PROFIT
The part of net output attributed to capital goods in use is called profit. The term suffered at the hands of neo-classical economists who sacrificed structural reality to their atomistic, analytical refinements. In their flair to stuff economic concepts with psychological content they read into stock in trade elements of enterprise and borrowing, separated these, ascribed profit to enterprise and interest to loan capital, and explained profit as reward for risk-taking and uncertainty-bearing. A category of profit such as this did not conform to facts of life. Attempts at its further differentiation into various kinds either ended in a blind alley or added confusion. With modern economic analysis converging to two broad categories of production – labour and capital- the classic concept of net output divided into wage and profit has re-asserted itself.
Entrepreneurial activity cannot be conceived of apart from capital. Whether carried on by single-man business owner, partners of a partnership or directors or managers of a joint stock company or public corporation, entrepreneurship is always exercised on behalf of capital and the impact of its success and failure is invariably on capital’s share of net output. Profit, thus, covers risk-and-uncertainty earnings, positive or negative, in conditions of disequilibrium. When there is equilibrium, risk-and-uncertainty earnings are nil and the actual rate of profit is equal to the expected rate.
The rate of profit as defined is conceptually and factually the same for micro-economic and macro-economic analysis, for capitalist and socialist economy.
For an adequate theory of profit we have to re-interpret and amplify the classical saving-investment nexus which is properly an explanation of profit and capital formation. A given investment has capital multiplying effect in the long run and income multiplying effect in the short run. Keynes considered the latter which alone could be relevant for his short period analysis. In the comprehensive theory of value and growth both capital and income multiplying effects have to be considered.
Keynes is wrong when he says, ‘The decisions to consume and the decisions to invest between them determine incomes.’ The mistake is obvious in terms of his own analytical system. Decisions to consume and decisions to invest together determine aggregate demand which, in conjunction with aggregate supply, determines output (income). Disequilibrium between investment and saving changes the amount of profit. The quantity of capital being fixed in the short run, the rate of profit is changed as a result of change in the amount of profit. Equality between investment and saving is brought about by a change in the amount of profit and consequently the rate of profit. Equilibrium between investment and saving keeps the rate of profit in equilibrium.
Given the aggregate demand, the quality and quantity of capital goods and their effective use determine the aggregate supply. A flow of investment alters the quality and quantity of capital, on the one hand, and the level of aggregate demand, on the other, and, through the latter, influences effective use of the former and, thus, the whole chain of gross output, net output, the ratio of net output to installed capital (or the Standard Ratio), amounts of profits and wages into which the net output is divided and the rate of profit.
1. Keynes: General Theory, p.64,
Investment is a function of the rate of profit, the stock of capital in existence, and the Standard Ratio and capital-labour ratio reflecting technology. The higher the rate of profit, the larger is investment. Given the technology, the larger the stock of capital beyond the point of saturation, the lower is the rate of profit and the smaller is the investment. A change is technology may raise the rate of profit and stimulate investment or else it may lower the rate of profit, cause obsolescence and encourage investment to meet the needs of new type of capital goods. The relations involved are complex. To make them amenable to systematic treatment we may first express it as a function of the amount of profits and net output per worker and then in terms of the independent variables stated above.
Let I represent amount of investment, K, L and P capital, labour and relative prices respectively, R the Standard Ratio, y′ net output per worker and α0, α1 and α2 parametric constants when prices are calculated at I = R and y′ is obtained on the basis of these prices.
We, thus, have I =a0+a1KPr+a2y′ (4.1.1)
Where (µ+R) KP= γP, r=R n√1-ω And y′= γ P-µKP L
Since y′ = γ P-µKP = γ P-µKP . KP = R KP
L KP L L
= r KP ,
n√1- ω L
we have KP r
I=a0 + a1KPr + a2
L n√1- ω
or I= a0 + (a1KP+ a2 KP ) r (4.1.2)
L n√1- ω ω
Where (µ+R) KP = γ P, y′ = γ P-µKP , ω = --
L y′
The optimum capital-labour ratio and the optimum Standard Ratio remain unchanged when technology is unaltered. In such circumstances if the economy moves from a sub-optimum state towards the optimum, output increases rapidly and net output labour ratio as well as net output capital ratio rises. This is the case of increasing return. If the economy moves from its optimum to a super-optimum state, output increases at a diminishing rate and net output labour ratio as well as net output capital ratio declines. This is the case of diminishing return.
