Saving and the saving function – Consumption, Saving, Investment and Multiplier (Senior 5 Economics) | Ganzaa

Consumption, Saving, Investment and Multiplier

Lessons

Senior 5 · Economics

Consumption, Saving, Investment and Multiplier

4 lessons

Lesson 2 of 4

Saving and the saving function

40 min

Saving less than it invests

Every year from 2021 to 2025, Rwanda invested far more than it saved: in 2025, saving was 23.1% of GDP and investment 34.1%. The gap was filled from abroad, by loans, grants and foreign investment. Raising domestic saving is therefore a long-standing goal of policy. This lesson studies saving as the other side of the consumption decision, and asks why saving is hard in a developing economy and how it can be encouraged.

Definition

Saving: the part of disposable income that is not spent on consumption, $S = Y - C$ .

Saving function: the relationship between saving and disposable income. If $C = a + b Y$ , then

S = Y - (a + b Y) = - a + (1 - b) Y

Average propensity to save (APS) $= \frac{S}{Y}$ . Marginal propensity to save (MPS) $= \frac{\Delta S}{\Delta Y} = 1 - b$ .

Two identities

Since every franc of income is either consumed or saved, $Y = C + S$ . Dividing by $Y$ , and then taking changes:

\frac{C}{Y} + \frac{S}{Y} = 1 \;\Rightarrow\; \text{APC} + \text{APS} = 1

\frac{\Delta C}{\Delta Y} + \frac{\Delta S}{\Delta Y} = 1 \;\Rightarrow\; \text{MPC} + \text{MPS} = 1

The saving function is the mirror of the consumption function. Where consumption is above the 45° line (incomes below 800), saving is negative: households are dissaving, by borrowing or using past savings. At the break-even income saving is zero, and above it saving is positive and grows by the MPS, 0.25, for each extra franc of income.

Worked example 1: from a consumption function to a saving function

Given $C = 300 + 0.6 Y$ (Frw billion):

S = Y - (300 + 0.6Y) = -300 + 0.4Y, \qquad \text{MPS} = 0.4 = 1 - 0.6

At $Y = 2\,000$ : $S = - 300 + 800 = 500$ , so $\text{APS} = \frac{500}{2\,000} = 0.25$ , and $C = 1\,500$ , so $\text{APC} = 0.75$ . Check: $0.25 + 0.75 = 1$ .

Break-even income: $S = 0 \Rightarrow 0.4Y = 300 \Rightarrow Y = 750$ .

Worked example 2: Rwanda's saving rate and saving gap

NISR's accounts give gross national saving of Frw 5,395 billion in 2025, out of gross national disposable income of Frw 23,973 billion, and investment of Frw 7,981 billion.

\text{APS (national)} = \frac{5\,395}{23\,973} = 0.225

\text{Saving gap} = I - S = 7\,981 - 5\,395 = 2\,586 \text{ billion Frw}

\text{Share of investment financed by national saving} = \frac{5\,395}{7\,981} \times 100 = 67.6\%

About two-thirds of Rwanda's investment in 2025 was financed by its own saving; the remaining third came from abroad.

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Saving in developing countries

Why saving tends to be low

Low incomes: when most income goes on food, rent and school fees, the MPC is close to 1 and little is left.
Large households and many dependants, which raise consumption needs.
Irregular incomes in farming and informal work, which households smooth by spending savings in lean months.
Limited access to financial institutions in rural areas, and distrust of banks after past failures.
Low or negative real interest rates: when inflation is above the deposit rate, money in the bank loses value.
Social obligations and the demonstration effect: ceremonies and imitation of richer lifestyles.
Saving in kind: wealth is held as livestock, land or building materials, which is not available to lend to investors.
Government dissaving: budget deficits subtract from national saving.

