(i) Autonomous Investment
(ii) Induced Investment

(i) Ceteris paribus (constant extraneous variable).
(ii) Existence of Normal conditions.
(iii) Existence of a Laissez-faire capitalist economy.

Formula for calculating APC =\(\frac{C}{Y}\) x 100
= \(\frac{120}{120}\) x = 1 x 100
∴ APC = 100

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

Muliplier is the ratio of the change in national income to change in Investment.
K = \(\frac{ΔY}{ΔI}\)

(i) The Average Propensity to Consume = \(\frac{C}{Y}\)
(ii) The Marginal Propensity to Consume = \(\frac{ΔC}{ΔY}\)
(iii) The Average Propensity to Save = \(\frac{S}{Y}\)
(iv) The Marginal Propensity to Save = \(\frac{ΔS}{ΔY}\)

Saving = Y - C
S = 1806 - 170
∴ S = 10
Formula for calculating
APS = \(\frac{S}{Y}\)
S = 10, Y = 180

∴ APS% = 5.56

(i) Payment towards past debts
(ii) Purchase of existing wealth
(iii) Import of goods and services
(iv) Non availability of consumer goods
(v) Full employment situation

(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

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.

Meaning of consumption function.
(i) Propensity to consume refers to income consumption relationship.
(ii) Consumption function is a "functional relationship between two aggregates viz. total consumption and gross national income."
(iii) C = f(Y)
(iv) C = Consumption
Y = Income
f = Function
(v) Thus the consumption function indicates a functional relationship between C and Y.
(vi) C is the dependent variable and Y is the independent variable. i.e. C is determined by Y.
(vii) Based on the ceteris paribus (other things being same) assumption, as only income consumption relationship is considered.
(viii) All possible influences on consumption are held constant.
(ix) A hypothetical consumption schedule is given in table.
Income - Consumption Schedule (Rs.Cores)

If we take C = 100 + 0.8Y, then MPC = 0.8
Here if Y = 0, C = 100; if Y = 100, C = 180
If Y = 200, C = 260
If Y =300, C = 340 (MPC = \(\frac{ΔC}{ΔY}\) = 0.8)
In mathematical terms
C = a + b Y or C = 20 + 0.8Y
Where a > 0 and b < 1
C = Consumptiona = Constant or intercept = 20
Y = Income
b = MPC (Marginal prosperity to consume)

8.0 = \(\frac{ΔC}{ΔY}\)
(x) The above table shows that consumption is an increasing function of income because consumption expenditure increases with increase in income.
(xi) When income is zero, people spend out of their past savings on consumption because they must eat in order to live (Autonomous consumption).

Here, when Y = 120, C = 120 (point B in the diagram)
When Y = 180, C = 170, S = 10 (point S in the diagram)
If oY increases to 360, C = 320, S = 40
(xii) In the diagram, income is measured horizontally.
(xiii) Consumption is measured vertically.
(xiii) In 45 line at all levels income and consumption are equal.
(xv) The consumption function measures not only the amount spent on consumption but also the amount saved.
(xvi) The propensity to save is merely the propensity not to consume.

Law
According to Keynes, "men are disposed as a rule and on the average to increase their consumption as their income increases but not by as much as the increáse in their income".
Propositions
1. When income increases, consumption expenditure also increases, but by a smaller amount
(a) 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.
2. The increased income will be divided in some proportion between consumption expenditure and saving
(a) When income increases to 180 and 240, it is divided between consumption (170 and 220) and saving (10 and 20)
3. Incrcascs in income always lead to in incrcase in both consumption and saving
(a) Increases in income to 180) and 240; lead to increased consumption 170 and 220; increased saving 10 and 20.
(b) It is clear from the widening area below the C curve and the saving gap between 45^o line and C curve.