If the economy keeps on to its optimum, output increases in the same proportion as the quantity of capital and net output labour ratio as well as net output capital ratio remains constant. This is the case of constant return. If the wage rate remains constant, the wage proportion1,
ω or ω declines in the first case, rises in the second and remains constant in the third; the rate of
y
profit rises in the first case, declines in the second and remains constant in the third. If wage rate changes, there could be no a priori rule. A simultaneous rise in wage rate, wage proportion and the rate of profit is possible in the first case. The three may remain constant in the third case. In the second case a rise in the rate of profit may go with a fall in the wage rate. Institutional factors may keep the economy stuck to a sub-optimal state and the rate of profit or wage rate depressed in any or all of these three cases. In absence of institutional deterrents, equilibrium prices would assert and keep investment going in all the three cases and raise or lower it according as the rate of profit rises or falls. If the economy sticks to a super-optimal state, the pressure of demand would impinge on the output capacity available and impart additional impetus to investment.
The greater the investment, the more rapidly the quantity of capital increases. As the process continues and capital saturation is approached opportunities for new investment shrink. The rate of profit declines. The rate of investment goes down.
A change in technology turns installed capital goods obsolete and opens new opportunities for investment. Both the capital labour ratio and the net-output capital ratio (or the Standard Ratio) change. The new opportunities for investment are reflected in a rise either in the rate of profit or in the amount of profit expected.
In the investment function (4.1.2) continuance of the same technology keeps the optimum capital-labour ratio, KP constant. A change in the quantity of capital of the same technology,L that is, a change in the scale of operations, keeps the optimum Standard Ratio constant. Variation in effective use of installed capacity alters r and ω simultaneously.
The optimum ratio, r , changes along with optimum capital-labour ratio, KP only
n√1- ω L
when the technology is changed.
It may be noted that r, ω and the ratio, r are key to the variation in relative prices. n√1- ω
It is through these that price structure is linked to the investment function. Secondly, investment is no monotonic function since the rate of profit may rise, fall and rise again in no definite order. Thirdly, in contrast to the infinite continuum of techniques in the neo-classical production function, the investment function (4.1.2) can admit no more than a few technologies at a time so that prices and wage in each are expressed in terms of the Standard Net Product on one of them and n is determined by the wage profit equations in the way shown in chapter 2 above and the appendix to this chapter.
Saving depends on the level of income (output) and division of net income into profits and wages. Level of income depends on the quantity and quality of capital and its effective use. Given the quantity of capital, its effective use and the resulting income (output), the larger is profit income, the greater is saving. And given the quality of capital, the higher is the rate of profit, the greater is saving. Let S be total saving in the economy and s1 and s2 respectively the portions of profits and wages saved. We then have
S = s1KPr + s2 L ω (4.2.1) Where (µ + R) KP = γ P, y′ = γ P-µ KP, ω = ω and r = R n√1- ω
L y
1. See chapter 2
Let parametric constants, β0, β1 and β2 be introduced into the function. We, thus, have
S = β0 + β1s1KPr+ β2s2L ω
where (µ+R)KP = γ P, y′ = γ P-µKP , ω = ω
L y′
Capital has, thus, an important place in both saving and investment functions. Saving depends on profits and wages which constitute income and the latter depends on the stock of capital and its effective use. Investment depends on the stock of capital in existence, the degree of its effective use and scope for further increases in the stock of capital with the same or new technology, largely reflected in the rate of profit.
The investment and saving functions determine between them the rate of profit subject to the constraint of wage-profit relation. When investment and saving are in equilibrium, we have equilibrium rate of profit. When investment and saving are in disequilibrium, the rate of profit moves and brings about equality between investment and saving. The rate of profit may, thus, be above or below the equilibrium rate of profit according as investment ex-ante is greater or less than saving ex-ante.
