Friday, 26 August 2016

Rate of Profit, Rate of Interest

The rate of profit and the rate of interest are at the core of capitalism’s dynamic, but there is a huge amount of confusion in what is written on these matters. This article aims to clarify some key points. I outline the relevant aspects of some theories of profit and interest, but focus on how to understand profit and interest rates from the perspective of a Marxist understanding of capitalism. Underlying these abstract concepts are the realities of class and power in the world economy.

Rate of profit calculations
Profitability is obviously important for capitalism. Paying attention to the rate of profit, not just the amount, also makes sense, since this gives the amount of profit per unit of capital advanced, and the more the better. But this simple point hides two important complications.
Firstly, the calculation must be timed. Commonly, calculations are for the rate of profit per year, so that the amount of profit in a year is measured against how much capital is advanced at any one time to achieve it. Other things equal, this also means that the shorter the time period between advancing the money capital, buying the necessary means of production, producing and then selling the commodities at a profit, the greater will be the rate of profit per year. This can make shortening the buying/selling process also appear to be a source of value and profit, not just the production process itself. A quicker method of buying/selling will speed up the circulation process for the producer, raise the amount and rate of profit per year and allow a greater profit to be shared between the producers and the commercial capitalists who are more involved in this process.
Secondly, the rate of profit will be affected by how much of the capital advanced is from the company’s owners and how much is borrowed from banks or other money capitalists providing it with extra investment funds. If we assume a given, annual rate of profit of 10% for the company, then the return on its total investment will also be 10%. But if it has borrowed half its investment funds from banks at a rate of just 5%, or issued bonds with a yield of 5%, then the rate of profit on the funds that the company’s owners have advanced will be higher. For example, for 200 invested at 10%, the annual return is 20. But if the company’s owners have invested only 100 of their own money plus an extra 100 they have borrowed, the company then gets as its profit the 20 total minus the 5 it needs to pay on its borrowings, etc. The result is that its rate of return will be higher: 15 (20 – 5) over the 100 invested, or 15%.
This extra profitability depends on the rate of interest paid on the borrowings being lower than the underlying rate of profit on the total investment. That is not always the case, but it shows how profitability calculations for capitalist owners will tend to change when borrowing funds is taken into account.
What rate?
A company’s borrowed funds raise an ambiguity, one that has not been dealt with well by Marxist theory. If the money is borrowed via bond issues or bank loans, then the payment for the borrowing falls under the heading of interest, so the previous calculation will hold. But if the extra funds come from new money advanced by money capitalists buying any new equity the company issues on the stock market, then how should these extra funds be treated and what is the form taken by the deduction from profits?
If the money capitalists have put their funds into the company’s new equity issue, or even just bought previously issued equity from others, then they own part of the company, just as much as the original owners. To that extent, they will receive a share of the profits in the form of dividends on the equity they own, just like the others. However, there are some distinctions to take into account.
As newer entrants, unless the new equity buyers become big shareholders, they will have fewer claims on the company’s resources through the large salaries they might otherwise get by becoming executives and directors, with special bonuses or other payments. Small-scale equity owners also have little voting power in company decisions, and some of the equity sold and bought may even be devoid of voting rights on these decisions. Insofar as they are in this latter camp, the equity dividends for them are not so different from the interest payments on the company’s bond or bank loan borrowings. But they are still in a different economic situation from bond holders or bank lenders. They benefit from any rise in the price of the equity, and may suffer a loss from a collapse of equity prices. They have none of the usual debt holder or bank lender protection of being first in line for payments, if the company gets in trouble, and their dividends might be zero or very high, while interest and coupon payments are determined at a market level or fixed in advance.
Aside from any possible director benefits, the return on equity for the companies’ owners can be taken to be not only the dividends paid on the value of the equities purchased, but also on the change in the price of the equity itself. So, holding a company’s equity that pays zero dividends may be better than holding one with high dividends, if its equity price has risen far enough above the investor’s purchase price. For example, buying shares in a company at 100 and receiving no dividend for two years will be disappointing for money capitalists. But the outcome will nevertheless look attractive if the company’s share price rises to 150 over those two years, because a large capital gain has been made.
This is accentuated further by the way in which all equity prices (and, indeed, bond prices) tend to rise as interest rates fall, and vice versa, due to the lower, or higher, rates of discount on future earnings by money capitalists. Such calculations show how far capitalist views on what it a profitable investment can become divorced from a measure of the company’s actual return on capital or its underlying profitability.
Company reports usually standardise data with annual rates of profit, and also distinguish the profit due to shareholders after interest on borrowings and other special factors. These commonly lead to different rankings of companies, not necessarily only by their reported profits, but also, especially in recent decades, by the volatility of the returns they get. Extra borrowing usually leads to extra volatility of returns. These are other factors that influence the choices made by money capitalists, and thus the allocation of capital, but they do nothing to change the actual profits produced.

