UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

The principle of marginal cost pricing Copes, Parzifal 1950

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1950_A8 C7 P7.pdf [ 6.36MB ]
Metadata
JSON: 831-1.0106875.json
JSON-LD: 831-1.0106875-ld.json
RDF/XML (Pretty): 831-1.0106875-rdf.xml
RDF/JSON: 831-1.0106875-rdf.json
Turtle: 831-1.0106875-turtle.txt
N-Triples: 831-1.0106875-rdf-ntriples.txt
Original Record: 831-1.0106875-source.json
Full Text
831-1.0106875-fulltext.txt
Citation
831-1.0106875.ris

Full Text

THE PRINCIPLE-OF MARGINAL COST PRICING A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF IN THE DEPARTMENT OF ECONOMICS, POLITICAL SCIENCE AND SOCIOLOGY. THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1950 PARZIVAL COPES MASTER OF ARTS \ Cd A • I ABSTRACT OP THE PRINCIPLE OF MARGINAL COST PRICING by PARZIVAL COPES A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS IN THE DEPARTMENT OF ECONOMICS, POLITICAL SCIENCE AND SOCIOLOGY THE UNIVERSITY OF BRITISH COLUMBIA APRIL, 1950 THE PRINCIPLE OF MARGINAL COST PRICING In this thesis an attempt i s made to describe the main features and some of the attendant problems of a system of price determination which has been recommended by several economists as the s o c i a l l y most desirable p r i c i n g system. The p r i n c i p l e on which th i s p r i c i n g method i s based is re-ferred to as "marginal cost p r i c i n g " , because i t requires that a l l prices for economic goods should equal the marginal costs of t h e i r production. The basic .reasoning which underlies the formula of marginal cost p r i c i n g i s simply that wherever society can produce an additional item of any product at a cost less than the value which any,'member of society i s w i l l i n g to surrender for that item, i t should be produced,. By making the priced of each good equal to the cost of producing an additional (marginal) item, consumers w i l l be encouraged to demand exactly the output thus produced. Two•analytical approaches to the matter are pre-sented. F i r s t a s^iummary is given of Professor Lerner 's theory of marginal cost p r i c i n g , based on the marginal sub-s t i t u t a b i l i t y concept of the indifference theory of value. However, most of the problems involved lend themselves better to analysis along the l i n e s of the u t i l i t y theory, in terms of which the remainder of the thesis i s written. Special emphasis is placed upon the equilibrium of the firm under marginal cost p r i c i n g and upon the influence of taxa-t i o n . A discussion of the main c r i t i c i s m brought out against the marginal cost p r i c i n g theory, both of a theoret .ical and a p r a c t i c a l nature, i s also presented. The conclusion reached i n the thesis is that i f price determination could be considered an isolated problem marginal cost p r i c i n g would indeed appear lo be desirable. I n s t i t u t i o n a l complications, however, make a universal ap p l i c a t i o n of the p r i n c i p l e appear both improbable and Inadvisable within the forseeable future. i CONTENTS I. INTRODUCTION 1. Subject of the thesis. 2. Development of the marginal cost p r i c i n g theory. 3. Outline of the discussion. II. THE MARGINAL SUBSTITUTABILITY APPROACH TO MARGINAL COST PRICING 1. Value'concepts of the marginal s u b s t i t u t a b i l i t y approach. 2. Professor Lerner's economic c r i t e r i a . 3. Optimum, conditions i n the f i e l d of d i s t r i b u t i o n . ,4. Optimum conditions i n the f i e l d of production -: the "Rule". -5. Social u t i l i t y - o f the price mechanism. 6. The "welfare equations" and perfect competition. 7. Imperfect competition and the "Rule". 8. The marginal cost schedule. 9. Application of the "Rule" i n decreasing average cost industries. III. THE UTILITY ANALYSIS OP MARGINAL COST PRICING .. . 24 1. The u t i l i t y theory of value and marginal cost p r i c i n g . 2. The constant marginal u t i l i t y of money. 3. The optimum d i s t r i b u t i o n of income. 4. The.demand function for a firm's product and consumers ' surpluses. 5. The cost function of a firm.' 6. The maximisation of private and s o c i a l p r o f i t . Producers' surpluses. 7. Social p r o f i t a b i l i t y of decreasing average cost industries. 8. The general equilibrium. 9. Comparison of maximum private p r o f i t p r i c i n g and marginal cost p r i c i n g . IV. TAXATION PROBLEMS RAISED BY THE PRACTICE OF MARGINAL COST PRICING 57 1. Forms of taxation. 2. Ef f e c t s of the excise .tax on the equilibrium of the firm. 5. The ultimate sources of tax revenue. 4. Direct taxation of surpluses. 5. Effects of taxation of surpluses on the general equilibrium. 6. Proportional excise taxes. V. THE RECORDED CRITICISM OF .MARGINAL COST PRICING . . 78 1. Sources of c r i t i c i s m . 2. Mr. Coase's model for multi-part p r i c i n g . 3. Analysis of multi-part p r i c i n g . 4. The r e d i s t r i b u t i o n of income under marginal cost p r i c i n g . 5. The'effects of marginal cost p r i c i n g on • taxation. 6. Estimation of s o c i a l p r o f i t a b i l i t y . VI. THE SIGNIFICANCE OF THE MARGINAL COST PRICING THEORY 92 1. Contention of the marginal cost p r i c i n g theory. 2. Limitations of the analysis presented. 3. Theoretical shortcomings. 4. P r a c t i c a l objections. 5. E x i s t i n g applications of marginal cost p r i c i n g . 6. Methods^ of introducing marginal cost p r i c i n g . 7. Conclusion. VII. APPENDICES i . SOME NOTES ON THE ANALYSIS OF SOCIAL COST . 106 i i . MARGINAL COST PRICING THROUGH SUBSIDISATION 111 i i i . MARGINAL COST PRICING THROUGH PRICE FIXING . 113 VIII. BIBLIOGRAPHY 119 A B B R E V I A T I O N S ape. average private cost apr. average private revenue ar (modified) average revenue asc average s o c i a l cost asr average s o c i a l revenue mc (modified) marginal cost mpc marginal private cost mpr marginal private revenue mr (modified) marginal revenue mso. marginal s o c i a l benefit msc marginal s o c i a l cost msr marginal s o c i a l revenue vmf value of the marginal factor ymp_. value of the marginal product THE PRINCIPLE OF MARGINAL COST PRICING INTRODUCTION 1, In t h i s thesis i t is proposed to investigate the claim put forward by a number of economists that i t is i n the interest of society to make the prices at which goods are sold equal to t h e i r respective marginal costs of pro-duction. A system of price determination operating along such l i n e s i s usually referred to as one of "marginal cost p r i c i n g " . The theory of the marginal cost p r i c i n g p r i n c i p l e has so far not encountered much c r i t i c i s m , i n part, perhaps, because i t has been given l i t t l e attention. Marginal cost p r i c i n g i s not understood outside the narrow ranks of econ-omists and even amongst that select group i t i s not a common topic of discussion-. It i s hoped that i t may be shown that the theory of t h i s p r i c i n g p r i n c i p l e i s not without import-ance and that a further study of i t s mechanics and i t s far-reaching implications may well be worth while. 2. The French engineer Jules Dupuit must be given credit for the origination of the marginal .cost p r i c i n g . theory. 1 The merit of his work, which i s based on u t i l i t y " 1 Dupuit, Jules, "De 1 ' u t i l i t e ' et de sa mesure", c o l l e c t -ed and reprinted by d i Bernardi, Mario, and Einaudi, L u i g i , La riforma s o z i a l e . Turin, 1932. c a l c u l a t i o n s , i s a l l the greater when one considers that he recorded his findings i n 1844, decades before the u t i l i t y -theory of value was accepted. Later, the marginal cost p r i c i n g p r i n c i p l e received the support of such eminent economists as Marshall and Pigou..^ That the question of marginal cost p r i c i n g has remained i n the background for such a long time i s probably a result of the fact that under conditions of perfect competi-ti o n marginal cost p r i c i n g i s automatically achieved. U n t i l f a i r l y recent times perfect competition was assumed to be the general case. Perhaps the only conditions of imperfect competition which were recognised were those a ^ r i s i n g i n the f i e l d of u t i l i t i e s and public works. Undertakings such as these were i n the mind of the c i v i l engineer Dupuit when his f i r s t publications on marginal cost p r i c i n g appeared in the Annales des ponts et chausse'es. By the introduction of the theory of imperfect competition^ further developments in the analysis of the marginal cost p r i c i n g p r i n c i p l e have been f a c i l i t a t e d . Under conditions which are generally considered imperfectly compet-i t i v e ^ recognition of t h i s p r i n c i p l e would require r a d i c a l changes i n p r i c i n g practices. A considerable f i e l d of econom-i c theory has thus been opened for exploration. Yet recent contributions, to the marginal cost p r i c i n g theory have.been " 1 Bergsoh, Abram, " S o c i a l i s t economics", in E l l i s , Howard""SV, ed., A survey of contemporary economics, Phila-delphia and Toronto, Blakiston, 1948, p. 425. 3 few and incomplete so that ample scope for further investiga-t i o n i s l e f t to the ambitious theoretician. 3. In the treatment of t h i s subject i t i s proposed to present, f i r s t , a summary of.Professor Lerner's version of the theory of marginal cost p r i c i n g . 1 His i s probably the only recent elaborate exposition of the theory. As Professor Lerner avoids the use of absolute measures of value as much as possible, his analysis cannot be applied d i r e c t l y to the theory of imperfect competition as developed by Mrs. Joan Robinson^ and Professor Chamberlin.3 Therefore i t i s proposed to apply the u t i l i t y analysis to marginal cost p r i c i n g so that the effects of t h i s p r i c i n g system on the imperfectly competitive firm may be traced. Next, the connection between various forms of taxation and marginal cost p r i c i n g w i l l be discussed. The major contribution to t h i s aspect of the theory has been made by Professor H o t e l l i n g . 4 C r i t i c i s m of the marginal cost p r i c i n g theory, as. i t stands today, w i l l also be con-sidered. The most extensive c r i t i c i s m , perhaps, has come I Lerner, Abba P., The economics of control. New-York, Macmillan, 1944. 2 Robinson, Joan V. , The economics of imperfect oompeti- tion, London, Macmillan, 1933. 3 Chamberlin, E.H., The theory of monopolistic competi- tio n, Cambridge, Harvard University Press, 1933. 4 "HotellingV Harold", "The general welfare i n r e l a t i o n to problems"of taxation and of railway and u t i l i t y rates", Econometrica. v o l . 6, pp. 242-269, 'July, 1938. from Mr. Coase. 1 In the conclusion some comment w i l l be attempted on the p r a c t i c a l a p p l i c a t i on of marginal cost p r i c i n g . It i s not suggested that i t w i l l be possible to present marginal cost p r i c i n g as a theory i n a complete form. Nor i s i t presumed that the arguments presented w i l l s e t t l e the question of price determination. It i s intended merely to stimulate interest i n an economic problem which has not perhaps yet received the attention warranted by i t s importance, both from an academic and a p r a c t i c a l point of view. I' Coase, R.-H., "The marginal cost controversy", Economic v o l . 13, pp. 169-182, August, 1946. THE MARGINAL SUBSTITUTABILITY APPROACH TO MARGINAL COST PRICING 1. The analysis of the problem of marginal cost p r i c i n g necessitates, by i t s very nature, the use of a value theory. In the u t i l i t y theory value i s based on the absolute magnitude of sa t i s f a c t i o n s lost or gained by individuals i n the process of production and subsequent consumption. This theory i s admirably suited for dealing with an aspect of welfare economics such as the problem of price determination. Yet, i n recent decadES, the u t i l i t y theory has been c r i t i c i s e d increasingly from the point of view of the d i f f i c u l t y associated with measuring s a t i s f a c t i o n . Eo^this reason, the indifference theory, which i s concerned only with the r e l a t i v e magnitude of values, has tended to displace the old u t i l i t y concepts. Probably mindful of the c r i t i c i s m to which the conventional u t i l i t y theory has been subjected, Professor Lerner, i n his treatment of the marginal cost p r i c i n g p r i n -c i p l e , avoids measuring absolute values whenever he can. As far as possible his analysis i s confined to r e l a t i v e values and. the., establishment of equilibrium at the margin. 1 Professor "1 In the conventional u t i l i t y theory most of the problems are also solved at the margin. But t h i s is done with the aid of the concept of marginal u t i l i t y i n which the measurability of u t i l i t y i s implicit". Objections to the use of the u t i l i t y cpnceplt\,;_in"this form as" well", are discussed i n Hicks, J.R., Value and c a p i t a l . Oxford, Clarendon, 1948, ch. 1. Lerner does not formally embrace the indifference analysis, but he does make extensive use of one of the c h a r a c t e r i s t i c tools of that analysis - the concept of marginal substi-t u t a b i l i t y , which indicates the proportions i n which goods must be arranged i n a s p e c i f i c instance i n order to obtain equivalence. For this reason his theory w i l l be re f e r r e d to as the "marginal s u b s t i t u t a b i l i t y approach". It w i l l be evident, however, that at various points i n his work he finds i t necessary to return to the conventional u t i l i t y approach. 2. .Professor Lerner maintains that the s o c i a l l y mosf desirable state, i n an economic sense, may exist when the following conditions obtain: (1) The optimum d i v i s i o n of income - t h e quantitative determination of how much, i n general, each con-sumer should receive of. available, goods. ( 2 ) The optimum a l l o c a t i o n of goods - the qu a l i t a t i v e determination of the kinds of goods which should make up each consumer's portion. -(3) The optimum d i v i s i o n of resources - the quanti-tative determination of how much, i n general, of the" available fe.ctdrs of production should be-devoted to the production of each good. (4) The optimum a l l o c a t i o n of factors - the qu a l i t a -t i v e determination of what factors should be used for the production of each good. Each of these four c r i t e r i a i s established with respect to given situations i n the f i e l d s covered by the. 7 others and an adjustment i n any.one f i e l d may necessitate changes i n the other f i e l d s i n order that optimum conditions may be re-established everywhere. An ov e r - a l l optimum, therefore, can be achieved only by simultaneous action in a l l the f i e l d s concerned. Til/hen discussing the c r i t e r i o n for a p a r t i c u l a r f i e l d , i t must be assumed that there are forces at work i n the other f i e l d s which w i l l maintain optimum conditions there, irresp e c t i v e of the operations carried out i n the f i e l d under observation. 