THE INVESTMENT FUNCTION

THE INVESTMENT FUNCTION

Meaning of Investment

            In Ordinary sense, investment means to buy shares, stocks, bonds and securities which are already existing in stock market. But, this is not real investment because it is simply a transfer of existing assets. Hence, this is called financial investment which does not affect aggregate spending. In Keynesian terminology, investment refers to real investment which adds to capital equipment increasing the production and purchase of capital goods. Thus, investment includes new plant and equipment, construction public works like dams, roads, buildings, etc. net foreign investment, inventories, and stocks and shares of new companies. In the words of Joan Robinson, "By investment is meant an addition to capital, such as occurs when a new house is built. Investment means making or a new factory is built. Investment means making an addition to the stock of goods in existence."

            Keynes again states that real investment means purchase of equities, bonds or securities of the companies to be newly set up. It means "addition to the existing stock of real capital assets". The essential condition is that investment should result in the construction of new capital assets, necessitating the employment of more labour and raw material.

            Investment function is related to private or induced investment. It implies inducement to invest or investment demand. For classical economists, investment demand was simply a decreasing function of rate of interest. I.e.,

               I = f (i)

Where,    i =rate of interest

and         I = investment

               It can be shown in figure below;

            In this figure, I_d I_d is investment demand curve. Rate of interest is measured along on OY-axis and investment on OX-axis. I_d I_d curve shows that there is inverse relationship between rate of interest and investment. Thus, investment is the function of rate of interest.

            According to Keynes, the volume of private investment depends upon two factors;

(i)   The marginal efficiency of capital (MEC) and

(ii) The rate of interest (i)

Thus,      I = f (r,i)

Where,    r = MEC

   However, in the modern theory, the investment is assumed to be the function of level of income. Other things remaining the same investment is the direct function of level of income. I.e.,

               I= f (Y)

Where,    Y= Level of income.

            As income increases, the investments will also increases and vice-versa. This modern investment function is shown in the following diagram.

            In the given figure, at Y₁ level of income, investment is I₁. When the level of income increases from Y₁ to y₂, investment increases from I₁ to I₂. It means that investment varies positively with the level of income. Thus, investment is the function of income.

Saving - Paradox of Thrift (Saving is a vice not virtue)

Paradox of Thrift (Saving is a vice not virtue)

            The classical economists considered saving to be a great virtue. They encouraged hard-work, maximum earning and minimum spending on consumption. They advised people to accumulate for future by maximizing earning and minimizing expenditure on consumption. Thinking aggregate savings as simply and aggregation of savings by individual members of the Community, they come to the conclusion that thriftiness improves the future of society. They also recognized that domestic saving was the major source of capital formation which is very necessary for economic progress.

            However, Keynes pointed out that when we consider the community as a whole, we can no longer assume that when community reduces its consumption, its income remains unchanged. The volume of saving defends upon the level of national income and the saving of the community can increase only when the total income of the community increases. Since expenditure of one person constitutes the income of another person, increase in savings of some individuals will lead to a decline in the incomes and hence expenditures of certain other individuals. Further, a decrease in demand for consumption goods in the economy will decrease the demand for capital goods. The decline in demand for consumption goods as well as for capital goods would lead to a decline in their prices and hence in profits. Declining Profits would discourage investment and thus result in a decline in income, output and employment. In short, a general reduction in consumption would cause a general defficiency of effective demand, leading to a lower level of equilibrium with considerable unemployment. Thus, though saving is a virtue for an individual, it is harmful for the society as a whole. Thus, 'saving is a vice but not virtue.

            So, saving decreases effective demand in the economy resulting a decrease in the price and profit. As a result, investors will be discouraged to invest. This will further decrease the employment, production and income which in turn decreases the saving. This will convert the saving into social evil. So, in the beginning saving is a virtue to the individual but to the society and the nation it will be harmful. Therefore, saving turns into misfortune. This is known as paradox of thrift.

