Part V, Chapter XVIII VARIOUS FORMULÆ FOR THE RATE OF SURPLUS-VALUE. - Karl Marx, Capital: A Critique of Political Economy. Volume I: The Process of Capitalist Production 
Capital: A Critique of Political Economy. Volume I: The Process of Capitalist Production, by Karl Marx. Trans. from the 3rd German edition, by Samuel Moore and Edward Aveling, ed. Federick Engels. Revised and amplified according to the 4th German ed. by Ernest Untermann (Chicago: Charles H. Kerr and Co., 1909).
About Liberty Fund:
Liberty Fund, Inc. is a private, educational foundation established to encourage the study of the ideal of a society of free and responsible individuals.
The text is in the public domain.
Fair use statement:
This material is put online to further the educational goals of Liberty Fund, Inc. Unless otherwise stated in the Copyright Information section above, this material may be used freely for educational and academic purposes. It may not be used in any way for profit.
- Editor's Note to the First American Edition By Ernest Untermann
- Author's Prefaces to the First and Second Editions, By Karl Marx
- I.—TO The First Edition.
- II.—TO The Second Edition.
- Editor's Prefaces, to the First English Translation and Fourth German Edition By Frederick Engels
- Editor's Preface to the First English Translation.
- Editor's Preface to the Fourth German Edition.
- Volume I. The Process of Capitalist Production.
- Book I. Capitalist Production.
- Part I. Commodities and Money.
- Part I, Chapter I Commodities.
- Section 1.—THE Two Factors of a Commodity: Use-value and Value (the Substance of Value and the Magnitude of Value).
- Section 2.—THE Twofold Character of the Labour Embodied In Commodities.
- Section 3.—THE Form of Value Or Exchange Value.
- A. Elementary Or Accidental Form of Value.
- 1. the Two Poles of the Expression of Value: Relative Form and Equivalent Form.
- 2. the Relative Form of Value.
- (a.) the Nature and Import of This Form.
- (b.) Quantitative Determination of Relative Value.
- 3. the Equivalent Form of Value.
- 4. the Elementary Form of Value Considered As a Whole.
- B. Total Or Expanded Form of Value.
- 1. the Expanded Relative Form of Value.
- 2. the Particular Equivalent Form.
- 3. Defects of the Total Or Expanded Form of Value.
- C. the General Form of Value.
- 1. the Altered Character of the Form of Value.
- 2. the Interdependent Development of the Relative Form of Value, and of the Equivalent Form.
- 3. Transition From the General Form of Value to the Money Form.
- D. the Money Form.
- Section 4.—THE Fetishism of Commodities and the Secret Thereof.
- Part I, Chapter Ii Exchange.
- Part I, Chapter Iii Money, Or the Circulation of Commodities.
- Section 1. The Measure of Values.
- Section 2.—THE Medium of Circulation.
- A. the Metamorphosis of Commodities.
- B. the Currency 82 of Money.
- C. Coin and Symbols of Value.
- Section 3.—MONEY.
- A. Hoarding.
- B. Means of Payment.
- C. Universal Money.
- Part II. the Transformation of Money Into Capital.
- Part Ii, Chapter Iv the General Formula For Capital.
- Part Ii, Chapter V Contradictions In the General Formula of Capital.
- Part Ii, Chapter Vi the Buying and Selling of Labour-power.
- Part III. the Production of Absolute Surplus-value.
- Part Iii, Chapter Vii the Labour-process and the Process of Producing Surplus-value.
- Section 1.—THE Labour-process Or the Production of Use-values.
- Section 2.—THE Production of Surplus-value.
- Part Iii, Chapter Viii Constant Capital and Variable Capital
- Part Iii, Chapter Ix the Rate of Surplus-value.
- Section 1.—THE Degree of Exploitation of Labour-power.
- Section 2.—THE Representation of the Components of the Value of the Product By Corresponding Proportional Parts of the Product Itself.
- Section 3.—SENIOR'S "last Hour."
- Section 4.—SURPLUS Produce
- Part Iii, Chapter X the Working Day
- Section 1—the Limits of the Working Day
- Section 2.—THE Greed For Surplus Labor, Manufacturer and Boyard
- Section 3.—BRANCHES Of English Industry Without Legal Limits to Exploitation
- Section 4.—DAY And Night Work. the Relay System
- Section 5.—THE Struggle For a Normal Working Day. Compulsory Laws For the Extension of the Working Day From the Middle of the 14th to the End of the 17th Century
- Section 6.—THE Struggle For the Normal Working Day. Compulsory Limitation By Law of the Working Time. the English Factory Acts, 1833 to 1864.
- Section 7.—THE Struggle For the Normal Working-day. Re-action of the English Acts On Other Countries.
- Part Iii, Chapter Xi Rate and Mass of Surplus-value.
- Part IV. Production of Relative Surplus-value.
- Part Iv, Chapter Xii the Concept of Relative Surplus-value.
- Part Iv, Chapter Xiii Co-operation.
- Part Iv, Chapter Xiv Division of Labour and Manufacture.
- Section 1.—TWOFOLD Origin of Manufacture.
- Section 2.—THE Detail Labourer and His Implements.
- Section 3.—THE Two Fundamental Forms of Manufacture: Heterogeneous Manufacture, Serial Manufacture.
- Section 4.—DIVISION Of Labour In Manufacture, and Division of Labour In Society.
- Section 5.—THE Capitalistic Character of Manufacture.
- Part Iv, Chapter Xv Machinery and Modern Industry.
- Section 1.—THE Development of Machinery.
- Section 2.—THE Value Transferred By Machinery to the Product
- Section 3.—THE Approximate Effects of Machinery On the Workman.
- A. Appropriation of Supplementary Labour-power By Capital. the Employment of Women and Children.
- B. Prolongation of the Working-day.
- C. Intensification of Labour
- Section IV.—THE Factory
- Section 5.—THE Strife Between Workman and Machine
- Section 6.—THE Theory of Compensation As Regards the Workpeople Displaced By Machinery.
- Section 7.—REPULSION And Attraction of Workpeople By the Factory System. Crisis In the Cotton Trade.
- Section 8.—REVOLUTION Effected In Manufacture, Handicrafts. and Domestic Industry By Modern Industry.
- A. Overthrow of Co-operation Based On Handicraft and On the Division of Labour.
- B. Re-action of the Factory System On Manufacture and Domestic Industries.
- C. Modern Manufacture.
- D. Modern Domestic Industry.
- E. Passage of Modern Manufacture, and Domestic Industry Into Modern Mechanical Industry. the Hastening of This Revolution By the Application of the Factory Acts to Those Industries.
- Section 9.—THE Factory Acts. Sanitary and Education Clauses of the Same. Their General Extension In England.
- Section 10.—MODERN Industry and Agriculture.
- Part V. the Production of Absolute and of Relative Surplus-value.
- Part V, Chapter Xvi Absolute and Relative Surplus-value.
- Part V, Chapter Xvii Changes of Magnitude In the Price of Labour-power and In Surplus-value.
- 1. Length of the Working Day and Intensity of Labour Constant. Productiveness of Labour Variable.
- II. Working-day Constant. Productiveness of Labour Constant. Intensity of Labour Variable.
- III. Productiveness and Intensity of Labour Constant. Length of the Working-day Variable.
- IV.— Simultaneous Variations In the Duration, Productiveness, and Intensity of Labour.
- (1). Diminishing Productiveness of Labour With a Simultaneous Lengthening of the Working-day.
- (2) Increasing Intensity and Productiveness of Labour With Simultaneous Shortening of the Working-day.
- Part V, Chapter Xviii Various FormulÆ For the Rate of Surplus-value.
- Part VI. Wages.
- Part Vi, Chapter Xix the Transformation of the Value (and Respectively the Price) of Labour-power Into Wages.
- Part Vi, Chapter Xx Time-wages.
- Part Vi, Chapter Xxi Piece-wages.
- Part Vi, Chapter Xxii National Differences of Wages.
- Part VII. the Accumulation of Capital.
- Part Vii, Chapter Xxiii Simple Reproduction.
- Part Vii, Chapter Xxiv Conversion of Surplus-value Into Capital.
- Section I.—CAPITALIST Production On a Progressively Increasing Scale. Transition of the Laws of Property That Characterise Production of Commodities Into Laws of Capitalist Appropriation.
- Section 2.—ERRONEOUS Conception By Political Economy of Reproduction On a Progressively Increasing Scale.
- Section 3.—SEPARATION Of Surplus-value Into Capital and Revenue. the Abstinence Theory.
- Section 4.—CIRCUMSTANCES That, Independently of the Division of Surplus-value Into Capital and Revenue, Determine the Amount of Accumulation. Degree of Exploitation of Labour-power. Productivity of Labour. Growing Difference In Amount Between Capital Empl
- Section 5.—THE So-called Labour Fund.
- Part Vii, Chapter Xxv the General Law of Capitalist Accumulation.
- Section 1.—THE Increased Demand For Labour-power That Accompanies Accumulation, the Composition of Capital Remaining the Same.
- Section 2.—RELATIVE Diminution of the Variable Part of Capital Simultaneously With the Progress of Accumulation and of the Concentration That Accompanies It.
- Section 3.—PROGRESSIVE Production of a Relative Surplus-population Or Industrial Reserve Army.
- Section 4.—DIFFERENT Forms of the Relative Surplus-population. the General Law of Capitalistic Accumulation.
- Section 5.—ILLUSTRATIONS Of the General Law of Capitalist Accumulation.
- ( A. ) England From 1846-1866.
- (b). the Badly Paid Strata of the British Industrial Class.
- C. the Nomad Population.
- (d). Effect of Crises On the Best Paid Part of the Working Class.
- (e.) the British Agricultural Proletariat.
- (1.) Bedfordshire.
- (2.) Berkshire.
- (3.) Buckinghamshire.
- (4.) Cambridgeshire.
- (5.) Essex.
- (6.) Herefordshire.
- (7.) Huntingdon.
- (8.) Lincolnshire.
- (9.) Kent.
- (10.) Northamptonshire.
- (11.) Wiltshire.
- (12.) Worcestershire.
- (f.) Ireland.
- Part VIII. the So-called Primitive Accumulation.
- Part Viii, Chapter Xxvi the Secret of Primitive Accumulation.
- Part Viii, Chapter Xxvii Expropriation of the Agricultural Population From the Land.
- Part Viii, Chapter Xxviii Bloody Legislation Against the Expropriated, From the End of the 15th Century. Forcing Down of Wages By Acts of Parliament.
- Part Viii, Chapter Xxix Genesis of the Capitalist Farmer.
- Part Viii, Chapter Xxx Reaction of the Agricultural Revolution On Industry. Creation of the Home Market For Industrial Capital.
- Part Viii, Chapter Xxxi Genesis of the Industrial Capitalist.
- Part Viii, Chapter Xxxii Historical Tendency of Capitalist Accumulation.
- Part Viii, Chapter Xxxiii the Modern Theory of Colonisation. 70
- Works and Authors Quoted In "capital"
Part V, Chapter XVIII
VARIOUS FORMULÆ FOR THE RATE OF SURPLUS-VALUE.
WE have seen that the rate of surplus-value is represented by the following formulæ.
The two first of these formulæ represent, as a ratio of values, that which, in the third, is represented as a ratio of the times during which those values are produced. These formulæ, supplementary the one to the other, are rigorously definite and correct. We therefore find them substantially, but not consciously, worked out in classical political economy. There we meet with the following derivative formulæ.
One and the same ratio is here expressed as a ratio of labour-times, of the values in which those labour-times are embodied, and of the products in which those values exist. It is of course understood that, by "Value of the Product," is meant only the value newly created in a working-day, the constant part of the value of the product being excluded.