How saving can be encouraged

Wider financial inclusion: Rwanda created an Umurenge SACCO (a savings and credit cooperative) in every administrative sector, and mobile money lets people save small amounts cheaply.
Long-term saving schemes: the Ejo Heza scheme, run by the Rwanda Social Security Board, lets informal workers save for old age, with incentives from the government.
Positive real interest rates, by keeping inflation low and stable.
Contractual saving through pensions and insurance, and tax incentives for saving.
Financial education, and strong supervision so that savers trust institutions.
Government saving: smaller budget deficits, or surpluses, raise national saving.
Informal groups (ibimina, rotating savings clubs) that can be linked to SACCOs and banks.

Important

The paradox of thrift. Keynes pointed out that if everyone tries to save more at once, consumption falls, firms sell less, incomes fall, and total saving may end up no higher than before. What is wise for one household can be harmful for the economy in a recession. In the long run, though, saving finances investment and growth, which is why developing countries try to raise it. Which view matters more depends on whether the economy has idle resources.

Warning

Watch the signs. In $S = - a + (1 - b) Y$ , the intercept is negative: at zero income households dissave by the amount of autonomous consumption. Students often write $S = a + (1 - b) Y$ . Check your saving function by confirming that $C + S = Y$ at any income.

UWindsor OpenLearning (University of Windsor), "Consumption and Saving Functions" (about 16 minutes). Follow how the saving function is derived from the consumption function, and check his result against the two-panel diagram in this lesson.

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Practice

Define saving, the APS and the MPS.
Show that APC + APS = 1 and MPC + MPS = 1.
Given $C = 120 + 0.7 Y$ , write the saving function and find the break-even income.
For $C = 120 + 0.7 Y$ , calculate S, APS and APC at Y = 1,000.
A household's income rises from Frw 150,000 to Frw 200,000 and its saving from Frw 6,000 to Frw 21,000. Calculate the MPS and the MPC.
In 2024, Rwanda's gross national saving was Frw 4,537 billion and investment Frw 6,916 billion (NISR). Calculate the saving gap and the share of investment financed by national saving.
Explain five reasons why saving is low in many developing countries.
"Rwanda should raise its saving rate as fast as possible." Evaluate this statement, with reference to the paradox of thrift.

Show answersHide answers

Saving is income not consumed (S = Y − C). APS = S ÷ Y. MPS = ΔS ÷ ΔY.
Y = C + S; dividing by Y gives APC + APS = 1. ΔY = ΔC + ΔS; dividing by ΔY gives MPC + MPS = 1.
S = −120 + 0.3Y; break-even where S = 0: Y = 400.
S = −120 + 300 = 180; APS = 0.18; C = 820, APC = 0.82.
MPS = 15,000 ÷ 50,000 = 0.30; MPC = 0.70.
Gap = 6,916 − 4,537 = Frw 2,379 billion; share = 4,537 ÷ 6,916 × 100 = 65.6%.
Any five: low incomes (high MPC); large households; irregular incomes; limited access to banks; low or negative real interest rates; social obligations and demonstration effect; saving in kind; government deficits.
For: more domestic saving finances investment without foreign debt and supports long-run growth. Against: a sudden rise in saving cuts consumption and, if investment does not rise, lowers income and jobs (paradox of thrift). Conclusion: raise saving gradually, while expanding the financial institutions that channel it into investment.

Sources and credits

Saving, investment, GDP and disposable income, 2021–2025: GDP National Accounts 2025 (annual tables, released 17 March 2026), National Institute of Statistics of Rwanda (NISR). Percentages calculated by Ganzaa.
Umurenge SACCOs and the Ejo Heza scheme: Rwanda Social Security Board and the Ministry of Finance and Economic Planning (MINECOFIN); described in general terms.
Video: Consumption and Saving Functions, UWindsor OpenLearning, embedded from YouTube.

Written by Ganzaa: the text, both diagrams, the worked examples and the practice items. The consumption functions and household figures are illustrative.

1Saving less than it invests

2Two identities

3Saving in developing countries

Why saving tends to be low

How saving can be encouraged

Saving less than it invests

Two identities

Saving in developing countries