# #FocusonExams: Economics GCE ‘A’ L – 30th April 2020

CLASS: UPPER SIXTHS

TOPIC: THE MULTIPLIER

OBJECTIVES: At the end of this lesson the learner should be able to:

• Define the multiplier and explain the multiplier process
• Illustrate the multiplier process
• Calculate the multiplier in the different sectors of the economy

MEANING OF THE MULTIPLIER

In macroeconomics a multiplier is a factor of proportionality that measures how much an endogenous variable changes in response to a change in some exogenous variable. It shows how a change in any of the autonomous components of aggregate demand leads to a more than proportionate change in income. That is, it determines how much income changes as a result of changes in expenditure.

For example, suppose variable X changes by 1 unit, which causes another variable Y to change by M units. Then the multiplier is M.

Also, the multiplier can also be seen as the coefficient by which an initial change in injection is multi plied to obtain the resultant change in income. That is,

K=

Where  is the change in income?

K is the multiplier
is the change in expenditure

Hence if investment increases by 100 million FCFA and this causes incomes to increase 500 Million FCFA then the value of the multiplier will be?

K=  =500/100= 5

ASSUMPTION OF THE MULTIPLIER

The multiplier is based on the following assumptions:

• The marginal propensity to consume is constant at all levels of income. That is, for any additional income received, a constant proportion of it is consumed.
• Firms obtain or borrow all their funds from households
• There is less than full employment of human and material resources like land, labour and capital
• Firms adjust production with the prevailing market demand
• Households adjust instantly their consumption at each level of income
• All injections are autonomous
• Techniques of production and prices remain fixed.

THE MULTIPLIER PROCESS

Let us assume that there is a constant MPC of 0.8 and that the government of Cameroon wants to spend 100 billion FCFA to construct a stadium. This 100billion is paid to the contractors who spends some of the money in buying equipment, materials, employing workers etc. Taking into consideration the MPC of 0.8 he spends 80billion.The various groups who receive this money now go and spend some of the 80 billion FCFA, of this ,64 billion may be spent by the various agents in the economy. The 64billionFCFA become incomes for another group, who spend some of it and the process continuous………….

From the extract, it is realized that the initial amount of 100billionFCFA creates a series of smaller increases in the economy in relation to spending.

ILLUSTRATION OF THE MULTIPLIER

From the extract, an increase in investment(I) of 100billionFCFA generates an increase in spending, given an MPC of 0.8 as shown by the series below:

100b +80b +64b +51.2+—-+ = K=

The total increase in income is the total of the successive rounds of spending caused by the initial increase in investment.  It would be realised that an initial increase in spending will eventually lead an increase in spending above the initial amount actually spent. The above series is a geometric series with a common ratio of 0.8

Note common ratio is gotten by dividing the next term by the previous term.

Eg 80/100 =0.8

64/80= 0.8

The resultant change in income () from an initial investment is given by:

=   First Term              =         a    =     100b     = 100/0.2  =500billion

Where ‘’ a’’ is the first term and r is the common ratio

Therefore, the multiplier K= = 500/100 = 5

Also, taking r to be the MPC                         1       = 1/1-0.8 =1/0.2 = 5

1-mpc

MULTIPLIER IN THE DIFFERENT SECTORS OF THE ECONOMY

• 2- SECTOR ECONOMY

In a two sector economy, the only withdrawal is savings. Therefore,

K=                  Or            this is also known as the investment multiplier. Mpc is the marginal propensity to consume, mps is the marginal propensity to save

• 3 – SECTOR ECONOMY

A three-sector economy has two withdrawals. That is savings and taxes. Here,

K =

Where mpt is the marginal propensity to tax

• 4- SECTOR ECONOMY (OPEN ECONOMY)

A four- sector economy now includes imports; therefore, the multiplier will be;         K=

OTHER TYPES OF MULTIPLIERS

• TAX MULTIPLIER

Kt =

• TRANSFER PAYMENT MULTIPLIER

Ktr    =

BALANCED BUDGET MULTIPLIER

BBM= =           = =           = 1

Generally, the multiplier could be seen as =           , where W is the marginal propensity to withdraw (mpm)

APPLICATION EXERCISES

1. The information below shows income resulting from a change in investment:

1000million + 700milion + 490million Qmillion+—+

Calculate,

1. The multiplier
2. The value of Q

SOLUTION

1. K =       and the mpc is gotten by dividing the next term by the previous term, that is the common ratio.    should be equal to  = 0.7

Therefore, K=   = 3.3

1. Q=0.7 X 490= 343 (We multiply by 0.7 because the mps is constant)
2. The present level of national income in a given economy is 100millionFCFA. Out of every 1000FCFA of additional income, savings are 150FCFA, taxes are 100FCFA and imports are 150 millionFCFA
3. Calculate the value of the multiplier in this economy
4. By how much must the government raise its expenditure to increase national income to a new level of 125millionFCFA

SOLUTION

1. MPS =         =O.15

MPT =        = 0.1

MPM=       =0.15

Therefore,    K =         ==           = =            = 2.5

1. K =

2.5 =    , this implies ==  =  10 millionFCFA

Hence for the government to increase national income to a new level of 125millionFCFA, she must increase her expenditure by 10millionFCFA.

1. Given that

C= 0.8Yd

Income tax =0.5Y

Indirect Tax = o.1

Import = 0.5C

Calculate the value of the multiplier.

SOLUTION

C=0.8(Y-0.5Y)

C= 0.4Y

S= 0.2Yd =0.2(Y-0.5Y)

S = 0.2(0.5Y)

S = 0.1Y therefore, MPS=0.1

Tax = 0.5Y +0.1Y = 0.6Y

Mpt = 0.6

MPM  = 0.5C = 0.5(0.4Y)=  0.2Y

Being an open economy, k =   =       =   =1.1111111

THANK YOU

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