A firm which earns a rate of profit higher than the equilibrium rate has the price of its product greater than its normal price. An economy is in equilibrium when every industry (sector) earns equilibrium rate of profit. Our system in chapters 2 and 3 moved with one degree of freedom and we managed to close it with the average of the existing rates of profit or the rate at which one state of the economy switched over to another state and in case of multiple switch-points, the rate closest to the previously existing rate. This expedient was adopted to help the exposition. An element of arbitrariness was accepted in selection from multiple switch-points. We can dispense with that expedient now. With an adequate theory of profit here we have the system closed.
We may remind ourselves that the rate of profit is not necessarily equal to marginal product of capital. As shown in chapter 2, it is equal to marginal product of capital only when capital-output ratio is the same in all sectors (industries) of the economy. The equality holds in the special case of uniform capital-output ratio. Such uniformity necessarily exists only in the Standard System.
The rate of profit determined by saving and investment has to be consistent with productivity of capital and labour as reflected in wage-profit relation. It has, therefore, been said that the rate of profit is determined by saving and investment functions subject to the constraint of wage-profit relation. Let us explain it with the help of diagrams:
In the diagram above saving and investment curves intersect each other at P, but the wage-profit curve passes to the left of P. In this situation P represents a position of metastable equilibrium. The point of intersection between the wage-profit curve and the investment curve is below P so that the rate of profit is above the rate which can be sustained by the economy. In such conditions relative prices would change. While changing in relation to one another the prices would all move downwards, heralding a fall in the general price level.
In the diagram above the point of intersection between the wage profit curve and investment curve is above P so that the rate of profit is less than what the economy would sustain. In such conditions, again, relative prices would change. While changing in relation to one another the prices would all move upwards, ushering in a rise in the general price level. Equilibrium would be stable only when the wage-profit curve intersects the investment curve at the same point at which the saving curve intersects the latter. This Situation is shown by the diagram above (fig, 4.1.3). We have, thus, a second approximation in the theory of profit: the rate of profit is determined by the investment function and the wage-profit relation, subject to the constraint of saving.
In the diagram (4.2.1) above investment curve and wage-profit curve intersect each other at P (subject to the saving constraint) and determine at the point the stable equilibrium rate of profit.
We may extend the investment curve to the left to meet the vertical axis. The point of intersection between investment curve and vertical axis would represent a situation of zero profit which obtains in a stationary state marked by zero net investment and zero rate of growth. The stationary state would exist either in a primitive society where net output is negligible or in a highly advanced society where capital is so large in relation to net output (net income) that the Standard Ratio is negligible. With the Standard Ratio zero in either case, the wage-profit curve is represented by the vertical intercept between the point of origin and the terminal point (extreme left) of the investment curve.
It is evident from the investment function (4.1.2) that, in case of different technologies or different levels of capacity use of the same technology, corresponding to each wage-profit curve there is a different investment curve. If we consider points of intersection of investment curves with their corresponding wage-profit curves and draw a curve by joining the points of intersection, the curve so drawn is the investment curve for different states of the same technology or for different technological systems. It need not be monotonic. It may go up and down and up again in no definite order. It is shown in the diagram on the next page.
In the diagram (fig.4.3.1) there the wage-profit curve denoted by R5 represents optimum state of a technology the Standard Net Product of which is adopted as unit of measurement. Curves R1 and R2 represent sub-optimum states of the technology denoted by R3. Curves R4 and R6 represent other two technologies respectively. The point of intersection of these curves with their corresponding investment curves are marked A,B,C,D,E and F respectively. The dotted curve passing through A,B,C,D,E and F is the investment curve for the sub-optimal and optimal states and for the different technologies. As we see, the dotted curve I goes up and down and up again. It must, however, be mentioned that the dotted investment function I is no continuous curve, for there is no assumption of infinite continuum of technologies. The points representing stable equilibrium rate of profit have been joined by a dotted line only to shoe the trend of these rates of profit and the corresponding rates of investment.
The figure (4.3.1.) shows the wage-profit curves and switch-point and equilibrium rates of profit and wage of the six miniature economies worked out it appendix to chapter 4.
The change in price level brought about by movement of the rate of profit from a position of metastable equilibrium to one of stable equilibrium is different in nature from a similar change caused by a difference between the rate of profit and the rate of interest. The latter, to anticipate our discussion on money, is a situation of monetary disequilibrium, or in a conceivable neutral money economy, one of credit disequilibrium. The difference is fundamental. It has invariably missed the attention of economists.