5 , The f i r s t two conditions - those dealing with the quantitative and qu a l i t a t i v e d i s t r i b u t i o n of goods - may be dealt with b r i e f l y . 1 It i s usually assumed that the optimum a l l o c a t i o n of goods i s achieved i n a market where the con-sumer 's choice between goods i s unrestricted. The indivudual secures the maximum.benefit from the goods he consumes by continuing the purchases of these ,goods to the point where t h e i r marginal s u b s t i t u t a b l l i t i e s for money - the i r marginal u t i l i t i e s i n terms of moneyjaf in the terminology of the u t i l i t y analysis - equal t h e i r prices i n the market. For i f the marginal s u b s t i t u t a b i l i t y of a commodity for money were greater than i t s price, the purchaser would gain by buying additional units of the commodity. Similarly, should the marginal s u b s t i t u t a b i l i t y of a good for money drop below the market price,, the consumer would incur a loss on every 1 Lerner, The economics of control, ch. 2 and ch. 3 , 8 unit of the commodity he were to purchase under-such con-1 d i t ions. ~ Owing to the im p o s s i b i l i t y , or, at any rate, great inaccuracy, of the comparison of s a t i s f a c t i o n s gained by d i f f e r e n t individuals from various incomes, the estab-lishment of an optimum d i v i s i o n of income must remain, to a great extent, i n the realm of theory. With the a i d of the p r i n c i p l e of diminishing marginal u t i l i t y of income and the assumption that different- individuals enjoy sat-i s f a c t i o n s of a similar character, Professor Lerner con-cludes that an optimum d i v i s i o n of income would be estab-l i s h e d at vthe point where the marginal u t i l i t i e s of income would be equal for a l l indi v i d u a l s , ^ For the t o t a l u t i l i t y enjoyed by society i s always increased by the s h i f t of a unit of income from a person with a lower marginal u t i l i t y of income to a person having a higher marginal u t i l i t y of income, and t h i s process could be continued to the point where diminishing marginal u t i l i t y would bring about the -equation of the marginal u t i l i t i e s of income of a l l persons. In practice, however, i t proves impossible to compare the marginal u t i l i t i e s of income of d i f f e r e n t i n d i v i d u a l s , even assuming, that. the. u t i l i t i e s , enjoyed are of. a. similar nature. 1 The v a l i d i t y of the p r i n c i p l e of diminishing marginal s u b s t i t u t a b i l i t y - the equivalent of the p r i n c i p l e of dimin-ishing marginal u t i l i t y i n the u t i l i t y analysis - i s pre-sumed. " " 2 Consistency in the'abandonment of"the u t i l i t y analysis would"require' the use of a concept such as "the diminishing marginal s u b s t i t u t a b i l i t y of the income, of one in d i v i d u a l for-the income of another i n d i v i d u a l " instead of that of diminishing marginal u t i l i t y . Professor Lerner, admitting t h i s , claims that the most probable p o s i t i o n for the equivalence of the marginal u t i l -i t i e s of income would be at the point of equal d i v i s i o n of income between a l l individuals concerned. 4." The c r i t e r i a i n the f i e l d of production required the optimum quantitative and q u a l i t a t i v e d i s t r i b u t i o n of the factors of production. Pro-fessor Lerner sets out to prove that the optimum relations i n the f i e l d of produc-t i o n are achieved when the following simple "Rule" i s obeyed: If the value of the marginal (physical) product of any  factor i s greater than the price of the factor, increase  output. If i t is l e s s , decrease output. If i t is equal  to the price of the factor continue producing at the  same rate. (For then the right output has been reached.) Fi r s t . of a l l , he w i l l investigates conditions i n a s i m p l i f i e d form of economy where i n every operation one homogeneous factor i s used tp produce one homogeneous com-modity. The two c r i t e r i a in the f i e l d of production are then resolved into the problem of devising the optimum d i v i s i o n of each factor amongst i t s various uses. To bring t h i s about, the marginal product of each factor must have . an equal value in every use. For as long as the value of the marginal product of a factor is greater i n commodity A than i n commodity B, society would gain by s h i f t i n g a 1 Lerner, op.cit., p. 64. 10 unit of the factor from the production of B to the produc-t i o n of A. 1 Assuming that the price mechanism has brought about the r e f l e c t i o n of the values of marginal products and the costs of factors i n t h e i r respective prices, the optimum d i s t r i b u t i o n of a factor amongst various uses i s brought about by obedience to the "Rule". The value of the marginal product of the factor must be equal i n every use since obedience to the "Rule" requires that t h i s value must equal the price of the factor. 5. Professor Lerner points out that the essential s o c i a l u t i l i t y of the price mechanism l i e s in the fact that it# equates the private marginal opportunity cost with the s o c i a l marginal opportunity cost:;-: by which he means the value of the alternative goods which the individual and society, respectively, must s a c r i f i c e i n order to obtain another unit of a p a r t i c u l a r good.2 If the price of a factor i s the same to every manager of production and every manager follows the "Rule" by.making the value of the marginal product equal to the price of the factor, the s o c i a l mar-ginal opportunity cost of any product w i l l be measured by i t s p r i c e . But as the individual consumer cannot influence prices, his private marginal opportunity cost of any com-1 The p r i n c i p l e of diminishing marginal productivity i s understood here, 2 Lerner, op.cit., p. 67. 11 modity w i l l also be measured by i t s p r i c e . Thus, the "Rule" equates the s o c i a l and private marginal opportunity costs so that the i n d i v i d u a l , i n t r y i n g to minimise h i s own s a c r i f i c e of alternatives when he spends his money income to his own best advantage, i s - l e d automatically and even unconsciously to minimise the s o c i a l s a c r i f i c e i n producing what gives him most s a t i s f a c t i o n . 6. Under certa i n circumstances private enterprise automatically leads to the optimum d i v i s i o n of resources as prescribed by the "Rule". 1 If there is perfect competition i n the purchasingof' factors, the entrepreneur's marginal cost i s equal to the price of the factor, for the entrepreneur cannot influence the price of the factor by the amount of his purchases. Similarly, i f there i s perfect competition i n the sale of factors, the price received for the product is equal to the marginal revenue, as the entrepreneur cannot influence t h i s price by the volume of his sales. The entre-preneur maximises his p r o f i t s at the point where his mar-ginal cost meets his marginal revenue. Where marginal cost equals the price of the factor and marginal revenue the price of the product, the most p r o f i t a b l e output coincides with the output which would be determined under the "Rule" -i . e . where the price of a factor equals the value of i t s marginal product. 1 Lerner, op.cit., pp. 72-75. 12 To i l l u s t r a t e the above relationship Professor Lerner has developed f i v e equations with the following six items: 1 i The marginal s o c i a l benefit (msb). This i s the benefit to society ( i . e . the net benefit to" a l l the members of society affected) from the par-t i c u l a r increment of output of product considered. i i The value of the marginal product (vmp). This i s the physical increment of output of product being considered, mul t i p l i e d by the price paid for i t by the consumer. i i i The marginal private revenue (mpr). This i s the~ increase i n revenue (positive or negative) received by the producer as a re s u l t of producing and s e l l i n g the increment i n output. iv The marginal private cost (mpc). This i s the " increase i n cost incurred by the producer as a result of increasing the quantity of factor he purchases i n order to be able to produce the increment of output. v The value of the marginal factor (vmf). This Is the physical increment of the factor of produc-t i o n (that i s needed to make the increment o f " product), mul t i p l i e d by the price per unit paid' for i t and received by the owner of the factor. v i The marginal s o c i a l cost (msc). This i s the s a c r i f i c e to society from having the marginal factor used up here so that i t is not available" for use elsewhere. It is the alt e r n a t i v e marginal' s o c i a l benefit that the marginal factor could have produced i f i t had been used elsewhere. The fiv e "welfare equations" are: (l) Marginal s o c i a l benefit = Value of marginal product This equation is s a t i s f i e d i f there is an optimum allocation, of goods and. i f the. purchaser pf. the. good 1 Lerner, op.cit., pp. 75-'77. The abbreviations added i n parentheses w i l l be used subsequently i n the text. 13 i s the only individual i n society who i s affected"" by the purchaser's use of the product. In that case the amount of money paid for i t measures the use-fulness of the product to the purchaser and" so to' the society of which he i s the only in d i v i d u a l affected. ( 2 ) Value of marginal product= Marginal private revenue This equation is s a t i s f i e d i f there i s perfect"com-p e t i t i o n in s e l l i n g the product. The producer is then not able to influence the price of the product by varying the output, so the extra revenue"he re-ceives from an increment in output i s simply the' physical' increment in output m u l t i p l i e d by i t s p r i c e . ( 3 ) Marginal priva.t.e revenue = Marginal private cost This equation is s a t i s f i e d i f the producer maximizes his p r o f i t . This involves expanding output as long as the marginal private revenue" i s greater"than the marginal private cost and contracting output as long as i t i s less; the equilibrium p o s i t i o n where" p r o f i t s are maximized thus being reached only when these two values are equat.ed. • ( 4 ) Marginal private cost=Value of marginal factor This equation is s a t i s f i e d i f there i s perfect com-p e t i t i o n i n buying factors of production. The pro-ducer i s then not able to influence the price o f the factor by varying the quantity of i t that^rf he buys, so the extra cost of buying the increment" of . factor i s simply the physical quantity of the fac-tor multiplied by i t s p r i c e . (5) Value of marginal fact or =Marginal so c i a l cost This equation is s a t i s f i e d i f the f i r s t four equa-tions hold for a l l the other production units in the economy using the factor so that the value of the marginal factor equals the alternative marginal s o c i a l benefit from using the factor i n these other uses.1 1 S t r i c t l y speaking,, i t i s not necessary that a l l of the f i r s t "four "equations hold for the alternative uses of the fac-tor' under"consideration so .long as, msbs vmf in every other use of that factor. • 14 These f i v e equations may conveniently be written i n abbreviated form thus: msb - vmp - mpr - mpc L vmf 4 msc The relationships expressed by the f i v e equations may be i l l u s t r a t e d as follows: Y msb Equalisation sought by society Equalised by production according to the""Rule" Equalised by private p r o f i t incentive ( 1 ) Opt imum vmp = mpr ( 2 ) mpc vmf (3) ( 4 ) (5) msc • Perfect Maximisation Perfect msb = vmf d i s t r i b u t i o n competition of p r o f i t competition i n the of produced i n s e l l i n g i n buying a l t e r n a t i v e goods product factor uses Prom the d e f i n i t i o n of msb and msc it- may be de-duced that the ultimate end of the productive processes of society is t h e i r equalisation. For S.Q long as msb exceeds msc society w i l l gain from additional production, whereas i f msc would be i n excess of msb society would gain from reduced production. To compare msb and msc d i r e c t l y i s too d i f f i c u l t 15 a task as this would, require an invesitgation into the gains and losses of a l l individuals r e s u l t i n g from every single increment in production. For i t i s the t o t a l of the e f f e c t s , direct and i n d i r e c t , on a l l individuals which determines msb and msc. It i s not necessary to compare msb and msc d i r e c t l y , however. The normal c r i t e r i o n of production i s the maximisa-t i o n of p r o f i t by a firm (equation 3) and so long as there i s an optimum d i s t r i b u t i o n of goods (equation l ) , conditions of perfect competition (equations 2 and 4) w i l l bring about' the desired equality of msb and msc (equation 5 automatically s a t i s f i e d ) . 7. The existence of imperfect competition raises the major problem. For i t is i n those cases where perfect corn-p e t i t ion. does not exist - i n those cases where equations (2) and (4) do not hold good - that the p r i n c i p l e of marginal cost p r i c i n g , as expressed by the "Rule", becomes important. Throughout the argument an optimum d i s t r i b u t i o n of goods w i l l be assumed ( s a t i s f y i n g equation l ) so that attention may be focussed on the dir e c t equalisation of vmp and vmf (equation 5 is then automatically s a t i s f i e d ) . Once more, the argument is not concerned ?