Investment Multiplier: Definition, Example, Formula to Calculate

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What Is the Investment Multiplier?

In our two-sector model, a change in aggregate demand may be caused by a change in consumption expenditure business investment, or in both. 

Since consumption expenditure is a stable function of income, changes in income are primarily from changes in the autonomous components of aggregate demand, especially from changes in the unstable investment component. We shall now examine the effect of an increase in investment (upward shift in the investment

schedule) causing an upward shift in the aggregate demand function. But before this, let us know about the investment multiplier. It is a process of multiple increases in equilibrium income due to an increase in investment and how much increase occurs depends upon the marginal propensity to consume. The process of increase in national income due to an increase in investment is illustrated below.

an increase in autonomous investment by Al shifts the aggregate demand schedule from C+1 to C+1+Al. Correspondingly, the equilibrium shifts from E to and the equilibrium income increases more than proportionately from Yo to Y₁. Why and how does this happen? This occurs due to the operation of the investment multiplier.

Multiplier refers to the phenomenon whereby a change in an injection of expenditure will lead to a proportionately larger change (or multiple changes) in

the equilibrium level of national income. The investment multiplier explains how many times the equilibrium aggregate income increases as a result of an increase in autonomous investment. 

When the level of investment increases by an amount say al, the equilibrium level of income will increase by some multiple amounts, A Y. The ratio of AY to Al is called the investment multiplier, k.

The size of the multiplier effect is given by AY=KAI.

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For example, if a change in investment of 2000 million causes a change in national income of 6000 million, then the multiplier is 6000/2000 =3. Thus multiplier indicates the change in equilibrium national income for each rupee change in the desired autonomous investment. 

The value 3 in the above example tells us that for every 1 increase in desired autonomous investment expenditure, there will be? 3 increase in equilibrium national income. Multiplier, therefore, expresses the relationship between an initial increment in autonomous investment and the resulting increase in equilibrium aggregate income. 

Since the increase in national income (AY) is the result of an increase in investment (AI), the multiplier is called ‘investment multiplier.”

The process behind the multiplier can be compared to the ‘ripple effect’ of water. Let us assume that the initial disturbance comes from a change in autonomous investment (AI) of 500 units. 

The economy being in equilibrium, an upward shift in aggregate demand leads to an increase in national income which in a two-sector economy will be, by definition, distributed as factor incomes. There will be an equal increase in disposable income. 

Firms experience increased demand and as a response, their output increases. Assuming that MPC is 0.80, consumption expenditure increases by 400, resulting in an increase in production. 

The process does not stop here; it will generate a second round of increase in income. The process further continues as an autonomous rise in investment leads to induced

increases in consumer demand as income increases.

We find at the end that the increase in equilibrium income per rupee increase in investment is:

3-MPC MTS (2.12)

From the above, we find that the marginal propensity to consume (MPC) is the determinant of the value of the multiplier and that there exists a direct relationship between MPC and the value of the multiplier. The higher the MPC more will be the value of the multiplier, and vice-versa. 

On the contrary, the higher the MPS, the lower the value of the multiplier and vice-versa. The maximum value of the multiplier is infinity when the value of MPC is 1 i.e. the economy decides to consume the whole of its additional income. We conclude that the value of the multiplier is the reciprocal of MPS.

For example, if the value of MPC is 0.75, then the value of the multiplier as per (2.11) is:

1-MPC025=4

The multiplier concept is central to Keynes’s theory because it explains how shifts in investment caused by changes in business expectations set off a process that causes not only investment but also consumption to vary. The multiplier shows how shocks to one sector are transmitted throughout the economy.

An increase in income due to an increase in initial investment, does not go on endlessly. The process of income propagation slows down and ultimately comes to a halt.

The causes responsible for the decline in income are called leakages. Income that is not spent on currently produced consumption goods and services may be regarded as having leaked out of the income stream.

