Investment Multiplier At a Glance

The working of the Multiplier assumes the following process:

multipler-process

Change in investment causes change in income. As a result, consumption changes. Consumption expenditure of one person is an income of the other.

Hence, change in consumption leads to change in income. This process continues till ∆C falls to zero.

MPC is the core factor in the process of income generation. Higher the MPC, greater is the conversion of income into consumption expenditure. Accordingly, greater is the generation of income. As, it is expenditure that is converted into income.

Expenditure is the injection into the income generation process, saving is the leakage.

For Detailed Study -

1. Investment Multiplier

2. Graphic Presentation of Multiplier

How Multiplier Mechanism Works

Let us understand the logic behind the direct relationship between MPC and multiplier through Multiplier Mechanism. It runs like this:

1) Suppose AB industry limited spends Rs. 100 crore in setting up a new plant i.e  ∆I = Rs. 100 crore.

This will lead to creating more demand for goods and services required for the setting up of this new plant. There will more demand for machinery, raw materials, labour etc.

This will generate income for all those people who are associated with the setting up this plant and leading to more output and income.

As a result national income in the first will increase by an amount equal to amount of investment i.e  ∆Y = Rs. 100 crore

2) This ∆Y = Rs. 100 crore would be split into ∆C and ∆S as a part of income is spent and a part of it is saved.

3) In round – 2, ∆C would be converted  into ∆Y as people who receive this new income (Rs. 100 crore) directly from the building of the factory will spend some of it on consumer goods like food, clothing, TV, cars, etc.

Here comes an important point:

The exact amount of additional consumption expenditure depend on the MPC(c).

Suppose MPC is 0.8, then 

MPC = ∆C / ∆Y (as discussed in consumption function)

∆C = MPC (∆Y)

∆C = 0.5(100)

     = Rs. 50 crore

If  MPC is 0.4, then

∆C = 0.4(100)

     = Rs. 40 crore

Relationship between Investment multiplier and Marginal propensity to consume

There is a direct relationship between multiplier and MPC. Higher the value of MPC, higher the multiplier affect and lower is the value of multiplier, lower the multiplier effect. 

We have already derived the multiplier formula i.e 

K = 1 / 1-MPC

Now we see the multiplier effect by taking different values of MPC

If MPC = 0.5 

K = 1 / 1-MPC

K = 1 / 1-0.5

    = 1 / 0.5

    = 2

Derivation of Investment Multiplier Formula

The multiplier formula can be derived by using the simple equilibrium condition for the two sector model i.e  

Y = C + I 

When there is an increase in investment by (∆I), it will lead to increase in income (∆Y) and this induces increase in consumption (∆C) i.e

∆Y = ∆C + ∆I 

Since, change in total consumption (∆C) equals change in income multiplied by MPC (marginal propensity to consume, “c”)

∆Y = c∆Y + ∆I

∆Y - c∆Y = ∆I

∆Y(1-c) = ∆I

∆Y = ( 1 / 1-c)  ∆I 

∆Y/ ∆I = 1 / 1-c

Graphic Presentation of Multiplier

Investment multiplier can also be explained with the help of the a diagram, as shown below:

investment multiplier

1) Income is shown along the X axis and Aggregate demand on Y axis.

2) The initial equilibrium is at point A, When AD = C + I

Determination of Equilibrium Income and output

After discussing about consumption and investment function in my previous posts, we are now in a position to study and analyse the equilibrium level of income and output.

Basic Assumptions:

1) Short Period analysis – Keynesian theory of equilibrium output is determined only with reference to short period of time.Short run is defined as a period of time during which level of output is determined exclusively by the level of employement in the economy. Technology is assumed to remain constant.

2) Closed economy – Keyenes discuss the theory of equilibrium GDP in the context of a closed economy.This is an economy which has no relations with  the rest of the world,there is no import or export.

Its two sector economy consisting of the household sector and business sector.All the decisions concering consumption expenditure is taken by the individiula household, while the business firms take decisions regarding investment.

Short run equilibrium of the firm perfect competition

The short-run equilibrium of the firm can be illustrated by combining the short-run cost curve with 
the demand curve (AR curve) faced by the firm.Since the firm is price- taker, it has to decide 
the amount of output it should produce at the given price so as to maximise its profits.
Thus, the firm is output adjuster under perfect competition.
In order to determine the profit maximising output, the firmhas to meet two conditions :

1) Short run marginal cost curve = Marginal revenue, and SMC curve cuts the MR curve from below.

Since in perfect competition MR = AR = price (p), it follows that SMC = P.