            The paradox of thrift can be illustrated graphically as follows:

            Above given diagram is showing "paradox of thrift". In this diagram, income is along on OX-axis and saving and investment along on OY-axis. SS and II curve are the original saving and investment curves respectively. They intersect each other at point E and give us the equilibrium level of income OY at which savings are equal to investment. Now suppose savings in the community increase shifting the SS curve upwards to S₁S₁ which intersects the old II curve at E₁. This lead to a decline in income from OY to OY₁. The decrease in income from OY to OY₁, results in a reduction in the volume of savings from YE to Y₁E₁. Thus, the community's efforts to save more have actually led to a decrease in income as well as savings. If the community attempts to further increase savings which shifts the saving curve to S₂S₂, then the equilibrium level of income will decline so much that savings as well as investment would become negative. This explains the paradox that attempts to increase aggregate savings would actually lead to a decrease in savings. Therefore, 'saving is vice not virtue'.

saving - Income consumption and saving

Concept of Saving

            From an individual's point of view saving is that part of his income which is not spent on consumption. Similarly, from the community's point of view aggregate saving is that part of national income which is not spent on consumption. In other words, saving is excess of income over consumption expenditure, i.e., S=Y-C, where, S=saving, Y=income and C=consumption expenditure. In Keynes' general theory, current savings depend upon current income but Robertson believes that current savings are more a function of past income. According to Robertson, saving is that part of income received in the immediately proceeding period which is not spent on current consumption. According to J.M. Keynes- "Saving is the excess of income over consumption expenditure or the difference between income and expenditure on consumption". He has made current savings is to depend upon current income. That is, saving is that part of the income which is left after consumption. Hence, there is functional relationship between saving and income. Thus, saving function can be written as:

S= f(Y)

Where, S= Savings

Y= Income

            There is positive relationship between saving and income. This means higher the income, higher will be the saving and vice-versa. Saving is different from hoarding. Hoarding is a part of savings which is held as stock of money. It constitutes a leakage in the income stream. Concept of saving can be explained by the help of table and figure below: 

Schedule of Income consumption and saving

Income (Rs.) (Y)	Consumption (Rs.) (C)	Savings (Rs.) (S) = Y-C
O	0	-50
50	75	-25
100	100	0
150	125	25
200	150	50

    Above given schedule shows that people spend on consumption without any income. After increase in income, people start to save some amount of income for further purposes. So, there is direct relationship between income and saving. The saving function can also be shown in figure below:

            From above given figure, saving curve 'SS' shows that saving tends to increase when the income increases. Likewise, it also shows that saving is negative and zero at low level of income. So, saving curve starts downward from X-axis.

            There are various forms of saving, such as average propensity to save (APS) and marginal propensity to save (MPS) which are explained below:

(i)   Average propensity to save (APS):

            The ratio of saving and income is known as average propensity to save. APS is the counterpart of the average propensity to consume (APC). It can be expressed as;

APS = =

or, APS = 1-APC [^..^. APC + APS = 1]

(ii) Marginal propensity to save (MPS):

            Marginal propensity to save is the ratio between the change in saving and change in income. In other words, MPS is the change in saving as a result of change in income. It can be expressed as;

MPS =

Where, DS = Change in saving

 DS = Change in income

or,  MPS= 1- MPC [\MPS+MPC=1]

            It shows the relationship between MPC and MPS. As MPC increases MPS declines and vice-versa, i.e., higher the MPC implies lower the MPS.

Determinants of Saving

            Saving is an important function of individual and business organization. Everybody likes to save some parts of their income in the view of solving the possible problems that may occur in the future. But main determinant of saving is the level of income. Therefore, the higher the level of income, the higher is the possibility of saving. So, part of the income left over after the consumption expenditure of people is known as saving. The factors, which influence the amount and ratio of saving is called determinant of saving. The factors determining saving can be explained as follows:

(1) Income Level:

            Saving of every individual and business organization depends upon the level of income. Higher the level of income, higher will be the saving. This is because of marginal propensity to consume (MPC) of rich people with high income will be low while the marginal propensity to consume of poor people with low income will be high. Hence, possibility of saving increases as income increase of the people. So, saving is impossible without adequate level of income.

(2) Rate of Interest:

            Rate of interest is also an important determinant of saving. In general, there is positive relationship between saving and rate of interest, i.e., higher the rate of interest results the higher level of saving and vice-versa. Keynes stated the concept that low rate of interest will increase the propensity to consume. This is because people are encouraged to save in order to obtain a high rate while they are discouraged to save with low rate of interest.

(3) Price level:

            The price level of the goods in the market also influences the saving. The consumers may react to any rise or fall in the price level by spending either more or less of their income for goods and services. If the price level is high, less is left for saving. But, if the market price level is low, the consumers can get goods cheaper and increase the saving. Hence, we can say that the condition of inflation is not favorable for saving. 