If the increased income goes out of the cycle of consumption expenditure, there is a leakage from the income stream which reduces the effect of the multiplier. The more powerful these leakages are the smaller will be the value of the multiplier. The leakages are caused by to:

1. Progressive rates of taxation which result in no appreciable increase in consumption despite the increase in income

2. High liquidity preference and idle saving or holding of cash balances and an equivalent fall in marginal propensity to consume

3. Increased demand for consumer goods being met out of the existing stocks or through imports

4. Additional income spent on purchasing existing wealth or purchase of government securities and shares from shareholders or bondholders

5. undistributed profits of corporations

6. Part of the increment in income used for payment of debts

7. In case of full employment additional investment will only lead to inflation, and

8. Scarcity of goods and services despite having high MPC

The MPC, on which the multiplier effect of an increase in income depends, is high in underdeveloped countries; but ironically the value of the multiplier is low. Due to structural inadequacies, an increase in consumption expenditure is not generally accompanied by an increase in production. E.g. increased demand for industrial goods consequent on increased income does not lead to an increase in their real output; rather prices tend to rise.

An important element of Keynesian models is that they relate to short-period equilibrium and contain no dynamic elements. There is nothing like Keynesian macroeconomic dynamics. When a shock occurs, for example when there is a change in autonomous investment due to a change in some variable, one equilibrium position can be compared with another as a matter of comparative statics. There is no link between one period and the next and no provision is made for an analysis of processes through time.

Aggregate demand in the three-sector model of the closed economy (neglecting foreign trade) consists of three components namely, household consumption (C), desired business investment demand (1), and the government sector’s demand for goods and services(G). Thus in equilibrium, we have

Y = C+I+G (2.13)

Since there is no foreign sector, GDP and national income are equal. As prices are assumed to be fixed, all variables are real variables and all changes are in real terms. To help interpret these conditions, we turn to the flowchart below. Each of the variables in the model is a flow variable.

The three-sector, three-market circular flow model which accounts for government intervention highlights the role played by the government sector. From the above flow chart, we can find that the government sector adds the following key flows to the model:

i) Taxes on households and business sector to fund government purchases

ii) Transfer payments to the household sector and subsidy payments to the business sector

iii) The government purchases goods and services from the business sector and factors of production from the household sector, and

iv) Government borrowing in financial markets to finance the deficits occurring when taxes fall short of government purchases However, unlike in the two-sector model, the whole of national income does not return directly to the firms as demand for output.

There are two flows out of the household sector in addition to consumption expenditure namely, saving flow and the flow of tax payments to the government. These are actually leakages. The saving leakage flows into financial markets, which means that the part that is saved is held in the form of some financial asset (currency, bank deposits, bonds, equities, etc.). 

The tax flow goes to the government sector. The leakages that occur in the household sector do not necessarily mean that the total demand must fall short of output. There are additional demands for output on the part of the business sector itself for investment and from the government sector. In terms of the circular flow, these are injections. 

The investment injection is shown as a flow from financial markets to the business sector. The purchasers of the investment goods, typically financed by borrowing, are actually the firms in the business sector themselves. Thus, the amount of investment in terms of money represents an equivalent flow of funds lent to the business sector.

The three-sector Keynesian model is commonly constructed assuming that government purchases are autonomous. This is not a realistic assumption, but it will simplify our analysis. Determination of income can also be explained with the help of aggregate demand and aggregate supply

AD=C+I+G

AS = C+S+T

The equilibrium national income is determined at a point where both aggregate demand and aggregate supply are equal, that is,

AD = Y = AS

C+1+G=Y= C + S+T

The variables measured on the vertical axis are C, I and G. The autonomous expenditure components namely, investment and government spending do not directly depend on income and are exogenous variables determined by factors outside the model. You may observe that in panel B , the lines that plot these autonomous expenditure components are horizontal as their level

does not depend on Y. Therefore, the C + 1 + G schedule lies above the consumption function by a constant amount.

The line S + T in the graph plots the value of savings plus taxes. This schedule slopes upwards because saving varies positively with income. Just like government spending, the level of tax receipts (T) is decided by policymakers.

The equilibrium level of income is shown at the point E where the (C + 1 + G) schedule crosses the 45° line, and aggregate demand is therefore equal to income (Y). In equilibrium, it is also true that the (S+T) schedule intersects the (1 +G) horizontal schedule.

