10

Theories of Investment Spending

INTRODUCTION

One of the most important components of the GNP is investment. In the earlier chapters of the simple model of income determination, investment was assumed to be given at some particular level. This chapter analyses the relationship between investment and the rate of interest and also the responsiveness of investment to the rate of interest.

 

Investment expenditure constitutes an extremely volatile component of the aggregate demand. The fluctuations in investment cause fluctuations in the production and income levels. They are responsible for much of the business cycles. In this chapter, we attempt at determining the factors that influence the investment decisions. We also examine some of the theories of investment spending.

 

BASIC CONCEPTS

Before we embark on our analysis of investment, we will discuss some of the concepts relating to investment.

Investment

Capital is the accumulated stock of plant and equipment, which is held by the business firms. It is the stock of the productive facilities, which are available to produce the output. Hence, capital is a stock concept. On the other hand, investment is a flow concept. In the simplest terms, investment can be defined as the value of that portion of an economy’s output for any period of time that takes the form of new producer’s durable equipment, new structures and the change in inventories. It is the flow of spending, which makes an addition to the physical stock of capital. In the long run, it is investment that determines the stock of capital and hence the long-run growth in the economy. It is to be noted that compared to the stock of capital, the flow of investment is quite small.

In Chapter 3, investment expenditure was defined as consisting of goods and services bought for use in the future. It was grouped into three categories: (i) business fixed investment is the purchase of new plant and equipment by firms, (ii) residential investment is the purchase of new housing by households and others, and (iii) inventory investment is the change in the inventory of goods by the firm. The present chapter focuses on, specifically, the business fixed investment.

It is obvious that different factors influence the different types of investment. Thus, there can be no single investment theory which is applicable to all the different types of investment.

Gross and Net Investment

Investment can be in net terms or in gross terms. Gross investment consists of two parts: the replacement investment, which is required to keep the capital stock intact and the net investment that is required to expand the existing capital stock. To arrive at net investment, a deduction is made from gross investment for producer’s durable equipment and the existing structures that are used in the production process. Net investment is equal to gross investment minus depreciation. In fact, net investment is an accretion to the stock of capital.

 

If in a particular period of time,

1. the gross investment is equal to the amount of capital that is used up in that particular period, (in other words the cumulative depreciation thereon) then there will no net investment.
2. the gross investment is greater than the amount of capital that is used up in that particular period, then there will be positive net investment that involves an increase in the stock of capital.
3. the gross investment is smaller than the amount of capital that is used up in that particular period, then there will be negative net investment or in other words there will be a disinvestment. This involves a reduction in the stock of capital.

Other things remaining unchanged, for example, given the labour force, technology and natural resources, an accretion to the stock of capital increases the economy’s productive capacity. However, in practice as the stock of capital increases the other things do not remain unchanged. But it is necessary to separate the growth in the other factors if one wishes to isolate the effect of the growth of capital stock on the potential output. Thus, for the sake of convenience we assume that all the variables like labour force, technology and natural resources are assumed to be constant. Hence, we can associate all the increases in the capital stock with increases in the productive capacity of an economy.

Public and Private Investment

It is important to differentiate between public investment and private investment. Public investment refers to the investment in the public sector and private investment refers to the investment in the private sector. The motivating factor behind public investment is social welfare where as private investment is guided by the profit motive. Our analysis primarily relates to the private investment.

 

Induced and Autonomous Investment

Investment can be divided into two categories:

Induced Investment

In general, the investment function can be expressed as

 

I = I (Y, i)

 

where,	I = investment
	Y = income level
	i  = rate of interest

 

While investment is positively related to the income level, there is a negative relationship between investment and the rate of interest. Investment that changes due to a change in income and the interest rate is called induced investment.

In the short run as income remains more or less constant, the investment function can be expressed as

 

I = I(i)

Autonomous Investment

Investment that does not change due to a change in income and the interest rate is called autonomous investment. This is the investment that depends on the other factors like inventions, population and future expectations. While most of the investments in the public sector are autonomous as they are made for considerations other than profit, some of the investments in the private sector may also be autonomous.

 

• In the long run, it is the investment that determines the stock of capital and hence the long-run growth in the economy.
• We can associate all the increases in the capital stock with increases in the productive capacity of an economy.
• Most of the investments in the public sector are autonomous as they are made for considerations other than profit, some of the investments in the private sector may also be autonomous.

THE DECISION TO INVEST

The decision to invest is different as compared to the decision to buy consumer goods. This is due to the following reasons:

1. A firm must make a decision whether to go for capital expansion or buy an existing asset like equity in another company.
2. Most of the capital goods have a long life and one can learn only several years later as to whether the investment in these capital goods has been profitable or not.
3. When a firm has decided to expand, it will have to decide as to whether the cost of borrowing is greater than the return expected on the new investment undertaken by the firm.