The rate of interest is a discount factor. The higher is the rate of interest, the lower is the discounted value of prospective yields of capital goods. Investment is, thus, a decreasing function of rate of interest while, as we have seen, it is an increasing function of the rate of profit. If investment as decreasing function of the rate of interest intersects the wage-profit curve at the same point at which investment as increasing function of rate of profit does, there is equilibrium between the monetary side and real side of the economy. Both relative prices and the general price level are stable. If the rate of interest is lower than the rate of profit, the general price level rises and relative prices may be distorted in the wake of upward movement of the price level. If the rate of interest is higher than the rate of profit, the general price level moves down and relative prices may be distorted in the wake of downward movement of the price level. The relation is shown in the diagrams:
In the figure (4.4.1) above the rate of interest, indicated at Q where I(i) intersects I (r), is less than the rate of profit determined at P, so that the
general price level moves up, disturbing the equilibrium at P and possibly changing the positions of the investment curve until equality between rate of interest and rate of profit is established, as shown in the diagram (4.4.3). In the diagram (4.4.2) the rate of interest indicated at Q is greater than the rate of profit at P so that the general price level moves down, upsetting the equilibrium at P and possibly changing the position of investment curve until equality between rate of interest and rate of profit is established, as shown in the diagram (4.4.3) below.
An optimal wage-profit curve would not change its position in any of the two conditions of disequilibrium while a non-optimal wage-profit curve (sub-optimal or super-optimal) would do in both the situations of disequilibrium.
A metastable rate of profit, as shown in figure (4.1.1-2), sets in motion a train of changes as does a difference between the rate of interest and the rate of profit. There is, however, a difference between the two types of changes. It is difference of sequence as well as of effect on stability. The first type of change starts with relative prices, involves movement of price level in its wake and takes the economy towards stable equilibrium. The other type of change starts with movement of the general price level, distorts relative prices in its wake and takes the economy away from equilibrium. Forces operating on the real side, unhampered by institutional factors, make for stability unless disturbed by those on credit or money side of the economy.
The rate of profit determined by investment function and the wage-profit relation, subject to the constraint of saving, has two distinct spectra on either side of it, one of internal rates of return and the other of rates of discount. While the rate of profit is a determinant of relative prices, these two spectra of rates of return are calculated on the basis of prices determined by it.
Keynes expressed the internal rate of return as marginal efficiency of capital and the social rate of time preference as rate of interest. He missed the rate of profit, the pivot around which an economy moves.
Of Bohm-Bawerk’s three reasons for the existence of rate of interest in a stationary economy, relative under-endowment of the present and perspective under-valuation of the future, and technical superiority of round-about method of production the first and the second explain the rate of discount and the third which could be rightly worded as technical improvement through round about method of production, is related to the internal rate of return. He confused the two distinct issues, mingled the two different rates into one and, like Keynes after him, missed the pivotal rate of profit.
In his strenuous search for truth for 25 years (1906-1930) Irving Fisher trod over a wide terrain and made himself vaguely aware of the three different sets of rates of return. What Pasinetti calls his first, second and third rates of return have resemblance with the rate of time preference, the internal rates of return and the rate of profit.
Ricardo was conscious of only two rates: the rate of profit and the social rate of time-preference. As he said, ‘ The rate of interest, though ultimately and permanently governed by the rate of profit, is, however, subject to temporary variations from other causes’.2
Every individual has time-shape of his needs and time stream of his income. The two can be reconciled to each other by a rate of discount at which he is prepared to substitute his present income (value of goods) for future income (value of goods).
Let V1(a), V2 (a) ….. VГ (a) be A’s income (value of goods) in periods 1.2, ….. , Г, Ƨ (a) the rate of his discount and V (a) the present value of his future income (value of goods). We then have Г
V (a) = ∑ Vt (a) e- Ƨ (a)t (4.3.1) t=1
1. ‘Switches of Technique and the "Rate of Return" in Capital Theory’ in the Economic Journal, Sept. 1969 pp 508-11.
