Chapter 4: Equilibrium Output and Multiplier Effect

8/10/2019 Chapter 4: Equilibrium Output and Multiplier Effect

1/27

CHAPTER 4EQUILIBRIUM OUTPUT

AND THE MULTIPLIER EFFECT


2/27

Equilibrium Output

Equilibrium output happenswhen aggregate expendituresequal aggregate income.Aggregate expenditures mayalso be labeled as aggregate

demand., while aggregateincome may also be labeled asaggregate supply. Hence,equilibrium output may beidentified as the point whereSa (aggregate supply)

intersects (aggregate demand)in the expenditure and incomegraph.


3/27

The Aggregate of Income and

Expenditure Aggregate income (Y) is

calculated by adding allincomes received in theeconomy by all owners offactor inputs within a one-year

period, hence, should equalaggregate supply. On the otherhand, aggregate expenditure isthat part of income spent onconsumption and investment(C + I). But since investment is

merely a part of saving (S), wemust understand in relation toincome.

The first general equationthat we need to be consider isthat Y = C + S, this equationgenerally tells us that, given acertain level of income, we can

only dispose it either byspending (C) or saving (S),nothing more, nothing less.The money (Y) can only usedeither way, so that Y can onlybe the sum of C and S.

Corollarilly, if w want todetermine savings (S), theequation is: S = YC


4/27

Table 4.1

Income, Consumption and Savings

Y

C

S

160 320 -160

200 350 -150

400 500 -100

800

800

0

1200 1100 100

1600 1400 200

2000 1700 300

Table 4.1 shows that negative savings may happen because even at zero income

need to spend, e.g., food and minimal clothing in order o keep themselves alive.

Where do they get the money? Maybe from borrowing, spot from relatives,

subsidies from government welfare agencies.


5/27


6/27

Consumption and Savings

Propensities1. Average Propensity to

Consume (APC). A portionof total income used forconsumption. It isexpressed as a percentage

income (Y). Algebraically.APC = C / Y

2. Average Propensity toSave (APS). A portion of

total income not used forpresent consumption, andtherefore, saved.Algebraically, APS = S / Y

Since Y = C + S, C / Y + S + Y= 1, hence, APC + APS = 1also, because income canonly be either spent orsaved. So adding two more

columns to Table 4.2 forAPC and APS, the result canbe seen as follows.


7/27

Table 4.2

Income, Consumption, Savings, Average Propensity to

Consumeand Average Propensity to Save

Y C S APC APS

160 320 -160 2 -1

200 350 -150 1.75 -0.75

400 500 -100 1.25 -0.25

800

800

0

1

0

1200

1100

100

0.92

0.08

1600 1400 200 0.86 0.14

2000 1700 300 0.85 0.15

Adding each row in the APC and APS columns gives us a uniform sum of 1. Also

in table 4.2, we can see that APC and APS move in opposite directions, that is,as APC decreases, APS increases. Conversely, as APC rises, APS moves down.

The APC and APS are useful tools in planning as they may be used by

planner (economists) to determine the spending and saving patterns of various

regions and localities of a country, which could guide decision makers in their

policy-making activities.


8/27

Consumption and Savings

Propensities

1. Marginal Propensity to Consume (MPC). A portion ofchange in total income that is used for consumption.It is expressed as the ratio of total change inconsumption C to change in income Y.

Algebraically. MPC = C / Y

2. Marginal Propensity to Save (MPS).A portion of thechange in income that is not used for spending, and

therefore, saved. It is expressed as the ratio of thetotal change in the amount saved to the change inincome. Algebraically. MPS = S / Y


9/27

Table 4.3

Relationship of Income, Consumption, Savings,

APC , APS, MPC and MPS

Y

C

S

APC

APS

MPC

MPS

160 320 -160 2 -1 - -

200 350 -150 1.75 -0.75 0.75 0.25

400 500 -100 1.25 -0.25 0.75 0.25

800 800 0 1 0 0.75 0.25

1200 1100 100 0.92 0.08 0.75 0.25

1600 1400 200 0.86 0.14 0.75 0.25

2000

1700

300

0.85

0.15

0.75

0.25

We can see that the first two row in the


10/27

Consumption Function

At equilibrium, income (Y) is equal to expenditure (C + I),and between C and I, C always comprises the larger shareof Y. This logical flow is an extension of Keynes observationthat saving is just a residual fund after an individual orhousehold had already satisfied his consumption needs,

and that investment (Y) is merely a portion of (S), and atequilibrium S = I.

From the equilibrium equation Y = C + I, we can see thatboth C and I are functions of Y. But because C comprises themore significant portion of Y, we need to study it moreclosely in relation to Y. Hence, we will state that C = f(Y),meaning the value of C depends on the value of Y.


11/27


From this graph, we can seethe value of C at any pointalong the C curve is C = a + bY.

So that we can forecast the

consumption behavior if weare able to establish the ratioof C and Y (change in C forevery change in Y). In thisassumed linear relationshipbetween C and Y, a = origin or

starting value of C and b =slope of the curve or C line.


12/27


Revisiting the date we generated

in Table 4.1, we will validate the

linear relationship of C and Y by

calculating its slopes are every

paired rows:

1. At Y = 160 and C = 320

Y = 200 and C = 350

Solve for B.

2. At Y = 200 and C = 350

Y = 400 and C = 500

Solve for B.

b=C

Y

b=150

200

b=0.75

b=C

Y

b= 350

320

200 160

b=30

40

b= 0.75


13/27


3. At Y = 400 and C = 500

Y = 800 and C = 800

Solve for B.