Rate of interest
At first sight, the rate of interest is more easily observable than the rate of profit on industrial or commercial investment. After all, the central bank’s key interest rates are published daily or intra-day, as are the yields on 3-month Treasury bills, 5-year or 10-year government bonds or rated corporate bonds. Nothing similar really happens for measures of company rates of profit. While there are many rates of interest – interbank borrowing rates, government Treasury bill or bond yields, corporate bond yields, borrowing rates for consumer loans or mortgages, etc – they are publicly observable in ways that a rate of profit on corporate investments is not.
How is this problem of many rates of interest dealt with in economic theory? Mostly, not at all. Instead, a sacred ‘rate of interest’ is often used in mainstream economic theory, with few, or no questions asked as to what kind of interest rate is meant. Financial theory may, for practical calculations, distinguish a corporate bond yield or government-borrowing yield, in order to determine the relevant price of a financial security, but there will be no serious investigation as to why this is at a particular level and not at any other. Instead, tautological assessments of ‘risk’ are offered, which make the banal observation that a more risky investment will probably have to offer a higher interest yield. But this does little to get around the problem that much mainstream financial theory, especially for financial derivatives, is based on the idea of there being, at bottom, a ‘risk-free’ interest rate, one that exhibits a zero, or negligible credit risk of not getting repaid by the borrower.
What rate is ‘risk free’? Usually this is assumed to be a government security yield, ignoring the inconvenient fact that governments have also been known not to repay in full. In the case of the US government’s security yields, the nec plus ultra of ‘risk free’ in financial theory, it is conveniently ignored that on several occasions the US government has run close defaulting on its debt repayments, owing to political turmoil in Congress. How far government yields can be seen as objective arbiters of the rate on ‘risk free’ debt is also questioned by a significant bias lower for this rate, especially in financial markets dominated by the major powers. Structural demand for the key government securities, from the domestic banking system, from international investor demand for the global currency security, and sometimes from their taxation policies (for example, exempting capital gains from tax), produces lower yields than would otherwise be the case.
The upshot is that ‘the’ rate of interest is as nebulous as ‘the’ rate of profit. Both sets of rates are determined in a chaotic capitalist market. Are there any laws determining these?

Relationships between interest and profit rates
A common view in mainstream economic theory is that the rate of profit and the rate of interest are either the same, or tend to equality over time. The logic is straightforward, but this logic also highlights the deficiencies of the argument. It is an example of the errors that arise when a focus on appearances is allowed to obscure the underlying processes of the capitalist economy. This happens when the social content of the relationship is ignored, with little attention paid to what the terms in an equation actually mean.
To illustrate this point, and even to make a mild concession to the argument, cast aside the messy reality that there are many rates of profit and many rates of interest, determined by all kinds of market pressures. Instead, assume that there is, in fact, one capitalist market rate of profit (r), available to industrial and commercial capitalists, and one market rate of interest (i) available to those putting funds into banks, buying bonds, etc. The basic case made by modern economics is that there is a tendency for r to equal i.
The rationale for this view is usually given from the perspective of the money capitalist. Let us call him (it is rarely her) Moneybags, and imagine him just sitting there with $1m in cash to play with. So what does Moneybags do with the cash when viewing the opportunities available?
            if i > r, just lend money in the market rather than invest directly in production
            if i < r, then invest in production rather than lend on the money markets
The actions of Moneybags supposedly tend to equalise the two rates, by investing or lending. How? The logic is rarely spelled out, but the mechanism assumed is as follows. If the rate of interest is above the rate of profit, the effect of offering more funds into the money market will tend to depress the rate of interest on loans towards the (lower) rate of profit. Alternatively, if Moneybags invested more in the higher rate of profit available on capitalist production, then that would tend to decrease the rate of profit on that activity towards the (lower) rate of interest on loans. Abracadabra, in a free market the rate of interest will therefore tend to equality with the rate of profit!
There is so much wrong with this argument, despite it often being taken as self-evident, or at least plausible. The problems can be seen in several steps.

