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

Marginal Propensity to Save(MPS) is the ratio of change in saving to change in income.\(MPS=\frac { \Delta S }{ \Delta Y } \)    

The value of APS can be negative when saving is negative or when consumption is greater than income.

(i) Open Market Operations: Open market operation is the policy of the central monetary authority to sell and buy the government securities in the market. The central bank purchases government securities from commercial banks and general public in a bid to correct the situation of deficient demand. This increases the stock of high powered money in the economy. As a result. the purchasing power of the people increases, which increases the Aggregate Demand in the economy.
(ii) Bank Rate: Bank rate is the minimum rate at which the central bank discounts the first class bills of exchange and provides credit to the commercial banks. The central bank decreases the bank rate to correct the situation of deficient demand in the economy. Lower bank rate increases the lending capacity of the commercial banks as they get funds at a lower interest rate from the central bank. Consequently, money supply expands in the economy as public borrows more at low rate of interest and Aggregate Demand rises.

Investment multiplier (K) is the relationship between the final change in income and the initial change in investment. It is estimated as the ratio of change in investment income due to' change investment. Marginal Propensity to Consume (MPC) is the ratio of change in consumption to the change in income, There is a direct relationship between investment multiplier and MPC.
We know that,
\(Y=C+I\)
Or; \(\Delta Y=\Delta C+\Delta I\)
Dividing both sides by \(\Delta I\), we get:
\(\frac { \Delta Y }{ \Delta Y } =\frac { \Delta C }{ \Delta Y } +\frac { \Delta I }{ \Delta Y } \)
\(\Rightarrow \) \(I=\frac { \Delta C }{ \Delta Y } +\frac { \Delta I }{ \Delta Y } \)
\(\Rightarrow \)  \(I-\frac { \Delta C }{ \Delta Y } =\frac { \Delta I }{ \Delta Y } \)
Or;\(\frac { I }{ I-\frac { \Delta C }{ \Delta Y } } =\frac { \Delta Y }{ \Delta I } \)
Since  \(\frac { \Delta C }{ \Delta Y } =\)Marginal Propensity to Consume
Thus,  \(\frac { \Delta Y }{ \Delta I } =\frac { I }{ I-MPC } \)
\(\therefore \)  \(K=\frac { I }{ I-MPC } \)
One man's expenditure is another man's income. Whenever there is an increment in investment expenditure, some individuals' income is increased by the amount of investment with which they buy goods and services. They spend a part of their increased income on consumption and keep some income for saving. The individuals' MPC determines the amount they spend or save. If MPC is greater than MPS, individuals will spend more on consumption; and if MPC is less than MPS, the individuals' expenditure on consumption will be less.The extent of the effect of multiplier depends upon the Marginal Propensity to consume. Higher the MPC, higher will be the value of multiplier.
If MPC\(=\frac { 1 }{ 2 } \),
\(K=\frac { 1 }{ 1-\frac { 1 }{ 2 } } =\frac { 1 }{ \frac { 1 }{ 2 } } =2\)
If MPC\(=\frac { 3 }{ 4 } \),
\(K=\frac { 1 }{ 1-\frac { 3 }{ 4 } } =\frac { 1 }{ \frac { 1 }{ 4 } } =4\)
At lower MPC, multiplier is 2 and at higher MPC, multiplier is 4.

Marginal Propensity to Consume (MPC) is the ratio of change in consumption to the change in income.
\(MPC=\frac { \Delta C }{ \Delta Y } \)
Marginal Propensity to Save (MPS) is the ratio of change in savings to the change in income.
\(MPS=\frac { \Delta S }{ \Delta Y } \)
The sum of the propensity to consume and propensity to save is always equal to one.
MPC + MPS = I
Or; MPC = I - MPS
Or;  MPS = I - MPC
MPC and MPS are inversely related. Higher the propensity to consume lower will be the propensity to save and vice-versa. For example, suppose propensity to consume is 0.80. The propensity to save will be
MPS = I - 0.80
= 0.20
If propensity to consume falls to 0.40, then the propensity to save will be
MPS = I - 0.40
= 0.60

The relationship between the consumption and the income is called the consumption function. The consumption function may be represented by the following equation:
C = a + bY; a> 0,0 < b Where,  C = Consumption Expenditure
Y = Level of income
a = Autonomous Consumption
b = Slope of consumption function\(\left( MPC=\frac { \Delta C }{ \Delta Y } \right) \)
Autonomous consumption is the amount of consumption expenditure at zero level of income. It is the intercept of the consumption expenditure and is assumed to be positive as people consume even at the zero level of income. Marginal Propensity to Consume (MPC) or b is the slope of the consumption function. It measures the rate of change in consumption per unit change in income. The value of MPC is positive and lies between 0 and I. This means that the consumption increases with the income.
Saving Function Equation
The relationship between saving and income is called the saving function. The following identity
expresses the relationship between saving (S) and income (Y).
Or,  Y = C + S
S = Y - C     ...(1)
The consumption function is represented as:
C = a + bY    ...(2)
Substituting (2) in (I); we get
S = Y - (a + bY)
S = Y - a - bY
S = -a + (I - bY)
Where,  S = Saving
a = Amount of saving when level of income is zero
(l- b) = Slope of the saving function\(\left( MPS=\frac { \Delta S }{ \Delta Y } \right) \)

Average Propensity to Consume (APC) is the ratio of total consumption (C) to total income (Y).
\(APC=\frac { C }{ Y } \)
Average Propensity to Save (APS) is the ratio of total saving to total income.
\(APS=\frac { S }{ Y } \)
Relationship between APC and APS
We know that,  \(Y=C+S\)
Dividing both sides by Y, we get:
\(\frac { Y }{ Y } =\frac { C }{ Y } +\frac { S }{ Y } \)
Substituting APC\(=\frac { C }{ Y } \)and APS\(=\frac { S }{ Y } \) , we get:
\(APC+APS=I\)
Thus, the sum of the APC and APS is always equal to one. This is because total income is either
consumed or saved.
The value of APS can be negative when saving is negative or when consumption is greater than income.

Equilibrium level of National Income is determined as:
\(Y=\overset { - }{ C } +cY+1\)  ....(1)               
Substituting appropriate values in (I); we get
2000 = 400 + c(2000) + 200
2000c = 2000 - 600
2000c = 1400
\(c=\frac { 1400 }{ 2000 } \)
= 0.7
Thus, the economy's Marginal Propensity to Consume is 0.70.