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Class 12 Macro Economics Notes · CBSE

Consumption-Saving Relationships and Equations

Consumption-Saving Relationships and Equations — Learn the relationship between APC and APS, MPC and MPS, and derived equations connecting consumption, saving, and income. CBSE Class 12 Macroeconomics notes.

Last updated: 24 Jul 2026

Notes

Consumption, Saving, and Their Relationships

Class 12 Macro Economics — How are consumption and saving connected? Let's find out.

APC + APS = 1

APC tells us what fraction of income is spent. APS tells us what fraction is saved. Together, they must add up to 1 — because every rupee you earn is either spent or saved.

Step-by-Step Proof

1

We know Y = C + S (Income = Consumption + Saving)

APC + APS = 1

APC+APS=1APC + APS = 1

Example

If your APC is 0.80 (you spend 80 paise of every rupee), then your APS must be 0.20 (you save 20 paise of every rupee). 0.80 + 0.20 = 1. Always.

MPC + MPS = 1

MPC is the fraction of additional income you spend. MPS is the fraction you save. Every extra rupee is either spent or saved — so they too must add up to 1.

Step-by-Step Proof

1

When income changes, both consumption and saving change: ΔY = ΔC + ΔS

MPC + MPS = 1

MPC+MPS=1MPC + MPS = 1

Example

If your MPC is 0.75 (you spend 75 paise of every extra rupee), your MPS must be 0.25. 0.75 + 0.25 = 1. Note: MPC + MPS always equals APC + APS = 1.

Linear Consumption Function

Consumption Function
A mathematical relationship between consumption (C) and income (Y), showing how much households plan to spend at each income level.

Linear Consumption Function

C=cˉ+bYC = \bar{c} + bY

c̄ — Autonomous Consumption

The spending that happens even when income is zero. You have to eat, pay rent, travel — even if you earn nothing. You fund this through savings, borrowing, or selling assets.

In our village story: farmers eat from last year's grain stock.

bY — Induced Consumption

The additional spending that comes from having income. b is the MPC — how much of each extra rupee you spend. Y is your current income.

When the baker

Solved Example

Problem

If autonomous consumption (c̄) = ₹40 crore, MPC (b) = 0.80, and national income (Y) = ₹500 crore, calculate total consumption (C). Use the formula: C = c̄ + bY

Solution

C = 40 + 0.80 × 500 = 40 + 400 = ₹440 crore

Linear Saving Function

Saving Function
A mathematical relationship between saving (S) and income (Y), derived from the consumption function.

Linear Saving Function

S=−cˉ+(1−b)YS = -\bar{c} + (1-b)Y

Derivation (Step by Step)

1

Start with S = Y - C

Solved Example

Problem

Given c̄ = ₹40 crore, MPC = 0.80, Y = ₹500 crore, find saving (S). Use: S = -c̄ + (1-b)Y where (1-b) = MPS.

Solution

S = -40 + (1-0.80) × 500 = -40 + 0.20 × 500 = -40 + 100 = ₹60 crore

Derivation of Saving Curve from Consumption Curve

Complementary Curves

The consumption curve and the saving curve are two sides of the same coin. Every point on the C curve has a corresponding point on the S curve. Where C = Y, S = 0 (break-even). Where C < Y, S is positive. Where C > Y, S is negative (dissaving).

Consumption Curve

45° lineCY (Income)C (Consumption)c̄

Saving Curve

S=0SY (Income)S (Saving)-c̄

Auto-Derive Process

✓

Step 1: Autonomous consumption (c̄) — spending even when income is zero

Click "Auto-Derive" to watch the process step by step.

Reverse Derivation: Consumption from Saving

The Reverse Works Too

Just as we derived the saving curve from the consumption curve, we can go backwards. Since S = -c̄ + (1-b)Y and C = Y - S, you can substitute to get C = c̄ + bY again.

Quick check:If S = -40 + 0.20Y, then C = Y - (-40 + 0.20Y) = Y + 40 - 0.20Y = 40 + 0.80Y. That's the consumption function!

Board Exam Tip: If the question gives you the saving function, simply use C = Y - S to find the consumption function.

Key Takeaways

Key Takeaways

  • APC + APS = 1 — every rupee of income is either spent (APC) or saved (APS).
  • MPC + MPS = 1 — every extra rupee of income is either spent (MPC) or saved (MPS).
  • Linear consumption function: C = c̄ + bY where c̄ = autonomous consumption (spending at zero income) and b = MPC.
  • Linear saving function: S = -c̄ + (1-b)Y = -c̄ + MPS × Y. Derived from S = Y - C.
  • The saving curve is the mirror image of the consumption curve — at break-even, C = Y and S = 0; below it, dissaving occurs.