(4) Fiscal Policy:

            The fiscal policy undertaken by the government also affects the saving. If the government increases the tax rate, then propensity to save will decrease. But on the other hand if tax rate is decreased, then the propensity to save of the people will increase.

            Fiscal policy adopted by government are of two types, i.e., expansionary and contractionary fiscal policy. Expansionary fiscal policy helps to rise saving where government reduced tax and increase government expenditure. Conversely, contractionary fiscal policy reduces the ratio of saving where government imposes high tax system and reduces the government expenditure.

(5) Distribution of Income:

            Distribution of income and wealth is also important determinants of saving. If distribution of national income and wealth is equal in the society, then the average propensity to consume will be high. But, if distribution of income and wealth is unequal, then average propensity to consume will be low because more part of income will be in the hands of a few people. In such a situation, their average and marginal propensity to consume will be very low.

(6) Social security:

            Social security system is also one of the main factors that determines the saving. The rate of saving will be very low in the country where various social security system are fully developed like pension to the retired government personnel, old-age allowance, handicapped and disabled allowance, unemployment allowance, widow allowance, medical insurance, etc. When social and economic security systems are appropriately available, then people will not  be worried about their future and try to enjoy with higher level of consumption,  which reduces saving. But on the other hand, if the government does not provide any kind of social securities in the own securities. For this, they will start saving and this will increase the propensity to save.

(7) Demonstration Effect:

            Demonstration effect is also one of the most important determinants of saving. The more the people get attracted to various advertisements and expensive foreign consumption goods, the more will be the consumption of such goods. This will result in the decrease in saving. On the other hand, if people of a country are not influenced by the demonstration effect, then the saving will be more.

            Betides these, the determinants of saving are; the development of banking and financial institutions, government policy of saving, economic structure, peoples desire in improving the living standard, etc. 

Revenues to a Price Taker A Firm in Pure Competition

Importance or Uses of Multiplier

            The introduction of multiplier analysis in income theory is regarded as one of path-breaking contributions of Keynes to the economic theory. It is not merely theoretical concept, but also important instrument of economic policy. The importance of multiplier can be explained as follows:

(1)  Importance in Investment:

            The concept of multiplier established the immense importance of investment as the major dynamic in pretence of investment as the major dynamic element in the economy. J.M. Keynes considers the theory of multiplier as an integral part of the theory of employment. The multiplier, he says, 'establishes a precise relationship, given the propensity to consume (MPC), between the aggregate employment and income and the rate of investment'. Thus, it underlines the importance of investment and explains the process of income propagation.

(2) Analysis of Trade Cycle:

            Cyclical fluctuations or business cycles characterized by alternating waves of expansion and contraction are the inherent features of market economies. The multiplier process by showing different phases of trade cycles helps the business to plan their transactions accordingly.

(3) Equality between Savings and Investment:

            It helps in bringing the equality between saving and investment. If there is a divergence between saving and investment, an increase in investment leads to a rise in income with the multiplier process by more than the increase in investment. As income increases, savings also increases and equals investment.

(4) Formulation of Economic Policy:

            The multiplier analysis is an important tool in the hands of modern governments in formulating economic policies and projecting their consequences. It can be used to estimate the quantitative government policy changes needed to smooth out some of the business cycles.

(5) Importance of Public Investment:

            The modern governments decide upon the amount of investment to be injected in to the economy so as to utilize the idle resources and remove unemployment. With the help of multiplier analysis policy makers project the required levels of investment to be made till the full employment level is reached.

(6) Deficit Financing:

            The multiplier principle highlights the importance of deficit financing. When the economy is reeling under a state of recession increased government spending through public investment programs, creates a budget deficit and helps in expanding income and employment by multiplier times the increase in investment.

            The above discussion reveals the importance of the multiplier in public investment policy and its assessment at various levels. Public investment refers to government spending on public works and other works meant to increase the public welfare. It is autonomous and free from profit motive. Thus, it applies with greater emphasis in overcoming inflationary and deflationary portents in the economy and in achieving and maintaining full employment.

Leakages of multiplier

           

In common practice, working of the multiplier is affected by a larger number of dynamic factors which work over time. Multiplier not goes on raising income indefinitely. This is because of there are several leakages from the income-stream as a result of which the process of income propagation is slowed down as time passes. All the income of the people is not fully used in consumption expenditure. Therefore, marginal propensity to consume is not 100%, i.e., 0<MPC<1.