A firm’s investment decision is based on the relationship between three elements:

1. Expected income flow from capital good under consideration: As the future is uncertain, a crucial decision for the firm in making its investment decision is regarding two aspects:
   1. An estimate of the future flow of income that the capital asset under consideration is expected to yield over its entire life.
   2. The expected life of the capital good, which may last more than expected or may become obsolete before its lifetime due to technological advancements.
2. The purchase price of the good in question: Often, there exists an uncertainty regarding the price at which the good is to be purchased. This is more for projects where new machines and equipment are involved and where the cost may undergo change over time.
3. The rate of interest prevailing in the market which again is subject to fluctuations.
   It is important to note that any calculations that relate to the future must take into consideration the fact that the returns over the future have a much lower worth as compared to the same returns today. While making an investment decision relating to the future, a calculation may be made regarding the present value of the capital asset and the discounted rate of return on the asset.

Present Value of a Capital Asset and Discounting

To make its investment decision, a firm compares the present value of the capital asset with its purchase price or the supply price.

The supply price of a capital asset is the cost of replacing the capital asset, which is under consideration, with a new one.

 

The present value of a capital asset is the sum obtained after discounting the expected future yields over its entire life at the market rate of interest. The higher is the market rate of interest the lower is the present value. In the extreme case if the market rate of interest is zero, then the present value is equal to the expected future yield.

The discounting process is the process by which a future sum is converted into its present value. It is just the reverse of the process by which a sum of money grows as it is invested in the future.

 

Suppose that an amount R₀ is invested for a period of one year at a market rate of interest, r. The amount the individual will receive at the end of year 1:

Suppose that the amount R₁ is invested for a period of another year.

The amount the individual will receive at the end of year 2:

 

	R1 = R1 (1 + r)
But	R1 = R0 (1 + r)
Thus,	R2 = R0 (1 + r)(1 + r) = R0(1 + r)2

If R₂ is invested for a period of another year, then at the end of year 3 the individual will receive:

 

R₃ = R₀ (1 + r)³

In general if an amount R₀ is invested for a period of n years at a market rate of interest, r, the amount the individual will receive at the end of the n years:

Equation (1) can be written as

where,

 

(1 + r) = discount rate

= the discounted present value of R₁

Numerical Illustration 1

Suppose that Rs. 100 is to be received by an individual after a period of 1 year. The market rate of interest is 10 per cent. How much must he invest today.

Solution

The discounted present value of Rs. 100 is

This implies that to get a sum of Rs. 100 at the end of 1 year, Rs. 90.91 must be invested today at an interest rate of 10 per cent.

Equation (2) can be written as

Where,

 

(1 + r) = discount rate

= the discounted present value of R_n

We consider the determination of the present value of a bond. A bond yields a yearly income, say R, until it reaches maturity at the end of n years when it returns the principal amount, P. the present value of the bond is

Alternatively, a machine is expected to yield an income stream of R₁, R₂, R₃,…, R_n over a period of its entire life. At the end, it has a scrap value of J. The market rate of interest is r. The present value of the returns from the machine is

Numerical Illustration 2

Suppose the annual expected returns from a machine are Rs. 35,000 over a period of 5 years, which is the expected economic life of the machine. The scrap value of the machine is Rs. 20,000. The market rate of interest is 10 per cent. The cost of the machine is Rs. 100,000. Find the present value of the expected returns from the machine. Is it profitable to invest in the machine.

Solution

The present value of the expected returns from the machine is

V = 31,818 + 28,925 + 26,296 + 23,905 + 21,732 + 12,418 = 1,45,904

As the discounted present value of the returns from the machine is Rs. 1,45,904 which is greater than the cost of the machine, Rs. 1,00,000 the investment in the machine is profitable.

The Marginal Efficiency of Capital

Till now we have focused on the determination of the present value of a given income stream and the market rate of interest. We now assume that we are given the following:

1. The income stream from the capital asset, R₁, R₂, R₃…, R_n
2. The cost or purchase price of the capital asset, C.

We wish to find the rate of interest that will make the cost or purchase price of the capital asset equal to the present value of a given income stream. Thus, given C and R₁, R, R,… R_n we wish to find i, which is the rate of return expected from a particular capital asset. It is also called the marginal efficiency of capital, MEC. Thus,

Numerical Illustration 3

Suppose the income stream from an investment project is R₁ = Rs. 500 million, R₂ = Rs. 600 million, R₃ = Rs. 600 million, R₄, = Rs. 400 million and R₅ = Rs. 400 million. The cost of the machine is Rs. 2000 million. Find the internal rate of return.

Solution

The marginal efficiency of capital is

We get the internal rate of return (IRR), i = 8.397 per cent, or in other words, the MEC as 8.397 per cent. Hence, if market rate of interest is greater than 8.397 per cent, the project is not profitable and hence not acceptable. If the cost of borrowing funds is lower than the IRR threshold of 8.397 per cent, the project can be taken up.

It is important to note that:

1. For a given level of the income stream the higher the cost or purchase price of the capital asset, C the lower is the value of i, the marginal efficiency of capital.
2. For a given level of the income stream the lower the cost or purchase price of the capital asset, C the higher is the value of i, the marginal efficiency of capital.

Once the MEC is determined, a comparison of the market rate of interest with the MEC will enable one to make a decision whether the investment in the capital asset is profitable or not. The level of r determines whether the capital asset will be purchased or not, given the MEC. However, r does not, in any way, determine the MEC of the capital asset.

