Essay on Investment Function | Economics

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Investment function provide micro foundation for our study of macroeconomics.

Investment is capital formation, i.e., the acquisition and creation of resources to be used in production. And capital goods are the creations of other goods.

The key concept in the theory of investment is the investment function. An investment function is the relation between the acquisition of capital and a set of explanatory variables.

In a market-based mixed economy like that of the USA or India private domestic investment has three components, viz.:

(i) Residential housing construction,

(ii) Business acquisition of new industrial plants, machinery and equipment and

(iii) Inventories of finished goods.

In the tradition of classical economics, it is held that business profits are partly or even entirely accumulated as capital investment. Thus, investment becomes a function of profits. The more profits are made, the larger is the volume of investment.

Keynes’s Ideas:

In 1936, Keynes emphasised that investment was an essential component of the total effective demand which determined the rate of output and, hence, of employment in the economy. The investment function projected by Keynes which was borrow from the American economist Irving Fisher, made investment depend upon its marginal efficiency or gross profitability.

This depended upon the expected returns from investment and its cost or supply price. And the profitability or marginal efficiency, in turn, must be related to the financial cost of investment or the rate of interest. Thus, firms would invest in additional plant, equipment or inventories only as long as the rate of return on each unit of investment exceeded the rate of interest, or only as long as the present discounted value of expected future returns, that is, the demand price of capital goods exceeded or was at least equal to the supply price or cost.

The Neo-Classical Theory:

Investment may be viewed as the acquisition of capital for replacement, including modernisation and for expansion. The rate of investment will then depend upon the rate at which existing capital is replaced and the expectation of increases in future demand. It will also depend upon the desired capital-output ratio or capital-labour ratio, which in turn, relates to technological factors (that is, the production function) and relative prices of capital and labour.

A meaningful price of capital would involve the initial cost or supply price of the capital goods being purchased, the expected rate of depreciation or wearing out or replacement requirements of the capital to be acquired, the interest or financial cost of the funds invested in the capital, and any expected capital loss due to changing prices of capital goods.

These elements, along with relevant tax parameters, have been incorporated by D. W. Jorgenson (1963) into a “rental price of capital”, which plays a key role in a neoclassical investment function. The lower the rental price of capital, the greater the capital stock that firms would find optimal or would desire in order to produce any given rate of output, or to increase output by any given amount. The greater the expected output, the greater will be the demand for capital; moreover, the greater the increase in expected output, the greater will be investment.

This leads to a general formulation of an investment function in which the rate of investment:

(1) Depends upon past changes in demand, sales, or output, which presumably generate changed expectations of future demand, sales, and output, and

(2) Also depends upon past changes in the rental price of capital, which generate changes in the desired and effective (actual) capital- output ratio.

We thus have a distributed lag function in which investment is related positively to past, current and—to the extent they are known—expected future changes in sales or output and changes in the rental price of capital.

Empirical studies have attempted to measure the influence of interest rates, taxes and expectations of future demand on investment. Producers are presumed to acquire capital to increase their expected profits. The profitability of additional capital depends on its cost, on its expected productivity, and on expectations of the price at which additional output can be sold.

Assuming that output is a fixed, ‘well-behaved’ function of capital and labour (strictly concave, with declining partial derivatives of output with respect to capital and labour and positive cross partial derivatives), producers will acquire capital to the point where its declining marginal product equals its cost.

This will then define both the desired, or equilibrium, capital-labour ratio and capital-output ratio. With the supply of labour and the rate of output fixed and no change in the relative price of capital and labour, investment in equilibrium will be equal to depreciation, which means that net investment will be zero. Positive net investment will then stem from increases in the demand for output or reductions in the relative price of capital. Increases in output will generate investment demand in order to maintain the equilibrium capital- output ratio.

A reduction in the cost of capital would generate investment in order to increase the capital-labour and capital-output ratios. In either case, maintaining increased amounts of capital will generate further investment to cover increased depreciation.

