptions: prices are fixed, supply of final goods is perfectly elastic at that price, and there is idle capacity. Then output is demand-determined.
Investment is treated as autonomous (fixed) in the simplest model. Of the components of AD, investment is the most unstable (NCERT).

Adjustment to equilibrium

If AD is less than output, firms see unplanned inventory accumulation and cut production.
If AD exceeds output, inventories fall below plan and firms raise production.
Ex ante = planned; ex post = realised. In equilibrium the two coincide.

The multiplier

A rise in autonomous spending ΔA raises income by ΔY = k × ΔA.
Process: initial spending becomes someone's income; a fraction c is spent again; and so on. Total = ΔA (1 + c + c² + ...) = ΔA / (1 − c).
With government and a proportional tax rate t: k = 1 / [1 − c(1 − t)].
Government expenditure multiplier = 1 / (1 − c). Tax multiplier = − c / (1 − c). It is negative and smaller in size than the expenditure multiplier.
Balanced budget multiplier (equal rise in G and T) = 1.

Paradox of thrift

If households raise the savings rate, consumption falls, AD falls and output falls. With investment fixed, total saving ends up unchanged or lower, even though each household tried to save more.
It works when there is unemployed capacity; it does not work at full employment.

Term	Meaning	Value
MPC	Extra consumption per extra rupee of income	Between 0 and 1
MPS	Extra saving per extra rupee	1 − MPC
Multiplier	Income change per unit autonomous spending	1 / MPS

Deeper

Fallacy of composition. The paradox of thrift is a standard example: what is rational for one person (saving more) is harmful in aggregate.
Keynes' fundamental psychological law. As income rises, consumption rises, but by less than the increase in income (0 < MPC < 1). So, with positive autonomous consumption, APC falls as income rises (MPC < APC).
Leakages reduce the multiplier. Taxes and imports act like saving: the larger the leakage rate, the smaller the multiplier. An import-heavy economy has a smaller domestic multiplier.
Multiplier works both ways. A fall in investment lowers income by a multiple; the "reverse multiplier" operates in a recession.
Limits of the simple model. It fixes prices and interest rates. The IS–LM model (Hicks, 1937) adds the money market. Crowding out, expectations and supply constraints can reduce the real-world multiplier. Estimates for India's fiscal multiplier depend on the model and period; capital expenditure is usually said to have a larger multiplier than revenue expenditure.
Effective demand versus Say's law. Keynes rejected the classical idea that supply creates its own demand.

Classical versus Keynesian theory of employment

Classical view: Say's law (J.B. Say): supply creates its own demand, so general overproduction cannot last. Flexible wages clear the labour market, and a flexible interest rate keeps saving equal to investment. Full employment is the normal state; any unemployment is voluntary or frictional and temporary.
Keynesian view: employment depends on effective demand, the point where the aggregate demand price equals the aggregate supply price. Money wages are sticky downwards, and saving depends mainly on income, not on the interest rate. Equilibrium can therefore persist below full employment (involuntary unemployment).
Policy: classical economists trusted laissez-faire; Keynes argued for public spending to raise effective demand in a depression.

Point	Classical	Keynesian
Normal equilibrium	Full employment	Can be below full employment
Saving–investment equality	Rate of interest	Changes in income
Wages	Flexible	Sticky downwards

Propensities: average and marginal

APC = C / Y and APS = S / Y, so APC + APS = 1 (because Y = C + S).
MPC = ΔC / ΔY and MPS = ΔS / ΔY, so MPC + MPS = 1.
Under the psychological law, MPC is below APC and APC falls as income rises. APC can exceed 1 at very low income (dissaving); MPC lies between 0 and 1.
Example: if Y rises from 1,000 to 1,200 and C from 800 to 950, APC at 1,200 = 0.79 (rounded), MPC = 150 / 200 = 0.75 and MPS = 0.25.

Investment: MEC and the rate of interest

Keynes: a firm invests until the marginal efficiency of capital (MEC) equals the rate of interest. MEC is the rate of discount that makes the present value of a capital asset's expected yields equal to its supply price (replacement cost).
MEC falls as more capital is installed (lower expected yields, higher supply price of machines), so the investment demand curve slopes downward. MEC depends heavily on business expectations, which is why investment is volatile.
Autonomous investment does not depend on income (public projects, inventions); induced investment rises with income or with the change in income.