The difference between the MEC and the market rate of interest is the net rate of return expected after allowance is made for all costs. Though both the MEC and r are percentages, they are totally different.

The MEC will increase when:

1. Given an unchanged price of the capital good, business expectations improve leading to an upward revision of the expected income flow from the capital asset.
2. There is a decrease in the purchase price of the capital asset, and no change in the expected income flow from the capital asset.

The MEC will decrease when:

1. Given an unchanged price of the capital good, business expectations worsen leading to a downward revision of the expected income flow from the capital asset.
2. There is an increase in the purchase price of the capital asset, and no change in the expected income flow from the capital asset.

Hence, we find that the basic rule for making a decision is that:

1. If the MEC is greater than the market rate of interest, then the purchase of the capital asset is worthwhile.
2. If the MEC is smaller than the market rate of interest, then the purchase of the capital asset is not worthwhile.

The Marginal Efficiency of Capital Schedule and the Rate of Investment

A firm has, often, variety of investment projects among which it has to make a choice. These may involve new projects or even the expansion of existing buildings and purchase of more equipment of a similar type. In making its decision, a firm will compare the MEC of the capital asset with the current market rate of interest. Once it has estimated the MEC from all the projects, the firm’s MEC would be as shown in Figure 10.1.

Figure 10.1 The Marginal Efficiency of Capital Schedule

Figure 10.2 The Aggregate Marginal Efficiency of Capital Schedule

In Figure 10.1, a firm can invest in four different projects. Project 1 requires an investment of 20 crores with an MEC of 10 per cent. Project 2 involves an investment of 15 crores with an MEC of 8 per cent. Project 3 requires an investment of 10 crores with an MEC of 6 per cent. Project 4 involves an investment of 5 crores with an MEC of 4 per cent. If the market rate of interest is 6 per cent the firm will invest in projects 1, 2 and 3 a total investment of 45 crores. Once the investment has increased to the point where the last project yields an MEC that equals the market rate of interest the firm will stop with its expansion drive unless there is a further change in the market rate of interest. The firm has achieved its desired capital stock. For an individual firm, the lower is the rate of interest the higher is its investment expenditures.

For every firm, the MEC schedule will resemble the stair like curve shown in Figure 10.1 with an obvious difference in the heights and the lengths of the steps depending on the investment opportunities available to the firm. However once the MEC’s for all the firms are added together horizontally, the steps would all even out and we can arrive at the aggregate MEC schedule as shown in Figure 10.2. The aggregate MEC schedule slopes downwards from left to right. The economy is in equilibrium at the point where the aggregate MEC equals the rate of interest. Thus, the equilibrium aggregate stock of capital is determined and there is no net investment and disinvestment. This equilibrium stock of capital is the desired stock of capital.

The determination of the equilibrium amount of investment has been depicted in Figure 10.3. Given a market rate of interest equal to 10 per cent, the equilibrium point will be at point E with the capital stock at I*. It is determined at the intersection of the aggregate MEC schedule and the curve representing the rate of interest.

A decrease in the rate of interest will lead to a larger investment where as an increase in the rate of interest will lead to a smaller investment.

The Marginal Efficiency of Investment

In Figure 10.3, we had focused on the determination of the equilibrium amount of investment. At a market rate of interest of 10 per cent, the equilibrium amount of capital stock was I*. This is the profit maximizing stock of capital where there is no net investment and disinvestment.

 

A decrease in the rate of interest to 7 per cent will lead to a larger profit, maximizing stock of capital at I₁ in Figure 10.3. This implies that there is a need to increase the capital stock to I₁, a net investment of I₁ – I*. How much time will be required for the firms to increase the capital stock from I* to I₁? This is a crucial question and needs considerable attention.

There can be two totally diverse situations:

Figure 10.3 Determination of the Equilibrium Investment

1. The capital goods industry has unlimited capacity with a supply curve, which is perfectly elastic. In such a case, the net investment will increase at a faster rate and the optimum capital stock will be achieved quickly.
2. The capital goods industry has limited capacity with a supply curve, which is upward sloping. The marginal costs increase as the level of output increases, which leads to increasing prices of the capital goods. In such a case due to the increasing prices of the capital goods, the rate of investment will slow down and thus more time will be taken to achieve the optimum capital stock.

   When we were analysing the investment expenditures by a single firm, we could increase the capital stock overnight because the capitals goods industry may be able to cater to the increased demands of a single firm at short notice and without much increase in the price of the capital goods. However, when all the firms in the industry increase their stock of capital the capitals goods industry will not only take a long time to produce the additional output but it may have to install extra capacity which may lead to increased costs and thus increase in price of the capital goods.

It is necessary at this stage of our analysis to distinguish between the marginal efficiency of capital and marginal efficiency of investment. The marginal efficiency of investment schedule depicts the relationship between the economy’s investment and rate of interest when the change in the price of capital goods is taken into consideration.

Figure 10.4 Marginal Efficiency of Capital Schedule and Marginal Efficiency of Investment Schedule

Figure 10.4 distinguishes between the marginal efficiency of capital and marginal efficiency of investment schedules.

