The concept of Super Multiplier Theory | Marginal Propensity to Investment and Marginal Propensity to Consumption

The multiplier that emerges from macroeconomic model in which is both induced consumption and induced investment is called the super multiplier. The value of the super multiplier is necessarily greater than the simple multiplier. It is believed that H.R. Hicks first used the term ‘super-multiplier’ in explaining his business cycle theory.

The concept of super multiplier develops from the point that increase in autonomous investment originates the increase in income. The initial increase in income will give rise to induced investment via the marginal propensity to invest (MPI). The increase in income / output indicates a condition of growing economic activities. So, the business community takes the increase in income as a positive incentive to increase further investment. The increase in income will also affect consumption via marginal propensity to consume (MPC). Induced investment and induced consumption produce further increases in income, and these increases in income still induce / motivate more investment and more consumption spending, and this process continues until a new equilibrium is established.

The super multiplier is derived by using the consumption and investment function along with national income accounting identity. In formulating the models, it is assumed that the economy is operating below full employment level (which means there are unemployed resource of production in the economy), general price level in the economy is more or less constant, effect of interest rate on investment demand as well as on consumption is neutral / unbiased, the economy is simple two sector closed economy.

Aggregate expenditure / demand (AE or AD) is the sum of households’ expenditure on the goods and services (C) and business sectors’ investment expenditure (I). This relationship is mathematically written as

AE = C + I …………………………. (i)

Macroeconomic equilibrium needs that aggregate expenditure / demand should be equal to the total value of income (Y).

Therefore, Y = AE ……………….. (ii)

By combining equations (i) and (ii), we get

Y = C + I ………………………….. (iii)

Equation (iii) is a national income accounting identity (unique condition hold true by definition). It simply tells that total income in equilibrium is equal to the sum of household consumption expenditure and business investment expenditure. In other words, represents macroeconomic equilibrium condition when aggregate demand / expenditure (C+I) is equal to the value of aggregate supply / income (Y).

Household consumption expenditure totally depends upon the level of current income (Y). Consumption is linearly dependent upon income. Keynes in explaining his consumption-affecting factors is insignificant. So, the relation of consumption (C) with income (Y) is algebraically expressed as

C = Ca + bY (0 < b < 1) ……………………. (iv)

Where, Ca is autonomous consumption, b is marginal propensity to consume (MPC) and Y is income level, it is the disposable income or after-tax income (income left after the payment of tax). We have been assuming a simple two sector private economy where there is no government tax, so Y is both national income and disposable income.

Autonomous consumption is independent of the level of income, it is the minimum level of consumption to be made to keep one’s life alive even if the current level of income earning is zero; Ca is the intercept term of the consumption function which represents the effect of all factors other than current income on consumption. Marginal propensity to consume (MPC) or ‘b’ in equation (iv) is the coefficient of Y, and it measures the change in consumption resulting from some change in the level of income. MPC is expressed as a ratio of the change in consumption to the change in income. So, 

MPC = (Change in consumption) / (Change in income) = ∆C / ∆Y

In equation (iv) the restriction / limitation on the MPC is that it is positive but less than one (0 < b < 1). 

This is fully justified by Keynes’ Fundamental Psychological Law of Consumption according to which human beings have a tendency of increasing consumption with the increase in income but not by as much as the increase in income. This means that consumption expenditure increases with the increase in income but all the increases in income is not spent in consumption. The relation of consumption to income is geometrically shown in figure.

Keynesian Consumption Function

The consumption function slopes upward indicating that consumption rises with the rise in income. In the equation "C = Ca + bY", the term ‘b’ or MPC also measures the slope of the consumption function. Every point on the consumption line represents a combination of the value of Y and C, and hence the ratio of C and Y is a measure of the average propensity to consume (APC = C / Y). Along the consumption increases with the increase in income but by less than the increase in income; some part of the increase in income goes for saving.

Total investment (I) is made of the sum of autonomous investment (Ia) and induced investment. Autonomous investment is not influenced by the change in income but induced investment is totally dependent upon the level of income. Then the investment equation is algebraically written as

I = Ia + βY (0 < β < 1) ………………………. (v)

Where β (Greek small letter beta) is the marginal propensity to invest (MPI); it measures the change in investment with the change in income / output (i.e. MPI = ∆C / ∆Y = β). The restriction on the MPI is that it is also positive but less than zero. The increase in induced investment due to the change in income is normally less than the increase in income.