Investment and ‘interest’
A money capitalist investor with funds of M can put them into a bank deposit, equity or bond investment, try to start up a business, or invest in someone else’s business. Assuming the investor is attracted by the relative yields, then this looks like a mechanism for equalising r and i, and the previous argument would hold.
However, that assumes there are diminishing returns on the M invested in industry and commerce, or in ‘financial’ ways, so that the flow of M into the different applications of funds will equalise the returns on the funds in each case. Rates of return may not initially move lower when M is applied a number of times to a particular type of investment, but eventually the extra supply of commodities produced, or of funds into an investment area, should presumably lower prices and reduce the rate of profit and also, in the alternate case, the interest return. Yet this seemingly valid logic ignores the nature of the investment that produces the return.
In one case, it is an advance of M to invest in means of production and labour-power to get a surplus value that results in a corresponding rate of profit. In the other case, it is an advance of M on the money markets, into bonds, etc, to get back a value of M plus interest. In the first case, the M may be advanced to expand the circuit of production. This could even raise the rate of profit if it boosted the productivity of a company versus its competitors, although, taken for the economy as a whole and over a period of time, probably not. The real problem for this proposed mechanism occurs for the advance of M for the ‘financial’ investment.
Moneybags wants to get back the invested funds, M, plus interest. But is Moneybags literally a bag of money hovering in the air, having no costs of investment that need to be deducted from the interest received? Also, what if Moneybags also borrows money from others to help fund the investment? Then the net investment return will depend on the difference between the borrowing and lending interest rates, as well as the deduction of his relevant costs. This means that the ‘rate of interest’, seen as a return on money capital advanced, is not as straightforward for Moneybags as the economists’ assertion of the letter i for interest would suggest.
Neither is the ‘r’ for the profit rate unambiguous. Industrial and commercial companies will borrow funds for investment as well as using their own funds. This means that their net profit is reduced by their interest payments; to give what Marx called the ‘profit of enterprise’. This latter profit is best measured over the money advanced by the industrial and commercial capitalists to get their ‘rate of profit’, but that will generally be a different number from the rate of return on the investment as a whole, as explained earlier.
The industrial and commercial capitalists will tend to borrow more, the lower is the rate of interest on borrowing versus the going rate of profit. They might also stop any extra borrowing when the rate of interest rises to equal the rate of profit that extra investment funds could generate. Yet, while that looks like a possible market mechanism for tending to equalise the rate of interest and the rate of profit, it is at best only a partial one. For example, companies would not borrow indefinitely with a lower rate of interest than the rate of profit. To do so would greatly increase their ‘leverage’ and expose them to the risk of having to service debt and pay interest even if the conditions of profitable production deteriorate. For such reasons, stockmarket investors usually frown upon highly leveraged companies.
In addition, there is the point, explained in my book, The City,[1] that the ‘profit rate’ of financial firms, such as banks who can create their own financial assets, or who depend upon attracting funds from other money capitalists and savers, such as asset managers, cannot sensibly be compared with the profit rate of industrial and commercial corporations advancing capital for their business. It is not comparing like with like.

