How to work out the rate of profit

This short paper discusses how to work out the rate of profit, using figures from the US government's Bureau of Economic Analysis (BEA). Any comments are welcome.

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Marx called the rate of profit, s/c+v, the most important law in political economy;

 

“The rate of self-expansion of capitalism, or the rate of profit, being the goal of capitalist production, its fall…appears as a threat to the capitalist production process.”

Capitalists invest in order to make profit, they use their capital M to buy commodities C with a view to receiving an increment or profit on the capital M’. This cycle M – C – M’ is the cycle of capital accumulation.

If profits are rising there are growing opportunities for capitalists to invest and they have more capital to invest. Rising profits provide both the incentive and the means to expand production.

Conversely if profits are falling, there are less opportunities for capitalists to invest, what investments capitalists do make accrue less profits and the mass of profit falls. Falling rates of profit both remove the incentive and the means for capitalists to invest. Consequently the scale of production falls.

Marxists regard changes in the capitalist economy as a necessary and inevitable outcome of the movements of the economy itself. They are objective movements over which the individual capitalist has no control.

How to work out the rate of profit

The value of a commodity consists of constant capital + variable capital + surplus value (C+V+S). The total value of the entire capitalist economy consists of the total value of production in a given year, the total of constant capital consumed in the production process, the total of wages paid and the total of surplus value produced. An individual commodity may be sold above or below its value, but as much as the seller either gains or loses, the buyer gains or loses by the same amount – so such fluctuations cannot determine the value of production.

Constant capital consists of the total depreciation of fixed capital, the value of raw materials, the value of repairs on machinery and investments in new fixed capital.

Variable capital consists of the total of wages earned by the entire working class, this includes some sectors of the ‘middle class’ or ‘labour aristocracy’ i.e. privileged layers, who are nonetheless necessary for capitalist production.

Surplus value – consists of the total of corporate profits, rents to landlords and directors salaries.

The value of the output of an entire economy therefore consists of the total of C+V+S produced in it.

Gross Domestic Product (GDP)

GDP is a measure the value of production of a given economy in a particular year. It is distinguished from Gross National Product (GNP) because it does not include receipts from foreign investments.

(For an explanation of how the income side of GDP is worked out see here

http://en.wikipedia.org/wiki/National_Income_and_Product_Accounts)

Both sides of GDP, output and income, should equal each other as every part of value production is also an income under capitalism, insofar as a proportion of output remains unsold, this will be measured as a deduction from profits.

The additive or the deductive method

The additive method

One typical method for trying to establish the rate of profit in the capitalist economy, is to try and work out the value of the different elements, constant capital, variable capital and profits and establish the rate of profit from them. This method certainly will provide an estimate of the rate of profit, but suffers from a number of problems, the two most important of which are:

Raw materials make up a very large part of constant capital but do not form a part of fixed capital, machinery, buildings etc. Raw materials are rather consumed in the production process itself. Raw materials are often not distinguished in national accounts and this can lead to difficulties in establishing the true value of constant capital consumed in production.

Unproductive sectors like retail do not produce surplus value, but nonetheless consume constant capital, variable capital and create profits – how are they measured?

The deductive method

The deductive method alternatively starts from the assumption that the total value GDP/GNP of a particular economy, must consist of the total of constant, variable and profits produced in a given year. There is no other source of value possible. Certain firms may make super profits, but these will be at the expense of other firms who will make less profits. The production of unproductive sectors is simply a deduction from productive sectors, but still originates in value production.

The national income figures also reflect the rising organic composition of capital, i.e. the historic accumulation of capital which does not take place in the given year, as depreciation rises alongside the growing mass of fixed capital and at a relatively constant rate. The annual write off of value is the root cause of the regular ten year business cycle after all. (Marx Volume II) Hence although, this method may (or may not!) be as accurate as the additive method described above, it does to a reflect the increases in the mass of constant capital undertaken in previous periods of production and therefore the rising organic composition of capital and the falling (or rising) rate of profit. (See note below for more information.)

The deductive method means that if it is possible to establish the mass of profit, then the rate of profit can be deduced simply by deducting it from total GDP so that the rate of profit = mass of profit / (GDP – mass of profits). GDP - mass of profit, must equal the total of constant and variable capital consumed in the production of a given year.

As Marx noted:

"Although the rate of profit thus differs numerically from the rate of surplus-value, while surplus-value and profit are actually the same thing and numerically equal, profit is nevertheless a converted form of surplus-value, a form in which its origin and the secret of its existence are obscured and extinguished. In effect, profit is the form in which surplus-value presents itself to view, and must be initially stripped by analysis to disclose the latter."

Marx Capital Vol III p47.

How to work out the rate of profit using the deductive method

The GDP on the income side of national accounts gives the total income of various participants in the production process, capitalists, middle class and workers and breaks down that income into profits, salaries, rents and proprietor’s income. As all income arises in production, the total income in a given year will equal the total value of production.

The publication of the quarterly national income figures for US output by the Bureau of Economic analysis, gives the most accurate and up to date statistics on the health of the US economy and therefore, is an important indicator for the health of the world economy, as the US continues to produce around 30% of world output and has an even larger share of foreign investments and profits.

It follows then that if we can work out the value of the total profit we can establish the mass of Surplus value S. By deducting profits from national income we can establish the value of Constant and Variable capital and then dividing profits by the total of constant and variable capital, we can establish the rate of profit.

The formula is;

profits/(GDP-profits).