Another individual’s income may similarly be denoted by V1(b), V2(b), ….., Vθ(b),his rate of discount by Ƨ (b) and the present value of his future income by V(b).
We then have θ
V (b) = ∑ Vt (b) e- Ƨ (b) Ƨ (4.3.2) t =1
Suppose Ƨ (b) is greater than Ƨ (a) . Then a would like to exchange his present goods with B in order to have from the latter in a future period within their common time horizon a quantity (value) of goods larger than he would by himself do. As A exchanges his present goods for B’s future goods, both A’s and B’s time streams of income expand and their rates of discount change. They may ultimately arrive at a common rate of discount, i, so that we have
Г Г θ θ∑ Vt (a) e- Ƨ (a)t -∑ Vt (a) e- Ƨ t=∑ Vt (b) e- Ƨ (b)t -∑ Vt (b) e- Ƨ t
t=1 t=1 t=1 t=1 (4.3.3)
Similar process of adjustment may occur among all individuals and other economic units. In a perfect market a uniform social rate of discount would emerge. In conditions of market imperfections several social rates of discount may be established.
Emergence of a social rate of discount divides related activities into lending and borrowing. Those individuals (or other economic units) who have their rates of time preference lower than the social rate of discount offer a part of their current resources for loans. Those who have their rates of time preference higher than the social rate of discount demand current resources on credit. The lower are individual rates of time preference from the social rate of discount, the larger is the supply of loans. Let Ƨq represent individual rates of time preference where q =1,2, ….. , Q and Ƨ represents social rate of discount as before. The criterion for credit transactions, then, is
>
I= Ƨ q
< (4.3.4)
(q=1,2, ……. , Q)
If Ƨ′ q stands for time preference rates lower than the social discount rate and Ƨ ′′ q for time preference rates higher than the social rate of discount, the condition for supply of loan is
Ƨ > Ƨ q′ (4.3.5)
and the demand condition for loan is
I< Ƨ q′′ (4.3.6)
Since the social discount rate equates the demand for loans with the supply of these and the rate of profit equates investment with saving subject to the constraint of wage-profit relation, there is full equilibrium in the economy when the social discount rate is equal to the rate of profit :
Ƨ = r (4.3.7)
2. Ricardo : Principles of Political Economy and Taxation, Everyman’s, 1962, p. 198.
In a world of certainty individual rates of time preference and social rate of discount emerge from individuals’ differences in their perspective under valuations of the future. As we move from the world of certainty to one of uncertainty, we have individuals and other economic units afflicted by ‘all sorts of vague doubts and fluctuating state of confidence and courage’. Events like obsolescence caused by a new invention cannot be insured against. Uncertainties arising from these are met by holding a part of resources in liquid form. Differing under valuations and liquidity preferences together bring into being various financial assets created or held and generally dealt in by banks and non-breaking financial institutions. Liquidity preferences of banks, non-banking financial institutions and individual economic units are together reflected in banks’ encashment function and maturity function, the difference between which determine the rates of interest or index of interest rates, representing the social discount rate.
When we express social discount rate in terms of rate of interest, denoted by i, we have the condition of financial equilibrium
i = r (4.3.8)
The rate of profit influences the social rate of discount and individual rates of time preference in two ways. First, as a determinant of prices at which goods are valued, it influences the value of goods which forms the time stream of income. Secondly, the rate of investment associated with it changes the stream of income and so the social rate of discount and individual rates of time preference.
The internal rates of return also influence the social rate of discount. Possibility of high internal rates would induce individuals and other economic units to spare large quantity of present goods for future ones and, thus, to change their rates of time preference and social rate of discount.
There is interaction among the three rates. A given rate of profit and the rate of investment associated with it influence social rate of discount and internal rates of return through the quantum of goods produced and their prices. Social rate of discount, spread of individual rates of time preference below or above the social rate and internal rates of return in their turn influence the amount of saving being available, the volume of loans and the amount of investment demanded. Social discount rate and individual rates of time preference below the social rate enter the saving function as a parameter. The internal rates structure enters the investment function as a parameter. A change in individual rates of time preference and social discount rate shifts the saving function. A change in internal rates of return shifts the investment function. As a result of shifts in these two functions a new equilibrium rate of profit is determined.