(i) Investment has a specific meaning in economics.
(ii) It means additions to the existing productive capacities (stock of capital and inventories).

(i) The multiplier assumes that those who earn income are likely to spend a proportion of their additional income on consumption.
(ii) In practice, people tend to spend their additional income on other items
(iii) Such expenses are known as leakages.

Accelerator is the ratio between induced investment and an initial change in consumption.
(β) = \(\frac{ΔI}{ΔC}\)

APS is the ratio of saving to income
APS = \(\frac{S}{Y}\)

APC is the ratio of consumption expenditure to any particular level of income
APC = \(\frac{C}{Y}\)

Proposition (1):
When income increases from 120 to 180 consumption also increases from 120 to 170 but the increase in consumption is less than the increase in income, 10 is saved.
Proposition (2):
When income increases to 180 and 240, it is divided in some proportion between consumption by 170 and 220 and saving by 10 and 20 respectively.
Proposition (3):
Increases in income to 180 and 240 lead to increased consumption 170 and 220 and increased saving 20 and 10 than before. It is clear from the widening area below the С curve and the saving gap between 45° line and С curve.

(i) Hicks combined multiplier and accelerator to measure the total effect of initial investment on income.
(ii) Both induced consumption and induced investment are combined.
(iii) Also called leverage effect, it may lead the economy to a very high or low level of income propagation.
\(\mathrm{Y}=\mathrm{C}+\mathrm{I}_{\mathrm{A}}+\mathrm{I}_{\mathrm{P}}\)
Y = aggregate income
C = consumption expenditure
I_A = autonomous investment
I_B = induced private investment

(i) When income incrcases, consumption expenditure also incrcases but by a smaller amount.
(ii) The increased income will be divided in some proportion between consumption expenditure and saving.
(iii) Increase in income always leads to an increase in both consumption and saving.

Since Y = C + I we can write Y = a + bY + I.
This equation can be rearranged to yield
Y - bY = a + I
Y(1 - b) = a + I
We can then solve for Y in terms of I by dividing through by (1 - b):
Y = (a + I) (1/1 - b)
Now we can see that an increase in I will increase Y by
ΔY = ΔI x (1/1 - b)
Since b D MPC, the expression becomes
ΔY = ΔI x 1/(1 - MPC)
Therefore, the multiplier is 1/1 - MPC or 1/MPS.

(i) The propensity to consume refers to the portion of income spent on consumption.
MPC = \(\frac{ΔC}{ΔY}\)
(K) = \(\frac{1}{1-MPC}\)
(ii) The multiplier is the reciprocal of one minus marginal propensity to consume.
(iii) Multiplier is 1/MPS
(iv) The multiplier is therefore define as reciprocal of MPS.
(v) Multiplier is inversely related to MPS and directly with MPC.
Numerically, if MPC is 0.75, MPS is 0.25 and K is 4.
Using formula K = \(\frac{1}{1-MPC}\)
⇒\(\frac{1}{1-0.75}\) = 1/0.25 = 4
∴ Multiplier (K) = 4

C = 100 + 0.8Y;
I = 10
Y = C + I
= 100 + 0.8 Y +9p00

0.2Y = 1000
∴ Y = 1000
Here, C = 100 + 0.8y
= 100 + 1000 = 900
S = 100 = I
After I is raised by 10, now I = 110
Y = 100 + 0.8y + 110
0.2y = 210 
y = \(\frac{210}{0.2}\) = 1050
Here, C = 100 = 0.8 (1050) = 940,
S = 110 = I
(i) It implies the variables in axis-and axis are equal.
(ii) The MPC is assumed to be at 0.8. (C = 100 + 0.8y)
(iii) The aggregate demand (C + I) curve intersects 45° line at point E.
(iv) The new aggregate demand curve is
C + I = 100 + 0.8Y + 100 + 10
Y = \(\frac{210}{0.2}\)
C = 940; S = 110 = Z

Introduction
J.M Keynes has divided factors influencing the consumption function into two namely Subjective factors and Objective factors
Subjective Factors
These factors are internal and related to psychological feelings. Keynes lists 8 motives which lead individuals to refrain from spending
Motive of precaution
To build a reserve against unforeseen contingencies. (eg.) Accidents
Motive of foresight
The desire to provide for anticipated future needs. (eg.) Old age
Motive of calculation
The desire to enjoy interest and appreciation.
Motive of improvernent
(i) The desire to enjoy for improving standard of living.
(ii) Motive of financial independence
(iii) Motive of enterprise - desire to do forward trading
(iv) Motive of pride - desire to leave a fortune
(v) Motive of avarice - miserly instinct
(vi) The government institutions, business corporations and firms may also consume mainly because of:
Motive of enterprise
The desire to get resources to carry out further capital investment without debt.
Motive of liquidity
The desire to secure liquid resources to meet emergency
Motive of improvement
The desire to secure a rising income and to demonstrate successful management
Motive of financial prudence
The desire to ensure adequate financial provision against depreciation, obsolescence and to discharge debt.
Objective Factors
They are the external factors which are real and measurable. They can be easily changed in the long run;
Income Distribution
According to VKRV Rao if incone is equally distributed propensity to consume increases
Price level
When price falls, real income rises; people consume more and save more.
Wage level
Consumption expenditure increases with a rise in wages.
Interest rate
Higher interest rate will encourage people to save more money and reduces consumption.
Fiscal Policy
When government reduces tax, disposable income rises and propensity to consume increases.
Consumer credit
The availability of consumer credit at easy installments will encourage people to buy consumer durables like car, fridge, computer
Demographic factors
(i) Size of family, stage in family life cycle, place of residence and occupation affect the consumption pattern
Duesenberry hypothesis
(i) Consumption expenditure depends on current income, past income and standard of living
(ii) As individuals are accustomed to a particular standard of living, they continue to spend the same amount on consumption
(iii) Consumption of the poor people is influenced by the rich. This is called Demonstration effect.
Windfall gain and loss
Unexpected changes in the stock market leads to gain or loss, so consumption function shifts upward or downward.
Conclusion
According to Keynes only the subjective factors do not change in the short-run, so consumption function remains stable in the short period.