In Marxist theory, there is no law determining the rate of interest, while profits are determined by the surplus value extracted from productive workers. That profit is measured over the capital invested, to determine a rate of profit for the system as a whole, and the profit remaining to the productive capitalists is determined after paying the amount of interest. [2] The only barrier to the rate of interest is that it cannot be sustained at a level that eats up all the profit of productive capital. In recent years, ‘real’ rates of interest have been negative (when compared to inflation levels), and have even been negative for some rates in nominal terms, but no statistician has so far claimed that corporate profitability has become close to zero or negative for the economy as a whole. This gives empirical support to the argument in this article that there is no equalisation of the rate of interest and rate of profit.
Developments in capitalist society mean that the 19th century picture of the industrial capitalist versus the money capitalist and, correspondingly, the rate of profit versus the rate of interest have taken on a new form today. While it is possible to identify capitalist entrepreneurs who have founded companies, from James Dyson (vacuum cleaners) to Mark Zuckerberg (Facebook), most of these have also evolved into being financial entrepreneurs, using borrowings from capital markets and financial operations to boost their market status and power. It is commonly the case that ‘entrepreneurs’ these days cannot readily be separated from ‘financiers’, given their often multiple shareholdings and other financial interests; still less can the initial investors in their projects from the financial elite be considered under the same heading as Marx’s industrial capitalists.
So there is not any longer, even if there once was in Marx’s time, a distinct class of ‘money capitalists’ versus the rest of the capitalist class. Individual capitalists will often have a portfolio of more important and less important holdings in companies, ones they pay more attention to and others, ones that are industrial, commercial or financial, together with the additional assets they hold in the form of government and corporate bonds, money market securities, bank deposits and so forth.
The activities of asset managers, insurance companies and pension funds complicate the situation further. In the rich countries, where financial operations are more prevalent, a significant proportion of the population indirectly owns a large share of corporate equity. No individual among these feels in control. Rightly so, since their monthly payments or accumulated savings are used to boost the corporate elite. But they nevertheless also benefit from and have a stake in the fortunes of the capitalist corporations in which they have invested. This has an impact on the politics of the populations concerned. But I do not cite this as the only political problem faced, since in the richer, imperialist societies the poorest will also commonly be among the most aggressive supporters of their state’s power.

Tony Norfield, 26 August 2016

[1] See here.
[2] Even this simple summary ignores the question of rent on land ownership, dealt with in the latter parts of Volume 3 of Capital. In this article, I do not cover the separate question of the tendency of the rate of profit to fall. My book, The City, discusses how measures of the rate of profit are impacted by financial developments, state intervention and, especially, by the position of a country in the world economic system.


  1. You say,

    "But if it has borrowed half its investment funds from banks at a rate of just 5%, or issued bonds with a yield of 5%, then the rate of profit on the funds that the company’s owners have advanced will be higher. For example, for 200 invested at 10%, the annual return is 20. But if the company’s owners have invested only 100 of their own money plus an extra 100 they have borrowed, the company then gets as its profit the 20 total minus the 5 it needs to pay on its borrowings, etc. "

    But, this is wrong. Marx rate of profit is calculated on the capital value of the productive capital invested, not any money amounts advanced. Marx makes quite clear that the reason he analyses the rate of profit in Volume III, prior to then analysing the rate of interest and rent, and the division of profit into interest, rent and profit of enterprise is precisely for this reason.

  2. Reply to Boffy: You have misread the sentences quoted. The value of the productive capital invested includes the 100 borrowed, that is why it is 200. The 100 borrowed is not left as money.

    1. Tony,

      No I haven't misread it. The money borrowed, and the money prices paid (including the money put up by the capital itself) only provide the historic price of the money advanced, not the value of the productive-capital advanced.

      In Volume II, Marx makes clear that the rate of profit is calculated on the current reproduction cost of the productive-capital. It is he says based upon the circuit of Productive-capital P...P. However, that circuit he goes on details the use values employed, which must be reproduced on a like for like basis. Consequently, he goes on, it is necessary to use the current money equivalent of the value of those use values, in order to perform a rational calculation. But, he emphasises that the money, M, here is only money as unit of account - it is NOT the money prices actually paid.

      I have set out all of the Marxist definitions of The Rate of Profit, Annual Rate of Profit, Rate of Interest, Rate of Rent and rate of profit of Enterprise on my blog, in the Glossary.

      Unfortunately, I'm having Internet problems at the moment, which makes it difficult to provide links etc.

      However, a reference to logic will suffice here. If we take your example, assume that a capital borrows all of the money it uses as money-capital, which it then uses to buy the elements of productive-capital.

      Let's say it borrows £1,000, and buys machines, materials and labour-power. This productive-capital produces a profit of £100, which is Marx's rate of profit, of 10%. Assume, the capital pays £50 in interest to the money lender, leaving £50 of profit of enterprise.

      On the basis you have set out the capital would have made £50 profit. So what is its rate of profit on your basis? It would be 50/0 x 100, because it has advanced, on your basis no capital of its own, having borrowed it all.