            The incomes of people are influenced by various factors limiting the process of multiplier. That is, due to leakages in income flow, the effect of multiplier reduced. leakages are the potential diversions from the income-stream which tend to weak the multiplier effect of new investment. Given the marginal propensity to consume, the increase in income in each round declines due to leakages in the income-stream and ultimately the process of income propagation to gradually becomes smaller. Due to the leakages, the national income does not increase fully. So, leakages in various forms are the leakages of multiplier. The following are the important leakages:

(1) Saving:

            Saving is the most important leakage of the multiplier process of income propagation. Since the marginal propensity to consume is less than one, the whole increment in income is not spent on consumption. A part of it is saved which gradually becomes smaller of the income stream and the crease in income in the next round declines. Thus, the higher the MPS, the smaller the size of multiplier and the greater the amount of leakage out of income-stream, and vice-versa. For instance, if MPS=1/6, the multiplier is 6, according to the formula K=1/MPS; and the MPS of 1/3 gives a multiplier of 3.

(2)  Strong Liquidity preference:

            If people prefer to hoard the increased income in the form of idle cash balances to satisfy a strong liquidity preference for the transaction, precautionary and speculative motives, that will act as a leakage out of the income stream. As income increases people will hoard money in inactive bank deposits and the multiplier process is checked.

(3)  Purchase of old stocks and securities:

            If a part of the increased income is used in buying old stocks and securities instead of consumer goods, the consumption expenditure will fall and its cumulative effect on income will be less than before. In other words, the size of the multiplier will fall with a fall in consumption expenditure when people buy old stocks and shares. 

(4) Debt cancellation:

            If a part of increased income is used to repay debts to banks, instead of spending it for further consumption, that part of the income peters out of the income stream. In case, this part of the increased income is repaid to other creditors who save or hoard it, the multiplier process will be slowed down.

(5) Price Inflation:

            Price inflation constitutes another important leakage from the income stream of an economy. If due to increased investment the inflation increases then most part of the increased income will be used to pay for the increased price. This will affect the multiplier. Increase in the price of goods decreases the real consumption of the people. The price inflation is also one of the main leakages of multiplier.

(6) Net Imports:

            If increased income is spent on the purchase of imported goods, it acts as a leakage out of the domestic income stream. Such expenditure fails to effect the consumption of domestic goods. This argument can be extended to net imports when there is an excess of imports over exports thereby causing a net outflow of funds to other countries.

(7) Undistributed Profits:

            If profits accruing to joint-stock companies are not distributed to the share-holders in the form of dividend but are kept in the reserve fund, it is a leakage from the Income stream. Undistributed profits with the companies tend to reduce the income and hence further expenditure on consumption goods thereby weakening the multiplier process.

(8) Taxation:

            Taxation Policy is also an important factor in weakening the multiplier process. Progressive taxes have the effect of lowering the disposable income of the tax payers and reducing their consumption expenditure. Similarly, commodity taxation tends to raise the prices of goods, and a part of increased income may be dissipated on higher prices. Thus, increased taxation reduces the income stream and lowers the size of the multiplier.

            All these factors constitute potential leakages from the income stream resulting from an expansion of new investment. The new income under such circumstances, does not give rise to secondary consumption expenditures as much as it should. 

Assumptions of multiplier Macroeconomics

Assumptions of multiplier

            Keynes' theory of the multiplier works under certain assumptions which limit the operation of the multiplier. They are as follows:

(i)     The marginal propensity to consume is constant.

(ii)    There is a closed economy unaffected by foreign influences.

(iii)   Consumption is a function of current income.

(iv)    There are no time lags in the multiplier process.

(v)     There are no changes in prices.

(vi)    The economic situation should be less than full employment level. If there is already full employment, MPC will not be effective.

(vii)   The new level of investment is maintained steadily for the completion of the multiplier process.

(viii)  Consumer goods are available in response to effective demand for them.

(ix)    Other resources of production are also easily available within the economy.

(x)     There is net increase in investment. 

Multiplier - macroeconomics the concept

  

The concept of multiplier

            The concept of multiplier was first developed by R.F. Kahn in his article "The Relation of Home Investment to unemployment" in the Economic Journal of June 1931. Kahn's multiplier was the employment multiplier. Keynes took the idea from Kahn and formulated the Investment multiplier. So, the concept of multiplier is regarded as one of the important contributions of J.M. Keynes to economics. The economists before Keynes were not unaware of the effect of an increment in investment on the increment of income. For example, Knut Wicksell, for the first time, had used multiplier in the context of inflation. Similarly, N. Johanson had explained it in 1903. But, the economists before Keynes had not been able to explain the concept of multiplier in a clear way.

