Determination of Income and Employment — Aggregate Demand and the Multiplier

This chapter asks what decides the level of output in the short run, and its answer is aggregate demand. The setting is deliberately simple: prices are fixed, and there are unemployed workers and idle machines, so firms will produce whatever is demanded. Output therefore settles where planned spending equals output — and a change in spending changes output by more than itself, through the multiplier. The paper asks four things here: the propensities (MPC, MPS, APC, APS), the equilibrium income from a consumption function, the multiplier and the change in income it produces, and the meaning of excess demand, deficient demand and the paradox of thrift.

The Consumption Function and the Four Propensities

Households spend more when income rises, but not by the full amount of the rise. Keynes wrote this as the consumption function C = c̄ + cY. Here c̄ is autonomous consumption — what households would spend even at zero income, by drawing on past savings or borrowing — and c is the marginal propensity to consume (MPC), the share of each extra rupee of income that is consumed. Whatever is not consumed is saved, so the saving function is S = Y − C = −c̄ + (1 − c)Y.

The four propensities, and the two identities that link them
PropensityFormulaRange and identity
Marginal propensity to consume (MPC)ΔC ÷ ΔY0 ≤ MPC ≤ 1
Marginal propensity to save (MPS)ΔS ÷ ΔYMPC + MPS = 1
Average propensity to consume (APC)C ÷ YCan exceed 1 at low incomes
Average propensity to save (APS)S ÷ YAPC + APS = 1; APS can be negative

Worked: with C = 100 + 0.8Y and Y = ₹1,000, consumption is 100 + 800 = ₹900 and saving is ₹100. So APC = 900 ÷ 1,000 = 0.9, APS = 0.1, MPC = 0.8 and MPS = 0.2. Notice that APC is larger than MPC: because of autonomous consumption, the average share consumed falls as income rises, approaching the MPC from above. At very low income, consumption exceeds income — APC above 1, saving negative — which is dissaving.

Aggregate Demand and Equilibrium Income

In a two-sector economy (households and firms only), aggregate demand is planned consumption plus planned investment: AD = C + I. Investment is taken as autonomous (Ī) — decided by firms on their expectations, not by the current level of income. So AD = c̄ + Ī + cY. Equilibrium is where planned output equals planned spending, Y = AD, which is the same thing as planned saving equals planned investment, S = I.

Setting Y = c̄ + Ī + cY and solving gives Y* = (c̄ + Ī) ÷ (1 − c). Worked: c̄ = 100, Ī = 200, c = 0.75. Y* = 300 ÷ 0.25 = ₹1,200. Check it both ways: consumption at ₹1,200 is 100 + 0.75 × 1,200 = 1,000, plus investment 200 gives AD = 1,200 = Y; and saving is 1,200 − 1,000 = 200 = I. If either check fails, the arithmetic is wrong.

  • Ex ante means planned or intended; ex post means actual or realised. Actual saving always equals actual investment after the event; equilibrium is the special case where the plans also agree.
  • If output is above AD, goods go unsold and inventories pile up unplanned; firms cut production and output falls towards equilibrium.
  • If output is below AD, inventories run down unexpectedly; firms raise production and output rises towards equilibrium.

The Investment Multiplier

Suppose investment rises by ₹100. The ₹100 is spent and becomes someone's income; with MPC = 0.8 they spend ₹80, which becomes another income, of which ₹64 is spent, and so on. The rounds add up to 100 + 80 + 64 + … = ₹500. The ratio of the change in income to the change in autonomous spending is the multiplier: k = ΔY ÷ ΔĪ = 1 ÷ (1 − MPC) = 1 ÷ MPS. Here k = 1 ÷ 0.2 = 5, and ΔY = 5 × 100 = 500.

The multiplier rises with the MPC
MPCMPSMultiplier k = 1 ÷ MPSΔY for ΔI = ₹100
011₹100
0.50.52₹200
0.750.254₹400
0.80.25₹500
0.90.110₹1,000
⚠️ The multiplier is 1 ÷ MPS, not 1 ÷ MPC
With MPC = 0.8, 1 ÷ 0.8 = 1.25 will always be among the options, and so will 0.2. The multiplier is never below 1 — the first round alone adds the whole of the new spending — and it grows as people spend more of each extra rupee. The minimum value, 1, comes when MPC = 0; as MPC approaches 1 the multiplier grows without limit.

Full Employment, Excess and Deficient Demand, and the Paradox of Thrift

Full employment is the level of output at which everyone willing to work at the going wage has a job; anyone without work at that point is voluntarily unemployed. Nothing guarantees that the equilibrium of the previous section lands exactly at full employment — it can fall short or overshoot it, and the two cases have names.

The two disequilibria at full employment
PointExcess demandDeficient demand
DefinitionAD exceeds the AD needed for full-employment outputAD falls short of the AD needed for full-employment output
The gapInflationary gapDeflationary gap
EffectOutput cannot rise further, so prices riseInvoluntary unemployment; output below capacity
RemedyReduce AD — raise taxes, cut government spending, tighten creditRaise AD — cut taxes, raise government spending, ease credit
🎯 The paradox of thrift
For one household, saving more is prudent. But if all households try to save more at once — the MPS rises — consumption falls, aggregate demand falls, and through the multiplier income falls. With investment unchanged, equilibrium still requires S = I, so total saving in the economy ends up unchanged or lower, not higher. What is wise for each is self-defeating for all: that is the paradox of thrift, and the paper asks it as a statement to be judged true or false.