We shall now see why other points on the graph are not points of equilibrium. Consider a level of income below Y. We find that it generates consumption as shown along the consumption function. When this level of consumption is added to the autonomous expenditures (1 + G), aggregate demand exceeds income; the (C + 1 + G) schedule is above the 45° line. 

Equivalently at this point, I + G is greater than S + T, as can be seen in panel B With demand outstripping production, desired investments will exceed actual investment and there will be an unintended inventory shortfall and therefore a tendency for output to rise. Conversely, at levels of income above Y₁, output will exceed demand; people are not willing to buy all that is produced. 

Excess inventories will accumulate, leading businesses to reduce their future production. Employment will subsequently decline and output will fall back to the equilibrium level. It is only at Y that output is equal to aggregate demand; there is no unintended inventory shortfall or accumulation and, consequently, no tendency for output to change.

 An important thing to note is that the change in total spending, followed by changes in output and employment, is what will restore equilibrium in the Keynesian model, not changes in prices.

The Government Sector and Income Determination

We have seen above that the government influences the level of income through taxes, transfer payments, government purchases, and government borrowing. A comprehensive discussion on the effect of government fiscal policy is beyond the scope of this unit; and therefore, we shall look into a few variables.

(i) Income Determination with Lump Sum Tax

We assume that the government imposes lump sum tax, i.e. taxes that do not depend on income, has a balanced budget (G=T), and that there are no transfer payments. The consumption function is defined as -1.82

C = a + bYd

Where Ya = Y -T (disposable income), T = lump sum tax Y= a + b (Y-T) + 1 + G

Y = 1-6 (a−bT+1+G)

The four sector model includes all four macroeconomic sectors, the household sector, the business sector, the government sector, and the foreign sector. The foreign sector includes households, businesses, and governments that reside in

other countries. The following flowchart shows the circular flow in a four-sector economy.

In the four-sector model, there are three additional flows namely: exports, imports, and net capital inflow which is the difference between capital outflow and capital inflow. The C+1+G+(X-M) line indicates the aggregate demand or the total planned expenditures of consumers, investors, governments, and foreigners (net exports) at each income level.

In equilibrium, we have

Y=C+1+G+ (X-M) (2.14)

The domestic economy trades goods with the foreign sector through exports and imports. Exports are the injections in the national income, while imports act as leakages or outflows of national income. Exports represent foreign demand for domestic output and therefore, are part of aggregate demand. 

Since imports are not demands for domestic goods, we must subtract them from aggregate demand. The demand for imports has an autonomous component and is assumed to depend on income. Imports depend upon marginal propensity to import which is the increase in import demand per unit increase in GDP. 

The demand for exports depends on foreign income and is therefore exogenously determined and autonomous. Imports are subtracted from exports to derive net exports, which is the foreign sector’s contribution to aggregate expenditures. 

Since import has an autonomous component (M) and is assumed to depend on income(Y) and marginal propensity to import (m), the import function is expressed as M= M + mY. Marginal propensity to import m = A M/A Y is assumed to be constant.

As noted above, the equilibrium level of national income is determined at the level at which the aggregate demand is equal to the aggregate supply. As the aggregate demand in the four-sector model is given in equation 2.14, the equilibrium condition is expressed as follows-

Y=C+I+G+(X-M)

Where C = a + b(Y-T)

M= M + MY

The equilibrium level of National Income can now be expressed by –

Y=C+I+G+(X-M)

Y = a+b (Y-T) + 1 + G + X-M - mY

Y- by + mY = a- bT+1+G+X-M

Y = (a- b T+I+G+X-M)

1-b+m

The economy being in equilibrium, suppose the export of the country increases by A X autonomously, all other factors remaining constant. By incorporating the increase in exports by AX, the equilibrium equation of the country can be expressed as

Y+AY= (a-b T+ 1+ G + X-M+ AX) or 1-b+m

1-b+m

Y+AY = 1 (a- bT+I+G+X-M) +AX 1-b+m

As, Y=1(a- bT+I+G+X-M)

I-b + m

We get, Y + AY =Y+= 1 AX 1-b+m

Subtracting Y from both sides, we get AY = ______AX 1-b+m

By rearranging AY = 1AX, we get 1-b+m

AY 1

AX 1-b+m

Or alternatively written as

AY 1

AX 1-(b-m)

The term 1-b+m is known as foreign trade multiplier whose value is determined by marginal propensity to consume (b) and marginal propensity to import (m).

