The Concept of Multiplier:

An economic 'multiplier' is just the ratio of an increase in aggregate government spending to an increase in aggregate GDP, calculated through econometric methods. I ran into a question about the Money Multiplier Model, and I realised that explaining it is a lot more complicated than I expected. The story of the model is how an initial cash deposit at one bank creates a chain of smaller and smaller loans, until the aggregate loan book has grown by a multiple of the initial deposit. The key to understanding the model is that it is based on a defective. The money multiplier in theory makes a number of assumptions that do not always necessarily hold in the real world. It assumes that people deposit all of their money and banks lend out all of the money they can (they hold no excess reserves). It also assumes that people instantaneously spend all of their loans. The formula for the gross income multiplier is simple: Property Price / Gross Annual Rental Income = Gross Income Multiplier. Here’s an example of how to use the formula. Imagine that you’re assessing a rental property that costs $600,000. The property might generate $55,000 in gross annual rent.

Real-world money multipliers refer to the process in which banks loan money and the result is more cash circulating in the economy. That is, the money supply is multiplied. Economists measure a basic money multiplier by calculating the inverse of the required reserve ratio set by the Federal Reserve, the institution responsible for regulating.

The theory of multiplier occupies an important place in the modern theory of income and employment. The concept of multiplier was first of all developed by F.A. Kahn in the early 1930s. But Keynes later further refined it. F.A. Kahn developed the concept of multiplier with reference to the increase in employment, direct as well as indirect, as a result of initial increase in investment and employment.

Keynes, however, propounded the concept of multiplier with reference to the increase in total income, direct as well as indirect, as a result of original increase in investment and income. Therefore, whereas Kahn’s multiplier is known as ’employment multiplier’, Keynes’s multiplier is known as investment or income multiplier.

The essence of multiplier is that total increase in income, output or employment is manifold the original increase in investment. For example, if investment equal to Rs. 100 crores is made, then the income will not rise by Rs. 100 crores only but a multiple of it.

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If as a result of the investment of Rs. 100 crores, the national income increases by Rs. 300 crores, multiplier is equal to 3. If as a result of investment of Rs. 100 crores, total national income increases by Rs. 400 crores, multiplier is 4. The multiplier is, therefore, the ratio of increment in income to the increment in investment. If ΔI stands for increment in investment and AY stands for the resultant increase in income, then multiplier is equal to the ratio of increment in income (Δy) to the increment in investment (ΔI). Therefore k = ΔY/ΔI where k stands for multiplier.

Now, the question is why the increase in income is many times more than the initial increase in investment. It is easy to explain this. Suppose Government undertakes investment expenditure equal to Rs. 100 crores on some public works, say the construction of rural roads.

For this Government will pay wages to the labourers engaged, prices for the materials to the suppliers and remunerations to other factors who make contribution to the work of road-building. The total cost will amount to Rs. 100 crores. This will increase incomes of the people equal to Rs. 100 crores.

But this is not all. The people who receive Rs. 100 crores will spend a good part of them on consumer goods. Suppose marginal propensity to consume of the people is 4/5 or 80%. Then out of Rs. 100 crores they will spend Rs. 80 crores on consumer goods, which would increase incomes of those people who supply consumer goods equal to Rs. 80 crores. But those who receive these Rs. 80 crores will also in turn spend these incomes, depending upon their marginal propensity to consume. If their marginal propensity to consume is also 4/5, then they will spend Rs. 64 crores on consumer goods.

Thus, this will further increase incomes of some other people equal to Rs. 64 crores. In this way, the chain of consumption expenditure would continue and the income of the people will go on increasing. But every additional increase in income will be progressively less since a part of the income received will be saved. Thus, we see that the income will not increase by only Rs. 100 crores, which was initially invested in the construction of roads, but by many time more.

Derivation of Investment Multiplier:

How much increase in national income will take place as a result of an initial increase in investment can be expressed in the following mathematical form:

Increase in income

Or

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ΔY = 100 + 100 x 4/5 + 100(4/5)² + 100(4/5)³ + 100(4/5)⁴

= 100[1 + (4/5) + (4/5)² + (4/5)³ + (4/5)⁴]

But the above series is one of geometric progression. Therefore, increase in income (ΔY)

= 100 1/1-4/5

⁼100 X 1/1/5

= 100 x 5

= 500

It is thus clear that if the marginal propensity to consume is 4/5, the investment of Rs. 100 crores leads to the increase in the national income by Rs. 500 crores. Therefore, multiplier here is equal to 5. We can express this in a general formula.

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If ΔY stands for increase in income, ΔI stands for increase in investment and MPC for marginal propensity to consume, we can write the equation (i) above as follows:

ΔY = ΔI 1/1-MPC

ΔY/ΔI = 1/1-MPC

ΔY/ΔI measures the size of the multiplier. Therefore,

Size of multiplier or k = 1/1-MPC

It is clear from above that the size of multiplier depends upon the marginal propensity to consume of the community. The multiplier is the reciprocal of one minus marginal propensity to consume. However, we can express multiplier in a simpler form. As we know that saving is equal to income minus consumption, one minus marginal propensity to consume will be equal to marginal propensity to save, that is, 1 – MPC = MPS. Therefore, multiplier is equal to

1/1 – MPC = 1/MPS https://urclever.amebaownd.com/posts/20624572.

Algebraic Derivation of Multiplier:

The multiplier can be derived algebraically as follows:

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Writing the equation for the equilibrium level of income we have

Y = C + I

As in the multiplier analysis we are concerned with changes in income induced by changes in investment, rewriting the equation (1) in terms of changes in the variables we have

ΔY = ΔC + ΔI

In the simple Keynesian model of income determination, change in investment is considered to be autonomous or independent of changes in income while changes in consumption are function of changes in income. In the consumption function,

C = a + bY

where a is a constant term, b is marginal propensity to consume which is also assumed to remain constant. Therefore, change in consumption can occur only if there is change in income. Thus

Theory of Multiplier

ΔC = bΔY

Substituting (3) into (2) we have

ΔY = bΔY + ΔI

ΔY – bΔY = ΔI

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ΔY (1 – b) = ΔI

Or

ΔY =1/1-b ΔI

ΔY/ΔI = 1/1 -b

As b stands for marginal propensity to consume

ΔY/ΔI = 1/1 – MPC = 1/MPS

This is the same formula of multiplier as obtained earlier. Note that the value of multiplier ΔY/ΔI will remain constant as long as marginal propensity to consume remains the same.

Calculating the Size or Value of Multiplier:

It follows from above that the size or value of multiplier is the reciprocal of marginal propensity to save. Therefore, we can obtain the value of multiplier if we know the marginal propensity to consume or the marginal propensity to save of the community. Given the size of multiplier form the net increase in investment, we can find out the total increment in income that will occur as a result of investment.

If the marginal propensity to consume of a community is equal to 2/3, we can find out the size of multiplier as under:

Multiplier, k = 1/1-MPC

1/1-2/3 = 1/1/2 =

The Real-world Money Multiplier