/ith production i n those f i e l d s where perfect competition reigns but only with production where buyers or s e l l e r s can influence prices through the quantity of t h e i r purchases or sales. This l a t t e r condition prevails i n many f i e l d s of economic endeavour i n modern 16 society. What happens to equations ( 2 ) and. (4) under con-d i t i o n s of imperfect competition? To the monopolistic s e l l e r the mpr i s not equal to the vmp. The marketing of the mar-ginal increment of his product is associated with a lower pr i c e and the mpr is less than the vmp by the amount to which the prices of a l l the items are reduced by the mar-keting of the marginal increment. Similarly, when perfect conditions exist i n buying, the purchase of the marginal increment of the factor sought by the monopsonist w i l l be associated with an increase i n the price of the'factor-and.' the mpc w i l l exceed the vmf by the amount to which the prices of a l l items of the factor sought on the market are increased by the purchase of the marginal increment. We see that under conditions of imperfect competition, while mpr s t i l l equals mpc, vmp exceeds mpr and mpc exceeds vmf. A f o r t i o r i vmp must be greater than vmf. Thus msb exceeds msc and society ..would have gained by an increase i n production.! The thesis that . monopolies r e s t r i c t output to the detriment of society, is. 1 There are l i m i t a t i o n s to this conclusion. Though msb must equal" vmp (by the assumptions of the model),, msc may' hot equal "vmf i f there is imperfect" c ompet i t ion" i n other f i e l d s of production'usihg the same factor. Where other factors are us"ed in" combination with t h i s factor, indirect effects of imperfection i n other f i e l d s yet may' be f e l t . Complementarity and suppl'ementarity, respectively, may influence the diverg-ence between msc and vmf i n one d i r e c t i o n or the other, but the resultant'is"not l i k e l y to be strong enough to affect • the o r i g i n a l conclusion. ' hereby confirmed, 1 The suggested solution to t h i s unsatisfactory condition brought about by- imperfect competition i s the -direct a p p l i c a t i o n of the "Rule-", equalising vmp and vmf, instead of the maximisation of private p r o f i t i n the f i e l d s of production concerned. The analysis, which was applied to the s i m p l i f i e d economy where factors.and products appear i n i s o l a t i o n i s carried over by Professor Lerner onto various combinations of factors and products.2 i n general?, he divides the mar-ginal product i n proportion to the productive contributions of the co-operating factors by determining the .increase in-the product r e s u l t i n g from the a p p l i c a t i o n of. each of the marginal factors.3 Thus the problem is' reduced to the simple form outlined above, v i z . where every marginal f a c t o r . i s considered to have an individual product, - i.e.. produced without the co-operation of other factors. Hence the op-. timum d i v i s i o n of respurces s t i l l corresponds to the o p t i -1 This statement must be taken i n a r e l a t i v e sense. I f there i s f u l l employment of manpower and resources, output, i n a physical sense,, of course, has not been r e s t r i c t e d . It simply-lmeans; that r e l a t i v e l y too l i t t l e - from the standpoint of the maximisation of s a t i s f a c t i o n to society - has been . produced i n those f i e l d s where imperfection manifests . i t s e l f and, as a consequence, r e l a t i v e l y too much has been produced of less preferred a r t i c l e s . The degree of imperfection w i l l determine, i n part,, the magnitude, of the r e s t r i c t i o n i n out-put of a p a r t i c u l a r item. See also below, pp.45"-46 and 54-5"5. ^ 2 Lerner, op.cit., ch. 10 and ch. 11. 3 The problem of fixed proportions i s abstracted from here. Professor Lerner deals with t h i s question i n ch. 10 of his work. 18 mum d i s t r i b u t i o n of factors amongst t h e i r various uses as prescribed by the "Rule". The i d e n t i f i c a t i o n of marginal factors by the share of the product for which they are responsible s i m p l i f i e s the analysis of the fourth condition c a l l i n g for the best combination of factors to be used i n each productive process. For now the "Rule" may be applied to each one of the con-t r i b u t i n g factors by equating the value of each marginal factor with i t s corresponding product. A greater a p p l i c a t i o n of the factor would raise i t s price above the value of i t s marginal product, r e s u l t i n g i n a s o c i a l l o s s . Failure to achieve the amount of employment of the factor c a l l e d for by the "Rule" would leave the factor price below the value of the marginal product, in d i c a t i n g that the net benefit accruing to society could be increased through further application of the factor concerned. The optimum a l l o c a t i o n of factors is obviously that which corresponds to the equa-t i o n of the value of each marginal factor with that of i t s product. Where the value of each marginal factor equals the value of. i t s share i n the marginal product,. thev value of the combination of marginal factors w i l l equal the. value of the j o i n t l y produced t o t a l marginal product. . . . ..' . . 8. With perfect d i v i s i b i l i t y of a l l the factors of production and perfect, . e l a s t i c i t y i n t h e i r supply - i . e . i n a p e r f e c t l y competitive market for factors - a firm would be subject to constant costs per unit of output. For under o 19 these conditions i t would always be possible to vary the scale of the productive process and maintain the same pro-portion of the factors. These conditions are seldom s a t i s -f i e d , however, and most firms show a range of production over which average cost,per unit of output declines followed by a range characterised by increasing average cost. This can be explained by the i n d i v i s i b i l i t y of c e r t a i n factors of production which must be applied i n larger (or smaller) units than t h e i r optimum proportion to co-operating factors would warrant. 1 Por the f i r s t (marginal) unit of a product the cost w i l l be high, since i t includes the* cost of the appropriate units of d i v i s i b l e factors (in proportion to t h e i r marginal products) as well as the cost of an entire unit of the i n d i v i s i b l e factor - the l a t t e r being i n excess of the need for that stage of production. For successive (marginal) units of the product, over a c e r t a i n range, the cost w i l l be considerably lower as outlays w i l l have to be made only"for the d i v i s i b l e factors - enough unused capacity of the i n d i v i s i b l e factor s t i l l being l e f t from the o r i g i n a l excessive purcha.se of an entire unit. Average costs w i l l thus continue to decline u n t i l the optimum combination of factors i s reached, v i z . whre the factors are applied i n proportion to the values of t h e i r marginal products. The marginal product of the i n d i v i s i b l e factor may be ascertained for this purpose by a mental c a l c u l a t i o n applied to a h-ypo-1 Lerner, op.cit., ch. 15 and ch. 16. 20 t h e t i c a l scale of production where units of t h i s factor are small enough, r e l a t i v e l y , to feature as marginal increments. Production beyond the stage of the optimum combination of .. factors w i l l r e s u l t i n increasing average costs. The capacity of the i n d i v i s i b l e factor i s then being overtaxed and applica-t i o n of successive units of the d i v i s i b l e factors w i l l y i e l d product increments diminishing i n s i z e . If demand warrants a further increase i n production, the increasing costs may be overcome by the a p p l i c a t i o n of another unit of the i n d i -v i s i b l e factor, bringing about another range of decreasing costs. Projected on a large enough scale, t h i s procedure would eventually see the disappearance of i n d i v i s i b i l i t y . . There are, however, c e r t a i n factors which are not only i n -d i v i s i b l e but, also, unaugmentable, e.g. the managerial function, and such factors w i l l ensure i n d e f i n i t e l y increas-ing costs once t h e i r capacity becomes overtaxed by the suc-cessive application of units of the other factors.1 9. As has been pointed out previously, the optimum d i v i s i o n of resources requires adherence to the "Rule" so that i n every productive process the value of the marginal product w i l l equate with the value of the marginal factor (or. factor combination). This has rather s t a r t l i n g con-sequences when applied to a decreasing average cost firm - . i . e . a firm where at. the output calle d for by the "Rule" 1 Lerner, op.cit., ch. 17. the range of increasing average cost has not yet begun. In order that average cost might decline marginal cost must be* below average cost. But the marginal cost must equal the value of the marginal product expressed by the price i t fetches i n the market. Except for the few markets where price discrimination i s f e a s i b l e , the price of the marginal item i s equal to the price of a l l other items of the com-, modity concerned and, thus, to the average revenue of a firm. This average revenue,' equalling marginal cost, i s now below the average cost.of a decreasing average cost firm and i t s adherence to the "Rule" can only-be f u l f i l l e d by producing at a f i n a n c i a l l o s s . That production at a f i n a n c i a l loss would benefit society may seem a contradict ion.- Y e t t h e marginal sub-s t i t u t a b i l i t y analysis of Professor Lerner would lead to the conclusion that any f i n a n c i a l loss would be immaterial, so long as an equation of the values of marginal "factors with the values of their respective products existed. The v a l i d i t y of the conclusions of the marginal s u b s t i t u t a b i l i t y analysis, however, stands and f a l l s with the v a l i d i t y of a t a c i t assumption on which t h i s analysis is based. The as-sumption i s that s o c i a l benefit exceeds s o c i a l cost for each item of output previous to the marginal item at which equality of s o c i a l benefit and s o c i a l cost i s established. (A "social p r o f i t " would be made on each item.) Eor each item of output following the item at the point of equilibrium i t i s assumed that s o c i a l cost exceeds s o c i a l benefit. (This 22 would constitute a " s o c i a l loss".) Under such circumstances , the item of output at which s o c i a l benefit equated with s o c i a l cost would be the demarcation between the ranges of s o c i a l p r o f i t and of s o c i a l l o s s . Hence t h i s item would c l e a r l y indicate the most p r o f i t a b l e output for society. It i s possible, however, that the output series of a firm would commence with a range of s o c i a l loss followed by a-range of s o c i a l p r o f i t and concluding with a f i n a l range of s o c i a l l o s s . Only a measurement i n absolute terms would determine whether the s o c i a l p r o f i t would offset the s o c i a l loss to an extent that i t would be b e n e f i c i a l for society to have production continued i n a p a r t i c u l a r instance. It ?/as the claim that no measurement of the value of s a t i s f a c t i o n i n absolute terms was possible" that-gave r i s e to the indifference and marginal s u b s t i t u t a b i l i t y theories i n opposition to the conventional u t i l i t y theory. But i t would appear that the problem under discussion cannot be resolved without an absolute measure of value. 1 Professor Lerner - while not s p e c i f i c a l l y renouncing h i s adherence to the marginal s u b s t i t u t a b i l i t y approach"- i n fact, returns 1 Bergson, Abram, " S o c i a l i s t economics", i n E l l i s , "< Howard S., ed., A survey of contemporary economics, Phila-delphia and Toronto, Blakiston, 1948, p. 428, n. 40. Pro-fessor Bergson states that the generally accepted solution to t h i s problem i s along the l i n e s of. the u t i l i t y analysis as presented by Professor Pigou i n The economies' of welfare. London, Macmillan, 1929, p. 808. Professor Bergson suggests that an a l t e r n a t i v e solution exists involving " . . . an index number problem, the objective being to compare the community's r e a l income in two d i f f e r e n t situations with d i f f e r e n t price structures." Apart from the p r a c t i c a b i l i t y of such a method, i t does not seem to dispense with the need for an absolute measure of value. 23 to.the u t i l i t y theory to solve t h i s problem. He makes, the a p p l i c a b i l i t y of the "Rule" dependent upon the average value of the product increments exceeding the average price of the factor increments for the entire range of production re-c a l l e d for b l i t h e "Rule".*1 The process of averaging c a l l s for summation of the values concerned, which can only take place on the basis of a common measure of value. Since Professor Lerner through h i s marginal sub-st i t u t a b i l i t y approach has been able to avoid the objections to the u t i l i t y theory i n only part of hi s analysis, i t may. well be asked whether i t was worth while to avoid these d i f f i c u l t i e s at a l l . An attempt w i l l be made to .demonstrate that, with the introduction of a few plausible assumptions, the objections to the u t i l i t y theory w i l l appear to be o.-f l i t t l e consequence i n the application of the u t i l i t y theory to the problems under discussion. . . 1 Lerner, o p . c i t p p . 196-198 THE UTILITY ANALYSIS OE MARGINAL COST PRICING 1. Marginal cost p r i c i n g is intended to a s s i s t i n maximising the general welfare of society in an economic sense. It must indicate the prices which, ceteris paribus, w i l l secure a maximum of s a t i s f a c t i o n from consumption of economic goods with a minimum of e f f o r t i n t h e i r production. As indicated above, the f i n a l solution of the problem appeared to require a standard of absolute value. This standard should be capable of measuring s a t i s f a c t i o n and e f f o r t , but i f e f f o r t i s considered to.be the surrender of s a t i s f a c t i o n (through loss of l e i s u r e , etc.), a simple unit of s a t i s f a c t i o n might s u f f i c e . With the a i d of the u t i l i t y analysis a measure of value w i l l be provided which w i l l render the problems involved subject to arithmetic manipulation. The capacity to s a t i s f y human wants,^directly or i n d i r e c t l y , i s a quality common to a l l goods. This common quality, u t i l i t y , may be measured i n a p r a c t i c a l way by means of money. Money may appear to be too crude and con-crete a concept to s a t i s f y the delicate requiremnets of economic abstraction. In order that i t might become a to o l suited to the broader problems of economic analysis, t h i s measure of value must be capable of comparing a l l the subjective u t i l i t y evaluations which are made i n society. Thus, i t must be the common denominator of 25 (a) the u t i l i t i e s of various goods to one person and (b) the u t i l i t i e s of goods to di f f e r e n t i n d i v i d u a l s . In order that money may be used i n this capacity with l o g i c a l jus-t i f i c a t i o n , two assumptions must be made. These assumptions constitute the main l i m i t a t i o n s of the u t i l i t y theory. If the assumptions are v a l i d , for a l l p r a c t i c a l purposes, f u l l use of the extremely valuable analytical.-.tools which the u t i l i t y theory provides may be j u s t i f i e d . 2. The f i r s t assumption, which is made with respect to the various u t i l i t y evaluations of one in d i v i d u a l , i s that the marginal u t i l i t y of money i s constant. In other words, there w i l l be no change i n the value , or u t i l i t y , of successive units of money spent by a person. This as-sumption underlies much of Marshall's u t i l i t y analysis.1 Of t h i s Professor Hicks - while himself favoring the i n -difference approach to value - says; . . the constancy of the marginal u t i l i t y of money is i n fact an ingenious s i m p l i f i c a t i o n , which i s quite harmless for most of_ the applications Marshall gave i t himself. Professor Hicks claims that the assumption pre-, sumes that changes i n the consumer's supply of money w i l l not af f e c t the marginal rate of substitution between money and any p a r t i c u l a r commodity. Por the marginal... rate of 1 Marshall, Alftfed, P r i n c i p l e s of economics, Macmillan, . London, 1938 (copyright 1920), pp. 132-133 and 842. 