In such a framework the desired capital stock may be written as:

K * = f( p, c, Y *) … (1)

where p is the price of output, c = q [i – (q°/q) + d] is the rental price or the user cost of capital, q is the supply price of capital goods, i is the opportunity cost of capital, d is the rate of economic depreciation, and Y* is desired output. If firms minimise expected cost of producing an exogenously given or expected output F, then the wage rate, w, would be substituted for p.

The rental price or user cost of capital, c, is the cost per period of holding and maintaining one unit of capital. If we ignore taxes, it is the price of capital goods multiplied by the sum of the real interest rate and the rate of economic depreciation.

The former measures the opportunity cost in terms of foregone net earnings from lending or otherwise investing money, plus the capital loss (or minus the capital gain) associated with changing prices of capital goods. On the basis of this neoclassical theory of the firm developed by Havelmo (1960) and assuming a Cobb- Douglas production function with output elasticity of capital, b, Jorgenson (1963, 1967) arrived at a demand function for capital with the following form

K* = b (p/c) Y* … (2)

With an implicit unitary elasticity of K* with respect to c, this formulation implies strong effects of monetary policy, via the rate of interest, and of tax policy so far as, by accelerated tax depreciation, investment subsidies, or exclusion of capital gains from taxation, it affects the value of c.

The more general constant-elasticity-of-substitution (CES) production function may be used to generate a demand for capital having the form:

K*= s (p/c) ^r(Y*) … (3)

where s, the elasticity of substitution between labour and capital, is the critical elasticity of demand for capital with respect to the relative price of capital, and r is the elasticity of demand for capital with respect to output. The elasticity r will be greater than, equal to, or less than unity as the returns to scale are decreasing, constant, or increasing.

The Acceleration Principle:

If relative prices are constant, or if technology requires that capital and labour be used in fixed proportions (in which case the elasticity of substitution is zero), then with constant returns to scale, desired capital is proportional to the demand for output.

This form of the demand for capital leads to the ‘acceleration principle’, according to which net investment demand—arising from a desire to change the stock of capital depends not on the level of demand for output but on the rate of change of the demand for output. The acceleration principle was developed by J. M. Clark in 1917. To induce firms to invest (acquire more capital), demand for output must keep on increasing year after year.

Application of the acceleration principle, relating investment to changes in the rate of output and the pressure of demand on capacity, has been complicated by the implication of notions of permanent income for investment. This suggests that changes in demand which are deemed essentially transitory will have little or no effect upon investment and only to the extent that such changes are viewed as permanent will be investment affected.

Flexible Accelerator and Distributed Lag Process:

Both the original formulation by Jorgenson of the demand for capital (2) and the more general formulation (3) underlying by a ‘flexible accelerator’, where the desired capital-output ratio is not constant, but depends on prices and on the scale of output and investment is subject to a distributed lag mechanism affected by adjustment costs and the dynamic process governing the formation of expectations of future variables.

Investment and Profits:

One major competing hypothesis was that investment depends on the level of profits, on the ground that realised profits measure expected profits, or that capital market imperfections cause firms’ capital expenditures to be constrained by the flow of internal funds.

Recent studies have attempted to capture profit expectations by including expectations of the major determinants of profits, namely, sales, prices, and wages, or to approximate them by stock market valuations of firms. The flow of internal funds may play some role in investment decisions, not as a determinant of the desired capital stock but as a factor influencing the speed of adjustment of capital.

Adjustment Costs:

According to Eisner and Strotz, the desired capital stock does not in itself indicate the rate of investment, which is the rate of replacement of existing capital plus the rate of net additions. Both entail a combination of financial considerations and costs of adjustments, which will, in turn, relate to costs of planning, and the supply function for capital goods, all filtered through the expectations of agents. If adjustment costs are an increasing function of the rate of investment, it will generally prove optimal not to adjust capital to the desired level immediately, but, instead to distribute changes in the capital stock over time.