1. When the rate of interest is 10 per cent, all the firms taken as a group decide to only replace worn out capital and not go in for any new investments. Thus, net investment is zero. The capital goods price remains unchanged. Thus, MEC equals MEI at a rate of interest of 10 per cent.
2. When the rate of interest decreases to 7 per cent, given the price of capital goods, all the firms taken as a group decide to not only replace worn out capital but to increase the new investment to I₁'. Thus, net investment is now greater than zero. As all the firms decide to increase their investment simultaneously, there is an increase in the demand for the capital goods which leads to an increase in their price. This leads to a decrease in the MEC or the internal rate of return for all the new investments. Hence, the firms reduce their investment to I₁ instead of I₁'. This is clearly the result of an increase in the price of capital goods. Thus, given a market rate of interest equal to 7 per cent the equilibrium point will be at point A (and not point C) with the capital stock at I₁. This gives one point on the MEI schedule.
3. Similarly, if the rate of interest falls to 5 per cent the equilibrium point will be at point B with the capital stock at I₂. This gives another point on the MEI schedule.
   By joining such points we can arrive at the MEI schedule, which represents the true investment demand schedule for the economy as a whole. The MEI schedule is downward sloping showing a negative relationship between the level of investment and the rate of interest.

• A firm’s investment decision is based on the relationship between three elements which are the expected income flow from capital good under consideration, purchase price of the good in question and the rate of interest prevailing in the market.
• For every firm, the MEC schedule is a stair like curve where as the aggregate MEC schedule is downward sloping and a smooth curve.
• When all the firms in the industry increase their stock of capital, there will be increases in the price of the capital.
• The MEI schedule is downward sloping showing a negative relationship between the level of investment and the rate of interest.

CHANGES IN THE RATE OF INTEREST, THE MEC AND CAPITAL ACCUMULATION

When do the firms attain the desired stock of capital? What is capital accumulation? This section is concerned with answering the above two questions.

A Fall in the Rate of Interest and Capital Accumulation

In this section, we attempt at explaining the process by which capital accumulation occurs in response to a decrease in the market rate of interest.

We assume that increased supplies of capital goods are possible only at higher prices. In such a scenario, the supply curve of capital goods is upward sloping or, in other words, it is upward bending.

In Figure 10.5 (a), the MEC is downward sloping. In Figure 10.5 (b) also, the MEI slopes downwards from left to right because the supply curve of capital is upward sloping. In fact, the concavity of the MEI schedule is due to the increasing cost of the capital goods. It is important to note that with a given stock of capital there is only one MEI.

Figure 10.5 A Fall in the Rate of Interest and Capital Accumulation

In Figure 10.5 (a), assume that:

1. At point A on the MEC, the economy’s actual stock of capital is of 400 crores. This is also the desired stock of capital as the MEC equals the market rate of interest, r₁. Thus the net investment is zero.
2. There is a decrease in the market rate of interest to r₄. At this rate of interest, the equilibrium occurs at point D (as the MEC equals the market rate of interest). The desired stock of capital increases to 500 crores. This is difference of 100 crores from the existing actual stock. Thus, 100 crores of net investment is required to increase the capital stock to the desired level.
   The important question here is how long will it take the firms to increase the capital stock by 100 crores? If the production capacity of the capital goods industry were unlimited, the firm could increase its capital goods to 500 crores in just one time period. However, the production capacity of the capital goods industry is limited and increasing the capital goods to the desired level will take more than one time period.

Figure 10.5 (b) shows that:

1. In period 1, given MEI₁, due to the decrease in the rate of interest to r₄, net investment will increase but only by 50 crores. This is because the horizontal line, which corresponds to the rate of interest r₄ meets MEI₁ at point J. Hence, the stock of capital increases to 450 crores at the end of period 1.
2. In period 2, the actual stock of capital in the beginning of the period is 450 crores. In Figure 10.5 (a), corresponding to this stock of capital of 450 crores, the equilibrium occurs at point B where the MEC equals the market rate of interest which is r₂. The corresponding MEI curve is MEI₂. The net investment will increase by 30 crores. Again this is because the horizontal line, which corresponds to the rate of interest r₄, meets MEI₂ at point I. The stock of capital increases to 480 crores at the end of period 2.
   Similarly in the next period, there will be a further increase in the capital stock and the process will continue till the actual stock of capital gradually increases over time to 500 crores, which is the desired capital stock. It is obvious from the above analysis that in each period the net investment is smaller as compared to the previous period.

Thus,

1. Given the MEC schedule (which does not shift), net investment is determined by the rate of interest and the size of the capital stock.
2. Given the stock of capital, MEC can be determined. If the MEC is greater than the market rate of interest, then there will be positive net investment and hence an increase in the capital stock.
3. The rate at which net investment will increase in every time period will depend on the steepness of the slope of the MEI schedule.
4. The steepness of the slope of the MEI schedule, in turn, depends on the slope of the supply curve of the capital goods.

A Shift in the MEC Schedule and Capital Accumulation

In this section, we attempt at explaining the process by which capital accumulation occurs in response to a shift in the MEC schedule, given the market rate of interest. We will analyse an upward shift in the MEC schedule, which leads to an increase in the profit maximizing capital and thus to capital accumulation.