Key takeaways

  • In the short run with fixed prices and idle resources, output is determined by aggregate demand.
  • C = c̄ + cY; MPC + MPS = 1 and APC + APS = 1; APC can exceed 1 at low incomes, which is dissaving.
  • Equilibrium: Y = AD, equivalently planned S = planned I; Y* = (c̄ + Ī) ÷ (1 − c).
  • Unplanned inventory accumulation means output is above AD and will fall; unplanned depletion means it will rise.
  • Multiplier k = 1 ÷ (1 − MPC) = 1 ÷ MPS, and ΔY = k × ΔI; it is at least 1 and rises with the MPC.
  • Excess demand at full employment creates an inflationary gap; deficient demand creates a deflationary gap and involuntary unemployment.
  • Paradox of thrift: if everyone tries to save more, income falls and total saving does not rise.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

  1. If the marginal propensity to save is 0.25, the marginal propensity to consume is:

    1. 0.25
    2. 4
    3. 0.75
    4. 1.25
    Show answer

    Answer: C — 0.75

    Every extra rupee of income is either consumed or saved, so MPC + MPS = 1 and MPC = 1 − 0.25 = 0.75. The figure 4 is the multiplier, 1 ÷ MPS, which is the answer to a different question, and 1.25 adds the two propensities instead of subtracting.

  2. If the marginal propensity to consume is 0.8, the value of the investment multiplier is:

    1. 5
    2. 1.25
    3. 8
    4. 0.2
    Show answer

    Answer: A — 5

    k = 1 ÷ (1 − MPC) = 1 ÷ 0.2 = 5. The value 1.25 comes from dividing by the MPC instead of the MPS, and 0.2 is the MPS itself; a multiplier can never be below 1, which rules both out at sight.

  3. When aggregate demand exceeds the level required to produce full-employment output, the result is:

    1. A deflationary gap and involuntary unemployment
    2. A rise in output well beyond full employment
    3. An inflationary gap and a rise in the price level
    4. No effect, because supply always adjusts
    Show answer

    Answer: C — An inflationary gap and a rise in the price level

    At full employment there are no idle resources left, so extra demand cannot be met by extra output and pushes prices up instead — an inflationary gap. A deflationary gap is the opposite case of too little demand, and output cannot rise much beyond full employment precisely because the resources are already in use.

  4. Investment rises by ₹200 crore and the marginal propensity to save is 0.2. The increase in equilibrium income is:

    1. ₹40 crore
    2. ₹1,000 crore
    3. ₹250 crore
    4. ₹160 crore
    Show answer

    Answer: B — ₹1,000 crore

    Multiplier = 1 ÷ MPS = 1 ÷ 0.2 = 5, so ΔY = 5 × 200 = ₹1,000 crore. ₹40 crore multiplies by the MPS instead of dividing, ₹250 crore uses 1 ÷ MPC = 1.25 as the multiplier, and ₹160 crore is only the second round of spending.

  5. In an economy, C = 50 + 0.5Y and autonomous investment is 100. Equilibrium income is:

    1. 150
    2. 200
    3. 75
    4. 300
    Show answer

    Answer: D — 300

    Y = (c̄ + Ī) ÷ (1 − c) = (50 + 100) ÷ 0.5 = 300. Check: C = 50 + 150 = 200, and 200 + 100 = 300 = Y. The value 150 is autonomous spending before the multiplier works, 200 is consumption at equilibrium rather than income, and 75 multiplies by 0.5 instead of dividing.

  6. At a low level of income, the average propensity to consume is greater than one. This means that:

    1. Consumption exceeds income, so households are dissaving
    2. The marginal propensity to consume is also greater than one
    3. Saving is positive but small
    4. The economy is at full employment
    Show answer

    Answer: A — Consumption exceeds income, so households are dissaving

    APC = C ÷ Y above 1 means C > Y, so saving is negative — households draw on past savings or borrow. This is possible because of autonomous consumption; it says nothing about the MPC, which stays between 0 and 1, and nothing about whether the economy is at full employment.

  7. According to the paradox of thrift, if all households in an economy decide to save a larger proportion of their income:

    1. Total saving rises in proportion to the rise in the saving rate
    2. Investment automatically rises to match the higher saving
    3. The price level rises because of excess demand
    4. Income falls, and total saving remains unchanged or falls
    Show answer

    Answer: D — Income falls, and total saving remains unchanged or falls

    Higher saving means lower consumption, so aggregate demand and, through the multiplier, income fall; since equilibrium still needs saving equal to the unchanged investment, total saving does not rise. Saving rising in proportion is the individual's intuition that the paradox overturns, investment is autonomous here and does not respond, and lower spending creates deficient rather than excess demand.

  8. In an economy, C = 200 + 0.75Y and autonomous investment is 300. If investment rises by 100, the new equilibrium income will be:

    1. 2,100
    2. 2,400
    3. 2,000
    4. 1,600
    Show answer

    Answer: B — 2,400

    Initial Y = (200 + 300) ÷ 0.25 = 2,000; the multiplier is 1 ÷ 0.25 = 4, so ΔY = 4 × 100 = 400 and the new income is 2,400 — the same as (200 + 400) ÷ 0.25. The figure 2,100 adds the extra investment without the multiplier, 2,000 is the old equilibrium, and 1,600 is the old equilibrium less four times the change.