If in the model proportional income tax and government transfer payments are incorporated, then only the denominator of the multiplier will change. If income tax is of form T=T+tY where T is constant lump-sum, t is the proportion of income tax, and TR > 0 and autonomous, then the four-sector model can be expressed as:

Y = C + I+G+ (X-M)

Where C = a + b(Y- T – tY + TR)

M= M + mY.

The equilibrium level of National Income can now be expressed as:

1 1-b(1-1)+m Y = (a-b7+b TR+1+G+X-M) 

We shall explain income determination in the four-sector model.

Equilibrium is identified as the intersection between the C+1+G+(X-M) line and the 45-degree line. The equilibrium income is Y. From panel B, we find that the leakages(S+T+M) are equal to injections (1+G+X) only at the equilibrium level of income.

We have seen above that only net exports (X-M) are incorporated into the four-sector model of income determination. We know that injections increase the level of income and leakages decrease it. Therefore, if net exports are positive (X > M), there is a net injection and national income increases. Conversely, if X<M, there is net withdrawal and national income decreases.

We find that when the foreign sector is included in the model (assuming M > X), the aggregate demand schedule C+1+G shifts downward with the equilibrium point shifting from F to E. The inclusion of the foreign sector (with M > X) causes a reduction in national income from Yoto Y₁. 

Nevertheless, when X > M, the aggregate demand schedule C+1+G shifts upward causing an increase in national income. Learners may infer diagrammatic expressions for possible changes in equilibrium income for X>M and X = M.

We have seen in section 2.5 above that equilibrium income is expressed as the product of two terms: AY = k Al; i.e. the level of autonomous investment expenditure and the investment multiplier. 

The autonomous expenditures multiplier in a four-sector model includes the effects of foreign transactions and is stated as (1-b+m) where ‘m’ is the propensity to import which is greater than ze You may recall that the multiplier in a closed economy

The greater the value of ‘m’, the lower will be the autonomous expenditure multiplier. The more open an economy is to foreign trade, (the higher mis) the smaller the response of income to aggregate demand shocks, such as changes in government spending or autonomous changes in investment demand A change in autonomous expenditures- for example, a change in investment spending, will have a direct effect on income and an induced effect o consumption with a further effect on income. 

The higher the value of m, the larger the proportion of this induced effect on demand for foreign, not domestic, consumer goods. Consequently, the induced effect on demand for domestic goods and hence on domestic income will be smaller. The increase in imports per unit of income constitutes an additional leakage from the circular flow of (domestic

income at each round of the multiplier process and reduces the value of the autonomous expenditure multiplier.

An increase in demand for exports of a country is an increase in aggregate demand for domestically produced output and will increase equilibrium income just as an increase in government spending or an autonomous increase in investment. 

In summary, an increase in the demand for a country’s exports has an expansionary effect on equilibrium income, whereas an autonomous increase in imports has a contractionary effect on equilibrium income. However, this should not be interpreted to mean that exports are good and imports are harmful in their economic effects. 

Countries import goods that can be more efficiently produced abroad, and trade increases the overall efficiency of the worldwide allocation of resources. This forms the rationale for attempts to stimulate the domestic economy by promoting exports and restricting imports.

CONCLUSION

According to the Keynesian theory of income and employment, national income depends upon the aggregate effective demand. If the aggregate effective demand falls short of that output at which all those who are both able and willing to work are employed, it will result in unemployment in the economy. 

Consequently, there will be a gap between the economy’s actual and optimum potential output. On the contrary, if the aggregate effective demand exceeds the economy’s full employment output (production capacity), it will result in inflation. Nominal output will increase, but it simply reflects higher prices, rather than additional real output. 