Figure 10.6 (a) depicts the effect of a shift in the MEC schedule on capital accumulation. The figure depicts the following:

1. The original MEC schedule is MEC₁. At a rate of interest of r₁, the profit maximizing or the desired capital stock is at 400 crores. As the actual capital stock is also 400 crores, net investment is zero.
2. Suppose the MEC schedule shifts upwards to MEC₂. At a rate of interest of r₁, the profit maximizing or the desired capital stock is now at 500 crores. As the actual capital stock is at 400 crores, there is a difference of 100 crores from the optimum or desired capital stock. Thus, 100 crores of net investment is required implying that net investment is positive or greater than zero.
   The important question here again is how long will it take the firms to increase the capital stock by 100 crores? As the production capacity of the capital goods industry is limited, increasing the capital goods to the desired level will take more than one time period.

Figure 10.6 (b) shows that:

1. In time period 1, given MEI₁, net investment will increase but only by 50 crores. This is because the horizontal line, which corresponds to the rate of interest r₁, meets MEI₁ at point J. Thus, the stock of capital increases to 450 crores at the end of period 1.
2. In period 2, the actual stock of capital in the beginning of the period is 450 crores. In Figure 10.6 (a), corresponding to this stock of capital of 450 crores is point B on MEC₂. The corresponding MEI curve is MEI₂. The net investment will increase by 25 crores. Again this is because the horizontal line, which corresponds to the rate of interest r₁, meets MEI₂ at point I. The stock of capital increases to 475 crores at the end of period 2. However, the actual stock of capital is still less than the desired stock of capital. Thus in the next period, there will be a further increase in the capital stock and the process of capital accumulation will continue till the actual stock of capital gradually increases over time to 500 crores, which is the desired capital stock.

Figure 10.6 The Shift in the MEC Schedule and Capital Accumulation

Thus,

1. Given the rate of interest, an upward shift in the MEC schedule generates conditions which are apt for investment.
2. Due to the upward shift in the MEC schedule, the MEC becomes greater than the current market rate of interest (given the actual capital stock). This leads to a situation, which initiates the investment activity or the net investment is greater than zero. The process of investment, or in other words the process of capital accumulation, will continue till the actual capital stock is equal to the desired capital stock. At this level, investment activity will cease as the MEC is equal to the market rate of interest.

• In each period, the net investment is smaller as compared to the previous period.
• The rate at which net investment will increase in every time period will depend on the steepness of the slope of the MEI schedule.
• Given the rate of interest, an upward shift in the MEC schedule generates conditions which are apt for investment.

THEORIES OF INVESTMENT

Many theories have been put forward to explain investment demand. It is a difficult and complex subject and one of the most controversial subjects. We throw light on some of these theories.

Accelerator Theory of Investment

The simple accelerator model states that investment is proportional to the change in the level of output and is not influenced by the cost of capital.

According to the accelerator theory, the desired stock of capital depends on the economy’s output level. An increase in the output leads to an outward shift in the MEC schedule implying that at each interest rate a larger capital stock is desired. Thus, changes in investment can be explained in terms of shifts in the MEC schedule. The increases in the output puts pressures on the existing stock of capital, or in other words on the existing productive capacity. An increase in the productive capacity is possible only by an expansion of the existing capital stock thus providing the incentive to the firm to obtain more capital goods and a higher rate of investment.

According to this approach, the rate of investment spending depends on the output level. To produce more output, more capital is required. Within limits it is possible to increase the output by using the existing capacity more intensively. But there exists a particular capital output ratio, which the firms consider to be the ideal ratio. This ratio differs from industry to industry being higher in some industries and lower in the others. However, at a particular point in time there exists a particular capital output ratio which is considered to be the desired ratio for the economy as a whole. As there occur technological and other changes in the economy, this ratio will undergo a change. However, for simplifying our analysis we assume that the ratio remains unchanged over time.

We have,

K = kY

where,	K = capital stock
	k = capital output ratio
	Y = output level

Given an unchanged capital output ratio, as the output changes, the desired stock of capital will also change. Suppose,

 

K_t-1 = k Y_t-1

where,	t =	some particular time period
	t – 1, t – 2 =	preceding time periods
	t – 1, t – 2 =	subsequent time periods

Suppose there is an increase in the output level in period t. Hence,

 

K_t = k Y_t

The increase in the desired stock of capital

 

= K_t – K_t–1.

The capital will increase only when net investment equals the increase in the capital stock, or

 

	It = Kt – Kt–1
where,	It = net investment in period t
We can also write,
	It = Kt – Kt–1 = kYt – kYt‒1 = k(Yt – Yt-1)

The above equation indicates that the net investment in time period t depends on the change in the output level between time periods t and t – 1 multiplied by the capital output ratio. It is clear that:

1. If Y_t > Y_t–1, there is a positive net investment in period t.
2. If Y_t < Y_t–1, there is a negative net investment or disinvestment in period t.
3. If Y_t = Y_t–1, there is a zero net investment in period t.

If replacement investment (which we assume to be equal to depreciation) is added to net investment, we get gross investment. Thus, we have

 

	It + Dt = k (Yt + Yt–1) + Dt
where,	Dt = depreciation in period t
Thus,
	Igt = k (Yt – Yt–1) + Dt
where,	Igt = gross investment

 

Investment will change if there is a change in the output level. However, it is assumed that there is no excess capacity. We allow for excess capacity by including X_t, which is the excess capacity in period t, in our analysis.

