CAPITULO IV. –PROPUESTA DE PLAN DE COMUNICACIÓN INTEGRAL
6.4 Principios y valores por grupos de interés
Y = AE identity AE2 (I2)
AE1(I1)
Real Income Y1 Y*
0 Agg. Exp
∆Y ∆Y ∆Y ∆Y +∆I +∆y
3.2 The Geometrical Illustration of Multiplier .
Figure: 4.2.1 Diagrammatic Illustration of the Multiplier Process
Figure 4.2.1 depicts the working of the multiplier. The initial change was an increase in investment expenditure depicted as (+∆I). This change caused an increase in income shown as ∆Y. The increase in income (∆Y) gave rise to increase in consumption expenditure depicted as ∆C and an increase in savings not shown in the diagram. Since consumption expenditure is a component of AE aggregate expenditure increased necessitating in income denoted as ∆Y. This sets in motion another chain of reactions until the economy converges to a new equilibrium income level depicted as Y* corresponding to aggregate expenditure AE2.
Self Assessment Exercise
i. Draw a diagram to illustrate the concept of multiplier 3.3 Algebraic Determination of the Multiplier
We will employ equation for the illustration.
Y = 1 ( a – bT0 +I0 + G0 + X0 – M0) ... 10 1– b( 1 – t) + m
Equation 10 has two main components. The expression for the multiplier 1 1+ b ( 1-t) +m and the autonomous components (a – bT0 + 10+G0 + X0 – M0 ).
From equation above, if any of the autonomous components changes for
∆Y = 1 (∆10) (11) 1 – b(1 – t) + m
From equation above the changes in Y with respect to I could be expressed as.
∆Y = 1
∆I 1 – b (1 – t) + m
Equation 1.16 is the investment spending multiplier. The value of equation 1.16 is the member of times by which a change in investment will be multiplied to obtain the resultant change in income.
Alternative Explanation to multiplier concept
The multiplier (k) is a number by which an initial change in investment (ΔI) is multiplier to obtain the final effect on the national income (Y).
Example 1:
Suppose an investment of N200 million brings about an increase in income of N1,000 million, the multiplier is.
m = 5 = N1.000
200 This is because 5 x N200million = N1.000 million Example 2:
If the increase in income, given the same level of investment, is N1,500 million, the multiplier is 7.5 (i.e. N1,500/200).
The crucial question is, why does a given change in the level of investment bring about a multiplier work? We shall examine this important question by the use of numerical illustrations.
The working of the multiplier: A numerical illustration
To explain the working of the multiplier, let us make two simple assumptions (a) that our small economy of Zamba decides to invest N100 million annually (b) that the MPC of Zamba is 0.75, This means that for every hundred naira received, 75 naira is spent and 25naira is saved.
let us assume that this economy has neither government nor external trade transactions.
If N100 million is invested in the Zamban economy annually, it will give rise to several rounds of expenditure, and each expenditure round will induce yet another expenditure round. Let us trace the details of this process of induced expenditure by examining Table 4.2.1 below;
Table 4.2.1: The multiplier process in Zamba (hypothetical) Period of
expenditure
Increase in income, ΔY N million
Increase in consumption with MPC = 0.75 N million
Increase in savings with MPS = 0.25 N million
Period one 100.00 75.00 25.00
Period two 75.00 56.25 18.75
Period three 56.25 42.00 14.00
Period four 42.00 31.50 10.50
Other subsequent periods
126.75 94.25 31.25
Total 400.00 300.00 100.00
It will be apparent from table 4.1 that the N100 million initial investment gives rise directly to a N100 million increase in income in the first round. Part of this income will be consumed and part of it saved. The part consumed is obtained by multiplying the income by the MPC, i.e. N100 million x 0.75 = N75 million (column 3). The part saved is N100 – 75 = N25million or N100 million x MPS = (0.25), column 4.
The second period of expenditure is the income of N75 million obtained from increased in consumption. Using the same process of multiplying this by the MPC of 0.75 and MPS of 0.25, the actual values for consumption and savings, respectively, will be found in Period 2, columns 3 and 4.
In general, each income period gives rise to an expenditure period as well as a savings period. Finally, the process of spending and re-spending will yield an income several times the initial amount. In our case, the ultimate amount will be N400 million. This is the multiplier effect of the yearly expenditure of N100.
What is the value of the multiplier in this case?
Note that from the multiplier effect of N400 goes to savings. Thus, the total reflects the size of both the MPC and the MPS. Note also that the final increment in income (the multiplier effect) is the multiplier of the reciprocal of MPS. This gives a clue on how to obtain the multiplier effect of any increase in investment.
Simply multiply the change in investment by the MPS turned upside down.
Using our case as an illustration, we have 100 x 4/1 = N400 million.
Self Assessment Exercise
i. Given the following equation determine the multiplier Y= C + I + G + X – M, where C = a + bYd , Yd = Y – T, I = Io, T = To + tY, G = G0, X = Xo, M = Mo. 4.0 Conclusion
This unit concludes that every economy has its definite marginal propencity to consume which is the main factor that determine the multiplier process, the larger the MPC the better
5.0 Summary
This unit looked at the concept of multiplier both algebraically and graphically and used these economic tools to explain in a clear term how multiplier process works. in addition, we used numerical analysis for better understanding.