Monday, 3 October 2016

Differential Value

Differential Value is a concept developed by Marx to deal with a logical problem arising from his theory of rent. Marx outlines the nature of this problem, and the basis of Differential Value as the means of resolving it in Theories of Surplus Value, Chapter 12.

The problem amounts to the following. Marx distinguishes between two types of rent – Absolute Rent, and Differential Rent. Differential Rent also divides into Differential Rent I, which arises from varying fertility of different types of land, and Differential Rent II, which arises from the addition of increasing amounts of capital to a given area of land, i.e. what orthodox economics would describe as the marginal productivity of land and capital respectively.

The Absolute Rent arises on all cultivated land, contrary to the belief of Ricardo, who denied the possibility of Absolute Rent. The basis of Absolute Rent, Marx sets out, is the existence of landed property. The owners of land have no reason to permit its use by capitalist farmers, unless they are paid a rent for its use. The economic basis of the Absolute Rent is the overall surplus profit obtained in agriculture compared to the general annual rate of profit in industry. That surplus profit arises because the organic composition of capital in agriculture is lower than in industry.

In industry, such surplus profits, between different spheres, are competed away, as capital moves from low profit areas to high profit areas, increasing the supply of commodities in the high profit areas, and thereby reducing their prices to the price of production, where only the general annual rate of profit is obtained. But, capital can only enter agriculture, if it is prepared to pay this absolute rent, and it will only do so, if it can also still make the average profit. Capital will then be restricted from entering agriculture, and reducing agricultural prices, and will remain in industry, keeping industrial prices lower than they would have been, and keeping the general annual rate of profit lower than it would have been.

The Absolute Rent, then, as its name suggests, is an Absolute Rent, a flat rate that must be paid by all cultivated land. The Differential Rent, is an amount of rent paid in addition to the Absolute Rent, and is determined by the specific surplus profit made on one type of land compared to another. The more surplus profit a piece of land produces the higher the Differential Rent. Absolute Rent acts as a limitation on additional capital investment, but Differential Rent does not. Absolute Rent limits capital investment, because capital will only be invested if market prices are high enough to cover both the general annual rate of profit, and the absolute rent, but Differential Rent requires that such a condition already exists. Additional capital investment, therefore, not only covers that absolute rent, but produces additional profit for the capitalist farmer. 

Total rent is then the sum of the Absolute Rent and the Differential Rent. However, the logical problem that Marx identifies is that under some market conditions, the market value of output is not determined by the least fertile land. Under those conditions, the market value of output, will not be sufficient to cover the payment of Absolute Rent, on some types of land. Marx sets out various scenarios where this occurs in a set of tables Tables A-E, presented in an insert between pages 264-265, of Chapter 12 of Theories of Surplus Value.

But, if the Total Rent on a piece of land is the sum of the Absolute Rent and the Differential Rent, and if, as must be the case, the Absolute Rent, is a flat rate payable on all cultivated land, if the actual rent paid is less than the Absolute Rent, that has to mean that the Differential Rent would be a negative amount. The idea of a negative rent, of a landlord paying a tenant to use their lower fertility land is irrational. It is in order to overcome this irrationality that Marx introduces the concept of Differential Value.

In Theories of Surplus Value, Marx uses the term “cost-price” for what in Capital Volume III, he defines as “Price of Production”. Wherever Marx uses the term “cost-price” here, therefore, it has to be born in mind that he does not mean cost-price as used in Capital, or as generally understood to mean the cost of production (c + v), but means price of production, the cost price plus the average profit, or k +p.

The basis of Absolute Rent is the surplus profit produced in agriculture compared to the general annual rate of profit in industry. Marx sets this out as follows.


c 80 + v 20 + s 10 = 110, r' = 10%.


c 60 + v 40 + s 20 = 120, r' = 20%.

If agriculture were like other industries, capital would flow into it, in search of this higher rate of profit. Agricultural prices would fall and industrial prices rise until both settled at the price of production of 115, where both sectors would make an annual rate of profit of 15%. But, landed property prevents such a free flow of capital. The landlord says, to the capitalist farmer, you have invested 100 of capital, and like other capitalists you are entitled to a 10% rate of profit. But, the value of your output is 120, so I will take 10 as an absolute rent, which means you will still make that average annual rate of profit.