Thus,

 

	Igt = k (Yt – Yt–1) + Dt – Xt
where,	Xt = excess capacity in period t

If k (Y_t – Y_t—1) + D_t is equal to or less than X_t, then I_gt will be zero.

The basic relationship that exists between the investment and the change in the output level is known as the accelerator principle. The capital output ratio, k, is known as the accelerator. The investment theory that is based on the above relationship is known as the accelerator theory.

 

The following points are important in the context of the theory:

1. If the economy is in a position where the existing capital stock is fully utilized and there is no excess capacity, and the capital output ratio is constant, then in that case an expansion of output is possible only with an expansion in the existing stock of capital.
2. If the accelerator is greater than one, then the increase in the capital stock will be greater than the increase in the output. Thus, the increase in the investment is greater than the increase in the output.

For the accelerator principle to work certain conditions must be satisfied as follows:

1. The firms must operate without any excess capacity. During periods of excess capacity, the accelerator principle is temporarily inactive.
2. The firms increase their capacity to be able to meet every increase in the level of real spending. This implies that whenever there is an increase in the quantity of goods sold there is an increase in investment by the firms and whenever there is a decrease in the quantity of goods sold there is a decrease in investment by the firms.
3. The capital output ratio, k, or in other words, the accelerator must be constant.
4. The gap between the desired output and the actual output of the firms is closed within a single time period. In practice, this will depend on the production capacity of the capital goods industries.

Criticism: Due to its rigid assumptions, the accelerator theory has been subject to severe criticisms. Also, it appears that the accelerator principle does not work during periods of recession when there exists excess capacity. The accelerator principle is based on calculations about the future, which are not necessarily accurate. Thus, doubts have been raised about the validity of the accelerator principle. However, its basic idea remains that investment depends upon changes in the level of output. It does not depend upon changes in the cost of capital.

The Flexible Accelerator Model

Many theories have been put forward regarding the speed at which firms fine tune their stock of capital over time. The main idea in the flexible accelerator model is that whenever there exists a large gap between the firm’s existing capital stock and the desired capital stock, the firm’s investment is swifter.

According to the model the firm, in each period, plans on bridging only a fraction of the gap that exists between the desired and the actual capital stocks.

At the end of current period, the actual stock of capital is

 

K₀ = K_–1 + β (K* – K_–1)

where,	K–1 =	capital stock at the end of preceding period
	K* =	desired capital stock
	(K* – K–1) =	gap between the desired and the actual capital stock

Net investment to be achieved by the firm is

 

I = K₀ – K_–1

I = β (K* – K_–1)

The larger is the value of β, the quicker is the reduction in the gap between the desired and the actual capital stock. The investment function shows that the desired stock of capital, K*, and the actual stock of capital, K_–1, together determine the level of current spending. Any factor that is responsible for an increase in the desired capital stock also leads to an increase in the rate of investment.

The factors that are responsible for an increase in the rate of investment are as follows:

1. An increase in the investment tax credit.
2. An increase in the expected level of output.
3. A decrease in the real rate of interest.

The flexible accelerator theory emphasizes that:

1. Net investment adjusts gradually over a period of time.
2. Investment shows the various aspects of a firm’s dynamic behaviour.

The q Theory of Investment

This theory is based on the relationship between investment and the stock market. The relationship between the stock market and investment was first put forward by James Tobin.

According to the theory, q is the ratio of a firm’s market value (capitalization) to the replacement cost of capital. Hence, it is an assessment of the value placed on the firm’s assets by the stock market in comparison to the cost of producing those assets.

A high q ratio implies that a firm will like to increase the production. Thus, there will be an increase in investment. Hence, a high q indicates a high investment. For example, if the value of q is larger than one it implies that a firm should increase the investment level. For every rupee worth of new machinery, a firm will be able to sell rupee q worth of stocks and hence make a profit equal to q – 1. Hence, when the value of q is greater than one it implies a flurry of investment.

• According to the accelerator theory, given an unchanged capital output ratio, as the output changes the desired stock of capital will also change.
• If the accelerator is greater than one, then the increase in the capital stock will be greater than the increase in the output.
• The flexible accelerator theory emphasizes that net investment adjusts gradually over a period of time.
• The q theory of investment is based on the relationship between investment and the stock market

INTRODUCTION

1. The chapter analyses the relationship between investment and the rate of interest and also the responsiveness of investment to the rate of interest.
2. We attempt at determining the factors that influence the investment decisions. We also examine some of the theories of investment spending.

BASIC CONCEPTS

1. Capital is the accumulated stock of plant and equipment, which is held by the business firms.
2. Investment can be defined as the value of that portion of an economy’s output for any period of time that takes the form of new producer’s durable equipment, new structures and the change in inventories. In the long run, it is the investment that determines the stock of capital and hence the long-run growth in the economy.
3. As different factors influence the different types of investment, there can be no single investment theory which is applicable to all the different types of investment.

