# Determinant and Derivation of Consumption and Saving Functions

Here students are introduced to the concepts of consumption and its
determinants. It explains in general form, what consumption expenditure
involves and clearly differentiates consumption function from saving function and the derivation of former from the latter.
This unit also introduce the students to the algebraic derivation of saving
function from consumption function and vice versa. It also explained the
determining factors of saving and it shows relationship between saving and
investment.
At the end of this unit, the student should be able to;
i. Recognize both saving and consumption functions.
ii. Derive saving function from consumption function
iii. Derive consumption function from a given saving function.
iv. Determine those factors that influence consumption expenditures.
v. Identify those factors that determine saving.
vi. Understand the relationship between saving and investment

### Derivation of consumption and saving function.

Derivation of Consumption Function from a given Saving Function
Given a saving function S = -α + sYd ; to derive consumption function we will
reflect on the classical assumptions and model that;
Y = C + S ……………………………………….1 or
Y d = C + S………………………………………..2 considering the equation (2)
C = Yd – S but S = -α + sYd ……………………..3
Therefore, C = Yd – (-α + sYd) ………………… 4
C = Yd + α - sYd …………………………………5
Collect like terms;
C = α + Yd – sYd ..................................................6
C = α + (1 - s) Yd…………………………………7
Recall that 1- s = 1 – MPS = MPC = b; therefore,
C = α + b Yd …………………………………….8 QED
Numerical Example
Given the following saving function S = - 25 + 0.3Yd, derive the consumption
function.
Since Yd = C + S
Therefore, C = Yd – S
C = Yd – (-25 + 0.3Yd)
C = Yd +25 – 0.3Yd
Collect like terms:
C = 25 + (1 – 0.3)Yd
C = 25 + 0.7Yd

### Derivation of Saving Function from a Consumption Function

Mathematically the saving function can also be derived from the consumption
functions
S = Y – C
Since C = a + by
Therefore;
S = Y – (a + bY)
S = Y – a – bY
S = -a + Y – bY
S = -a + (1 – b) Y
If 1 – b = β
Then
S = -a + βY
Numerical example;
Given a consumption function C = 25 + 0.75Yd
Recall that S = Y – C ………………………………..(1)
Therefore; S = Y – (25 + 0.75Yd) …………………….(2)
S = Y – 25 – 0.75Yd ………………………..(3);
Let Y = Yd………………………………………(4)
Therefore equation 3 becomes;
S = Y – 25 – 0.75Y……………………………...(5)
Collect like terms from eqn. 5 above, to have,
S = -25 + Y - 0.75Y …………………………….(6)
Factor out Y in eqn. 6 above, to have;
S = -25 + (1 – 0.75)Y ……………………………(7) S
= -25 + 0.25Y ………………………………….(8) The equation (8) above is the required saving function.

Self Assessment Exercise
i. Differentiate between bY and b from the above analysis
ii. Differentiate between b and 1 - b
iii. Clearly explain saving concept and derive saving function from a
hypothetical schedule.

### Determinants of aggregate saving and consumption expenditure

There are a number of factors that determine or influence household level of
consumption. These include, among others, the following;
i) The level of disposable income
ii) Stock of durable goods on hand
iii) Wealth
iv) Expectations
v) Total household indebtedness
vi) The price level
vii) Government fiscal policy
i. The level of disposable income: The level of income is the basic determinant of how much households will consume. An increase in disposable income will increase consumption expenditure and vice versa.

ii. Stock of durable goods on hand: In an economy, the stock of durable
goods on hand determines the amount of current consumption. If
consumers in an economy find themselves well supplied with various
durable goods, e.g. cars, television, etc. all worthy of years of service than
the current level of consumption may fall. This is because many
households will be out of the market for such products with the result that
consumers will be willing to spend less at each level of disposable income

iii. Wealth: This refers to the stock of accumulated purchasing power stored
up from the past. For example, savings done in the past can be used to finance
current consumption. The higher an economy‘s wealth, all other things being
equal the higher will be current consumption.