2 Hicks, Value and c a p i t a l , pp. 26-27. 26 s u b s t i t u t i o n equals the ration' of the marginal u t i l i t i e s of the_ commodity and money. The error to which th i s would lead is obvious. If a consumer's income increased and the price of the commodity remained constant, t h i s . p r i c e would s t i l l equal the marginal rate of substitution, and no change would take place i n the amount of the commodity bought. In other words, a consumer's demand for commodities would be independent of his income. This is not the in t e r p r e t a t i o n which should be given to the assumption of constant marginal u t i l i t y of money. This assumption should not be taken to mean that the consumer's supply of money w i l l not a f f e c t the marginal rates of substitution but, rather, that the consumer's .supply of money i t s e l f w i l l be constant.. .Where the money supplies of mosl/people are augmented, by regular flows of income (from p e r i o d i c a l l y received wages, s a l a j r i e s , e t c . ) , and depleted by flows of equal intensity (consumptive expenditures and savings), i t is not d i f f i c u l t to r e a l i s e that the marginal s u b s t i t u t a b i l i t y of money for other com-modities - under such circumstances - w i l l be subject to l i t t l e v a r i a t i o n . What the assumption.really entails i s a constancy of incomes (or, rather, of rates of income), a constancy of price l e v e l s , and the absence of hoarding or dishoarding of money supplies. 1 So long as tfhe analysis i s . limited to a period over which t h i s is substantially true, 1 For the sake of completeness, i t should be stated that changes in i n d i v i d u a l s ' scales .of preference, =as between goods, are abstracted from for the period under consideration. 27 the o r i g i n a l assumption holds. 1 In actual practice, i t is true that, except i n periods of s i g n i f i c a n t economic change, individuals as v/ell as firms use fixed d o l l a r values to express and compare t h e i r material desires and s a c r i f i c e s , or calculate t h e i r gains and losses. If the marginal u t i l i t y of money remains constant, the u t i l i t y evaluations of each individual may be expressed in terms of d o l l a r s . For each d o l l a r that a man spends has an equal value to him. Thus, i f a man is g.ust w i l l i n g to pay two dollars for an a r t i c l e and he considers that the ac q u i s i t i o n of a different a r t i c l e is just enough induce-ment to part with one d o l l a r , i t may be concluded that, to the man concerned, the f i r a t a r t i c l e has exactly twice the value of the l a t t e r . 3 . The u t i l i t y evaluations of each individual have been reduced to a form in.which they are subject to a r i t h -metic manipulation. A common denominator for the u t i l i t y " ' units of d i f f e r e n t individuals i s s t i l l necessary. Although to each i n d i v i d u a l , separately, a d o l l a r always represents the same quantity of u t i l i t y , i t has not yet been made acceptable that the d o l l a r ' s u t i l i t y i s equal to a l l i n d i -viduals... To.this, end., the. introduction, of a. second assump-1 The problems to which the indifference analysis i s most frequently applied, and with which i t i s uniquely q u a l i -f i e d to deal, concern changes in income and changes i n r e l a -t i v e p r i c e s . For the purposes of such questions, the assump-t i o n of constant marginal u t i l i t y of money wo.uld, indeed, be most f a l l a c i o u s . As, however, such, changes are abstracted from, the u t i l i t y analysis need suffer no d i s o u a l i f i c a t i o n with respect to the problems at hand. 28 t i o n is necessary - the assumption of the existence of an optimum d i v i s i o n of income. The d i f f i c u l t i e s which Professor Lerner encountered i n attempting to determine the optimum d i v i s i o n of income i n i society have already been pointed o u t / His conclusion that an equal d i v i s i o n of,income i s most l i k e l y to approximate the equality of the marginal u t i l i t i e s of income of various individuals i s not convincing.2 As he himself observed, u t i l i t i e s as between persons are, s t r i c t l y speaking, i n -commensurable. It seems more plausible and in keeping with the present general attitude towards human ra l t i o n s h i p s that an optimum d i v i s i o n of income should be established on the basis of some et h i c a l c r i t e r i o n . 0 Such an e t h i c a l c r i t e r i o n could be based on need, or on quantity and qual-i t y of productive contributions, to society, or, perhaps, on a combination of these and other factors. Whatever eth i c a l considerations may be applied, once the optimum d i v i s i o n has been established, i t w i l l be impossible for society, on the basis of the e t h i c a l p r i n c i p l e s involved, to gain from the transfer of income from one person to 1 Cf. above, pp. 8-9.' 2 Bergson, " S o c i a l i s t economics.!', pp. 413-414. Accord-ing to Professor Bergson, Marshall and Pigou tfended towards the views held by Professor Lerner i n t h i s respect. 3 Ibid., p. 414. This attitude i s attributed to Pareto and Barone by Professor Bergson. An ingenious attempt at re c o n c i l i n g the two attitudes has been offered by Dr. Lange. See "On the. economic theory of socialism", in Lippincott, Benjamin E., ed., On the economic'theory' of socialism. Minneev poliis, University of Minnesota Press, 1948 (copyright' 1938) vol..2, pp. 101-103. , ' 29 another. For i f society could gain from such a transfer, the d i v i s i o n of income could not be j u s t l y considered to be an optimum one. But saying that no gain can be made by the transfer of income from one person to another i s tantamount to s t a t i n g that the marginal u t i l i t i e s of income to a l l persons are equal. The comparison of u t i l i t i e s as between persons i s not now based on any objective s c i e n t i f i c stand-ards of measurement of s a t i s f a c t i o n which, as already stated, is impossible. Instead, the u t i l i t i e s of goods to various persons are compared on the basis of some e t h i c a l p r i n c i p l e . It may be f e l t that the u t i l i t y of a d o l l a r spent by a man with an income of ten thousand d o l l a r s w i l l be less than the u t i l i t y of a d o l l a r spent by a man with an income of but one thousand do l l a r s , i n terms of the i n t r i n s i c s a t i s f a c t i o n s enjoyed, but thi s cannot be corroborated by any s c i e n t i f i c t e s t . However, the concept of u t i l i t y as between individuals can be revised so as to make i t not a measure of i n t r i n s i c s a t i s f a c t i o n enjoyed but a measure of the right to enjoy s a t i s f a c t i o n s . In that light' the marginal u t i l i t y of income to thenman receiving ten thousand d o l l a r s would indeed be equal to the marginal u t i l i t y of income to the man drawing only a thousand d o l l a r s , i f those p a r t i c u l a r a l l o c a t i o n s of income were j u s t i f i e d by the e t h i c a l c r i t e r i o n of the optimum d i v i s i o n of income.in society. From the point of view of the et h i c a l c r i t e r i o n society would., recognise that the right s of each man to enjoy the s a t i s f a c t i o n from the expenditure of his 30 l a s t d o l l a r of income were equal. 1 On the basis of this interpretation, u t i l i t y would remain a measure of the inte n s i t y of s a t i s f a c t i o n enjoyed by indiv i d u a l s , but on the understanding that society recognises, for i t s own et h i c a l purposes, the equivalence of the s a t i s -factions enjoyed by di f f e r e n t individuals from equal amounts-of income when the optimum d i v i s i o n of income has been estab-l i s h e d . The assumptions and interpretations are e n t i r e l y i n keeping with the dual welfare objective of establishing the most equitable d i s t r i b u t i o n of income between individuals, while maximising the sa t i s f a c t i o n s which each of the i n d i -viduals might enjoy from his own p a r t i c u l a r income. Since the main concern of thi s essay is the problem of determining prices which will., maximise the t o t a l s a t i s f a c t i o n s of i n d i -viduals, ceteris paribus, i t is assumed that an optimum d i s t r i b u t i o n of income exists and i s maintained. In summary, the two assumptions have established that every d o l l a r has an equal u t i l i t y value and - with a market which does not discriminate as between consumers - an equal power of command over goods offered for sale, i r r e s p e c t i v e of the individual who presents i t , and irrespective of which part of that individuals's income the presented d o l l a r con-1 Objective s c i e n t i f i c standards have f a i l e d to provide a basis for measuring u t i l i t i e s as between in d i v i d u a l s . The assumption has merely established a p r i n c i p l e which provides .for an evaluation of alternatives which otherwise would be incommensurable. See Bergson, " S o c i a l i s t economics", p. 418. 31 sists.^-.By leaving theyactual d i v i s i o n of income undetermined, the analysis can be applied to almost any specific.condit i o n s which might be attached to the optimum d i v i s i o n of income. Many people.may take exception to the actual d i s t r i b u t i o n of purchasing power, but very few object on either e t h i c a l or-p r a c t i c a l grounds to the recognition of the d o l l a r as the unit of account to be used. The actual d i v i s i o n of income i s not l i k e l y ever to receive unanimous endorsement as an optimum d i v i s i o n i n any p a r t i c u l a r society, yet i t may be considered the resultant of the ind i v i d u a l concepts of s o c i a l j u s t i c e embodied i n the general philosophy of that society. With the assumptions of the constancy and equality of the marginal u t i l i t y of money to a l l individuals, the d o l l a r i s established as. the universal unit>:,of u t i l i t y . There i s one other provision which must be made, however, in order to use individual u t i l i t y evaluations as a measure of s o c i a l benefit. A good acquired by any in d i v i d u a l , at a certain cost, must be assumed to affe c t that individual only.2 1 Professor Nordin seems to have had t h i s concept i n mind, i n an a r t i c l e on the marginal cost controversy, when he spoke of "dollar democracy". See "The marginal cost con-troversy: a reply", Economica, v o l . 14, p. 147, May, 1947.. A related concept, that of "consumers' sovereignty", was introduced by Professor W^ H. Hutt in "The concept of con-sumers ' sovereignty", Economic gournal, vol.' 50, p. 66, March, 1940. Professor Bergson comments on t h i s concept i n "S o c i a l i s t economics", pp. 417-418. 2 This s t i p u l a t i o n is also made by Professor Lerner. See The economics of control, p. 76. To j u s t i f y t h i s assump-t i o n an adjustment i n s o c i a l cost may have to be made. Cf. below, p.40, n . l . 32 In other words, no other person should benefit by, or suffer from, an individual's possession of a good, since t h i s would af f e c t the t o t a l u t i l i t y to society beyond the individual !s u t i l i t y c a l c u l a t i o n . To make the assumption more r e a l i s t i c , the u t i l i t y evaluations of "households", rather than of individuals, should perhaps be considered, since incomes and expenditures are usually pooled by households. In cases of " c o l l e c t i v e consumption" the u t i l i t y evaluations of com-munities, as expressed by t h e i r representative bodies, should be considered. 1 The u t i l i t y of public parks or police pro-tecti o n , obviously, can be determined best b y a c o l l e c t i v e agency. No d i f f i c u l t i e s are involved i n the u t i l i t y calcu-l a t i o n s of the corporate bodies in the productive process. A l l u t i l i t i e s passing through their hands have objectively market-determined values; they are never required to assess e f f o r t or enjoyment. 4. The graphs pertaining to the equilibrium of the-firm, which Mrs. Joan Robinson2 and Professor Chamberlin^ 1 Bergson, " S o c i a l i s t economics", pp. 415-416. Professor Bergson comments on the appropriate spheres for government determination of values. He refers to the detailed, analysis of Dobb and Dickinson. See Dobb, M., P o l i t i c a l economy and  capitalism, New York, 1940, pp. 298-299 and 309-312. Idem, "Economic theory and the problems of a s o c i a l i s t economy", Economic Journal,. v o l . 4.3, pp.. 588-598, December, 1933. Dickinson, H.D., Economics of socialism. Oxford, 1939, p. 51 f f . 2 Robinson, The economics of imperfect competition. 3 Chamber!in, The theory of monopolistic competition.-33 es p e c i a l l y have helped to develop; and which now feature prominently amongst the standard a n a l y t i c a l equipment of the economist, w i l l a s s i s t greatly at t h i s point. The usual s i m p l i f i c a t i o n of defining a firm as a productive unit which turns out a single homogeneous product w i l l be made. No t h e o r e t i c a l error i s committed i f we consider each firm to be producing a d i s t i n c t i v e product. In the f i n a l analysis, every firm has a monopoly over i t s own output, which i s distinct, from the product of any other firm. The products of two firms are rarely .completely i d e n t i c a l (physically), -and even then, since they cannot be produced i n exactly the same location, variations i n distance to centres of con-sumption w i l l d i s t i n g u i s h them. This observation is made only to j u s t i f y the practice adopted in considering the demand for the product of any firm as the demand of society for that product. The conventional graphical representation of demand by a curve, such as the l i n e d in figure 1, i s f a m i l i a r . The v e r t i c a l axis measures prices i n d o l l a r s , which at the same time, because of the assumptions, expresses s a t i s f a c t i o n or u t i l i t y . The horizontal axis measures units of output of the product concerned. ,AS a firm produces successive units and offers them for sale, the maximum price at which the l a s t unit added may be sold declines. For each consumer the maximum d o l l a r values which he would be w i l l i n g to surrender for successive units of the product have been taken and these evaluations of a l l the consumers together have been combined 34 in one graph, where they are arranged in order of th e i r magnitude, irrespective of the p a r t i c u l a r consumers by which they were made-. The area under curve d now represents the t o t a l u t i l i t y to consumers - and, thus, to society - of the amount of output of the product described by the curve. If ON units are produced and sold to the people placing the highest u t i l i t y evaluations on those ON units, the t o t a l u t i l i t y enjoyed in the consumption of those units w i l l be described by the area MPNO. True At O /? s ^ _ X p §^ tnpr A/ Figure 1 Q u a n t i t y •As a general practice, firms charge a uniform price for a l l units of th e i r product.-The highest (uniform) price which the firm can charge i n the case of thi s example, and s t i l l f i n d enough buyers to dispose of the entire out-put ON, i s FN d o l l a r s . The revenue of the firm from the sale of that output w i l l then be given by the area LPNO. 35 If.the firm had a complete knowledge of the eval-uations which individual consumers placed on the product they bought, i t could practice price discrimination and charge every individual consumer the maximum price he would be w i l l i n g to pay to acquire a unit of that product. In that case, the revenue of the firm would equal the u t i l i t y of the output sold and cover the area MPNO. In the general ca.se, such price discrimination i s not feasible, and the maximised revenue of a firm w i l l be described by a rectangle, determined for a given output ON by a point P on the demand curve, i n d i c a t i n g a revenue of PN per unit. The demand curve, then, is i n fact anaverage revenue curve for the firm, for which the abbreviation apr (average private revenue) w i l l be used. The f i r s t derivative of the apr curve could be ca l l e d a marginal private revenue (mpr) curve of the firm. Por each unit added# to the output sold, the ordinate of the corresponding point on the mpr curve w i l l indicate the i n -crease in t o t a l revenue of the firm - the marginal private revenue - r e s u l t i n g from t h i s addition. It w i l l measure the price of the marginal unit minus the diminution i n price on a l l preceding units necessitated by the addition of the mar-ginal unit to the marketed output.' The t o t a l area under the mpr curve w i l l indicate the t o t a l revenue of the firm. Por . an output of ON th i s revenue w i l l be shown by the area MQ.NO, which w i l l thus equal the area LPNO. Thus the demand curve performs the same function 36 with respect to society as the mpr curve performs with respect to the private firm. By analogy, the demand curve could be ca l l e d the marginal social' revenue (msr) curve. 1 Por i t i s the area under t h i s curve which indicates the t o t a l benefit to society - the s o c i a l revenue in.terms of u t i l i t y - accruing from the sale and subsequent consumption of the output i t denotes. The ordinate of a point on the msr curve shows the increase i n t o t a l u t i l i t y enjoyed by consumers - the marginal s o c i a l revenue - r e s u l t i n g from the addition of the corresponding unit to the output sold. An average s o c i a l revenue (asr) curve could be. constructed, so that there would be.the a l t e r n a t i v e of measuring; .the t o t a l u t i l i t y enjoyed by society from a cer-t a i n output by a rectangle, determined for that output by the ordinate of the corresponding point on the asr curve. Thus, in figure 1, the t o t a l u t i l i t y of the output ON is not only given by area MPNO under the msr curve, but also by the rectangle KRNO. The slope of the demand curve - i t s e l a s t i c i t y -w i l i depend upon the degree to which r i v a l products can substitute i n the s a t i s f a c t i o n ofnoonsumers '-."demands for the commodity concerned. A highly desired commodity, which has few or imperfect substitutes amongst other goods on the market, w i l l have an i n e l a s t i c demand, characterised by. a steep, curve..., .Where,, on the. other, hand,, consumers ' 1 This marginal s o c i a l revenue w i l l correspond to Professor Lerner's marginal s o c i a l benefit. Cf. above, p. 12. 37 desires for a good may be, to a great degree, s a t i s f i e d by the products of other firms, the demand w i l l be r e l a t i v e l y e l a s t i c and the demand curve w i l l be less steep. When a,very great number of firms produce p r a c t i c a l l y i d e n t i c a l goods for the same market, i'fc i s said that perfect competition exis t s , and the demand curve for/the product of any one of the firms w i l l be, to a l l intents and purposes, a horizontal l i n e . In that case, the demand curve w i l l not only represent the apr and msr curves, but i t w i l l also coincide with the mpr and asr curves (figure 2). ce d- apr - *r>sr-»>pr = asr O A/ Figure 2 Quantity The general case of the sale of ON units of a product has been depicted i n figure 3 . The t o t a l u t i l i t y enjoyed by society from the consumption of these goods is indicated by the area MPNO. Consumers have had to s a c r i f i c e LPNO d o l l a r s to acquire the ON units of the product - the price of one unit being PN d o l l a r s . The d o l l a r value of the money surrendered by consumers (representing claims to alternative u t i l i t i e s ) i s less than the maximum amount, con-sumers would have been w i l l i n g to s a c r i f i c e for the ac q u i s i -t i o n of the goods concerned - the t o t a l u t i l i t y enjoyed. The net gain in u t i l i t y made by consumers is represented by the v e r t i c a l l y shaded area, MPL. This net gain i s c a l l e d consumers 1 surplus. 1 The concept of consumers* surplus was Z Figure 3 <Rua-<nt;ty 1 The appearance.of consumers' surpluses necessitates a reconsideration of the concept of income. The "real income" of a person (inclusive of the consumers' surpluses he may enjoy) and h i s "money income" might be distinguished. Both may be measured i n terms of do l l a r s and the i r divergence is a r e s u l t not of a difference i n value of the d o l l a r units of money income, but of the di f f e r e n t uses to which these d o l l a r units are put when purchasing goods to which d i f f e r e n t consumers ' surpluses are attached. As the analysis i s inde-pendent of any p a r t i c u l a r c r i t e r i o n applied to the optimum d i s t r i b u t i o n of income, i t i s immaterial whether th i s dis-tribution, l i s established on the basis of money income (which would seem the more f e a s i b l e ) 0 r of r e a l income. 39 f i r s t introduced by Dupuit, 1 the originator of the marginal cost p r i c i n g p r i n c i p l e , and has been elaborated by others including Marshall.2 5. The cost aspect of .production analysis w i l l now be considered. The cost to any firm w i l l be the amount paid for the factors of production i t employs. In t h i s study cost to a firm i s of less concern than cost to society - "real c o s t " . 0 The relationship between cost to society and cost to the firm must be investigated then. Along the l i n e s of the opportunity cost theory, Professor Lerner defined the marginal s o c i a l cost of a factor in any one firm as the s a c r i f i c e to society from having the marginal factor used in that firm, rather than, i n another firm where i t could have been y i e l d i n g a certain marginal s o c i a l revenue.4 He explained further, that 'this marginal s o c i a l cost would equal the market value of the marginal factor i f the "Rule" were adhered to i n a l l other uses of the factor. In turn, the value of the marginal factor would equal the, mar-ginal private cost provided that perfect competition.existed in the markets for the factors of a firm. Previously i t has been convenient to consider monop-l y conditions i n the markets for outputs of firms the rule, . a l lowing the' degree of monopoly to be p r a c t i c a l l y n i l i n case 1 Dupuit, "De l ' u t i l i t e ' e t de sa mesure", p. 63. 2 Marshall, Principles* of economics,pp. 124-133 and 830-831. 5 Ibid., p. 339. 4 Cf_ above, p. Z'12... of perfect competition. Now i t is equally convenient to assume perfect competition in the firm's markets for inputs the gen-eral case. This is not e n t i r e l y u n r e a l i s t i c . The v a r i e t y of factors of production, on the basis of most c l a s s i f i c a t i o n s , i s smaller than the variety of products, many firms producing quite d i f f e r e n t products with the same factors. Most' factors of firms are either bought i n crimpe'titive markets (e.g. labor, loans, and raw materials), or they are used i n large i n d i v i s -i b l e units (e.g. plant), i n which case they cannot be varied i n order to influence the price by the quantity bought. This assumption of perfect competition i n the realm of factor pur- • chases i s ma.de only to j u s t i f y the i d e n t i f i c a t i o n of the mar-ginal s o c i a l cost with the marginal private cost.'-1- The iden--1 There are some further possible l i m i t a t i o n s to the equality of marginal private cost and marginal so c i a l cost. Many s o c i a l costs, such as those connected with the t r a i n i n g and maintenance of the labor force, are evaded by individual firms and are thus not included i n private cost. See Clark, J.M., Studies i n the economics of overhead costs, Chicago, 1923, pp. 25-27, 397-403, and 463-464, cited i n Lange, "On the economic theory of socialism", p. 104. Also, external econo-' mies and diseconomies of scale are 'omitted from private cost. See.,<Lange, op. c i t . , p. 105. Other s o c i a l costs often evaded by private enterprises are those r e s u l t i n g from smoke nuisance, p o l l u t i o n of. water, etc. When the a c q u i s i t i o n of a good by one person a f f e c t s the u t i l i t i e s enjoyed by others, an adjustment i n s o c i a l cost takes place which does not feature in private cost. The overcrowding of a t r a i n w i l l diminish the u t i l i t i e s enjoyed by those who acquired the f i r s t seats and a corres-ponding amount must be r e f l e c t e d in an addition to the s o c i a l cost of places offered to those responsible for the overcrowd-ing. It should also be noted that in deciding whether to put a new firm into operation or not, s o c i a l as well as private cost c a l c u l a t i o n w i l l include the sums necessary for the construc-t i o n of buildings, i n s t a l l a t i o n of heavy equipment, etc. Once a plant has been constructed, however, the s o c i a l cost of fur-ther operation of the plant may include only that part of the value of such o r i g i n a l investment as could be r e a l i s e d by the current sale of those assets and t h e i r subsequent use i n other processes. Private cost of continued operation often includes quasi-rents, such as fixed debt charges, 41 t i t y of these/cwo magnitudes w i l l greatly simplify the anal-y s i s of the implications of marginal cost p r i c i n g . A l l calculations w i l l have to be i n terms of s o c i a l cost, i f the general welfare i s the c r i t e r i o n , and -the marginal private cost w i l l have to be converted into the marginal s o c i a l cost i n the oase of imperfect markets for factors. This may be done by c a l c u l a t i n g what -the mar-ginal private cost would be were the firm to leave the increase in price on a l l units of the factor out of con-sideration i n determining the cost of employing additional units of the f a c t o r . 1 Although the opportunity cost theory seems to have provided a l o g i c a l d e f i n i t i o n of the s a c r i f i c e s which make up s o c i a l cost, i t may not appear to be quite convinc-ing. In the process of production i n society as a whole, the only s a c r i f i c e s which can be observed are those involved i n the exertion, drudgery, and danger of labor and, perhaps, i n the temporary abstinence involved i n c a p i t a l saving. When, on the other hand, thes cale of the investigations i s re-duced to that of the firm, the use of land, for example, a free g i f t of nature, i s a cost item, since i t s use by one. firm involves the loss of alternative uses i n producing u t i l i t i e s by other firms. For the time being, the opportunity cost d e f i n i t i o n wiasi be used and the l o g i c a l connection with the o r i g i n a l human s a c r i f i c e s i n the process of production — 1 Lerner, op.cit., pp. 128-151, 42 (the "real cost" of production) w i l l be explained l a t e r . 1 Graphically cost may be represented i n the same manner as revenue. In figure 4 a marginal s o c i a l cost (msc) curve has been constructed by marking o f f the social cost involved i n each successive unit of output. From t h i s an average s o c i a l cost (asc) curve may be derived. In the assumed general case the msc curve w i l l coincide with the marginal private cost (mpc) curve and the asc curve w i l l be the same as the average private cost (ape) curve. "Pr, ce M H L 0 \ \ —. • Jnsc = tvi/oc \ \ . N X N ^/ y O.SC = a/oc ^ ^ ^ ^ ^ ^ ^ *" ~* - Imjor-A/' Figure 4 Q u a r t tiiy 6. Maximisation of p r o f i t s to the firm w i l l be de-termined by point PJ_, the int e r s e c t i o n of the mpr and mpc curves, establishing an output ON*. Up to that point private revenue exceeds private cost for each unit of output; beyond that point private cost exceeds private revenue for each 1 See Appendix i , pp. 106-110. 43 unit of output. Total private revenue at output ON* w i l l be represented by the area MPJJPO, t o t a l private cost by the area KP'N'O. Net private revenue, or private p r o f i t , i s given by the area MP'K. The maximised net s o c i a l revenue, or s o c i a l p r o f i t , can be determined by an analogous argument as the area MPK; P representing the intersection of the msr and msc curves, Por up to point P s o c i a l revenue exceeds s o c i a l cost, while beyond i t s o c i a l cost i s i n excess of s o c i a l revenue for each unit of output. According to whether the outputs of firms i n an economic system are determined by the maximisation of net private revenue, or of net s o c i a l revenue, the economy could be termed a private p r o f i t economy, or a s o c i a l p r o f i t econ- omy. How w i l l prices be determined in either economy? Dis-counting the p o s s i b i l i t y of price discrimination, the price of a good at any p a r t i c u l a r output w i l l be determined by the point on the demand curve corresponding to that output. Social p r o f i t w i l l be maximised for output ON at P, the i n t e r s e c t i o n of the msc and msr curves. Similarly, private p r o f i t w i l l be maximised for output ON' at P 1, the in t e r s e c t i o n of the mpc and mpr curves. Here the analogy ends. As the demand curve, d_, coincides with the msr curve, the price charged i n the s o c i a l p r o f i t economy for the output ON w i l l be PN. However, the price charged for the output ON* i n thejprivate p r o f i t economy w i l l not be P 'N' but Q,N'. Por to the firm maximising i t s private p r o f i t the demand curve w i l l be an apr curve, not a/- mpr curve. 44 It i s now evident why the s o c i a l p r o f i t economy i s said to adhere to the "marginal cost p r i c i n g p r i n c i p l e " . For i n the s o c i a l p r o f i t economy price (demand) equals marginal s o c i a l cost at the equilibrium output. In figure 4 both are given by the distance PN. The p r i c i n g pobicy of the private p r o f i t economy i s sometimes wrongly referred to as "average cost p r i c i n g " . 1 There is no reason why the ape curve, as a rul e , should pass through point C^, the point i n d i c a t i v e of price i n the private p r o f i t economy. Only i n the exceptional case that the average private cost would equal the average private revenue, when neither a p r o f i t nor a loss i s made, would t h i s be true. The p r i c i n g p o l i c y of a private p r o f i t economy Gould probably not be described any more l u c i d l y than as "maximum private p r o f i t p r i c i n g " . Previously the phenomenen of consumers.' surplus (the area, MPL i n figure 4) was mentioned. It should be noted that the t o t a l s o c i a l p r o f i t includes not only a consumers ' . surplus, but, i n addition, what may be c a l l e d a producers '  surplus (area LPK). This producers' surplus, i n an orthodox sense, is nothing but the firm's p r o f i t - the excess of i t s revenue (area LPNO) over i t s cost (area KPNO). Under con-di t i o n s of the private p r o f i t economy, consumers' and pro-ducers' surpluses would be given by .the areas MQ.H and HQ.P 'K respectively. ^  . . . 1 Coase, R.H., "The marginal cost controversy", Economica. v o l . 13, p. 173, August, 1946. Also Lange, "On the economic theory of socialism", p. 98, n. S2. 2 Under the private p r o f i t economy the producers ' surplus, being the firms p r o f i t , could, of course, be given, a l t e r -natively, by the areas MP 'K and HQP 'K. 45 The maximised s o c i a l p r o f i t of the firm depicted i n figure 4, established at output ON, covers the area MPK. The s o c i a l , p r o f i t of the same firm at output ON', where the private p r o f i t i s maximised, covers only the area MQ.P*K. Under the conditions of the s o c i a l p r o f i t economy, the t o t a l s o c i a l p r o f i t appears to be greater by an area Q.PP'. There are c e r t a i n l i m i t a t i o n s to t h i s conclusion, however,.The equality of marginal private cost and marginal s o c i a l cost may only be assumed when; in addition to the perfect competi-t i o n in the markets' for factors, which was already assumed, marginal cost p r i c i n g i s practiced i n a l l the other firms .in the economy, either by design, or as a result of perfect competition.-1- In that case, the factors used i n the produc-t i o n of the output between NJ_ and N would, i n alt e r n a t i v e uses (other firms), as marginal units, earn no s o c i a l p r o f i t . Here they are responsible for a s o c i a l p r o f i t given by area QPPWhere, however, an economy has a great number of firm's not adhering to marginal cost p r i c i n g , i t becomes extremely d i f f i c u l t to assess the s o c i a l loss, i n any in d i v i d u a l firm, r e s u l t i n g from private p r o f i t maximisation. The msc curve -depending fen the alternative uses of the factors - could not be determined without investigating how the s h i f t of factors towards the firm concerned would affect the s o c i a l p r o f i t i n every other firm. It is even possible that the s h i f t from output ON1 to output ON.'jffould result i n a diminution of s o c i a l p r o f i t . . This would be the case i f factors were with-1 Cf. above, p. 13. 46 drawn from other firms where they were earning a greater s o c i a l p r o f i t at the margin than they would earn between the outputs ON' and ON of the firm under considera'tion. When, on the other hand, factors would be withdrawn from firms earning less s o c i a l p r o f i t at the margin, or none at a l l (in the case of p e r f e c t l y competitive firms), an increase i n s o c i a l p r o f i t would be assured. Por the sake of completeness, i t should be mentioned that the t o t a l of consumers' surpluses enjoyed fromnioutputs of firms w i l l exceed that indicated by a summation of con-, sumers ' surpluses given on the graphs of the in d i v i d u a l firms. Consumers' surpluses are r e l a t i v e l y low (approaching zero i n the case of perfect competition between i d e n t i c a l products) when the maximum amount s. purchaser i s w i l l ing. to pay for a s p e c i f i c a r t i c l e i s influenced by his knowledge of the a v a i l -a b i l i t y of goods with a degree of s u b s t i t u t a b i l i t y at r e l a -t i v e l y low prices. Should the demand curves for an entire group of products having a great degree of s u b s t i t u t a b i l i t y amongst each other be combined, the t o t a l demand curve would be much more i n e l a s t i c than would the demand curves for the component products - would therefore provide for greater consumers' surpluses. This would be the case as purchasers would now have only very imperfectly substitutable a l t e r -natives l e f t to the type of product they wish to buy. 7 . As i t has been constructed, the msr curve of a firm - the demand curve for i t s product - w i l l always slope 47 downwards. If the mso curve would always slope upwards no doubt would ever arise as to the output maximising s o c i a l p r o f i t . Clearly, t h i s would be given by the interse c t i o n of the msr and.msc curves. For every item of output before the intersection of these curves the msr would exceed the msc, r e a l i s i n g a soc i a l p r o f i t . From, the production of every item a f t e r that intersection, however, a s o c i a l loss would resu l t since the msc would be i n excess of the msr. Under such c i r -cumstances Professor Lerner's marginal analysis would be satis f a c t o r y . As suggested by the indifference theorists,. -the u t i l i t y analysis might be dispensed with altogether then. As w i l l be seen, however, the relationship between s o c i a l revenue and s o c i a l cost very often i s not that simple. An understanding of the true relationship, i n many cases, cannot be gained without a study of the cost and revenue values over the entire range of output. The usual shape of aj^ msc curve, as mentioned before, is that of a "U". There are many ways i n which a U-shaped msc curve could intersect with a downvirard sloping msr curve. The relationship between the two curves may be much more complicated than i n the convenient example used above. Various possible relationships between msc and msr curves w i l l be investigated, in the l i g h t of v<?hich a re-examination of the conclusion that social p r o f i t i s maximised at the- intersection of the msc and msr curves w i l l be made. Corresponding to the previous example, figure 5 shows a firm responsible for a consumers' surplus (area MPL) and a producers ' surplus (area LPK) on every item of the s o c i a l l y most p r o f i t a b l e output (ON). 48 Pr, Figure 5 Quantity Figure 6 C2..u.antity 49 In figure 6 consumers enjoy a surplus equal to area MPL and the firm has a producers ' surplus (area QPR) over a l i m i t e d range. The firm suffers a f i n a n c i a l loss (area KQ.L) on part of i t s output. From a s o c i a l p r o f i t standpoint t h i s same area must be deducted from the consumers' surplus to make the s o c i a l p r o f i t equal to the area MPRQ.K. Firms which are i n the stage of decreasing cost for the entire range of output at the maximum s o c i a l p r o f i t p o s i t i o n , are often referred to as "decreasing cost f i r m s " . 1 Figure 7 shows a firm of t h i s type, suffering a f i n a n c i a l loss (area KPL) on i t s output. Such a firm may s t i l l r e a l i s e a, s o c i a l p r o f i t since i t i s evident that, a f t e r deduction of the f i n a n c i a l loss, a considerable amount of the consumers' surplus i s s t i l l l e f t (shaded area MPK). A decreasing average cost firm must incur a f i n a n c i a l loss i n order to produce at the s o c i a l l y most pr o f i t a b l e output. This j u s t i f i e s the. prac-1 The term "decreasing cost firm" i s ambiguous in that i t does not specify whether cost means marginal cost or average cost. In t h i s case referrence i s to decreasing average cost. The mathematical relationship between the" mpc and ape curves is such that the mpc curve w i l l always pass through the point of lowest average cost, R (figure 7). If point p, the intersection of the mpc and apr curves, i s "to the l e f t of point R, the apr w i l l be less than the ape and a private loss w i l l be incurred. On the other hand, a private p r o f i t w i l l be r e a l i s e d when P i s to the right of R the apr then exceeding the ape. A private loss w i l l be i n -curred when, and" only when, average cost i s decreasing at the maximum s o c i a l p r o f i t output. It i s possible, however, that a'firm suffering a f i n a n c i a l loss at t h e ' s o c i a l l y most pr o f i t a b l e output w i l l be.working under increasing marginal cost at that output, for mpc increases over a l i m i t e d range before the ape curve i s met. 5 0 T n c e ° A/' A/ Figure 7 Gi^^h t i c e of complete subsidisation of such "industries 1 1 as roads and bridges (where the marginal s o c i a l cost i s prac-t i c a l l y zero), and the p a r t i a l subsid-isation of railways. In the private p r o f i t economy, without subsidisation, decreasing average cost firms can only avoid, bankruptcy by using the monopolistic practice of r e s t r i c t i n g output. The firm i n figure 7 would maximise private p r o f i t s (area MQ.K) with an >• output ON' at the intersection of the mpr and mpc curves. Perfect competition could not pe r s i s t in a de-creasing average cost industry. Por under perfect competi-t i o n the msr and mpr curves would be the same horizontal l i n e (figure 8). With a downward sloping marginal cost curve t h i s would s p e l l a s o c i a l as well as a private loss . on the operations of the p e r f e c t l y competitive firm (area P r i ce Figure 8 Q u a n t i t y For some firms - as for the one i n figure 9 - mar-ginal cost may start at a higher point on the Y-axis than marginal revenue.^ i f the msc curve l i e s e n t i r e l y above the msr curve, no s o c i a l p r o f i t can be made on any unit of the. 1 It might be proposed to expand output to the point where the msc curve would r i s e and intersect with the msr curve again. A p r o f i t might be made there. But the industry would then no longer be a decreasing average cost.industry. Most l i k e l y the attempt -at such an expansion of output i n the firms of a. decreasing average cost industry would simply lead to lower msr curves through the increased supply of the commodity concerned on the market. 2 Actually, the majority of firms could be included i n th i s category. For many firms the cost of the f i r s t item of output - which includes a l l fixed costs - w i l l , exceed the highest possible revenue (demand) for the f i r s t item. But by enlarging the unit i n which output i s expressed, the msc might be reduced r e l a t i v e l y to the msr over the i n i t i a l range of output. • T r i c e 0 Figure 9 output series. Similarly, i f the mpc curve l i e s e n t i r e l y above the mpr curve (as i s the case here) no private p r o f i t can be made on any unit of output. Should the msc curve now intersect math the msr curve, i t must cross the l a t t e r at two places, -pl_ and P2_. (Whereas the msr curve continues a downward trend, the msc curve eventually turns upward.) Up to the f i r s t i n t e r s e c t i o n a s o c i a l loss i s incurred for each item of the product. Between PI and P2 the output r e a l i s e s a s o c i a l p r o f i t . After P2 an i n d e f i n i t e range of losses sets i n . The t o t a l s o c i a l p r o f i t area, P1P2Q, is maximised at P2 with output ON. Depending on whether th i s s o c i a l p r o f i t area is larger or smaller than the s o c i a l loss area KP1M, the existence of the firm w i l l or w i l l not be j u s t i f i e d . In a private p r o f i t economy, ob-viously, the firm depicted could not survive. 8. Care must he taken to the manner i n which the analysis of the firm is applied to that of the economy as a whole. The u t i l i t y evaluations made i n a society working under a system of private p r o f i t maximisation are, s t r i c t l y speaking, not comparable to the evaluations which would be made i n that same society were i t to change suddenly to a regulation of price and output according to s o c i a l p r o f i t maximisation. For, according to the assumptions made, com-p a r a b i l i t y of u t i l i t i e s i s made possible only by the exist-ence of an optimum d i s t r i b u t i o n of income. Any:.,change i n the outputs or prices of products, whether they be a result of applying a di f f e r e n t p r i n c i p l e of price determination, or whether they be a result of dynamic developments i n an unmodified p r i c i n g system, w i l l inevitably lead to a new and d i f f e r e n t d i s t r i b u t i o n of income. The new d i s t r i b u t i o n may be an optimum one again i f i t i s carried out according to the eth i c a l c r i t e r i o n for an optimum d i s t r i b u t i o n set by the society concerned. But the important point i s that the new optimum d i s t r i b u t i o n w i l l not l i k e l y be the- same one as the o r i g i n a l optimum d i s t r i b u t i o n and the u t i l i t y evaluations made under conditions of the one w i l l then not be comparable to those ma.de under conditions of the other. How i s i t now possible to prove that a switch from private p r o f i t maximisation' to s o c i a l p r o f i t maximisa-t i o n w i l l benefit society? A change from one system to another w i l l destroy the basis for a l l the u t i l i t y evalua-tio n s . However, i f a change towards s o c i a l p r o f i t maximisatio is broken down into stages, i t i s not d i f f i c u l t to prove that benefits to society w i l l ensue. Por example, an economy o r i -g i n a l l y working on the.principle of private p r o f i t maximisa-t i o n may be considered. The output of a firm making a large s o c i a l p r o f i t at the margin can be increased by one item and t h i s can be given to the person next on the demand schedule of that firm. The factors necessary for the pro-duction of that item can be withdrawn from a firm - (or firms) where they are producing for that same person goods on which no s o c i a l p r o f i t or a r e l a t i v e l y small p r o f i t i s r e a l i s e d . The value of the goods lost to the person under consideration is now less than than the value of the goods gained by him. But no one else i n the society has been affected by the change. Clearly society has gained i f i t increases the u t i l i t i e s to one of i t s members without a f f e c t i n g those enjoyed by others. The complete change from the private p r o f i t economy to the s o c i a l p r o f i t econo-my is nothing other than the t o t a l of such f r a c t i o n a l changes, each one of which w i l l benefit an in d i v i d u a l without detracting from the s a t i s f a c t i o n s enjoyed by others. After completion of the entire process some individuals may be found to have gained more than others. A r e d i s t r i b u t i o n of income could then establish'a new optimum d i s t r i b u t i o n which would equitably divide the benefits gained. Certain changes i n the scale of production w i l l 55 take place when moving from a private p r o f i t economy to a s o c i a l p r o f i t .economy. Under a l l but p e r f e c t l y competitive conditions, the outputs of firms would be pushed beyond the maximum private p r o f i t position, and some enterprises would be put into operation which could not exist at a l l in a private p r o f i t economy. It does not necessarily follow.from t h i s that o v e r - a l l production, and therefore employment, w i l l be increased. Employment, abstracting from involuntary unemployment, w i l l depend on how workers, i n general, balance the u t i l i t i e s of t h e i r income i n goods with those of le i s u r e time under the new circumstances. The increase i n production which the s h i f t from private p r o f i t maximisation to s o c i a l p r o f i t maximisation e.ntails must be taken i n a r e l a t i v e sense. If, under the new circumstances, t o t a l employment were to remain the same, an increased production (in terms of employment) in one firm would be at the expense of pro-duction i n other firms. It would simply mean that i n those firms where s o c i a l p r o f i t maximisation brought with i t a great increase in s o c i a l p r o f i t , the increase i n production wou3id be at the expense of production i n firms where no additional s o c i a l p r o f i t or only l i t t l e could be r e a l i s e d . 9. Summarising the investigations made so far, i t can be said that the l o g i c in both the private p r o f i t econ-omy and the s o c i a l p r o f i t economy i s the same. Both deter-mine output by equating t h e i r marginal cost with t h e i r mar-ginal revenue. The difference between the two economies i s , 56 i n the general case analysed, a result of the divergence of the mpr and msr curves. This divergence i s caused by:,the monopolistic p o s i t i o n of the firm, which can influence i t s revenue by varying the amounts of i t s product marketed. Only i f the monopolistic firm could be pe r f e c t l y d i s c r i m i -natory i n i t s p r i c i n g , i . e . i f i t could charge the maximum amount each individual would be w i l l i n g to spend for h is purchase of the firm's product, would the mpr curve coincide with the msr c u r v e . l . I f such perfect price discrimination were fea s i b l e , the intersection of the marginal revenue and marginal cost curves would indicate both private p r o f i t -maximisation and s o c i a l p r o f i t maximisation. In that case the search for an alte r n a t i v e p r i c i n g system would be un-necessary. • The general effect on the firm of the change from a policy of maximum private p r o f i t p r i c i n g to marginal cost p r i c i n g w i l l be a diminution of the firm's f i n a n c i a l surplus, or even i t s conversion into a f i n a n c i a l loss i f i t i s a decreasing average cost firm. 1 Cf. above, pp. 34-35. 57 TAXATION PROBLEMS RAISED B Y MARGINAL COST PRICING 1. Many forms of taxation materially a f f e c t both the r e l a t i v e and absolute outputs of firms. In fact, many taxes assume the form of cost items to the firms involved. No theory on marginal cost p r i c i n g can be complete then X without a chapter on the effects of taxation. Por the purposes of t h i s essay, forms of taxation may be grouped into "taxation of costs" and "taxation of surpluses". A tax. on costs w i l l be any tax the rate of which is defined i n terms of the price of an economic good or of any element of that p r i c e . A tax on surpluses, on the other hand, w i l l be one the magnitude of which depends upon the amount of a consumers' or producers' surplus. 2. As a proto-type of taxation of costs an excise tax i n the form of a fixed levy per unit of output sold may be used. What effect wiSUl such a tax have on the s o c i a l p r o f i t 1 The most prominent contribution toJthe taxation aspect of marginal cost p r i c i n g has been made by Professor H o t e l l i n g i n "The general welfare i n r e l a t i o n to problems of taxation and of railway and u t i l i t y rates", Econometrica, v o l . 6, pp. 242-269, July, 1958. A.discussion of certa i n t e c h n i c a l i t i e s of his presentation developed between Professor Hotelling and Professor Prisch. See Prisch, Ragnar, "The Dupuit taxa-t i o n theorem", Econometrica,- v o l . 7, pp. 145-150, A p r i l , 1939; Hotelling, Harold,^."The r e l a t i o n of prices to marginal costs i n an optimum system", Econometrica, v o l . 7, pp. 151-155, A p r i l , 1939; Prisch, Ragnar, "A further note on the Dupuit taxation theorem", Econometrica. v o l . 7, pp. 156-157,' A p r i l , 1939; and.Hotelling,.Harold, "A f i n a l note", Economet- r i c a , v o l . 7, pp. 158-160, A p r i l , 1939. economy? If the government decides to c o l l e c t the tax from the producing firm, the cost of production for each -item, of output, to the firm, w i l l be increased by the amount of the .tax. Thus,, i n figure 10, 1 the firm's o r i g i n a l msc curve w i l l be raised by the tax per unit of output, p'Q. A new marginal cost curve, mc_, w i l l result and i t s intersection, with the msr curve w i l l determine an output ON', instead of ON, and a price P'N', instead of FN. The consumers • surplus w i l l decline from area MPL to area MP 'L'. and - the producers' surplus from area LPK to area L'P'K'. Part of t h i s diminu-t i o n of the surpluses amounts to a transfer of purchasing power to the government, v i z . the tax represented by the area K'P'O.K. But the t o t a l s o c i a l p r o f i t ..has declined fr.om. area. MFK.to area MP 'Q,K, the diminution being measured by area P'P&. Through t h i s taxation procedure the t o t a l social, p r o f i t , apparently, has been reduced. Such a type of taxa-t i o n , obviously, i s inconsistent with marginal cost p r i c i n g , which seeks to maximise.the s o c i a l p r o f i t . However, the r a i s i n g of the msc curve. may., not be j u s t i f i e d i n the f i r s t place, since a tax cannot be regarded as a legitimate s o c i a l cost of production. If the firm were compe 11 ed to cont inue produeing at the maximum s o c i a l pr of i.t output, ON, and; s e l l i n g at the marginal s o c i a l c.os.t, PN, the tax (area. K'RPK) would very, lik e l y . oxce.e'd. the.,producers,• surplus (area LPK). In a -decreasing average. co.st.. .firm, the -.1 Professor Hotelling. uses a si m i l a r diagram put applies i t to an, industry,. instead of a firm. See "The general welfa.re p. 243, 59 tax would simply add to the f i n a n c i a l loss already suffered by the firm.. Insofar as the excise tax would be adding to the f i n a n c i a l losses of firms, i t would be defeating i t s own purpose. Por the d e f i c i t s of firms i n a s o c i a l p r o f i t econo-my would, . presumably, have to be financed, out of taxation. Only insofar as the excise tax could be paid out of producers;?' surpluses would i t f u l f i l i t s purpose. But i f the tax were to be determined by the producers' surpluses, i t would no longer have the.character of an excise tax - a tax proportional to the price of an a r t i c l e . Charging the tax to consumers, instead of producers, would have the same res u l t s . In this case, the msr - the maximum amount consumers would be w i l l i n g to s a c r i f i c e to acquire the successive•items of the product - would be lowered by P 'Q, per item, the amount of the tax. The msr curve would. 0 A/' N Figure 10 Quantity 6 0 be replaced by another marginal revenue curve, the mr curve. Again,the propriety of deviating from the msr curve i n the f i r s t place might be questioned. The tax does not r e a l l y constitute a diminution i n the t o t a l s a t i s f a c t i o n derived from the consumption of the goods concerned. But i t would be impossible to compel people to maintain t h e i r o r i g i n a l u t i l i t y evaluations of the product i f a tax were coupled to the purchase of each item. The output established at the intersection Q_ of the mr and msc curves is again ON'. The t o t a l s o c i a l p r o f i t i s again diminished by the area P 'PQ,. Charging consumers an excise tax is then also incompatible with s o c i a l p r o f i t maximisation. From the foregoing i t would appear that wherever a tax on an item i n the output series of a firm would exceed the s o c i a l p r o f i t (the combined producers ' and consumers ' surpluses) which could be r e a l i s e d on that item - t h i s applies to a l l items between outputs ON' and ON - the item would not be produced and whatever surplus could have been r e a l i s e d on i t would be l o s t . Yet a tax which would cause no loss of surpluses may s t i l l be t i e d to the price, of a good under exceptional circumstances. A glance at figure 1Q w i l l show that the steeper-the msr or msc curves are near t h e i r point . of intersection, the smaller w i l l be the area of s o c i a l p r o f i t lost (P 'PQ,) as a result of an excise tax. The loss may be zero whenever there is a good of limited quantity for which the demand has not been exhausted at a price equal to the marginal s o c i a l cost of producing the l a s t 61 item.'1 For i n that case, the msc curve w i l l be. v e r t i c a l at i t s point of intersection with the msr curve. A tax on the si t e value of land provides an example. In figure 11, the tax, QJfl, on a.particular grade of land with s i t e value PIT raises the msc curve to the mc_ curve without i n t e r f e r i n g v\fith output or s o c i a l p r o f i t . The tax, area K'QNO, i s drawn exclusively from the producers' surplus, area LPNO. Figure 11 Qua<nti ty 3. Taxation, i n the f i n a l analysis, must take the form of transfers of purchasing power, from, individuals or 1 Hotelling, "The general welfare", p. 257. 2 •,Here the c o l l e c t i v e owners of the""particular grade of land are consideredas the operators o f a single-firm. The maximum uniform price which they can charge for t h e i r land i s , of course, PN." As nature provides each grade of land free of charge, the msc w i l l be zero for the limited amount availa b l e , r i s i n g to i n f i n i t y when the supply i s exhausted. Cf. also Appendix i , p. 109. 62 corporate bodies to the government. The individuals or-cor-porations must pay the-t axe ajar out of the i r money incomes. Real incomes, as defined previously, w i l l exceed money i n -comes by the consumers' surpluses. Consumers' surpluses constitute an intangible form of income a r i s i n g out of the expenditure of money income i n a manner advantageous to the spenders. With the removal of the underlying money income from the spenders, the consumers' surpluses, so to say, vanish i n t h i n a i r . Money incomes consist of the revenues of firms. They include incomes from labor, since a worker may b e j a ^ considered to be a p a r t i c u l a r type of firm, producing l a b o r . 1 Individual incomes are, of course, i d e n t i c a l with those of firms, the income of any p a r t i c u l a r firm going to i t s owner or group of owners. Net money incomes,., i . e . money incomes a f t e r de-duction of production costs (including d i s u t i l i t y of labor), i make up producers' surpluses. Only these producers' surpluses can be removed as taxes. Any taxes i n excess of producers' surpluses w i l l cause a net loss to the firm concerned. The firm w i l l either have to suspend operations or draw a sub-sidy from the government, which would defeat the purpose for which the tax was collected i n the f i r s t place. • Although, by d e f i n i t i o n , purchasers never pay money for consumers ' surpluses, i t would be possible-to 1 Of. Appendix i , p. 108. / transfer their equivalent value from individuals to the government. A government can attach a tax to an a r t i c l e and s t i l l induce.' an individual to buy i t , as before, so long as the tax does not exceed the consumers' surplus which could be enjoyed. As consumers' surpluses are a res u l t of i n d i -v i dual u t i l i t y evaluations, of which no government can have a perfect, or even an approximate, knowledge, i t w i l l be almost impossible for a government to levy a. tax only where the- tax i s smaller than the consumers * surplus of an a r t i c l e . Even i f the government had a knowledge of the respective, consumers' surpluses enjoyed, i t could not levy a tax of the excise type. For, as the msr curve has. been constructed, the consumers' surplus w i l l , as a r u l e , decline with each successive unit of output of a product. The marginal item of output w i l l then have a zero consumers' surplus and, therefore, w i l l not be able to support a tax (unless there were a p e r f e c t l y i n e l a s t i c demand, characterised by a ver-t i c a l . msr_ curve). Only by an unthinkable process of "tax discrimination", taxing on the basis of presumed consumers • surpluses, could a government prevent a contraction of demand following i t s taxation of consumers ' surpluses. It should be noted that, even i f consumers' sur-pluses were taxed, the actual revenue would be drawn from producers' surpluses. For the surpluses surrendered i n taxes by the consumers would consist of part of t h e i r moaey incomes. The net money incomes ( i . e . net of costs, not net of taxes) of individuals are the producers' sur-64 pluses of the firms they own. Where taxes exceed producers ' surpluses (,i.e. net money incomes), proprietors w i l l abandon t h e i r enterprises. 4. As taxes, i n the f i n a l analysis, are drawn from pro-ducers' surpluses, the most l o g i c a l form of taxation would appear to be one which taxed these surpluses d i r e c t l y . Besides the tax on the s i t e value of land, inheritance and income taxes have been suggested. 1 It is not clear, however, that the estate of a deceased man i s a pure producers' surplus. Estates are l i k e l y to consist of c a p i t a l investments, to a large extent, and i t would seem unwise for a government to operate on funds drawn from the l i q u i d a t i o n of a country's i n d u s t r i e s . Income taxes are a d i f f e r e n t matter. I f the tax i s based on net money incomes, i t a f f e c t s s o l e l y producers;.' sur-pluses and could be levied without harmful e f f e c t s . However, personal incomes are very often gross money incomes. The cost of the worker, his d i s u t i l i t y of labor, i s not deducted from hi s income for taxation purposes.2 When an income tax is a tax on wages, i t is i n effect an excise tax on the labor performed by the worker.3 To the worker the tax i s an addi-1 Hotelling,' l o c . c i t . '"2"Certain tax exemptions are often granted," but these are seldom" connected with the d i s u t i l i t y of the all-import-ant marginal items of labor performed. 