On this basis, the general annual rate of profit is that set in industry of 10%. Both industrial and agricultural capitalist obtain this same average rate, whilst the landlord appropriates the surplus profit of 10, as absolute rent. The basis of the Absolute Rent then is the difference between the market value of output (120) and the price of production of that output (110). Ricardo's assumption in his theory of rent, is that it is the least fertile land that determines this market value. Because Ricardo does not understand the difference between market value, or exchange value, and price of production, he cannot understand the basis of Absolute Rent, which is why he denies its possibility.

But some agricultural producers operate on more fertile land than others. If the least fertile land determines the market value, then these other producers, using more fertile land, will have lower costs of production, and so will make surplus profits, resulting from this advantage. This additional surplus profit, is the basis of the Differential Rent. The Differential Rent is then equal to the difference between the Individual Value of output from a particular type of land, and the Market Value of that output.

By extension, therefore, the total rent for a particular type of land is the difference between its individual price of production and the market value. Marx sets these relations out as follows.

“In order to put this down in the form of equations, we shall call the absolute rent AR, the differential rent DR, the total rent TR, the market-value MV, the individual value IV and the cost-price CP. We then have the following equations:

1. AR=IV-CP=+y

2. DR=MV-IV=x


If MV>IV then MV-IV=+x. Hence: DR positive and TR= y+x.

And MV-CP=y+x. Or MV-y-x=CP or MV=y+x+CP. 

If MV < IV then MV - IV = -x.  Hence DR negative and TR = y - x.
And MV-CP=y-x. Or MV+x=IV. Or MV+x-y=CP. Or MV=y-x+CP.

If MV=IV, then DR=0, x=0, because MV-IV=0.


If MV=CP [then] TR or MV-CP=0”

(Theories of Surplus Value, Chapter 12, p 294)

But, its then obvious, on the basis of these formulas, that, under certain market conditions, as Marx sets out in the Tables A-E, that although in each case, Total Rent (TR), should be greater than zero, Differential Rent (DR) could be negative.

Marx introduces the concept of Differential Value to deal with this anomaly. He writes,

“As regards products of separate classes, it is quite possible, that their [individual] value is above or below the market-value. If it is above the market-value, the difference between the market-value and their cost-price is smaller than the difference between their individual value and their cost-price. But as the absolute rent equals the difference between their individual value and their cost-price, the market-value cannot, in this case, yield the entire absolute rent for these products. If the market-value sank down to their cost-price, it would yield no rent for them at all. They could pay no rent, since rent is only the difference between value and cost-price, and for them, individually, this difference would have disappeared, because of the [fall in the] market-value. In this case, the difference between the market-value and their individual value is negative, that is, the market-value differs from their individual value by a negative amount. The difference between market-value and individual value in general I call differential value.”

(Theories of Surplus Value, Chapter 12, p 268) 

The Differential Value is calculated per unit of output as the difference between its market-value, and individual value. On more fertile lands, the market value of output per unit should always be higher than the individual value per unit of output, and so the differential value will be positive, but on the less fertile land, the market value per unit could be lower than the individual value per unit resulting in a negative differential value. To take one of the examples that Marx gives, to illustrate where such a situation could arise, if some new land is brought into use that is very fertile, so that the supply of commodities (Marx in these examples uses the output of mines) increases, it could push market prices for these commodities down.

At these lower market prices, demand may expand so that all of the output from all land can be absorbed. But, if this market price is lower than the individual value of production on the least fertile land, not only will it not, be able to pay any Differential Rent, but it will not be able to pay the full amount of Absolute Rent. But, producers on this land would be unable to raise prices to a level where the full Absolute Rent was payable, because if they did, demand for the commodities would fall, and their particular output would not be saleable.

Suppose, £1,000 of capital is employed on this land comprising £600 c + £400 v, and the rate of surplus value is 50%, so s = £200. If 1,000 units are produced, there individual value is £1.20 per unit. If the average rate of profit is 10%, the individual price of production is £1.10 per unit. If the market value of these commodities is also £1.20 per unit, then an Absolute Rent of £10 is payable. However, suppose some new more productive land comes into production, which causes the market value of these commodities to fall to £1.15 per unit. This new production means that now 1,200 units are produced each year. At this lower price of £1.15 per unit, all of these 1,200 units can be sold, but at £1.20 per unit, only 1,000 units can be sold, which means that 200 units of the first capital's output would be unsaleable.

Yet, at £1.15 per unit, it still produces a profit of £0.15 per unit over its cost of production of £1, and moreover, this profit of £0.15 per unit, or 15%, is more than the average rate of profit in industry of 10%. So, there is still an incentive to produce, but it would then not be possible to pay the full amount of absolute rent.

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