      What rate of profit is 50/0 x 100? As with anything divided by zero, it is infinity, which is usually an indication that there is something wrong with the formulation that leads to it.

  3. Reply to Boffy: Your first point, which argues that the amount of money advanced by the capitalist may not represent the value of the means of production and labour-power employed, is not relevant to the argument I am making in this article about the rate of profit and rate of interest.

    Your second point does not follow from the first, and bears no relationship to reality. You would struggle to find an example of a capitalist borrowing all the money required to set up a business, advancing nothing of his own. Banks, hedge funds, bond investors and others doing the lending may do stupid things, but they are not that stupid. If the capitalist did somehow manage to borrow 100%, then the ‘rate of profit’ (or, more accurately, ‘rate of profit of enterprise’ or ‘return on equity’) calculation is undefined. If a calculation turns out to be ‘infinity’, then that is not unusual. In this case, it would just mean that the calculation is an inappropriate one to make. There would be nothing odd about that, except that it never happens.

  4. The first point clearly is relevant, because you are saying that you are calculating a Marxian rate of profit, when in fact you are not. The circuit you are describing here is that which Marx sets out as M - M - C ... P... C' - M' - M'. But, Marx makes clear that the portion M - M, and M' - M', actually stands outside the circuit of capital, because the first M involved here is fictitious capital, it is the same money-capital that functions a second time as the money-capital, which metamorphoses into productive-capital. It can only expand, earn interest, because the actual productive-capital self expands and produces profit. The phase M' - M', similarly is outside the circuit of capital, because it simply reflects the return of the loaned money-capital plus the interest.

    It doesn't matter where the money-capital comes from that metamorphoses into productive-capital, because Marx calculates the rate of profit on the capital value of the productive-capital advanced.

    Your second objection does not stand up. Marx uses thought experiments lots of times of things do not exist in reality, to prove a point. In fact, in explaining the relation between the rate of profit and rate of interest in Capital III, Marx cites the example, not of someone borrowing money, but of borrowing a machine which operates as productive-capital.

    Marx's definition of the rate of profit is based upon the capital value of the productive-capital advanced. So, in his example, he says if a machine is borrowed with a value of say £1,000, and the average annual rate of profit is 10%, then the capital will make £100 profit, if it makes the average rate of profit.

    Marx makes clear again, thereby that the rate of profit is calculated on this capital value of the productive-capital advanced, not on the money-capital advanced as the historic price of means of production and labour-power. He then demonstrates how, payments of interest and rent are deductions from that profit.


  5. What you have done by calculating a rate of profit on the basis of the money advanced by the capitalist, is to confuse capital with capitalists. You have calculated a rate of return on the one hand for the money capitalist who advanced an amount of money-capital, and a rate of return for the money-capital advanced by the productive capitalist.

    But, neither of these ar the calculation of the rate of profit as set out by Marx. neither, in fact are they Marx's calculation of the rate of interest, or even his method of calculating the rate of profit of enterprise.

    As Marx sets out it is first necessary to calculate the annual rate of profit on the productive-capital advanced, which in your case above was £200. If it produces a profit of £10, and the capital turns over once during the year, then the annual rate of profit,and rate of profit is 5%. The reason Marx insists on this, is precisely because it is this productive-capital that is the capital that self expands and produces the profit. The rate of profit measures the amount of that self-expansion. P...P, expressed in money terms as unit of account.

    If a money-lending capitalist advanced £100, M- M, and obtains the return of this capital, plus interest of £5, M' - M', then it has obtained a rate of interest of 5%. That leaves £50 of profit of enterprise, which means that it has produced a return of 5%.

    But, as Marx sets out the reason that the rate of interest and rate of profit of enterprise amount to these proportions of the rate of profit here, is only because the annual rate of profit, and rate of profit have been made the same here, and also because no change in the value of the productive-capital advanced, other than its self-expansion has been assumed.


  6. For example, suppose the capital turned over twice during the year rather than once. The rate of interest would remain 5%. But, the annual rate of profit for this capital would rise. The profit produced by the advanced capital of £200, would rise from £10 to £20, so the annual rate of profit rises from 5% to 10%.

    After paying the interest due to the money lender, the capital retains £15 of profit, which means the rate of profit of enterprise rises to 15%, which is a reflection of what is available for accumulation.

