# Aggregate Demand Multipler

__Introduction__

A change in the equilibrium income or output is the result of a shift in the aggregate demand function or the C + I curve. The aggregate demand curve can either shift upwards or downwards. The amount of the change in the income will be a multiple of the amount of the shift in the aggregate demand curve. The multiplier is the amount by which there is a change in equilibrium income or output when autonomous aggregate expenditure increases by one unit. It is this condition necessary for the multiplier to work.

__Shifts in the Aggregate Demand and the Multiplier__

In a two sector economy, the aggregate demand is a sum of consumption and investment expenditures. It is generally agreed that though both consumption and investment functions undergo a change from one period to another, the consumption function is relatively more stable than the investment function. Thus, the initial changes in income occur more due to the shifts in the investment function.

A few illustrations could explain us clearly the shifts in the aggregate demand as well as the multiplier.

__Illustration 16__

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

__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 17__

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__

__Δ Y__ = m

Δ I

Also,

m = __ 1 __

1 – mpc

Thus, Δ Y = Δ I

m = 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 S

-160 = Δ C – 40

The autonomous investment decreases by 40 millions, the saving will also decrease by 40 millions

Δ C = - 160 + 40

Δ C = - 120

**(2) The consumption expenditure decreases
by 120 millions**

__Illustration 18__

Compute the value of the investment multiplier when the marginal propensity to continue 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 – mpc

Hence,

**(1)** m = __ 1 __

1 – 0.8

** = 1
/ 0.2 = m = 5**

**(2)** m = __ 1 __

1 – 0.65

** = 1
/ 0.35 = m = 2.87**

**(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 2.87 = 172.2**

** = 60
x 1.67 = 100.2**

** = 60
x 1.33 = 79.8**

__Illustration 19__

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

- The change in the equilibrium level of income
- The change in autonomous demand
- The induced change in the consumption expenditure

__Solution__

__Δ Y__ = m

Δ Ȳ

But, m is the investment multiplier

Also,

m = __ 1 __

1 – mpc

Thus,

Δ Y = ΔIm = ΔI __ 1 __

1 – mpc

= -
60 x __ 1 __

1 – 0.50

= - 120

**Hence, the decrease in autonomous investment causes a decrease in the equilibrium level of income by 120 millions.****The decrease in investment by 60 millions is the change in the level of autonomous demand.****The Consumption expenditure falls by 60 millions**

Y = C + I

Therefore,

Δ Y = Δ C
+ ΔS

-120 = ΔC – 60

Δ C = -120 + 60

__Illustration 20__

Presume that in two sector economy, the income is $ 1000 million while the marginal propensity to consume is 0.40.

Suppose the government wants to increase the income to $ 1600 million, by an amount of $ 600 million.

By how much should the autonomous investment be increased?

__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 = m ΔI __ 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 1.67

Δ I = 600 / 1.67

**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**

**Online Live Tutor Equilibrium level, Consumption expenditures:**

We have the best tutors in Economics in the industry. Our tutors can break down a complex Equilibrium level, Consumption expenditures problem into its sub parts and explain to you in detail how each step is performed. This approach of breaking down a problem has been appreciated by majority of our students for learning Equilibrium level, Consumption expenditures concepts. You will get one-to-one personalized attention through our online tutoring which will make learning fun and easy. Our tutors are highly qualified and hold advanced degrees. Please do send us a request for Equilibrium level, Consumption expenditures tutoring and experience the quality yourself.

**Online Shifts In The Aggregate Demand and The Multiplier Help:**

If you are stuck with an Shifts In The Aggregate Demand and The Multiplier Homework problem and need help, we have excellent tutors who can provide you with Homework Help. Our tutors who provide Shifts In The Aggregate Demand and The Multiplier help are highly qualified. Our tutors have many years of industry experience and have had years of experience providing Shifts In The Aggregate Demand and The Multiplier Homework Help. Please do send us the Shifts In The Aggregate Demand and The Multiplier problems on which you need help and we will forward then to our tutors for review.

**Other topics under National Income and Its Determination:**

- Classical Theory of Employment
- Determination of Effective Demand
- Determination of Equilibrium Income or Output in a Three Sector Economy
- Keynesian Model of Income Determination in A Two Sector Economy
- Keynesian Model of Income Determination in a Four Sector Economy
- Refutation of Say's Law
- Principle of Effective Demand: Aggregate Demand and Aggregate Supply
- Propositions and Implications of the Law
- Say's Law of Market