The US governments Bureau of Economic Analysis (BEA) gives precise definitions of what it includes in the categories of these three major forms of profit (see appendix below) therefore, while the total is not absolutely precise for example;

Profits are also included in expense accounts, which are classed as a deduction from profits but are often a portion of surplus value;

Some small proprietors who are not capitalists are included when they should not be; the figure for capital consumption excludes dividends and expenses, which are a form of surplus value (although they should be included in proprietors income)

Nonetheless, these three sources of profit are certainly accurate enough to provide a very good approximation for the mass of profit and if it is possible to establish the mass of profit it is straightforward to establish the value of constant plus variable capital by subtracting the mass of profit from national income to establish the value of constant plus variable capital.

Go to the website for the BEA here National Income by Type of Income:

http://bea.gov/bea/dn/nipaweb/TableView.asp?SelectedTable=53&FirstYear=2004&LastYear=2006&Freq=Qtr

Download all data for the most uptodate figures, import the data into a spreadsheet.

Next work out the mass of profit.

Add up, non-farm proprietors income both after Capital Consumption Allowance and IVA (see precise definition below), non – farm rental income with CCA and IVA, and corporate profits after CCA and IVA.

(Row: Non farm proprietors income with CCA and IVA row 35; Rental income with CCA and IVA row 39; Corporate profits with CCA and IVA row 42)

Divide the mass of profit by national income minus the mass of profit i.e. the value of constant and variable capital together to establish the rate of profit i.e. s/c+v.

Insert this formula (mass of profit/(national income – mass of profit)) to work out the rate of profit.

Replicate the formula across the cells to reveal the rate of profit through history.

Testing the profit rate

The accuracy of this method of establishing the rate of profit can be tested by measuring changes in the profit rate against recessions. Profit rates should fall before recessions and rise during booms.

And indeed the rate of profit described here very accurately follows the movements in the business cycle. 

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Definitions from US Census Dept;

"Methodology for Net Stocks and Depreciation

The primary measure of the value of fixed reproducible tangible wealth is the net stock, that is, the value of the stock adjusted for depreciation. Depreciation is the decline in value due to wear and tear, obsolescence, accidental damage, and aging. For business and government, in addition to its use in calculating net stocks, the same depreciationc onsumption of fixed capitalis presented as part of the NIPA's. Consumption of fixed capital is a charge for the using up of fixed capital, and as such, it is, along with compensation of employees and other components of gross domestic income and gross national income, one of the costs incurred and the profits earned in the production of gross domestic product (GDP) and gross national product (GNP). Consumption of fixed capital is deducted from GDP and GNP to derive net domestic product and net national product. In addition, government consumption of fixed capital is a component of government consumption expenditures (and GDP) as a measure of the value of the services of government fixed assets. "

http://www.allcountries.org/uscensus/888_net_stock_of_fixed_private_capital.html

The similarity of the results can be demonstrated by comparing these graphs with those developed by Freeman and Dumenil and Levy.

See the graphs here and here

Compare with Alan Freeman What makes the US Profit Rate Fall? A response to Robert Brenner’s ‘Economics of global turbulence” page 4

Dumenil and Levy The Real and Financial Components of Profitability (USA 1948-2000) page 7

And of course using this method or one like it, has the huge advantage of providing a relatively up to date and accurate estimate of the rate of profit, to a point that it is if nothing else a very good lead indicator i.e. a measure which indicates trends in the economy as the close correspondance between changes in profit rates and GDP growth figures demonstrates.

See graph here

 

Appendix

The Bureau of Economic Analysis break up the national income measure of GDP into various parts according to the source of income, for the purposes of this discussion we need to know how the sources of profit are measured. This is how they define their measures of rent, proprietors income and profit:

“Proprietors’ income with inventory valuation and capital consumption adjustments (1–8) is the current production income (including income in kind) of sole proprietorships and partnerships and of tax-exempt cooperatives. The imputed net rental income of owner-occupants of farm dwellings is included; the imputed net rental income of owner-occupants of nonfarm dwellings is included in rental income of persons. Proprietors’ income excludes dividends and monetary interest received by nonfinancial business and rental income received by persons not primarily engaged in the real estate business; these incomes are included in dividends, net interest, and rental income of persons. (The inventory valuation and capital consumption adjustments are described below.)

Rental income of persons with capital consumption adjustment (1–9) is the net current-production income of persons (except those primarily engaged in the real estate business) from the rental of real property, the imputed net rental income of owner-occupants of nonfarm dwellings, and the royalties received by persons from patents, copyrights, and rights to natural resources.

Corporate profits with inventory valuation and capital consumption adjustments (1–10) is the net current production income of organizations treated as corporations in the NIPA’s. These organizations consist of all entities required to file Federal corporate tax returns, including mutual financial institutions and cooperatives subject to Federal income tax, private noninsured pension funds,18 nonprofit institutions that primarily serve business, Federal Reserve banks, and federally sponsored credit agencies. With several differences, this income is measured as receipts less expenses as defined in Federal tax law. Among these differences are the following: Receipts exclude capital gains and dividends received, expenses exclude depletion and capital losses and losses resulting from bad debts, inventory withdrawals are valued at replacement cost, and depreciation is on a consistent accounting basis and is valued at replacement cost using depreciation profiles based on empirical evidence on used-asset prices that generally suggest a geometric pattern of price declines. Because national income is defined as the income of U.S. residents, its profits component includes income earned abroad by U.S. corporations and excludes income earned in the United States by the rest of the world.”

(Source: A Guide to the national income and product accounts of the United States, 1929–97 (p10))

http://bea.gov/scb/pdf/misc/nipaguid.pdf

 

Wed 04, April 2007 @ 13:38