            Keynes used the concept of multiplier in the form of investment multiplier. According to Keynes, "Investment multiplier tells us that when there is an increment of aggregate investment, income will increase by an amount which is K times of the increment of investment", i.e., DY=K×DI, where Y is income, I is investment, D is change (increment or decrement) and K is the multiplier. Then the multiplier is expressed as;

K=  [ratio of change in income to the change in investment]

            The multiplier expresses a relationship between an initial increase in investment and final increase in aggregate income. So, the multiplier theory shows that how many times the income increases as a result of an initial increase in investment or it is the ratio of an increase of income to given increase in investment. For example, if increase in investment is made by Rs. 10 lakhs. As a result, after some time period the total income increases to Rs. 50 lakhs. The income has increased by five times. Hence, the multiplier is 5. In the multiplier theory, the important element is the multiplier coefficient, K which refers to the power by which any initial investment expenditure is multiplied to obtain a final increase in income.

·    Relationship Between the Multiplier and Marginal Propensity to Consume (MPC):

            The value of multiplier is determined by the marginal propensity to consume. The multiplier is large or small according as the marginal propensity to consume is large or small. Thus, higher the marginal propensity to consume, the higher is the value of multiplier, and vice-versa. The relationship between the multiplier and the marginal propensity to consume is as follows:

Total Income (Y) = Total consumption (C) + Total Investment (I)

or,  Y = C+I

or,  DY= DC+DI

or,  DI =DY-DC ---- ® (i)

Now,    by definition we know that

K=  or, DY= K. DI

or, DI =  ----® (ii)

Now substituting the value of DI from (ii) into (i), we get

 = DY- DC ----®(iii)

Further, dividing (iii) by DY, we get

= 1 -  ------®(iv)

or, Inverting (iv), we get

K =  =  =

            Since K stands for multiplier, DC/DY stands for marginal propensity to consume and 1- DC/DY stands for marginal propensity to save (MPS) The multiplier can also be derived from the marginal propensity to save (MPS) and it is the reciprocal of MPS, i.e., K=1/MPS. There is an inverse relation ship between multiplier and MPS. Higher the MPS, lower is the multiplier. Thus, the multiplier is directly related to MPC and inversely related to MPS.

            From this formula, we can compute the various values of the multiplier corresponding to various 'MPC' as follows:

DC/DY (MPC) [1-MPS]	DC/DY (MPS) [1-MPC]	K (multiplier coefficient) [K= = ]
0	1	1
1/2	1/2	2
2/3	1/3	3
3/4	1/4	4
4/5	1/5	5
8/9	1/9	9
9/10	1/10	10
1	0	¥(infinity)

            The table shows that the size of the multiplier varies directly with the MPC and inversely with the MPS. Since the MPC is always greater than zero and less than one (i.e., O<MPC<1), the multiplier is always between one and infinity (i.e., 1<K<¥). If the multiplier is one, it means that the whole increment of income is saved and nothing is spent because the MPC is zero. On the other hand, an infinite multiplier implies that MPC is equal to one and the entire increment of income is spent on consumption. It will soon lead to full employment in the economy and then create a limitless inflationary spiral. But these are rare phenomena. Therefore, the multiplier coefficient varies between one and infinity.

            The process of multiplier operation can be shown in figure below:

            In the figure, the 45º line represents OY income curve. C is the consumption curve having a slope of 0.5 to show the MPC is equal to one-half. C+I is the initial consumption and investment curve, which intersects the 45º line at point E, so point E is initial equilibrium point where aggregate income is equal to aggregate demand (C+I), in this condition equilibrium level of income is OY₁.

            Now, suppose that investment increases by DI, as a result C+I curve shifts upward to C+I+ DI curve. This curve intersects 45º line at the point E, which is the new equilibrium level where aggregate income also increased by DY level of income, i.e., which is double than the increase in investment.

            Multiplier works both in the forward direction as well as in the backward direction. If investment decreases, the multiplier operates in the reverse direction. A reduction in investment leads to contraction in income and consumption which causes cumulative decline in income. On the other hand, if consumption and investment increases, the multiplier operates in the positive direction. Thus, higher the MPC, the greater is the value of the multiplier and vice-versa.