What is Investment Multiplier?

The term Investment Multiplier is an important contribution made by Prof. J.M. Keynes. Keynes felt that an initial rise in investment multiplies overall income by a large factor. The relationship between an initial increase in investment and the subsequent rise in total revenue is expressed by the multiplier. In reality, it has been seen that when investments are increased by a particular amount, the change in income does not only reflect the initial investment’s value but also increases by several times. In other words, a multiple of a change in investment equals a change in income. A multiplier explains how many times an increase in investment causes an increase in national income.

Hence, Multiplier (k) is the ratio of an increase in national income (ΔY) due to an increase in investment (ΔI).

Assume that an extra ₹5,000 crores of investment (ΔI) in an economy result in extra ₹20,000 crores of income (ΔY). In this scenario, multiplier (k) will have the value:

= 4

It indicates that a single increase in investment resulted in a 4 times increase in income.

Multiplier and MPC

MPC and multiplier value are directly related to one another. The value of the multiplier increases with an increase in MPC, and vice versa. The concept of multiplier was developed based on the view that the expense of one person is another person’s income. The increase in investment raises the income of the people, a portion of which is used by people for consumption. The value of MPC; however, determines how much of the new income is to be spent on consumption. People will spend a large portion of their increased income on consumption in the case of higher MPC. The multiplier’s value will be higher in such a situation. However, people will spend a smaller percentage of their increased income on consumption when the MPC is low. It means that the MPC determines the value of multiplier.

Algebraic relationship between Multiplier and MPC

The following method can be used to derive the algebraic relationship between Multiplier and MPC. We already know that:

Y = C + I

This means that any change in income (ΔY) will therefore equal (ΔC+ΔI).

ΔY = ΔC + ΔI

Dividing both sides by ΔY:

OR

 Multiplier (k) in terms of MPS

Also, 1-MPC = MPS

So,

Multiplier is directly related to MPC and inversely related to MPS

The multiplier’s value is based on the marginal propensity to consume. In other words, when MPC is higher, multiplier (k) is higher, and vice versa. On the contrary, the higher the MPS, the lower will be the multiplier value and vice versa. It can be clearly understood with the help of the following table:

MPC	MPS (1-MPC)
0	1
0.60	0.40
0.67	0.33
0.72	0.28
1	0

The above table clearly shows that the multiplier has a direct relationship with MPC and an inverse relationship with MPS.

Maximum value of the Multiplier

From the above table, it can be seen that when the MPC value is 1, the multiplier can have a maximum value of infinite. MPC = 1 shows that the economy has decided to spend the entire increased income and has decided to retain not even a small part of its increased income. Consumption expenditures will continue to rise, and the multiplier’s value will be infinite.

Proof:

When MPC = 1, then:

k = ∞

Minimum value of the Multiplier

From the above table, it can be seen that when the MPC value is zero, the multiplier’s minimum value is one. When the MPC value is zero, the economy has decided to save all additional income and has made no consumption expenditures. Hence, there will be no further growth in income. As a result, ΔY = ΔI, or the overall rise in income (ΔY) will equal the total increase in investment (ΔI). In this case, the multiplier’s value is 1.

Proof:

When MPC = 0, then:

k = 1

Working of Multiplier

The principle of One person’s expenditure equals another person’s income explains how multiplier works. When you make an additional investment, your income rises many times faster than your investment. This can be understood with the help of an example:

• Consider that a ₹200 crore (ΔI) additional investment is made to build a road. This additional investment will result in an additional ₹200 crores in revenue in the first round. 
• If MPC is taken to be 0.80, then those receiving this increased income will spend ₹160 crores, or 80% of ₹200 crores, on consumption, and the remaining amount will be saved. The second round will increase the revenue by ₹160 crores.
• In the next round, 80% of the extra income of ₹160 crores, or ₹128 crores, will be spent on consumption, with the remaining amount saved.
• The multiplier process will continue, and every round’s consumer expenditure will be equal to 0.80 times the extra income earned in the previous round. 

To better understand this process, consider the table given below:

It can be concluded that an initial investment of ₹200 crores has resulted in a total increase of ₹1,000 crores in income.

Thus, the multiplier will be,

k = 5

Diagrammatic Presentation of Multiplier

The AD and AS approach can also be used to graphically represent the multiplier. In the above graph, the X-axis represents income, and the Y-axis represents Aggregate Demand. Assume that the initial equilibrium is established at point E, where the AD curve and AS curve intersects. OY is the equilibrium level of income. Assume that investment rises by ΔI, causing the new Aggregate Demand curve (AD₁) to cross the Aggregate Supply curve (AS) at point ‘F’. As a result, OY₁ is the new equilibrium level of income. Due to an initial increase in investment, the income increases from OY to OY₁. The graph clearly shows that the income growth (YY₁ or ΔY) is more than the investment growth (ΔI). Thus the value of the multiplier is provided by: