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The Saving Function

The Saving Function — Learn S = f(Y), the saving schedule and curve, dissaving at zero income, break-even point, APS, and MPS. CBSE Class 12 Macroeconomics notes.

Notes

The Saving Function

Class 12 Macro Economics \u2014 How much do people save at different income levels? Let's find out.

Meaning of Saving Function

Saving is the part of income that is NOT spent on consumption. If you earn \u20B9500 and spend \u20B9440, you save \u20B960.

Saving (S)
Saving is the difference between income and consumption expenditure. S = Y \u2212 C. It represents the portion of income that households do not spend on goods and services.
Saving Function
The saving function shows the relationship between saving and income. It is a derived concept \u2014 since S = Y \u2212 C and C depends on Y, saving also depends on Y. Mathematically: S = f(Y).

Saving Function

$$S = f(Y)$$

Derivation: Since C = \u0101 + bY and S = Y \u2212 C:

S = Y \u2212 (\u0101 + bY) = \u2212\u0101 + (1 \u2212 b)Y

Where \u2212\u0101 is dissaving at zero income and (1\u2212b) = MPS.

Saving Schedule: Saving at different income levels
Income (Y) ₹ croresConsumption (C) ₹ croresSaving (S = Y−C) ₹ crores
040−40
100120−20
2002000
30028020
40036040
50044060
60052080

Saving Curve Explorer

Click any point on the curve to see details:

0100200300400500600-60-40-20204060801000Income (Y) \u2192 \u20B9 croresSaving (S) \u2192 \u20B9 croresAt Y=0, dissaving = \u2212c\u0304 = \u2212\u20B940 crBreak-even (Y=200, S=0)DissavingSaving

Important Observations

Click through to uncover key observations about the saving curve:

Starts on the negative Y-axis

At Y = ₹0, saving = −₹40 crore (dissaving). People still consume even with zero income — they pay for it from past savings, selling assets, or borrowing. This dissaving equals autonomous consumption (ā = ₹40 cr).

1/4

Average Propensity to Save (APS)

APS tells us what fraction of total income people save.

Average Propensity to Save

$$APS = \\frac{S}{Y}$$
APS
Average Propensity to Save is the ratio of total saving to total income. It shows the percentage of income that is saved. For example, if Y = \u20B9400 cr and S = \u20B940 cr, APS = 40/400 = 0.10 or 10%.

Example

If Y = \u20B9400 crore and S = \u20B940 crore,
APS = S/Y = \u20B940 / \u20B9400 = 0.10 or 10%.
This means 10% of your income is being saved.
APS Schedule
Income (Y) ₹ crSaving (S) ₹ crAPS = S/Y
100−20−0.20
20000
300200.067
400400.10
500600.12
600800.133

Key Takeaways

  • APS can never be 1 or more — you cannot save more than what you earn (S ≤ Y).
  • APS = 0 at the break-even point (when all income is consumed).
  • APS can be negative when S < 0 (dissaving at low income levels).
  • APS rises as income rises — richer people save a larger proportion of their income.
  • APS + APC = 1 always. If you consume 80% of income, you save 20%.

Marginal Propensity to Save (MPS)

MPS tells us what fraction of additional income people save.

Marginal Propensity to Save

$$MPS = \\frac{\\Delta S}{\\Delta Y}$$
MPS
Marginal Propensity to Save is the ratio of change in saving to change in income. It shows how much of every extra rupee earned is saved. For example, if income rises by \u20B9100 and saving rises by \u20B920, MPS = 20/100 = 0.20.

Example

When income rises from \u20B9400 to \u20B9500 (\u0394Y = \u20B9100),
saving rises from \u20B940 to \u20B960 (\u0394S = \u20B920).
MPS = \u0394S/\u0394Y = \u20B920 / \u20B9100 = 0.20

Key Property

The slope of the saving curve is MPS.
In our example, MPS = 0.20 (constant).
This means the saving curve is a straight line with slope 0.20.
MPS Schedule \u2014 Note MPS stays constant at 0.20
Income ChangeΔY (₹ cr)ΔC (₹ cr)ΔS (₹ cr)MPS = ΔS/ΔY
0 → 10010080200.20
100 → 20010080200.20
200 → 30010080200.20
300 → 40010080200.20
400 → 50010080200.20
500 → 60010080200.20

MPS Live Calculator

Adjust the sliders to see how MPS changes with different income and consumption values:

Experiment 1

\u0394Y (Income change):\u20B9100 cr
\u0394C (Consumption change):\u20B980 cr

\u0394S = \u0394Y \u2212 \u0394C

₹20 cr

MPS = \u0394S/\u0394Y

0.20

MPC = 1 \u2212 MPS

0.80

Experiment 2

\u0394Y (Income change):\u20B9200 cr
\u0394C (Consumption change):\u20B9150 cr

\u0394S = \u0394Y \u2212 \u0394C

₹50 cr

MPS = \u0394S/\u0394Y

0.25

MPC = 1 \u2212 MPS

0.75

Experiment 3

\u0394Y (Income change):\u20B9300 cr
\u0394C (Consumption change):\u20B9220 cr

\u0394S = \u0394Y \u2212 \u0394C

₹80 cr

MPS = \u0394S/\u0394Y

0.27

MPC = 1 \u2212 MPS

0.73

Experiment 4

\u0394Y (Income change):\u20B9500 cr
\u0394C (Consumption change):\u20B9400 cr

\u0394S = \u0394Y \u2212 \u0394C

₹100 cr

MPS = \u0394S/\u0394Y

0.20

MPC = 1 \u2212 MPS

0.80

APS vs MPS

Both measure saving, but in different ways:

APS vs MPS Comparison
AspectAPSMPS
MeaningRatio of total saving to total incomeRatio of change in saving to change in income
FormulaS/YΔS/ΔY
Value < 0Can be negative (when S < 0 at low income)Never negative — lies between 0 and 1
Value = 0At break-even point (Y = C)Only when ΔS = 0 (saving does not change)
Trend with incomeRises as income risesUsually constant if consumption function is linear
RelationAPS + APC = 1MPS + MPC = 1

Important: Slope of Saving Curve is MPS

The saving curve slopes upward at a rate equal to MPS.
In our example, MPS = 0.20, which means for every \u20B9100 increase in income, saving rises by \u20B920.
This is why the saving curve is a straight line with a constant slope.

Key Takeaways

Key Takeaways

  • Saving (S) = Income (Y) − Consumption (C). It is the part of income not spent on goods and services.
  • APS = S/Y (average propensity to save). It rises with income but can never be ≥ 1.
  • MPS = ΔS/ΔY (marginal propensity to save). It is the slope of the saving curve. MPS + MPC = 1.
  • At the break-even point, S = 0 and APS = 0. Below break-even, S is negative (dissaving). Above break-even, S is positive.
  • MPS is constant in a linear saving function. In our example, MPS = 0.20 at all income levels.