The Saving Function
Class 12 Macro Economics — 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 ₹500 and spend ₹440, you save ₹60.
Saving Function
Derivation: Since C = ā + bY and S = Y − C:
Where −ā is dissaving at zero income and (1−b) = MPS.
| Income (Y) ₹ crores | Consumption (C) ₹ crores | Saving (S = Y−C) ₹ crores |
|---|---|---|
| 0 | 40 | -40 |
| 100 | 120 | -20 |
| 200 | 200 | 0 |
| 300 | 280 | 20 |
| 400 | 360 | 40 |
| 500 | 440 | 60 |
| 600 | 520 | 80 |
Saving Curve Explorer
Click any point on the curve to see details:
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).
Average Propensity to Save (APS)
APS tells us what fraction of total income people save.
Average Propensity to Save
Example
APS = S/Y = ₹40 / ₹400 = 0.10 or 10%.
This means 10% of your income is being saved.
| Income (Y) ₹ cr | Saving (S) ₹ cr | APS = S/Y |
|---|---|---|
| 100 | -20 | -0.20 |
| 200 | 0 | 0 |
| 300 | 20 | 0.067 |
| 400 | 40 | 0.10 |
| 500 | 60 | 0.12 |
| 600 | 80 | 0.133 |
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
Example
saving rises from ₹40 to ₹60 (ΔS = ₹20).
MPS = ΔS/ΔY = ₹20 / ₹100 = 0.20
Key Property
In our example, MPS = 0.20 (constant).
This means the saving curve is a straight line with slope 0.20.
| Income Change | ΔY (₹ cr) | ΔC (₹ cr) | ΔS (₹ cr) | MPS = ΔS/ΔY |
|---|---|---|---|---|
| 0 → 100 | 100 | 80 | 20 | 0.20 |
| 100 → 200 | 100 | 80 | 20 | 0.20 |
| 200 → 300 | 100 | 80 | 20 | 0.20 |
| 300 → 400 | 100 | 80 | 20 | 0.20 |
| 400 → 500 | 100 | 80 | 20 | 0.20 |
| 500 → 600 | 100 | 80 | 20 | 0.20 |
MPS Live Calculator
Adjust the sliders to see how MPS changes with different income and consumption values:
Experiment 1
ΔS = ΔY − ΔC
₹20 cr
MPS = ΔS/ΔY
0.20
MPC = 1 − MPS
0.80
Experiment 2
ΔS = ΔY − ΔC
₹50 cr
MPS = ΔS/ΔY
0.25
MPC = 1 − MPS
0.75
Experiment 3
ΔS = ΔY − ΔC
₹80 cr
MPS = ΔS/ΔY
0.27
MPC = 1 − MPS
0.73
Experiment 4
ΔS = ΔY − ΔC
₹100 cr
MPS = ΔS/ΔY
0.20
MPC = 1 − MPS
0.80
APS vs MPS
Both measure saving, but in different ways:
| Aspect | APS | MPS |
|---|---|---|
| Meaning | Ratio of total saving to total income | Ratio of change in saving to change in income |
| Formula | S/Y | ΔS/ΔY |
| Value < 0 | Can be negative (when S < 0 at low income) | Never negative — lies between 0 and 1 |
| Value = 0 | At break-even point (Y = C) | Only when ΔS = 0 (saving does not change) |
| Trend with income | Rises as income rises | Usually constant if consumption function is linear |
| Relation | APS + APC = 1 | MPS + MPC = 1 |
Important: Slope of Saving Curve is MPS
In our example, MPS = 0.20, which means for every ₹100 increase in income, saving rises by ₹20.
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.