iv. Expectations: Household‘s anticipation regarding future prices of goods,
their nominal income and the availability of goods may have an impact on
their current spending. Anticipation of rising prices and product shortages
tend to cause more spending.

v. Total household indebtedness: Debts are paid with current income. If in
an economy total household debts are huge there is the likelihood that current
level of consumption expenditure will be low and vice versa

vi. Level of prices: In an economy, the higher the level of prices the lower
the volume of real consumption expenditure

vii. Government fiscal policy: Fiscal policy in its simplest form implies
government spending and means through which revenue are generated
(taxes). However, if taxes are raised, disposable income will reduce and by
implication consumption will also reduce and vice versa.

### Determinants of Saving

The determinants of saving are replica of those of factors that determine
consumption except in some few cases.
i. The level of disposable income: The level of income is the basic determinant
of how much households will consume or save. An increase in disposable
income will increase consumption expenditure and vice versa.

ii. Stock of durable goods on hand: In an economy, the stock of durable goods
on hand determines the amount of current consumption. If consumers in an
economy find themselves well supplied with various durable goods, e.g. cars,
television, etc. all worthy of years of service than the current level of
consumption may fall. This is because many households will be out of the
market for such products with the result that consumers will be willing to spend
less and save more at each level of disposable income.

iii. Wealth: This refers to the stock of accumulated purchasing power stored up
from the past. For example, savings done in the past, the higher this wealth the
lower is the willingness to save further and vice versa.

iv. Inflation Expectations: Household‘s anticipation regarding future prices of
goods, their nominal income and the availability of goods may have an impact on
their current saving. Anticipation of rising prices and product shortages tend to
cause less saving.

v. Total household indebtedness: Debts are paid with current income. If in an
economy total household debts are huge there is the likelihood that current level
of saving will be low and vice versa

vi. Level of prices: In an economy, the higher the level of prices the lower the
volume of saving.

vii. Interest rate: The higher the money market rate of interest the higher would
be the level of saving, because current consumption could be postpone for more
wealth.

viii. Return on investment: The higher the return on investment the lower will
be saving level and vice versa.

ix. Government Fiscal Policy: The direction of fiscal policy to a great extend
has impact on current saving, for instance contractionary fiscal policy will reduce
disposable income and as a result reduce saving.

Self Assessment Exercise
i. List and explain various determinants of consumption expenditure.

### Relationship between Consumption and Saving

The main relationship between saving and consumption is that the income level
is shared between the two. Every level of income is either saved or consumed,
so income is the major factor that influences the both of them.
Algebraically, C= f(Y) and also S = f(Y)
i.e. Y= C + S therefore; C = Y – S while also S = Y – C
Saving is always equal to income less consumption and consumption is also
always equal income less saving..

Self Assessment Exercise
i. Show the relationship between consumption and saving

### CONCLUSION

We explained various determinants of consumption expenditure as well as
algebraic derivation of consumption expenditure from a given saving function
and conclude that income is a major determinant of consumption expenditure.
This unit also concludes that saving function could be derived from a given
consumption function and vice versa. We equally conclude that all things being
equal other than income level there are numbers of factors that influence the
aggregate level of saving.

### SUMMARY

This unit looked at concept of consumption and its determining factors, it also
expresses consumption, numerically (function). We also, derive consumption
function from a given savings function and explain the marginal propensity to
consume.
It also looked at concept of saving and its determining factors, it also expresses
Saving, algebraically (function). We also, derive savings function from a given
consumption function and explain the marginal propensity to save.

### TUTOR MARKED ASSIGNMENT

i. Define consumption
ii. List and explain components of consumption function
iii. Given that S = -25 + 0.6Yd derive the consumption function and
illustrate the result on a curve.
iv. Define Saving
v. List and explain components of Saving function
vi. Given that C = 5 + 2/3Yd derive the Saving function and illustrate
the result on a curve.
vii. Differentiate between saving function and curve.

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