GROSS AND NET INVESTMENT

1. Gross investment consists of two parts: the replacement investment, which is required to keep the capital stock intact and the net investment which is required to expand the existing capital stock.
2. Net investment is equal to gross investment minus depreciation. In fact, net investment is an accretion to the stock of capital.
3. Other things remaining unchanged, for example, given the labour force, technology and natural resources, an accretion to the stock of capital increases the economy’s productive capacity.

PUBLIC AND PRIVATE INVESTMENT

1. Public investment refers to the investment in the public sector and private investment refers to the investment in the private sector.
2. The motivating factor behind public investment is social welfare where as private investment is guided by the profit motive.

INDUCED AND AUTONOMOUS INVESTMENT

1. Investment that changes due to a change in income and the interest rate is called induced investment.
2. In general, the investment function can be expressed as I = I (Y, i). While investment is positively related to the income level, there is a negative relationship between investment and the rate of interest.
3. Investment that does not change due to a change in income and the interest rate is called autonomous investment.
4. Most of the investments in the public sector are autonomous as they are made for considerations other than profit, some of the investments in the private sector may also be autonomous.

THE DECISION TO INVEST

1. The decision to invest is different as compared to the decision to buy consumer goods.
2. Most capital goods have a long life and one can learn only several years later as to whether the investment in these capital goods has been profitable or not.
3. A firm’s investment decision is based on the relationship between three elements: (i) expected income flow from capital good under consideration, (ii) the purchase price of the good in question and (iii) the rate of interest prevailing in the market.

PRESENT VALUE OF A CAPITAL ASSET AND DISCOUNTING

1. To make its investment decision, a firm compares the present value of the capital asset with its purchase price or the supply price.
2. The supply price of a capital asset is the cost of replacing the capital asset, which is under consideration, with a new one.
3. The present value of a capital asset is the sum obtained after discounting the expected future yields over its entire life at the market rate of interest. The higher the market rate of interest the lower is the present value.
4. The discounting process is the process by which a future sum is converted into its present value.
5. In general if an amount if an amount R₀ is invested for a period of n years at a market rate of interest, r, the amount the individual will receive at the end of the n years: R = R₀ (1 + r)ⁿ
6. the discounted present value of R_n
7. The present value of the bond is
   
8. The present value of a machine is
   

THE MARGINAL EFFICIENCY OF CAPITAL

1. We assume that we are given the following: the income stream from the capital asset, R₁, R₂, R₃ …, R_n and; cost or purchase price of the capital asset, C.
2. Given C and R₁, R₂, R₃, …, R_n we wish to find i, which is the rate of return expected from a particular capital asset. It is also called the marginal efficiency of capital, MEC.
3. Once the MEC is determined, a comparison of the market rate of interest with the MEC will enable one to make a decision as to whether the investment in the capital asset is profitable or not.
4. The difference between the MEC and the market rate of interest is the net rate of return expected after allowance is made for all costs.
5. The basic rule for making a decision is that if the MEC is greater than the market rate of interest, then the purchase of the capital asset is worthwhile and if the MEC is smaller than the market rate of interest, then the purchase of the capital asset is not worthwhile.

THE MARGINAL EFFICIENCY OF CAPITAL SCHEDULE AND THE RATE OF INVESTMENT

1. A firm, often, has variety of investment projects among which it has to make a choice.
2. In making its decision, a firm will compare the MEC of the capital asset with the current market rate of interest.
3. For every firm, the MEC schedule will resemble the stair like curve in Figure 10.1.
4. Once the MECs for all the firms are added together horizontally, the steps would all even out and we can arrive at the downward sloping and a smooth aggregate MEC schedule.
5. The equilibrium amount of investment is determined at the intersection of the aggregate MEC schedule and the curve representing the rate of interest.

THE MARGINAL EFFICIENCY OF INVESTMENT

1. When all the firms in the industry increase their stock of capital, the capitals goods industry will not only take a long time to produce the additional output but it may have to install extra capacity which may lead to increased costs and thus increasing price of the capital goods.
2. The marginal efficiency of investment (MEI) schedule depicts the relationship between the economy’s investment and rate of interest when the change in the price of capital goods is taken into consideration.
3. The MEI schedule represents the true investment demand schedule for the economy as a whole. The MEI schedule is downward sloping showing a negative relationship between the level of investment and the rate of interest.

FALL IN THE RATE OF INTEREST AND CAPITAL ACCUMULATION

1. Here we attempt at explaining the process by which capital accumulation occurs in response to a decrease in the market rate of interest.
2. We assume that the supply curve of capital goods is upward sloping.
3. The concavity of the MEI schedule is due to the increasing cost of the capital goods.
4. There is a decrease in the market rate of interest. The desired stock of capital increases.
5. The important question here is how long it will take the firms to increase the capital stock to the desired level.
6. In each period, there is an increase in the capital stock and the process will continue till the actual stock of capital gradually increases over time to the optimum level.
7. In each period, the net investment is smaller as compared to the previous period.
8. Given the MEC schedule (which does not shift), net investment is determined by the rate of interest and the size of the capital stock.

