## Sunday, 18 March 2018

### Average Profit

Summary
• Average profit is an amount rather than a ratio
• The amount of average profit is calculated on the basis of the average annual rate of profit
• The average annual rate of profit is calculated on the total advanced capital. It is the surplus value produced in a year, S, as a proportion of the total advanced capital, C. It is then S/C, or put another way, it is the surplus value produced in one turnover period, s, multiplied by the number of turnovers of the circulating capital (effectively of the variable-capital,v), n, as a proportion of the total advanced capital for one turnover period, i.e. s x n/C.
• This amount of average profit, p, is added to the cost of production (d + c + v), or k, to give the price of production of a commodity.
• The rate of profit, or profit margin is equal to p/k. The rate of profit, or profit margin, is then different to the annual rate of profit, because the amount of average profit represents a different ratio where it is measured against the total laid-out capital, or cost of production, as opposed to where it is measured against the total advanced capital.
• Wherever the advanced capital is greater than the laid out capital, the annual rate of profit will be lower than the rate of profit, and vice versa. The higher the rate of turnover of capital, the more the laid-out capital will rise relative to the advanced capital.
• The rate of turnover is also partly a function of productivity, and productivity rises as more, and better fixed capital is introduced. Whilst a higher level of fixed capital investment, increases the amount of capital advanced, it simultaneously, thereby raises the level of productivity, and so increases the rate of turnover, and so reduces the proportion of advanced capital to laid-out capital.
• As the amount of fixed capital increases, the annual rate of profit rises, as productivity and the rate of turnover rises, and the mass of profit rises, but as the mass of laid-out capital rises by a larger proportion, due to this rise in productivity, so this mass of profit is spread across a larger mass of laid-out capital, resulting in a lower rate of profit, and across a larger volume of output, thereby also manifest in a lower profit margin, per unit of output.

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Average Profit is distinguished from the average rate of profit, in the same way that profit is distinguished from the rate of profit, or surplus value is distinguished from the rate of surplus value. In other words, it is an amount rather than a ratio.

Surplus value, as an amount, represents a different ratio if it is measured against the variable-capital, i.e. the rate of surplus value, as against the total laid-out capital, which gives the rate of profit or profit margin, and a different ratio still, if it is measured against the total advanced capital, which gives the annual rate of profit.

When Marx defines the average rate of profit, it is based upon the annual rate of profit. That is in order that the same thing is being measured, in the same way that lenders have to provide borrowers with an annual percentage rate (APR), or Annual Equivalent Rate (AER), of how much it will cost them to borrow money, rather than say a rate of interest for a day, week or month, so with the average rate of profit; it must be based upon the total capital advanced, for a given period of time, i.e. a year.

The total capital advanced, is not the same thing as the total capital laid-out, because the advanced capital turns over at different rates in different spheres, and even for different capitals within the same sphere. Take a capital, involved in producing cars, using the latest factory, with lots of robots. The factory may be expected to last for 20 years, whilst the robots may have a lifespan of 10 years. This fixed capital, might amount to say, £100 million, but perhaps only adds £5 million of value, each year to output via wear and tear. The high-tech, high productivity nature of the production, may mean that it turns over its circulating capital very quickly. In other words, if it needs to produce 1,000 cars in a working period, before sending them to market, it may achieve this every day. So, the circulating capital tied up in the raw materials, and so on, along with the variable-capital used to pay wages, may turn over say every three days. Suppose this circulating capital amounts to £60 million, for the 3 days, or £20,000 per car. This is the total amount of circulating capital, that the firm must advance, because, at the end of the three days, it will get this capital back from the sale of the cars, and so can simply advance this same capital once more.

However, that is not the only capital it must advance, because it has also advanced the £100 million of fixed capital, in the shape of the factory, and the robots. Had it not engaged in this type of production, it could have utilised this capital in some other activity. It expects, therefore, to obtain the average rate of profit on this fixed capital, as well as on the circulating capital. If the average rate of profit is 10%, therefore, this capital will expect to make £10 million on the fixed capital it has advanced, plus £6 million on the circulating capital it has advanced, making a total of £16 million of average profit. If it doesn't make this annual rate of profit, capital will move to other spheres of activity, so that competition will bring about an average annual rate of profit.

But, the industry produces and turns over its capital every three days. Assume that amounts to 100 turn overs per year. Its total laid out-capital is then £5 million for the wear and tear of fixed capital, which is transferred to the value of the year's output, plus £60 million x 100 = £6 billion for circulating capital. That gives total laid out capital, or cost of production of £6.05 billion. Adding the £16 million pound of average profit to this cost of production, gives a price of production of the total output of £6.21 billion. This represents a rate of profit or profit margin of 2.64%. In terms of each car, if in a year, 300,000 cars are produced and sold, the cost of production for each car is £20,166, and the profit margin is 2.64%, or £533, giving a price of production of £20,700.

But, other capitals may have less fixed capital, whilst having circulating capital that is tied up for long periods, due to the nature of the production. A shipbuilder, for example, may have less capital tied up as fixed capital, whilst having a large amount of capital tied up in materials, and wages, which takes a long time to be turned over, simply because of the nature of the product. It takes much longer to produce a large ship than it does to produce a car, and the ship cannot be sold, and the capital tied up in it turned over until it is complete.

Suppose it takes a year for the shipbuilder to turn over its capital. If the shipbuilder has £20 million of fixed capital, with an average lifespan of 10 years, thereby adding £2 million of value to output via wear and tear, each year, but has £140 million of capital advanced for circulating capital, its total advanced capital is the same as that for the car producer, of £160 million. With an average rate of profit of 10%, it thereby produces the same amount of average profit of £16 million. But, the total laid-out capital for the shipbuilder, its cost of production, is £2 million wear and tear of fixed capital, plus £140 million of circulating capital, in the shape of materials and wages. Taking the average profit of £16 million, that gives the price of production of the ship as £142 million, plus £16 million = £158 million, which is a rate of profit/profit margin of 11.27%. So, here, the rate of profit/profit margin is higher than the annual rate of profit/average rate of profit, of 10%.

Marx sets this out in Capital III, Chapter 9, where he says,

“These different rates of profit are equalized by competition to a single general rate of profit, which is the average of all these different rates of profit. The profit accruing in accordance with this general rate of profit to any capital of a given magnitude, whatever its organic composition, is called the average profit. The price of a commodity, which is equal to its cost-price plus the share of the annual average profit on the total capital invested (not merely consumed) in its production that falls to it in accordance with the conditions of turnover, is called its price of production. Take, for example, a capital of 500, of which 100 is fixed capital, and let 10% of this wear out during one turnover of the circulating capital of 400. Let the average profit for the period of turnover be 10%. In that case the cost-price of the product created during this turnover will be 10c for wear plus 400 (c + v) circulating capital = 410, and its price of production will be 410 cost-price plus (10% profit on 500) 50 = 460.”

In other words, here the average annual rate of profit is 10%, giving average profit of £50 on the total advanced capital of £500. However, the cost of production, i.e. the total laid-out capital, for the year amounts not to £500, but only to £410. The average profit of £50 is added to this cost of production, to give a price of production of £460, whilst the rate of profit/profit margin here is 50/410 = 12.20%.

From this, it is clear that the higher the rate of turnover of capital, the higher will be the mass of laid-out capital relative to the advanced capital. As the average profit is a function of the advanced capital, not the laid-out capital, it is also clear then that as the rate of turnover of capital increases the more the rate of profit/profit margin will fall relative to the annual rate of profit, and consequently the more the rate of profit/profit margin for the total social capital will fall relative to the average annual rate of profit.