Consumption and Saving Functions Explained: MPC, MPS, APC, APS

The consumption function is the heart of Keynesian economics. It describes the single most predictable relationship in macroeconomics: as income rises, consumption rises too — but not by as much. Understanding this relationship, and its mirror image in saving, unlocks the entire Keynesian framework.

The Consumption Function

What It Is

The consumption function describes how household spending changes as income changes.

The Linear Consumption Function

C = a + bY

Autonomous Consumption (a)

This is the consumption that happens even at zero income — the baseline spending on food, shelter, and necessities that people maintain by borrowing or drawing down savings.

Example: Even if a household temporarily has no income, it still buys groceries. That spending is autonomous consumption.

Induced Consumption (bY)

The portion of consumption that rises with income — the more you earn, the more you spend. The rate at which it rises is determined by the MPC.

Marginal Propensity to Consume (MPC)

MPC = ΔC ÷ ΔY

MPC measures how much of each additional rupee of income is spent on consumption.

Example: Income rises by ₹100. Consumption rises by ₹80. MPC = 80 ÷ 100 = 0.8

Properties of MPC

• Always between 0 and 1 → 0 < MPC < 1

• A person with MPC = 1 spends every extra rupee; MPC = 0 saves every extra rupee

• Higher-income groups tend to have lower MPC — the rich save a larger fraction of additional income than lower-income households

Average Propensity to Consume (APC)

APC = C ÷ Y

APC measures total consumption as a proportion of total income — not just what happens at the margin, but the overall picture.

Properties of APC

• Can exceed 1 at very low incomes — if someone earns ₹1,000 but spends ₹1,200 (by borrowing), APC = 1.2

• Falls as income rises — higher earners spend a smaller proportion of their income

• APC > MPC at all positive income levels — because autonomous consumption (a) always pulls the average up above the marginal rate

APC vs MPC: Quick Comparison

Deriving the Saving Function

Since all income is either consumed or saved:

Y = C + S Therefore: S = Y − C

Substituting C = a + bY:

S = Y − (a + bY) S = −a + (1 − b)Y

This gives us the saving function, where:

• −a is autonomous dissaving (at zero income, saving is negative because people are borrowing to consume)

• (1 − b) is the Marginal Propensity to Save (MPS)

Marginal Propensity to Save (MPS)

MPS = ΔS ÷ ΔY = 1 − MPC

MPS measures how much of each additional rupee of income is saved.

Example: MPC = 0.75 → MPS = 1 − 0.75 = 0.25 For every ₹100 of extra income, ₹75 is consumed and ₹25 is saved.

The Key Identity

MPC + MPS = 1

This must always hold — additional income can only be consumed or saved. There is no third option.

Average Propensity to Save (APS)

APS = S ÷ Y = 1 − APC

APS measures total saving as a proportion of total income.

The Key Identity

APC + APS = 1

Again, total income is entirely accounted for by consumption and saving.

All Four Measures: Summary Table

Always true: MPC + MPS = 1 APC + APS = 1

Worked Numerical Example

Given: Autonomous consumption = ₹200 MPC = 0.8 Income level = ₹1,000

Step 1: Calculate consumption C = 200 + 0.8 × 1,000 = 200 + 800 = ₹1,000

Step 2: Calculate saving S = Y − C = 1,000 − 1,000 = ₹0

Step 3: Calculate APC APC = C ÷ Y = 1,000 ÷ 1,000 = 1.0

Step 4: Calculate APS APS = 1 − APC = 1 − 1.0 = 0

Now let income rise to ₹1,500:

C = 200 + 0.8 × 1,500 = ₹1,400 S = 1,500 − 1,400 = ₹100 APC = 1,400 ÷ 1,500 = 0.93 (fallen from 1.0) APS = 100 ÷ 1,500 = 0.067

The Paradox of Thrift: A Warning About Saving

Saving is virtuous for an individual — but if everyone tries to save more simultaneously, a paradox emerges:

1. Households increase saving → Consumption falls

2. Falling consumption → Lower aggregate demand

3. Lower AD → Lower national income

4. Lower income → Less total saving overall

The individual’s rational behavior produces a collective outcome no one wanted. This is the Paradox of Thrift — one of the most counterintuitive and important insights in Keynesian economics.

Policy implication: During a recession, urging everyone to save is the wrong advice. It deepens the downturn. Government spending (dissaving by the public sector) can counteract the contractionary effect.

Exam Tips

For short-answer questions:

• Always state the formula before solving

• Verify your answer by checking MPC + MPS = 1

For derivation questions:

• Show the full algebraic steps when deriving S = −a + (1−b)Y from C = a + bY

Common MCQ traps:

• APC can exceed 1 — MPC cannot

• MPS = 1 − MPC (not MPC = 1 − MPS… same thing, but write it right)

• At break-even income, APC = 1 and APS = 0

Continue reading: The Investment Multiplier: How ₹200 Crore of Investment Creates ₹800 Crore of Income

Topics covered: Consumption function, Saving function, MPC, MPS, APC, APS, Autonomous consumption, Paradox of thrift, Keynesian identities | CBSE Class 12 Economics, CUET Preparation