The investment concepts used in deriving the super-multiplier is shown in figure:

Autonomous, Induced and Total Investment

Autonomous investment is constant at some value (equal to Ia in the example) and totally unresponsive to income; the autonomous investment line is parallel to the horizontal income axis; it tells us that autonomous investment remains fixed for a particular period of time whatever may be the level of income. On the other hand, the induced investment line (βY) starts from the origin and is fully dependent upon income level. If income level is zero, induced investment is also zero, and as income rises induced investment also rises. As, total investment is the sum of autonomous and induced investments (I = Ia + βY), the total investment line (I) starts from above the origin with some positive value equal to the autonomous investment (Ia).

In order to derive the value of super-multiplier, we first of all find the equilibrium level of income. For this, we substitute equations (iv) and (v) into equation (iii) which gives:

Y = Ca + bY + Ia + βY

Or, Y –bY – βY = Ca + Ia (collecting Y terms in one side)

Or, Y (1 – b – β) = C0 + Ia

Then the equilibrium level of income (Ye) is

Ye = (Ca + Ia)/(1 – b – β) ………………………. (vi)

Now let us suppose that there is some increase in autonomous investment equal to ‘∆Ia’. This increase in autonomous investment will bring increase in the equilibrium level of income / output by some amount ∆Y. Then the new equilibrium is

Ye + ∆Y = (Ca + Ia + ∆Ia)/(1 – b – β) ……………………. (vii)

Then subtracting equation (vii) from equation (vi), 

Ye + ∆Y – Ye = (Ca + Ia + ∆Ia) / (1 – b – β) - (Ca + Ia) / (1 – b – β)

Simplifying,

∆Y = (Ca + Ia + ∆Ia – Ca – Ia) / (1 – b – β)

Finally, we get,

∆Y = ∆Ia / (1 – b – β)

That is, ∆Y / ∆Ia = 1 / (1 – b – β)

= 1 / {1 – ( b + β)}

= 1 / 1 – (MPC+MPI) ………………… (viii)

The right hand expression “= 1/{1 – ( b + β)} = 1/1 – (MPC+MPI)” in equation (viii) is what is called the super-multiplier. The restriction in the super-multiplier is that the sum of marginal propensity to consume (MPC = b) and marginal propensity to invest (MPI = β) is not greater than one, that is b + β = MPC + MPI ≠ 1. If b + β > 1 (i.e., MPC + MPI > 1) the value of the super-multiplier will be negative which would mean that increase in investment reduces income/output and this is nonsensical/ illogical in economic explanation because increase in investment is assumed to increase income. If b + β = 0 (MPC + MPI = 0), the value of the super-multiplier will be one which would mean that the increase in equilibrium income is exactly equal to the increase in investment; and if b + β = 1 (MPC + MPI = 1) the value of the super-multiplier tends to infinity (it becomes very large), this would mean that the increase in autonomous investment brings very large increase in the equilibrium level of income, and increased investment is highly productive.

We can now make a comparison of the simple and super-multipliers. The multiplier that emerges in a model where investment includes only the autonomous investment and no induced investment is called simple investment multiplier

∆Y / ∆Ia = 1 / 1 – b = 1 / 1 – MPC

By comparison, it is obvious that as long as the marginal propensity to invest is positive (i.e., MPI > 0), the super-multiplier is greater than the simple multiplier because an initial rise in income created by a rise in autonomous investment leads to both induced consumption spending and induced investment spending and for this reason the overall rise in income will be greater than if only consumption spending had responded to the rise in income. Symbolically, we can write this as

1 / {1 – (MPC + MPI)} > 1 / (1 – MPC)

Or, Using the symbols of the equation, 1 / {1 – (b + β)} > 1 / (1 – b)

We can check this by taking some hypothetical values for MPC and MPI. Suppose MPC = 0.60 and MPI = 0.20. Then,

   1 / {1 – (MPC + MPI)} 

= 1 / {1 – (0.60 + 0.20)} 

= 1 / 1-0.80 

= 1 / 0.20 = 5

And, 1 / (1 – MPC) = 1 / (1 – 0.60) = 1 / 0.40 = 2.5

It is obvious that 5 > 2.5 or super-multiplier is greater than simple multiplier. This would mean that the combined effect of autonomous and induced investment on the rise/increase in income (output) is more powerful than the effect of autonomous investment alone.

