We know that,
Y = C + 1
Or;  \(\Delta Y=\Delta C+\Delta 1\)
Dividing both sides by \(\Delta Y\), 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,   \(\frac { \Delta Y }{ \Delta I } =\frac { I }{ I-MPC } \)        .....(1)
\(K=\frac { I }{ I-I } \)
Also, 
\(=\frac { I }{ 0 } \) 
\(=\infty \)     ......(2)
From (1) and (2); ​​​​​​​​  \(K=\frac { I }{ I-MPC } \)                                                                                                          

Deflationary gap refers to the excess of available supply of output over the anticipated expenditure at constant prices of base period. It is also known as deficient demand.
Inflationary gap, on the other hand, refers to the excess of anticipated expenditure over the available supply of output at constant prices of base period. It is also known as excess demand.
Following are the two measures that can be used to correct the problem of deflationary and inflationary gap:
(i) 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 increases the bank rate to correct the situation of inflationary gap or excess-demand in the economy. Higher bank rate reduces the lending capacity of the commercial banks as they get funds at a higher interest rate from the central bank. Consequently, money supply contracts in the economy as the public borrows less at high rate of interest and Aggregate Demand falls. Similarly, the central bank decreases the bank rate to correct the situation of deflationary gap or 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.
(ii) 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 sells government securities to commercial banks and general public in a bid to correct the situation of inflationary gap or excess demand. This decreases the stock of high powered money in the economy. As a result, the purchasing power of the people declines, which decreases the Aggregate Demand in the economy. Similarly, the central bank purchases government securities from commercial banks and general public in a bid to correct the situation of deflationary gap or 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.

Equilibrium is attained when planned expenditure is equal to the planned output in the economy. If this equality is achieved at a level less than full employment level of output then the economy will be in a situation of under employment equilibrium.
The two policy measures that the government can take are:
(i) Increase in Public Expenditure: Government can correct the situation of underemployment by increasing public expenditure on goods and services such as transportation, dams, electricity industry development expenditure, education, health etc. This increases the purchasing power of the public which, in turn, increases the demand for goods and corrects deficient demand. Moreover, increase in public expenditure also helps in eradicating poverty.
(ii) 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.

Excess demand refers to a situation in which Aggregate Demand in the economy is greater than the Aggregate Supply (AD> AS) at full employment level. Excess demand is also known as inflationary gap. It measures the gap between AD' and AS at full employment level of output. Since Aggregate Demand remains more than essential demand at full employment level, there is a significant increment in monetary income. Thus, there is an over employment equilibrium. This increases the Aggregate Demand but production cannot be increased as Aggregate Supply is perfectly inelastic. The problem of excess demand can be explained with the help of a diagram.
In the diagram, point E represents the state of over employment equilibrium in the economy. At E, the gap between Aggregate Demand and Aggregate Supply is AE, That is AE, is the excess demand. The problem of excess demand can be corrected only by the interference of the government (increasing taxes and reducing public expenditure).
Open market operation is the policy of the central monetary authority to sell and buy the government securities in the market. The central bank sells government securities from commercial banks and general public in a bid to correct the situation of excess demand. This decreases the stock of high powered money in the economy. As a result, the purchasing power of the people decreases, which decreases the Aggregate Demand in the economy.
Reverse repo rate refers to the rate at which central bank borrows from the commercial banks. The central bank increases the reverse repo rate to correct the situation of excess demand. Higher reverse repo rate would induce commercial banks to lend more to the central bank and hence, would reduce the supply of money in the economy. As a consequence, Aggregate Demand would fall.

The problem of deficient demand or deflationary gap can be corrected by adopting following monetary measures:
(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 i~creasesthe 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) Margin Requirement: Margin requirement of loan is the minimum security price charged by the commercial bank for granting loans. A decrease in margin requirement will correct the situation of deficient demand in the economy. Lower margin requirement implies lower security price for a loan. Thus, people will borrow more loans from the banks and the Aggregate Demand will increase.