It is not necessary that the equilibrium aggregate output will also be the full employment aggregate output. It is undesirable and a cause of great concern for society and government if a large number of people remain unemployed. In the absence of government policies to stabilize the economy, incomes will be unstable because of the instability of investment. 

Full employment could be maintained in a capitalist economy only if governments are willing to incur countercyclical budgetary deficits to offset the inbuilt tendency towards private over-saving. By making appropriate changes in government spending (G) and taxes, the government can counteract the effects of shifts in investment. 

Appropriate changes in fiscal policy by adjusting government expenditure and taxes could keep the autonomous expenditure constant even in the face of undesirable changes in investment.

SUMMARY

John Maynard Keynes in his masterpiece The General Theory of Employment Interest and Money’ published in 1936 put forth a comprehensive theory to explain the determination of equilibrium aggregate income and output in an economy.

The equilibrium analysis is best understood with a hypothetical simple two-sector economy that has only households and firms with all prices (including factor prices), supply of capital, and technology constant; the total income produced Y, accrues to the households and equals their disposable personal income.

The equilibrium output occurs when the desired amount of output demanded by all the agents in the economy exactly equals the amount produced in a given time period.

In the two-sector economy, aggregate demand (AD) or aggregate expenditure consists of only two components: aggregate demand for consumer goods and aggregate demand for investment goods, / being determined exogenously and constant in the short run.

The consumption function expresses the functional relationship between aggregate consumption expenditure and aggregate disposable income, expressed as C = f (M). The specific form consumption function, proposed by Keynes C = a + by

The value of the increment to consumer expenditure per unit of increment to income (b) is termed the Marginal Propensity to Consume (MPC).

The Keynesian assumption is that consumption increases with an increase in disposable income (b>0), but that the increase in consumption will be less than the increase in disposable income (b <1).

The propensity to consume refers to the proportion of the total and the marginal incomes that people spend on consumer goods and services.

The proportion or fraction of the total income consumed is called ‘average propensity to consume (APC)= Total Consumption /Total Income

• Since Y = C + S, consumption and saving functions are counterparts of each other. The condition for national income equilibrium can thus be expressed as C + 1 = C + S

Changes in income are primarily from changes in the autonomous components of aggregate demand, especially from changes in the unstable investment component.

The investment multiplier k is defined as the ratio of change in national income (AY) due to change in investment (AI)

The marginal propensity to consume (MPC) is the determinant of the value of the multiplier. The higher the marginal propensity to consume (MPC) the greater the value of the multiplier.

The more powerful the leakages are, the smaller the value of the multiplier.

Aggregate demand in the three-sector model of the closed economy (neglecting foreign trade) consists of three components namely, household consumption (C), desired business investment demand (1), and the government sector’s demand for goods and services(G).

The government sector imposes taxes on households and the business sector affects transfer payments to the household sector and subsidy payments to the business sector, purchases goods and services, and borrows from financial markets.

In equilibrium, it is also true that the (S+T) schedule intersects the (I + G) horizontal schedule.

• Taxes act as leakage from the economic system. Thus, tax multiplier when, T-T-ty, is 1-b(1-1) (1-b)

The four-sector model includes all four macroeconomic sectors, the household sector, the business sector, the government sector, and the

foreign sector and in equilibrium, we have Y = C+1+G+(X-M)

The domestic economy trades goods with the foreign sector through exports and imports.

Imports are subtracted from exports to derive net exports, which is the foreign sector’s contribution to aggregate expenditures. If net exports are positive (X > M), there is a net injection, and national income increases. Conversely, if X<M, there is net withdrawal and national income decreases.

The autonomous expenditure multiplier in a four-sector model includes the effects of foreign transactions and is stated as a closed economy. (1-b+m) against (-b) in a

The greater the value of m, the lower will be the autonomous expenditure multiplier.

An increase in the demand for exports of a country is an increase in aggregate demand for domestically produced output and will increase equilibrium income just as would an increase in government spending or an autonomous increase in investment.

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