Definition Calculating the value of multiplier Importance of multiplier Uses of multiplier Limitations of multiplier Mathematics

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.

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

Definition of Multiplier

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.

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).

Calculating the value of multiplier

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.

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:

INCOME CONSUMPTION

120 120

180 170

Calculating the value of multiplier

Here ; Therefore, or 83%. For example, suppose you receive a bonus with your paycheck, and it's $500 on top of your normal annual earnings. You suddenly have $500 more in income than you did before. If you decide to spend $400 of this marginal increase in income on a new business suit, your marginal

propensity to consume will be 0.8 ( ).

MPC and the Multiplier MPC’s importance depends on the multiplier theory. The value of the multiplier—is determined by MPC. The higher the MPC, the higher the multiplier and vice-versa. The relationship between the multiplier and the propensity to consume is as follows:We know

(i.e.,total national income=total Consumption)

(where is )

(where , is multiplier and

Since is the MPC, the multiplier is, by definition, equal to . The multiplier can also be derived from MPS (marginal propensity to save) and it is the reciprocal of MPS,

Importance of multiplier

1. Saving Investment Equality

The multiplier theory highlights the importance of investment in theory of income and employment. As the consumption function is stable during the short run, fluctuations in income and employment are result of the fluctuations in the level of investment. A rise in investment causes a cumulative rise in income and employment through the multiplier process and vice-versa. The multiplier theory not only explains the process of income propagation as a result of rise in the level of investment, it also helps in bringing equality between saving and investment. In case of divergence between the two, change in the level of investment leading to a change in the level of income via the multiplier process, ultimately equalizes saving and investment

2. Business Cycles

The multiplier process explains and helps in controlling different phases of business cycles occurring due to fluctuations in the level of income and employment. The boom period (high level of income and employment) can be controlled by a reduction in investment, which leads to a cumulative decline in income and employment in the multiplier process. On the other hand, during the depression phase of business cycle (low level of income and employment), an increase in investment leads to revival. If this process continues, boom may be the result.

3. Formulation of Economic Policies

The government can decide upon the amount of investment to be injected into the economy to reduce unemployment. The multiplier theory helps the government in formulating an appropriate employment policy during depression. During depression, Government’s public works programmes are more effective than cheap money policy due to multiplier effect of investment. It is important to note that any increase in the investment in one sector should not be accompanied by a decrease in the investment in the other sector. An inter-sectoral transfer of the investment will not raise the value of the multiplier. Further, it is necessary to ensure a steady injection of the investment. That is, the increments in the investment should be repeated at regular intervals so as to raise the level of the income and the employment to the full employment level. Further, modifications in the Keynes theory of the Multiplier will enhance the utility of the multiplier concept.

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.

Uses of Multiplier

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

Uses 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.

Limitations of Multiplier

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.

Illustration 1

In an economy, the basic equations are as follows: the consumption function is C = 300 + 0.8Y and investment is

I= Tk 360 millions. You are required to ascertain the following

1. The equilibrium level of income

2. The equilibrium level of income when planned investment increases from 360 to 400 millions, a total increases of 40 millions

3. The multiplier effect of the 40 millions increases in planned investment.

Solution

The equilibrium condition is given as Y = C + I

                                                Y         =          300 + 0.8Y + 360

                                    Y – 0.8Y         =          300 + 360

                                   0.2Y                =          660

                                               Y         =          3,300

1.         The equilibrium level of income is Y           =          3,300

The equilibrium condition is given as Y = C + I

Thus,                                                Y         =          300 + 0.8Y + 400

                                    Y – 0.8Y         =          300 + 400

                                   0.2Y                =          700

                                               Y         =          700 / 0.2

2.         Hence, the equilibrium level of income is 3,500

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                                                                  1 – 0.8

                                                =              1                                                                     0.2

3.         The multiplier effect is m is  5

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,

1. The change in the equilibrium level of income

2. The change in consumption expenditures

Solution

                We know        Δ Y      =          m                        Δ I

Also,                        m         =              1                                                                  1 – b

 

So Δ Y      =                      1                                   Δ I                            1 – b

  Δ Y           =          Δ I     1                                          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.

Y         =          C + I

            Therefore,       ΔY       =          Δ C + Δ I

                                   -160     =          Δ C – 40

                                    Δ C      =          - 160 + 40

                                    Δ C      =          - 120

(2)        The consumption expenditure decreases by 120 millions

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

Solution

The value of m, the investment multiplier is

                                    m         =              1                                                                  1 – b

Hence,

                        (1)        m         =              1                                                                  1 – 0.8                                                =          1 / 0.2              =          m         =          5

                        (2)        m         =              1                                                                  1 – 0.65

                                    =          1 / 0.35            =          m         =          2.86

(3)        m         =              1                                            1 – 0.4

                 =          1 / 0.2 =          m         =          1.67

(4)        m         =          1                                     1 – 0.25

                       =   1 / 0.75    =          m         =          1.33

           

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 2.86         =          171.6

                                        =         60 x 1.67         =          100.2

                                       =          60 x 1.33         =          79.8

Illustration 4

In an economy the marginal propensity to consume is 0.50. The level of autonomous investment decreases by 60 millions. Find the following

1. The change in the equilibrium level of income

2. The induced change in the consumption expenditure

Solution

                        Δ Y                  =          m                        Δ I

But, m is the investment multiplier

Also                        m         =               1                                                     1 – b

Thus,                         Δ Y      =          ΔIm     =               ΔI                   1                                                                                          1 – b

                                                            =          - 60 x       1                                                                                          1 – 0.50

                                                            =          - 120

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

Y         =          C         +          I

Therefore,                                     Δ Y      =          Δ C + ΔI

                                   -120     =          ΔC – 60

                                   Δ C      =          -120 + 60

Δ C      =          -60

2.The Consumption expenditure falls by 60 millions

Illustration 5

Presume that in two sector economy, the income is Tk 1000 millions while the marginal propensity to consume is 0.40. Suppose the government wants to increase the income to Tk 1600 millions, by an amount of Tk 600 millions.

1.By how much should the autonomous investment be increased?

Solution

The income level         =         Tk 1000 millions

The planned income level = Tk 1600 millions

Change in income       =          Δ Y      =          1600 – 1000

                                                            =         Tk 600 millions

But                                                Δ Y      =          m         =          1                                                        Δ I                                          1 – b

                                                Δ Y      =          Δ I         1                                                                                            1 – b

600      =  Δ I         1                                                                                            1 – b

                                                            =          Δ I       1 / 1-0.4

                                                            =          Δ I       1 / 0.6

                                                600      =          Δ I       1.66667

                                                Δ I       =          600 / 1.66667

Δ I = 360

Thus, the autonomous investment should be increased by Tk 360 millions for the income to increase to Tk 1600 millions. An increase in income by Tk 600 millions