In all of these formulæ (II.), the actual degree of exploitation of labour, or the rate of surplus-value, is falsely expressed. Let the working-day be 12 hours. Then, making the same assumptions as in former instances, the real degree of exploitation of labour will be represented in the following proportions.
From formulæ II. we get very differently,
These derivative formulæ express, in reality, only the proportion in which the working-day, or the value produced by it, is divided between capitalist and labourer. If they are to be treated as direct expressions of the degree of self-expansion of capital, the following erroneous law would hold good: Surplus-labour or surplus-value can never reach 100%. Since the surplus-labour is only an aliquot part of the working-day, or since surplus-value is only an aliquot part of the value created, the surplus-labour must necessarily be always less than the working-day, or the surplus-value always less than the total value created. In order, however, to attain the ratio of 100:100 they must be equal. In order that the surplus-labour may absorb the whole day (i.e., an average day of any week or year), the necessary labour must sink to zero. But if the necessary labour vanish, so too does the surplus-labour, since it is only a function of the former. The ratio Surplus-labour/Working-day or Surplus-value/Value created can therefore never reach the limit of 100/100, still less rise to (100+x)/100. But not so the rate of surplus-value, the real degree of exploitation of labour. Take, e.g., the estimate of L. de Lavergne, according to which the English agricultural labourer gets only ¼, the capitalist (farmer) on the other hand ¾ of the product or of its value, apart from the question of how the booty is subsequently divided between the capitalist, the landlord and others. According to this, the surplus-labour of the English agricultural labourer is to his necessary labour as 3:1, which gives a rate of exploitation of 300%.
The favourite method of treating the working-day as constant in magnitude became, through the use of the formulæ II., a fixed usage, because in them surplus-labour is always compared with a working-day of given length. The same holds good when the repartition of the value produced is exclusively kept in sight. The working-day that has already been realised in a given value, must necessarily be a day of given length.
The habit of representing surplus-value and value of labour-power as fractions of the value created—a habit that originates in the capitalist mode of production itself, and whose import will hereafter be disclosed—conceals the very transaction that characterises capital, namely the exchange of variable capital for living labour-power, and the consequent exclusion of the labourer from the product. Instead of the real fact, we have the false semblance of an association, in which labourer and capitalist divide the product in proportion to the different elements which they respectively contribute towards its formation.
Moreover, the formulæ II. can at any time be reconverted into formulæ I. If, for instance, we have (Surplus-labour of 6 hours)/(Working-day of 12 hours) the necessary labour-time being 12 hours less the surplus-labour of 6 hours, we get the following result,
(Surplus-labour of 6 hours)/(Necessary-labour of 6 hours) = 100/100
There is a third formula which I have occasionally already anticipated; it is
After the investigations we have given above, it is no longer possible to be misled, by the formula (Unpaid-labour)/(Paid labour), into concluding, that the capitalist pays for labour and not for labour-power. This formula is only a popular expression for (Surplus-labour)/(Necessary labour). The capitalist pays the value, so far as price co-incides with value, of the labour-power, and receives in exchange the disposal of the living labour-power itself. His usufruct is spread over two periods. During one the labourer produces a value that is only equal to the value of his labour-power: he produces its equivalent. Thus the capitalist receives in return for his advance of the price of the labour power, a product of the same price. It is the same as if he had bought the product ready made in the market. During the other period, the period of surplus-labour, the usufruct of the labour-power creates a value for the capitalist, that costs him no equivalent. This expenditure of labour-power comes to him gratis. In this sense it is that surplus-labour can be called unpaid labour.
Capital, therefore, is not only, as Adam Smith says, the command over labour. It is essentially the command over unpaid labour. All surplus-value, whatever particular form (profit, interest, or rent), it may subsequently crystallise into, is in substance the materialisation of unpaid labour. The secret of the self-expansion of capital resolves itself into having the disposal of a definite quantity of other people's unpaid labour.