    But, in Volume III, Chapter 6 and elsewhere, Marx again demonstrates that the rate of profit is calculated on the capital value of the productive-capital, not the money advanced to purchase it. So, for example, if £100 is borrowed and £100 advanced to buy elements of productive-capital this tells us nothing about the rate of profit.

    As Marx sets out, in that Chapter and in many more places, if the value of the productive-capital changes during the production process, the example Marx gives is of a change in the value of cotton as an input in the production of yarn, then this will impact the calculation of the rate of profit.

    In other words, if we assume that half of the value of the £200 of productive-capital comprised cotton, whose value doubles after it has been bought, but before it is processed and sold as yarn, then the value of advanced capital will have risen from £200 to £300, irrespective of the fact that only £200 of money had initially been advanced.

    Marx goes into great detail, in Volume I, and in Theories of Surplus Value, to show the difference between the effects of such changes in the value of the constant capital as against a rise in the value of labour-power (variable-capital) on both the value of the end product, and on the rate of profit.

    So, here, the increased value of cotton is passed on into the value of the yarn. previously, the value of output was £200 advanced capital (one turnover) plus £10 profit = £210. Now it is £300, value of advanced capital, plus £10 = £310, value of output. The profit does not rise, because the labour-power produces the same amount of surplus value as before.

    But, the effect here is that the rate of profit falls from 5%, to just 3.33%, reflecting the reduced amount of self-expansion of the productive-capital. But, on your basis the rate of profit would remain the same.

  7. Tony,

    I made a computational error in a previous comment due to working within the confines of the comments box. In detailing the situation where the productive-capital turns over twice, I calculated the rate of profit of enterprise as rising to 15%. I should have said rises to 7.5%. That is the profit rises to £20, £5 was deducted as interest, leaving £15 of profit of enterprise, which is 7.5% on the advanced productive-capital of £200. It is the amount available for accumulation.

    Nowhere in the three volumes of Capital, nor in the three parts of theories of surplus value does Marx come even close to calculating the rate of profit on the basis that you have done. The rate of profit is calculated on the capital value of the advanced productive-capital. Noweher does Marx calculate the rate of profit by making a distinction as to whether the money used for the purchase of that productive-capital was provided by the private owner of the capital (in any case irrelevant in the case of socialised capital) or was borrowed.

    In Capital II, Chapter 9, Marx writes,

    “... even if by far the greater part of the advanced productive capital consists of fixed capital whose period of reproduction, hence also of turnover, comprises a cycle of many years, the capital-value turned over during the year may, on account of the repeated turnovers of the circulating capital within the same year, be larger than the aggregate value of the advanced capital.” (p 187)

    Its important to note here that what Marx is calculating is not the actual money laid out, but the capital-value in money form. He is using M – M, rather than P...P, only to be able to make that calculation. What is still at issue, what is actually being turned over is still physical capital, not money-capital. If, the machine suffers some form of depreciation, so that its value falls to £5,000, the fact that £10,000 in money had originally been laid out for it is irrelevant. What M – M is considering is the actual capital-value advanced, and returned. Now, the capital advanced at the start of this circuit, is £5,000 – the new capital value of the machine. If it continues to lose 10% of its value in wear and tear, then it will transfer now, £500, rather than £1,000 to the end product. That will be realised in the sale of the end product, so that £500 will then flow back as money, i.e. M – M, becomes £5,000 - £500. The advanced capital-value continues to turn over at the rate of 0.1% a year.

    As Marx states,

    “In calculating the aggregate turnover of the advanced productive capital we therefore fix all its elements in the money-form, so that the return to that form concludes the turnover. We assume that value is always advanced in money, even in the continuous process of production, where this money-form of value is only that of money of account. Thus we can compute the average.” (p 187)

    Note Marx's terminology here. Firstly he begins by making clear that what he is talking about is “the advanced productive capital”. To make clear it is not the advance of the money-capital used to purchase that productive capital, that Marx is talking of, he then says that what he is doing is only to “fix all its elements in the money-form”. Finally, to make clear that his analysis here is one based on the actual capital-value advanced, and not on the money-capital advanced, the historic price, he makes clear that the use of money here, is merely a convenience of calculation, and that he is using it essentially only in its role as “money of account”.