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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.

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

C/YS/Y

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

ΔC/ΔYΔS/ΔY

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

$$C = \bar{c} + bY$$

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

$$S = -\bar{c} + (1-b)Y$$

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

CYC,S

Saving Curve

-c̄Y

Auto-Derive Process

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Step 1: Autonomous consumption c̄ on the consumption curve — spending even at Y=0

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.