The Putty-Clay Model:

The speed of adjustment of capital to changes in its desired (or equilibrium) level may depend on the causes and magnitudes of the changes. An increase in the demand for output may generate strong investment demand as expectations become firm with regard to the permanence of the increased demand.

If the increased demand for capital is due, however, to a fall in its relative price (due to, let us say, a fall in the rate of interest), thus generating a demand for more durable and, hence, more substantial and expensive capital, the rate of investment may be slowed by the availability of existing capacity sufficient for current production.

These considerations underlie the ‘putty-clay’ model in which the capital-labour ratio can be varied on newly installed capacity but cannot be altered on existing capacity. A demand for additional housing services will bring on investment in housing as rapidly as cost increases permit. A lower rate of interest, causing substantial investment in more durable brick houses to replace less durable houses of wood or straw, would cause the rate of investment to increase only as existing houses of wood and straw wear out and are replaced.

Investment equations should thus include separate distributed lag responses to changes in relative prices and to changes in output. They should also admit the possibility that the lag distribution is not fixed and may vary with other economic parameters and the expectations function.

Tobin’s q Theory:

The critical role in current investment of unobservable adjustment cost and uncertain, shift­ing (and generally not directly observable) expectations of the future, stressed by Keynes, sparked interest in a formulation of an investment function which directly relates demand prices and supply prices of capital.

In Keynes’s General Theory (1936), investment is under­taken to the point where the expectation of marginal profit on investment (the ‘marginal efficiency of investment’) is equal to the rate of interest or, alternatively, the present value of expected returns from the marginal investment, using the rate of interest as the discount factor, is equal to the marginal supply price of newly produced capital goods. Building on this, Tobin (1969) presented a q-theory’ which sees investment as a positive function of a ratio, called q.

Tobin’s q is the ratio of an index of the value of capital taken from stock market quotations, presumed to be a measure of demand price or the value of expected future returns from capital, to an index of the replacement cost of capital, taken to be a measure of the supply price.

If this ratio exceeds 1, firms will find it profitable to construct new capital, that is, investment. If this ratio is less than 1, purchase of existing firms to acquire existing capital would be cheaper than constructing new capital and new investment in plant, equipment and machinery would not take place.

The main advantage to be secured from using the q-model is that it offers a market measure of otherwise unobservable expected profits in the form of their present value. It has presented serious problem in statistical estimation, however, due to problems relating to tax considerations, distinctions between the valuation of firms and the prices of the few shares traded at any one time, and the fact that the stock market valuations reflect much more than the physical capital that would be included in the traditional measures of investment.

Suggested explanations of the difficulties include the fact that market values of firms may relate to much more than the tangible capital generally included in business investment and the failure to distinguish marginal and average values of the cost of new capital versus the acquisition costs of existing firms.

Public Policies to Promote Investment:

In the ultimate analysis it appears that changes in the rate of average demand and output are very likely to be of prime importance in the aggregate investment function. In equilibrium terms, the faster the rate of growth of aggregate demand, the greater the rate of investment demands.

Government fiscal policy and, particularly, the government budget surplus (government saving) or deficit (government dissaving), affect total saving and, hence, total investment. However, the rate of investment may be more influenced by government policy when the economy is slack than under conditions of full employment.

Fiscal concession in the form of investment tax credit, accelerated depreciation and preferential treatment of capital gains promote investment. Monetary restraint, in the form of higher interest rate, reduces residential investment disproportionately.

Conclusion:

It is important that public policy towards investment relates to all types of investment, human and intangible as well as tangible, and by households, government and public enterprises, and non-profit institutions as well as by business. Ultimately, investment is viewed as a function of its expected profitability or contributions to value and net worth, dependent, in turn, upon expected or projected demand or output; relative prices of capital and other inputs; rates of discount, or future expected returns, which are likely to be increased by higher perceptions of risk; and costs of adjustment and of obtaining information.

The pay-off in higher productivity and a higher path of consumption in the future is greater in all types of public investment—in R and D, in social infrastructure, and in health and education. All these types of investment generate positive externalities in the sense that social benefit far exceeds private benefit.