(i) 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 increases the bank rate to correct the situation of excess demand in the economy. Higher bank rate reduces the lending capacity of the commercial banks as they get funds at a higher interest rate from the central bank. Consequently, money supply contracts in the, economy as the public borrows less at high rate of interest and Aggregate Demand falls.
(ii) 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 sells government securities to commercial banks and general public in a bid to correct the situation of excess demand. This decreases the stock of high powered money in the economy. As a result, the purchasing power of the people declines, which decreases the Aggregate Demand in the economy.

Following are the monetary measures for correcting i.nflationary and deflationary gap:
(i) Open Market Operation: Open market operation is the policy of the central monetary authority to sell and buy the government securities in the market. RBI purchases or sells government securities to the general public in a bid to correct deficient or excess demand in the economy.
(ii) Bank Rate Policy: 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. Higher bank rate reduces the lending capacity of the commercial banks as they get funds at a higher interest rate from RBI. Consequently, credit contracts in the economy as public borrows less at high rate of interest. It reduces excess demand. Similarly, lower bank rate increases the lending capacity of the commercial banks as they get funds at a lower interest rate from RBI. Consequently, credit expands in the economy as public borrows more at low rate of interest. It solves the problem of deficient demand.
(iii) Varying Reserve Requirements: Cash Reserve Ratio (CRR) is the minimum fraction of the total deposits with the commercial banks, which they are required to keep with the central bank. Statutory Liquidity Ratio (SLR), on the other hand, is the minimum fraction of the total deposits with the commercial bank, which they are required to maintain in the form of specified liquid assets.A high (low) value of CRR or SLR helps increase (decrease) the value of reserve deposit ratio, thus diminishing (increasing) the value of the money multiplier and money supply in the economy.
(iv) Rationing of the Credit: Rationing of the credit implies controlling the quantity in the form of loan. Here, amount of loan is determined for speculative purpose. Hence, total demand can be increased by rationing of credit. It will increase the purchasing power of people and hence, deficient demand will be corrected. Rationing of credit should be increased by central bank for correcting the excess demand or inflationary gap.

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.

Investment means addition to the stock of capital goods in the nature of structures, equipment or inventory.
The equilibrium is determined at the level of income where Aggregate Demand is equal to the Aggregate Supply. That is,
We know that,
AD = AS     ...( 1)
AD = C + I     ...(2)
AS = C + S   ...(3)
By substituting (2) and (3) in (I), we get;
C + I = C + S
Or;  I = S
Thus, the equilibrium level of income and output is attained when planned saving (S) and planned investment (I) are equal. The determination of equilibrium level of income using saving-investment approach can be explained with the help of a schedule.

In the schedule, S is the planned saving at different levels of income and I is the investment as given and constant at 10'0.Planned saving and investment are equal (S = I = 100) at income level of 300. At this level of income, Aggregate Demand is also equal to Aggregate Supply, that is,
Y = AD = AS = 300
At the income level of 200, planned saving is less than planned investment (50 < 100). It implies that at this level of income, what businessmen plan to invest is more than what households plan to save.There is a situation of excess demand in the economy. Thus, producers will decrease inventory and output would expand until equilibrium is attained. Similarly, at the income level of 400, planned saving is greater than planned investment (150 > 100). It implies that at this level of income, what businessmen plan to invest is less than what households plan to save.There is a situation of deficient demand in the economy. Thus, producers will increase inventory and output would contract until equilibrium is attained.

Equilibrium is attained when planned expenditure is equal to the planned output in the economy. If this equality is achieved at a level less than full employment level of output then the economy will be in a situation of underemployment equilibrium. The two policy measures that the government can take are:
(i) Increase in Public Expenditure: Government can correct the situation of underemployment by increasing public expenditure on goods and services such,!-S transportation, dams, electricity industry development expenditure, education, health etc. This increases the purchasing power of the public, which in turn, increases the demand for goods and corrects deficient demand. Moreover, increase in public expenditure also helps in eradicating poverty.
(ii) 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.