                   You may also like to read:                  

• National Income: Various concepts of National Income | Gross Domestic Product (GDP), Gross National Product (GNP)

• Calculation of National Income and Difficulties in the Calculation of National Income

• Fiscal Policy: Role and Evolution of Fiscal Policy

• The dispute between Monetarism and Keynesianism

• Inflation and Demand Pull Inflation | Causes of Demand Pull Inflation

The Theory / Principle of Acceleration | Limitations and Assumptions of Acceleration Theory

The multiplier and accelerator are not rivals but parallel concepts. While the multiplier shows the effect of investment on consumption (and employment), the accelerator shows the effect of a change in consumption on investment.

According to Hayek, “Since the production of any given amount of final output usually requires an amount of capital several times larger than the output produced with it during any short period (say a year) any increase to final demand will give rise to an additional demand for capital goods several times larger than the new final demand.”

 

The principle of acceleration states that if demand for consumption goods rises, there will be an increase in the demand for the product. The accelerator therefore makes the level of investment a function of the rate of change in consumption. In other words, the accelerator measures the changes in investment goods industries as a result of changes in consumption goods industries.

The idea underlying the accelerator is not so much one or ever-rising demand as of a functional relationship between the demand for consumption goods and the demand for the machines, which make them. The acceleration coefficient is the ratio between the induced investments to a net change in consumption expenditure.

Symbolically, 

α = ∆I / ∆C 

where, α stands for acceleration coefficient;

           ∆I denotes the net changes in investment outlays and 

           ∆C denotes the net change in consumption outlays.

Suppose an expenditure of 10$ billion on consumption goods leads to an investment of 20$ billion in investment industries, and then the accelerator is 2. It could be one or even less than that. In actual practice, however, increased expenditures on consumption goods always lead in increased expenditures on capital goods. Hence accelerator is usually more than zero. Where a good deal of capital equipment is needed per unit of output, acceleration coefficient is positive and more than unity.

Sometimes, the production of increased consumer goods does not lead to an increase in the capital equipment producing these goods. The existing machinery also wears out on account of the constant use, with the result than the increased demand for consumer goods cannot be met. In the absence of induced investment and the acceleration effects, the increase demand of consumption goods leveled off and the accelerator, which measures the effects of induced investment as a result of changes in consumption, did not seem to work during these years.

The actual basis of the acceleration principle is the knowledge that the fluctuations in output and employment in investment goods industries are greater than in consumption goods industries. Acceleration has greater applicability to the industrial sector of the economy and as such it seeks to analyze the problem as to why fluctuations in employment in the capital goods industries are more violent than those in the consumption goods industries. There would be no acceleration effects in an economy that used no capital goods. Hence, acceleration principle has been widely used to explain fluctuations in economic activity, especially in the investment goods industries.

Thus, the acceleration principles hold that investment demand is dependent on increases in output, because such increases put pressures on firms to expand their stocks of capital goods. In this theory, investment occurs to enlarge the stock of capital because more capital is needed to produce more output. Firms may be able to produce more output with existing capital through more intensive use, but there is, at any time, a particular ratio of capital to output that firms consider optimum. At any time, there is a particular ratio that is the desired ratio for the economy as a whole over time, this ratio will changes as the mix or output changes. In order to reduce the complication, it is assumed that this ratio remains unchanged or constant over time. With K representing the capital stock, Y the level of output and W the capital output ratio, we have 

K = W Y

K (the desired stock of capital) will change over successive time periods only with changes in output (Y). Denoting a particular time period by t, preceding time periods are t – 1 and t – 2 and future of subsequent time periods are t + 1 and t + 2. Assume that in the preceding period (t – 1) the desired capital stock was enough to produce the level of output of the period t – 1. That is

Kt-1 = W Yt-1

Its output rises from Yt-1 to Yt, the desired capital stock would also rise from Kt-1 to Kt that is:

Kt = WYt

This increase in the desired stock of capital is Kt – Kt-1

To get this increase in capital stock, additional net investment is needed – this net increase in net investment expenditure is equal to the change in capital stock, that is,

It = Kt – kt-1 ………………………. (i) 

Where, it is not investment in period t. By substituting WYt for Kt and WYt-1 for Kt-1, we get

It = WYt – WYt-1 = W(Yt – Yt-1) …………………………….. (ii)

This equation simply means that investment during a particular time period (t) depends on the changes in output from ‘t-1’ to t multiplied by capital output ratio (W). If Yt > Yt-1, the equation shows that there is positive and investment during the period ‘t’. If, however, we want to show gross rather than net investment, all that it needed is to add replacement investment to both sides of the equation. This replacement investment is taken to be equal to depreciation and in shown by Dt, we have thus;

It + Dt = W (Yt – Yt-1) + Dt

The sum of It and Dt cannot be less than zero. If Ig represents gross investment in period t. We have, 

Igt = W (Yt – Yt-1) + Dt …………………………. (iii)

Investment will respond to changes in the level of output shown by the equation only if certain assumption are satisfied, the most important being the absence of excess capacity, if Xt shows the excess capacity at the beginning of the period t, we may rewrite equation (iii) as;

Igt = W (Yt – Yt-1) + Dt – Xt

Whatever the level of gross investment might otherwise be in t, it will be reduced by the amount of Xt. It’s the value of W(Yt – Yt-1) + Dt happened to be equal to an less than Xt then Igt would be zero, the minimum possible for gross investment in plant equipment.

Limitations and Assumptions of Acceleration Theory

The acceleration value may be considerably reduced as account of some practical limitations and assumptions:

1. No excess capacity: If there is already excess capacity in the consumer goods sector, a rise in demand for consumer goods will not lead to any induced investment or acceleration effects, because the increased demand may be met from the existing capital and machinery without producing additional capital goods. This will be a case of zero gross investment and is the typical case during the initial period of recovery phase of the trade cycle.
2. Surplus capacity: The operation of the principle depends upon the presumption that there is surplus capacity in the investment goods industries. If it were not so and no excess capacity existed in machine making industries, an increase in the derived demand for machines could not result in an increased supply of machines. Hence, the principle of acceleration depends upon very tough conditions that there shall be excess capacity in one industry (investment industry) but no excess capacity in other (consumer goods industries).
3. Capital output ratio: It is based on the assumption that there is a constant ratio of the output of consumer goods and capital equipment needed for their production. In reality thus ratio is not constant. Apart from the inventions and improvements in the technique of production, existing capital equipment may be worked more intensively. The capital output ratio also varies in different phases of the business cycle and does not remain constant.
4. Nature of demand: An increase in the demand for consumption goods must be more or less permanent in nature to have acceleration effects. A purely temporary increase in the demand for consumer goods will not lead to any addition in the capital goods. Durable capital goods are expensive and no producer will order capital goods that increases in demand in short level. This also shows that the acceleration is not based on merely technological factors but also no profit expectation.
5. Availability of resources: The working of acceleration principle is further impaired by the availability of resources and the ability of the machine making industry to produce more machines. In order that the increased demand for capital goods is followed by an increase in the production. There must be enough unemployed factors available for employment in the capital goods industries. This is possible only when there is widespread unemployment in the economy.
6. Elastic credit supply: The elastic supply of money and credit is another factor, which helps, in the smooth working of the acceleration principle. Whenever there is induced investment as a result of induced consumption, enough money and credit should be forthcoming for investment in investment goods industries. A scarcity of money and credit will raise the rate of interest and will make investment financed by borrowed funds easier. It is, therefore, essential that the rate of interest not be allowed to rise and that there is enough credit to allow for the acceleration effects to flow.

                You may also like to read:              

• The concept of Super Multiplier Theory | Marginal Propensity to Investment and Marginal Propensity to Consumption

• How monetary policy helps to control inflation? | What are the objectives/goals of fiscal policy of underdeveloped countries?

• Calculation of National Income and Difficulties in the Calculation of National Income

• National Income: Various concepts of National Income | Gross Domestic Product (GDP), Gross National Product (GNP)

• The dispute between Monetarism and Keynesianism