4. At Y = 800 and C = 800

Y = 1200 and C = 1100

Solve for B.

b=C

Y

b=300

400

b=0.75

b=C

Y

b=300

400

b=0.75


14/27

5. At Y = 1200 and C

=1100

Y = 1600 and C = 1400

6. At Y = 1600 and C

=1400

Y = 2000 and C = 1200

b=C

Y

b=300

400

b=0.75

b=C

Y

b=300

400

b=0.75


15/27


Since the slope of s straightline is the same at any pairedpoints along the line, we areable to prove the linearrelationship between Y and C

in our sample date. With thislinearity, we can forecast thevalue of C at any level of Y.

Example:

Y = 900

a = 200

Solve for C. C = ?

Solution:

C = a + bY

C = 200 + 0.75 (900)

C = 100 + 675C = 875


16/27

Planned Investments

And Its Multiplier Effect The second component of aggregate spending (aggregate demand) is

planned investment; I. Planned investment is the type of investment madeby the firm voluntarily of intentionally. This is differentiated fromunplanned investment, which has a negative effect on output because itoccurs due to weakness in demand, therefore, is undesirable.

Unplanned investment happens when inventories rise because of the fallin demand. For example, San Miguel Corporation expects to sell 100million bottles of beer for the year, but because of a change in consumerpreference, it is only able to sell 90 million bottles. So, without wanting it,SMC will have increased its investment (trough increase inventory) by theamount equivalent to 10 million unsold beers. This kind of investment

(unplanned) definitely has a negative effect on output. It is for this reasonthat we will only consider planned investment as relevant to our presentanalysis.


17/27

Planned Investments

And Its Multiplier Effect

With this clarification, henceforth, we willconsider planned investments as investment

Investment may be defined as that part ofsavings used to create future value, e.g.,sewing machine to create clothes I the future,

beer mixing machines to crease future beers,buildings to create more space foewarehousing, etc.


18/27

Planned Investments


Planned investment is normally not

dependent on income. Firms do not normally

alter its investments expenditures as planned

for a given year. Why? Because a capitalexpenditure plans which was made in prior

years is very costly for the firm to change in

terms of additional man-hour cost, which willrework the plan, and for cost opportunities in

doing other things rather than reworking plan


19/27


20/27

Planned Investments

And Its Multiplier Effect If for example, a typhoon damaged the facilities of

Meralco so, say in Manila. Meralco will have no choice butto increase its investment to rehabilitate its facilitiesimmediately. They cannot wait for the next budget cyclebefore repairing its facilities. Otherwise, they will be in big

trouble from its customers.

After deducting the reduction in income brought about bythe damaged facilities, will a 100 million increase ininvestment in Meralco to repair the facilities bring anadditional income of 100 million in the economy? Since Y= C + I, hence an increase by 100 million of I will result in100 million of I will result in Y also increase by 100million.


21/27

Planned Investments

And Its Multiplier Effect After deducting the reduction in income brought about by

the damaged facilities, will a 100 million increase ininvestment in Meralco to repair the facilities bring anadditional income of 100 million in the economy? Since Y= C + I, hence an increase by 100 million of I will result in

100 million of I will result in Y also increase by 100million.

The answer is flat NO. Why? Because an increase inplanned investment has a multiplier effect in the economy.Income, Y, will actually increase by a multiple of I. This isbecause an increase in I will also include an increase in C.


22/27

Planned Investments

And Its Multiplier Effect Let us explain this phenomenon. Initially, income will increase by

the same amount as the increase in I. But the money from theinvestment will be paid o additional workers who will work to repairthe damaged facilities and/or to those existing employees who willrender overtime; some will be paid to suppliers of equipment,wires, transformer, bus-station spare parts, etc.

The recipient of this investment money will naturally spend all or apart of this additional disposable income on consumption.Therefore, C will also be effectively increased. For the rest nextround, further recipients of this investment money paid to workers

and suppliers will spend part of it for their own familysconsumption needs. Then, there will be another round of spending,and another and another, until there will be no more residualmoney left for further spending.


23/27

Planned Investments


The graph in Figure 4.4

shows the effect of I to

Y. By ocular inspection,

we can easily see that the

distance from Y0to Y1is

longer than the distance

from I0to I1. Hence, Y >

I because of the

multiplier effect of I in

the economys income.


24/27

The Value of the Multiplier

The value of the investmentmultiplier can be derived byputting together the variousequilibrium relationships that wehave established in this chapter.

First we have to establish that:Y = C + S

But since at equilibrium,

S = I

Hence, Y = C + I at equilibrium

It was also established that:

C= a + bY

Therefore, Y = a + bY + I

By rearranging this equation, wefind:

Y by = a + I, and

Y (1 b) = a + I, and

Y= a + I

1 bor Y= a + I 1

1 b


25/27


Since a is the

intercept (starting

value) of C, its value is

assumed to beconstant.

Hence, if I is increased

by I,

Y=

I 1b

and because b=MPC

Y= I1

1-MPC

Hence, the value of the multiplier is1

1-MPC


26/27


Example:

Using the computed MPC of 0.75 in Figure 4.4, estimate the effect onincome at equilibrium of the change in planned investment using thefollowing data:

Given:I0 = 850

I1= 900

a = 350

b = 0.75

Calculate:

I change in investment= ?

Y change in income= ?

Y (resulting income)= ?

Y0income before I appears= ?


27/27


Solution:

1. I=I1-I0

= 900 850

= 50

2. Y = I 1

1-MPC

= 50

1

0.25

= 200

3.Y = C + I + I

= a + bY + I +

I

=350 + 0.75Y + 50

Y 0.75Y = 350 + 50

0.25Y = 400

Y=400

0.25

Y=1,600

4.Y0= Y Y

= 1600 200

= 1400

Documents

Chapter 4: Equilibrium Output and Multiplier Effect