The investment multiplier

k = ΔY / ΔI = 1 / (1 − MPC) = 1 / MPS. With MPC 0.75, k = 4, so a rise of 100 in investment raises income by 400.
Assumptions: constant MPC, idle capacity, a closed economy and no induced investment. R.F. Kahn (1931) first set out an employment multiplier; Keynes built on it for investment.

The accelerator

Acceleration principle (J.M. Clark, 1917): induced net investment depends on the change in output (or consumption), not on its level.
If the capital–output ratio (accelerator, v) is fixed, the capital stock required is K = vY, so net induced investment Iₜ = v (Yₜ − Yₜ₋₁). Gross investment = net investment + replacement.
Example: v = 3 and output rises from 500 to 540: induced investment = 3 × 40 = 120.
Output must keep rising to keep net investment positive; if output growth slows, net investment falls, and if output falls, net investment turns negative. Gross investment cannot fall below zero.
Assumptions: no idle capacity, a fixed capital–output ratio, a permanent rise in demand, and capital goods and credit easily available. Excess capacity weakens it.

Multiplier–accelerator interaction (Samuelson, 1939)

The multiplier turns a change in investment into a larger change in income; the accelerator turns that change in income into further (induced) investment. Together they produce cumulative expansion and contraction, i.e. trade cycles. The combined effect is also called the leverage effect.
Samuelson's model: Yₜ = Gₜ + Cₜ + Iₜ, with Cₜ = c Yₜ₋₁ and Iₜ = v (Cₜ − Cₜ₋₁). Depending on the values of c and v, income may move smoothly to a new level, fluctuate in damped, constant or explosive cycles, or rise explosively without cycles.
Super-multiplier (Hicks): when induced investment is added, k = 1 / (1 − c − i), where i is the marginal propensity to invest; it is larger than the simple multiplier.
Contrast: the multiplier links ΔI → ΔY; the accelerator links ΔY (or ΔC) → I.

Common traps

✗ "Multiplier = 1 / MPC." ✓ Multiplier = 1 / (1 − MPC) = 1 / MPS.
✗ "MPC + MPS can be greater than 1." ✓ They always add to 1.
✗ "A higher MPC lowers the multiplier." ✓ A higher MPC raises the multiplier.
✗ "In the paradox of thrift, saving rises because people save more." ✓ Total saving stays the same or falls, as income falls.
✗ "Tax multiplier is positive." ✓ A tax increase lowers income, so the tax multiplier is negative.
✗ "Keynes wrote his General Theory in 1929." ✓ It was published in 1936.

Quick revision

C = C̄ + cY; MPC + MPS = 1.
Multiplier = 1 / (1 − MPC) = 1 / MPS.
MPC 0.8 gives a multiplier of 5.
Equilibrium: Y = AD, or planned S = planned I.
Unplanned inventories signal AD below output.
Tax multiplier is negative; balanced budget multiplier = 1.
Paradox of thrift: more saving by all lowers income, not raising total saving.

Go deeper: Mains writing (beyond what APPSC Paper I usually asks)

Mains writing Mains writing

Frame: "Keynesian logic justifies counter-cyclical fiscal policy: when private demand is weak, the state can fill the gap."
Analysis points:
- during Covid-19 and slowdowns, governments raised spending to support demand
- capital expenditure has a larger multiplier than subsidies, because it also raises productive capacity
- the multiplier is lower where imports and tax leakages are high
- fiscal space is limited by deficit and debt, so quality of spending matters
Way forward: a front-loaded capital expenditure programme, with medium-term fiscal consolidation.
Example: the Union Budget's rise in capital expenditure since 2020-21 is justified in part on multiplier logic.

Medha AI writes its own notes and checks them against the sources listed. Medha AI is an independent preparation service. It is not affiliated with, endorsed by or connected to APPSC, TSPSC, MPSC, UPSC or any other commission or government body.

6.1.1.4 Keynesian income determination: consumption function, multiplier and the paradox of thrift

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