A SHIFT IN THE MEC SCHEDULE AND CAPITAL ACCUMULATION

1. In this section, we attempt at explaining the process by which capital accumulation occurs in response to an upward shift in the MEC schedule, given the market rate of interest.
2. Suppose the MEC schedule shifts upwards. Given the market rate of interest, there is an increase in the profit maximizing or the desired capital stock.
3. The important question here again is how long it will take the firms to increase the capital stock.
4. In each period, there is an increase in the capital stock and the process will continue till the actual stock of capital gradually increases over time to the optimum level.
5. Thus given the rate of interest, an upward shift in the MEC schedule generates conditions which are apt for investment.
6. The process of investment, or in other words the process of capital accumulation, will continue till the actual capital stock is equal to the desired capital stock. At this level, investment activity will cease as the MEC is equal to the market rate of interest.

ACCELERATOR THEORY OF INVESTMENT

1. The simple accelerator model states that investment is proportional to the change in the level of output and is not influenced by the cost of capital.
2. According to this approach, the rate of investment spending depends on the output level. At a particular point in time, there exists a particular capital output ratio which is considered to be the desired ratio for the economy as a whole.
3. The net investment in time period, t, depends on the change in the output level between time periods t and t – 1 multiplied by the capital output ratio.
4. Investment will change if there is a change in the output level. However, it is assumed that there is no excess capacity.
5. The basic relationship that exists between the investment and the change in the output level is known as the accelerator principle. The capital output ratio, k, is known as the accelerator. The investment theory that is based on the above relationship is known as the accelerator theory.
6. If the accelerator is greater than one, then the increase in the capital stock will be greater than the increase in the output. Thus, the increase in the investment is greater than the increase in the output that is responsible for the increase in it.
7. Due to its rigid assumptions, the accelerator theory has been subject to severe criticisms. Also it appears that the accelerator principle does not work during periods of recession when there exists excess capacity. The accelerator principle is based on calculations about the future, which are not necessarily accurate.

THE FLEXIBLE ACCELERATOR MODEL

1. The main idea in the flexible accelerator model is that whenever there exists a large gap between the firm’s existing capital stock and the desired capital stock, the firm’s investment is swifter.
2. According to this model the firm, in each period, plans on bridging only a fraction of the gap that exists between the desired and the actual capital stocks.
3. The investment function shows that the desired stock of capital and the actual stock of capital together determine the level of current spending.
4. qThe flexible accelerator theory emphasizes that net investment adjusts gradually over a period of time.

THE q THEORY OF INVESTMENT

1. This theory is based on the relationship between investment and the stock market. The relationship between the stock market and investment was first put forward by James Tobin.
2. According to this theory, q is the ratio of a firm’s market value (capitalization) to the replacement cost of capital.
3. A high q indicates a high investment.

TRUE OR FALSE QUESTIONS

1. Investment that changes due to a change in income and the interest rate is called autonomous investment.
2. The present value of a capital asset is the sum obtained after discounting the expected future yields over its entire life at the market rate of interest.
3. The supply price of a capital asset is the cost of replacing the capital asset, which is under consideration, with an old one.
4. For every firm, the MEC schedule is a stair like curve where as the aggregate MEC schedule is a downward sloping curve.
5. The MEC schedule represents the true investment demand schedule for the economy as a whole.

VERY SHORT-ANSWER QUESTIONS

1. What is the difference between induced and autonomous investment
2. Differentiate between public and private investment.
3. Which are the three elements, which determine a firm’s investment decision
4. What is the difference between a firm’s MEC schedule and the aggregate MEC schedule? Discuss.
5. What is the marginal efficiency of investment schedule?

SHORT-ANSWER QUESTIONS

1. What is capital? How is it different from investment?
2. Distinguish between gross investment and net investment.
3. ‘The decision to invest is different as compared to the decision to buy consumer goods.’ Comment.
4. On which three factors does a firm’s investment decision depend? Discuss.
5. ‘MEI schedule represents the true investment demand schedule for the economy as a whole’. Comment.

LONG-ANSWER QUESTIONS

1. Write short notes on the following:
   1. Capital and Investment
   2. Gross and Net Investment
   3. Public and Private Investment
   4. Induced and Autonomous Investment
2. What is the present value of a capital asset? How is it related to discounting? Explain.
3. What is the marginal efficiency of capital? How can we arrive at the aggregate marginal efficiency of capital schedule?
4. (a) Analyse the effect of a decrease in the rate of interest on capital accumulation.

   (b) Analyse the effect of an upward shift in the MEC schedule on capital accumulation.

5. Write short notes on the following theories of investment:
   1. Accelerator Theory of Investment
   2. The Flexible Accelerator Model
   3. The q Theory of Investment

TRUE OR FALSE QUESTIONS

1. False. Investment that changes due to a change in income and the interest rate is called induced investment.
2. True. The higher is the market rate of interest the lower is the present value. In the extreme case if the market rate of interest is zero, then the present value is equal to the expected future yield.
3. False. The supply price of a capital asset is the cost of replacing the capital asset, which is under consideration, with a new one.
4. True. For every firm, the MEC schedule will resemble the stair like curve. However, once the MEC’s for all the firms are added together horizontally the steps would all even out and we can arrive at the aggregate MEC schedule which is a downward sloping and smooth curve.
5. False. The MEI schedule represents the true investment demand schedule for the economy as a whole.