This is the profit maximisation rule.
2) Perfect competition firms may be earning super-normal profits, incurring losses or 
just earning normal profits.Whether a firm makes abnormal profits or normal profits or losses 
depends on its cost and revenue conditions.Three equilibrium conditions can be seen.

a) AR > SAC, it means the firm is earning abnormal or supernormal profits.

As shown by the graph above, as short run average cost is below the P = AR = MR 
line at equilibrium, the firm earns super – normal  or pure profits as shown by the shaded area.

As the firm is covering all its cost thereby earning abnormal profits.

b) AR < SAC (but > AVC), then the firm is incurring losses

If the AR (P) > AVC, then he is covering entire variable costs and part of fixed costs as well. 

Here, losses in production would be less than losses in case of shut down, and the firm will definitely produce.

As shown by the below graph:

As explained above, SAC lies above the price ( P= AR= MR), the firm is incurring losses shown by the shaded area. Since price exceeds AVC, the firm continues to produce in the short run (since loss is of fixed factors only so continue production) 

c) AR = SAC, it means firm is making only normal profits.

As shown by the graph above, SAC is tangent to P = AR = MR line, the firm covers 
only its SAC,which includes normal profits. The firm, therefore earns normal profits 
(no profit no loss situation)

Short run supply curve of the firm in perfect competition

In a state of perfect competition, price is given to a firm.

Implying that, AR is constant for different levels of firm’s output.

Constant AR implies that AR=MR, 

so that the equilibrium condition that MR=MC can also be stated as P=MC.

At a given Price (P) a firm strikes its equilibrium when P=MC and MC is rising. Supply curve of the 
firm shows that various quantities of a commodity a firm is willing to supply at different prices.

The quantity which a firm is willing to supply at a particular price is determined by the equality 
of SMC and MR (=AR=P). By finding out equilibrium output at different prices and by joining 
different equilibrium points we an derive the short-run supply curve of the firm as shown by the 
below graph:

1) At P_o price (P_o = AR_o = MR_o), SMC curve cuts MR_o from below at E_o, giving  E_o as 
the equilibrium point and OQ_o as the equilibrium quantity. 
At P_o price, firm is able to cover only variable cost since P=AVC.
The firm will not operate below this point and stop production since P <  AVC (firm is unable to 
cover variable as well as fixed cost). 
Eo is known as shut-down point because the firm would not like to operate below this.

OQ_o is the minimum supply of the firm in the short run.

2) If the price rises to P₁, equilibrium point shifts to E₁, where SMC = MR, and AR = SAC, and the 

equilibrium quantity increases to Q₁.

Point E₁, where SMC curve cuts the minimum point of SAC, is known as ‘break-even point’ 

because the firm is able to cover all costs at OP₁ price.

Firm is just covering all its cost i.e. AR = AC.

At P₁ price the firm will supply OQ₁ quantity.

3) At P₂ and P₃ prices, equilibrium is at E₂ and E₃ respectively, and the amount supplied is OQ₂ and 

OQ₃ respectively. While producing OQ₂ and OQ₃ quantities of output, the firm is earning super 

normal profits since AR > SAC.

4) By joining E_o, E₁, E₂ and E₃, we get the firm’s short run supply curve.

The part of short run MC curve which lies above the minimum point of AVC curve is the 

supply curve of the firm in the short run.

Supply curve of the firm in the short run is always upward sloping. 

Break even point and shut down point

Break-even point

Break even is said to occur when:

TR = TC

Or, TR / Q = TC / Q

Or, P = AC

A firm is just covering all its costs

break even point

Break – even occurs at point Q. Here AR (price) = AC= or TR = TC. The firm is just making normal profits.

AC = LQ = OP

A firm is just covering its costs as price (=OP) happens to be equal to AC (average cost) = LQ

It is a situation of  no - profit no - loss situation.

Marginal revenue and Marginal cost approach

The second method of showing equilibrium of the firm is in terms of marginal revenue and marginal cost curves.

There are three condition that must be satisfied for the profits to be maximum.

Rule 1 :

In the short run, a firm should produce 

if and only if P or AR > AVC  OR TR > TVC

1) A firm has to incur fixed cost even if there is no production, firm sometimes continues to produce even when it is facing losses.

If a firm decides to shut down and produce nothing, the losses would be equal to its fixed cost.

2) A profit earning firm will never lose more than its fixed cost, if the revenue is so low that the firm is unable cover its variable cost, to avoid this cost a firm can stop (cease) production, but if the firm still has the capital to resume production later, 

so this is a situation of Shut down ( a firm produce no output to minimise its lose).