1. Multiplier Definition Calculating the value of multiplier
Importance of multiplier
Uses of multiplier
Limitations of multiplier
Mathematics

2. Definition of Multiplier
A number which indicates the magnitude of a particular macroeconomics policy measure. In other words, the multiplier attempts to quantify the additional effects of a policy beyond those that are immediately measurable.
This is true of most macroeconomics policy measures, because the actual effect of the measure cannot be quantified by the effect of the measure itself.
What is a simple definition of the multiplier?
It is the number of times a rise in national income exceeds the rise in injections of demand that caused it

3. Contd..
We propose to study how much or how many times income increases as investment is done. This can be known from the concept of Multiplier.

4. Calculating the value of multiplier
Marginal propensity to consume.
In economics the marginal propensity to consume (MPC) is an empirical metric that quantifies induced consumption the concept that the increase in personal consumer spending consumption occurs with an increase in disposable income (income after taxes and transfers).
The proportion of the disposable income which individuals desire to spend on consumption is known as propensity to consume. MPC is the proportion of additional income that an individual desires to consume. For example, if a household earns one extra dollar of disposable income, and the marginal propensity to consume is 0.65, then of that dollar, the household will spend 65 cents and save 35 cents.

5. Mathematically, the function is expressed as the derivative of the consumption function with respect to disposable income . or
, where is the change in consumption, and is the change in disposable income that produced the consumption.
Marginal propensity to consume can be found by dividing change in consumption by a change in income, or . The MPC can be explained with the simple example:

6. Calculating the value of multiplier
INCOME
CONSUMPTION
120
180
170

9. Importance of multiplier

12. Uses of Multiplier
The multiplier principles occupies a very important place not only in economic theory but also in shaping economic policy.
It plays a vital role as an instrument of income building.
It tells us how a small increase in investment can result in large increase in income.
Multiplier uses control of business cycles.
It furnishes guidelines for appropriate income and employment policies.

13. Uses of Multiplier
It also explains the expansion of public sector in modern times.

14. Limitations of Multiplier
Efficiency of production: If the production system of the country cannot cope with increased demand for consumption goods and make them readily available, the income generated will not be spend as visualised. As a result the MPC may decline.
Regular investment: The value of multiplier will also depend on regularity repeated investment.

15. Multiplier period: Successive doses of investment must be injected at suitable intervals if the multiplier effect is not be lost.
Full employment celling: As soon as full employment of the idle resources is achieved, further beneficial effect of the multiplier will practically cease.

16. Illustration 1
In an economy, the basic equations are as follows: the consumption function is C = Y and investment is
I= $ 360 millions. You are required to ascertain the following
The equilibrium level of income
The equilibrium level of income when planned investment increases from 360 to 400 millions, a total increases of 40 millions
The multiplier effect of the 40 millions increases in planned investment.

17. Solution
The equilibrium condition is given as Y = C + I
                                                Y         =          Y + 360
                                    Y – 0.8Y         =         
                                   0.2Y                =          660
                                               Y         =          3,300
1.         The equilibrium level of income is Y           =          3,300
Thus,                                                Y         =          Y + 400
                                    Y – 0.8Y         =         
                                   0.2Y                =          700
                                               Y         =          700 / 0.2
2.         Hence, the equilibrium level of income is 3,500

18. The equilibrium level of income increases from 3,300 to 3,500crores when planned investment increases from 360 to 400 millions. There is an increase in income by 200 millions. Hence the multiplier effect is
                                    m         =              1                                                                                 1 – b
                                                =              1                                                                  – 0.8
                                                =              1                                                                    
3.         The multiplier effect is m is  5

19. Illustration 2
Presume in an economy the marginal propensity to consume is 0.75 and the level of autonomous investment decreases by 40 millions. Find,
The change in the equilibrium level of income
The change in consumption expenditures
Solution
                We know        Δ Y      =          m                         Δ I

20. Also,                         m         =              1                                                                  1 – b
So Δ Y      =                      1                                   Δ I                            1 – b
  Δ Y           =          Δ I     1                                          – b
                                    =          -40 x         1                                                                 1 – 0.75
                                    =          -160
(1)        Thus, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 160 millions. This effect occurs due to the reverse multiplier.

21. Y         =          C + I
            Therefore,       ΔY       =          Δ C + Δ I
                                   -160     =          Δ C – 40
                                    Δ C      =         
                                    Δ C      =          - 120
(2)        The consumption expenditure decreases by 120 millions

22. Illustration 3
Compute the value of the investment multiplier when the marginal propensity to consume is
(1) 0.80, (2) 0.65, (3) 0.40 and (4) 0.25
Find the effect of a decrease in the equilibrium income when autonomous investment decreases by 60 millions when the marginal propensity to consume is (1) 0.80, (2) 0.65, (3) 0.40 and (4) 0.25

23. Solution
The value of m, the investment multiplier is
                                    m         =              1                                                                  – b
Hence,
                        (1)        m         =              1                                                                  – 0.8                                                 =          1 / 0.2              =          m         =          5
                        (2)        m         =              1                                                                  – 0.65
                                    =          / 0.35            =          m         =          2.87

24. (3)        m         =              1                                            1 – 0.4
                 =          1 / 0.2 =          m         =          1.67
(4)        m         =          1                                     1 – 0.25
                       =   1 / 0.75    =          m         =          1.33
           

25. Thus, the decrease in the equilibrium income when autonomous investment decreases by 60 millions is
Δ Y      =          Δ Im              =        60 x 5              =          300
                                          =          60 x 2.87         =          172.2
                                        =         60 x 1.67         =          100.2
                                       =          60 x 1.33         =          79.8

26. Illustration 4
In an economy the marginal propensity to consume is The level of autonomous investment decreases by 60 millions. Find the following
The change in the equilibrium level of income
The induced change in the consumption expenditure

27. Solution
                        Δ Y                  =          m                         Δ I
But, m is the investment multiplier
Also                         m         =               1                                                     1 – b
Thus,                         Δ Y      =          ΔIm     =               ΔI                   1                                                                                          – b
                                                            =          - 60 x       1                                                                                          1 – 0.50
                                                            =          - 120

28. Hence, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 120 millions.

29. Y         =          C         +          I
Therefore,                                     Δ Y      =          Δ C + ΔI
                                   -120     =          ΔC – 60
                                   Δ C      =         
Δ C      =          -60
3.The Consumption expenditure falls by 60 millions

30. Illustration 5
Presume that in two sector economy, the income is $ million while the marginal propensity to consume is Suppose the government wants to increase the income to $ 1600 million, by an amount of $ 600 million.
1.By how much should the autonomous investment be increased?

31. Solution
The income level         =          $1000 millions
The planned income level is $1600 millions
Change in income       =          Δ Y      =          1600 – 1000
                                                            =          $600 millions
But                                                 Δ Y      =          m         =          1                                                        Δ I                                          1 – b
                                                Δ Y      =          Δ I         1                                                                                            1 – b

32. 600      =  Δ I         1                                                                                            1 – b
                                                            =          Δ I       1 / 1-0.4
                                                            =          Δ I       1 / 0.6
                                                600      =          Δ I      
                                                Δ I       =          600 / = =
Thus, the autonomous investment should be increased by $360 millions for the income to increase to $ 1600 millions. An increase in income by $ 600 millions