3 Professor Ho t e l l i n g admits this i n his second a r t i c l e . See""The r e l a t i o n of prices to marginal costs i n an optimum system", p. 154. He ref e r s to Professor Lerner's treatment of this problem i n The economics of control, pp. 234-240. 65 t i o n to h i s cost, the d i s u t i l i t y of his labor. If, i n figure 12, the marginal d i s u t i l i t y of labor to a worker i s given by the msc curve, an income tax, P'Q,, on the wage, given by the msr curve, would rais e the d i s u t i l i t y to the worker to the mc curve. 1 The worker w i l l now f i n d i t unprofitable to work that time for which the d i s u t i l i t y of his labor, gross of 2 taxes, exceeds his wages. In consequence, the worker w i l l M JvSC K' H -AV' A/ Figure 12 L a b o r 1 Alt e r n a t i v e l y , i t could be said that the u t i l i t y of the wage, given by the msr curve, would be diminished by P_J_ As explained above (pp. 59-60), t h i s would have i d e n t i c a l r e s u l t s . 2 "This argument may sound too t h e o r e t i c a l i n that i t disregards the r i g i d i t y with which working hours tend to be fixed."Yet, i n the long run, the balance between the d i s -u t i l i t y of labor and i t s remuneration .'may have a deciding influence"on the f i x i n g of standardised hours of work. Even in t h e s h o r t run the implications of the above argument may b"e""'felt. "Absenteeism i n the ' Br i t i s h coal mines i s attributed p a r t l y to high income taxes. reduce his output of labor from ON to ON'.1 Of his o r i g i n a l producers' surplus (area MPK), the government w i l l receive an amount, given by area KfP?Q,K, in taxes. But another part (a©ea P'PQ,) w i l l be lost e n t i r e l y , which w i l l mark a corre-sponding decrease i n s o c i a l p r o f i t . The objections to income taxes on wages could be n u l l i f i e d by. a change i n the taxation formula. If an annual tax were determined by the hourly wage earned by a worker during the hours he worked, a reduction i n the number of hours worked would bring no tax r e l i e f . The tax would, be independent of the actual number of hours worked and would not influence the worker's preference between labor and l e i s u r e . Another d i f f i c u l t y , which even this improved 2 income tax might encounter, is the following. The higher tax per unit of labor on larger incomes, which i s charged with progressive and even proportional income taxes, might induce workers to seek less remunerative, but easier jobs ( i ^ e . with a smaller d i s u t i l i t y attached to them). This would indeed be the case i f the t o t a l producers' surpluses on better paid jobs were equal or ©nly s l i g h t l y greater (i.e.. less, than ..the. difference in. taxes.) than. on poorer 1 It i s not necessarily true that the tax w i l l a c t u a l l y reduce the amount of labor performed. A reduction i n a work-erfe income may induce him to work longer i n order to make up f o r : the"" income lost i n taxes. Only where taxes are not returned in' the form of benefits to the worker would th i s apply. The analysis of such a s i t u a t i o n i s beyond the com-petence of this essay, since the assumption of constant mar-ginal u t i l i t y of money implies,constant rates of income. 2 Lerner, op.cit.. p. 237. paid jobs. For then increased taxation would more than off-set any gain i n producers' surplus a worker could make by accepting the better paid job. The producers' surplus fore-gone by the worker means, of course, a corresponding loss -in s o c i a l p r o f i t . Usually, however-, producers ' surpluses w i l l grow more than proportionately to the pay of a job and w i l l thus be able to support progressively higher income taxes. Only where the d i s u t i l i t y of labor increases less-than proportionately to wages, i s a progressive or propor-t i o n a l rate of income tax inadvisable and should i t be replaced by a fixed sum. In that case the tax (no longer an income tax) would be independent of the wage-rate. Any gain i n producers ' surpluses would accrue to the worker only, who would thus be encouraged to maximise s o c i a l p r o f i t by s e l e c t i n g the job which would give him the highest pro-ducers' surplus. E t h i c a l considerations of society have been abs-tracted from to the extent that no decision has been made whether or not c a p i t a l investment should, be determined by individual .preferences tofyby c o l l e c t i v e u t i l i t y evaluations. 1 A decision i n favor of the f i r s t a l ternative r a i s e s two other complicat ions to the income' tax. Savings may be sub-jected to "double taxation", since interest on saved income is. usually, regarded, as, income, again,. and so. is., taxed..twice. 1 Cf. Appendix i , p. 110. 2 Lerner, op.cit., pp. 235-237. The return to the saver i s then less than the rate of i n t e r e s t . The rate of interest should correspond to the inter s e c t i o n of the msr and msc curves of investment to the saver, determining the s o c i a l l y optimum output of h i s investment. With double taxation savers would be inclined to, reduce t h i s output. Their msc curves would be raised by the amount of the tax on in t e r e s t . A new inter s e c t i o n with the msr curve would c a l l for a.smaller output and would cause a loss i n s o c i a l p r o f i t . Exemption of income from investment from the income tax would seem the only remedy. S t r i c t l y speaking, only a return on investment equal to the going rate of interest would have to be exempted from income tax, since i t i s t h i s rate which determines new investment. Corporate income taxes could be levied i f corporations 1 incomes were calculated net of "normal p r o f i t s " corresponding to the prevalent rate of i n t e r e s t . If the investment.process i s to be l e f t i n the hands of private individuals, a progressive income tax might have another shortcoming. Risky investments, whieh otherwise might be made, could be discouraged. 1 This would-ft©4- only be the case where the r i s k were of such a magnitude as to involve p r o f i t s which could bring the investor into a d i f f -erent income bracket with a d i f f e r e n t rate of taxation. The increased tax rates of a higher income bracket would decrease the possible gains from such an investment. But even then th i s might be. offset by the decrease of. possible, losses, which 1 Lerner, op.cit., pp. 238-239. 69 the decreased tax rates ,of a lower income bracket would offer.. Moreover, r i s k s of such magnitude are seldom taken by one person. 5. Taxes on surpluses have been found which can take the place of the s o c i a l l y unprofitable taxes on costs. But care must be taken that the taxes on surpluses do not involve greater decreases i n s o c i a l p r o f i t i n some roundabout manner,. A tax on surpluses means that an equivalent amount of pur-chasing power i s withdrawn, from in d i v i d u a l s . This means that fewer goods w i l l be bought d i r e c t l y by these i n d i v i d -uals. In figure 13, the effect, of reduced purchasing power of individuals on a firm i s pictured. As purchases are with-drawn, prices (net of taxes) w i l l drop from FN to P'N', following the msc curve. At the margin, the s o c i a l p r o f i t l o s t , OjP', w i l l always equal the consumers' surplus fore-gone by a withdrawn purchase, for the price w i l l there be P T h e reduction i n purchases w i l l be such that p^t" w i l l , at any time, be the same for a l l firms. Por with consumers free to channel the reduction of t h e i r purchases (which, i n money value, equals the amount of the tax collected) i n any d i r e c t i o n they wish, they w i l l seek toi,;minimise t h e i r losses in consumers' surpluses per unit of tax paid by them. They w i l l never decrease purchases i n one d i r e c t i o n i f by doing that they would lose a greater surplus than they would lose by decreasing purchases i n a d i f f e r e n t d i r e c t i o n . Thus the r a t i o of the marginal decrease i n s o c i a l p r o f i t (consumers • 70 surplus i n t h i s case), Q.P', to the marginal amount of tax paid (purchasing power l o s t ) , P'N', must be equal for a l l goods i n the market. Where taxes are used to subsidise decreasing cost firms,the same r a t i o w i l l apply, and where taxes are used to provide government services, the same r a t i o again should apply to the output of these services (this time u t i l i t y evaluations w i l l be c o l l e c t i v e l y determined). In t h i s manner a maximum of s o c i a l p r o f i t w i l l be retained for society. P r i c e o y tr>SC - — ^ A/' A/ Figure 13 Quantity This analysis, of course, has been quite hypothet-i c a l . It began with a s i t u a t i o n where no taxes were levi e d and yet, presumably, a l l a c t i v i t i e s sustained by taxation continued. This was done i n order to show, c e t e r i s paribus, the effect of the imposition of taxation of surpluses. In any actually operating society taxes would be c o l l e c t e d 71 continuously. U t i l i t y c alculations, on;, the basis of pur-chasing power available to individuals, would.be such that the equilibrium p o s i t i o n for each firm (the i n t e r s e c t i o n of the msr and msc curves) would be established immediately at output ON', rather than f i r s t at output ON. 6. It i s now possible to reconsider the previous condemnation of excise taxes. Taxes on surpluses w i l l also reduce the s o c i a l p r o f i t which can be made by the operations of any firm, though i n such a manner as to r e t a i n a maximum of s o c i a l p r o f i t for society. A system of excise taxes which would reduce the outputs of various firms by exactly the same amounts as did the tax on surpluses, would be p e r f e c t l y in accord with s o c i a l p r o f i t maximisation. Such a system would c a l l for excise taxes, Q,P', on a l l goods proportional to the prices (net of taxes), P'N1, e x i s t i n g a f t e r the imposition of these taxes.1 For i n that p o s i t i o n no s h i f t of tax from one good to another could increase the t o t a l s o c i a l p r o f i t , but could only diminish i t . With a movement of N 1 towards N, ^£ w i l l diminish, and with a movement of — — P'N N' towards 0. w i l l increase. The expansion of produc-t i o n of any p a r t i c u l a r good (N' moving towards N) through a reduction in excise taxes w i l l have to be offset by a con-1 Professor Frisch corrects Professor Horelling's con-demnation of excise taxes with a somewhat si m i l a r argument along econometrlcal l i n e s . See "The Dupuit taxation theorem", pp."145-150. His conclusion, however, is that excise taxes should be proportional to prices before the imposition of the taxes. The difference with the conclusion here arises out of Professor Frisch's assumption that, with the imposition of excise taxes, prices (net of taxes) would remain unaltered. Such an assumption would seem unnecessarily u n r e a l i s t i c . 72 t r a c t i o n of production moving towards 0_) through increased excise taxes elsewhere. In t h i s manner, less s o c i a l p r o f i t would he gained through the expansion of production on the p a r t i c u l a r good than would be l o s t by contracted production elsewhere.. Considerations of p r a c t i c a b i l i t y should determine which tax system-is to be used. Taxation of producers' sur-pluses has, of course, the added advantage that i t may . simultaneoulsy be used i n the process of r e d i s t r i b u t i o n of income to suit society's c r i t e r i o n of the optimum d i v i s i o n of income. One other observation with regard to excise taxes should be made. Starting with an imperfect system of excise taxes on some goods, but not on others, or, at any rate, with non-proportional excise taxes, the imposition or increase of an excise tax on any one particular'good need not diminish the t o t a l s o c i a l p r o f i t enjoyed. 1 For i n the terms of the OP' previous analysis, the r a t i o p^, w i l l be quite d i f f e r e n t for various goods. The question i s whether the imposition or . increase of an excise tax on one good, and the subsequent decrease i n production of that good, w i l l be offset by an increase i n production of goods with, on the average, a QP' greater or a smaller r a t i o . In general, i t might be said, that, s o c i a l p r o f i t could be increased by any adjustment 1 Fri'sch, "The Dupuit taxation theorem", p. 145. Professor Hotelling accepts t h i s q u a l i f i c a t i o n to his o r i g i n a l argument. See "The r e l a t i o n of prices to costs i n an optimum system" pp. 153-154. ' 73 which would bring the various r a t i o s -p^, closer together. R e l a t i v e l y high, excise .taxes should then be reduced and... r e l a t i v e l y low excise taxes should be. increased. Disproportionately high excise taxes may s t i l l be j u s t i f i e d .in c u r t a i l i n g s o c i a l l y undesirable consumption (e.g. of liquor or tobacco). 1 In such cases individual, u t i l i t y scales would be modified by c o l l e c t i v e l y determined, evaluations. The tax would simply be the instrument of that modification. . Monopolistic practices of firms r e s t r i c t produc-t i o n i n the same manner that an excise tax r e s t r i c t s pro-duction. If excise/taxes proportional to prices are compatible with s o c i a l p r o f i t maximisation, so should monopolistic r e s t r i c t i o n s of output i n a manner keeping .prices (msr) . proportional to costs (msc) be i n accord with s o c i a l p r o f i t maximisation. In terms of figure 13, the r a t i o of taxes over prices (net of taxes), i n the f i r s t instance, i s given by ~ , and the .ratio of prices (gross .of p r o f i t s ) over costs, i n the second .instance, i s given by . Any conclusions P'A/' drawn from the constancy of the r a t i o -6— must have equal a p p l i c a t i o n to the constancy of the .ratio -^7, . The two problems, of proportionality are e s s e n t i a l l y the same. Whether the difference between the msr and.the msc i s made up of an excise tax or of a monopoly fs p r o f i t (which could 1 Lerner, op.cit., pp. 22, 3.08 and 314. Also Hotelling, "The relationship of .prices to marginal costs in an optimum system", p. 155. 74 e a s i l y be transformed into a tax)...makes no difference in* the determination of the s o c i a l l y most p r o f i t a b l e output. Several economists have disputed the adequacy of propo r t i o n a l i t y between msr and msc. in a s o c i a l p r o f i t economy and have maintained that equality of these mag-nitudes is required. 1 The p r i n c i p l e objection to propor-t i o n a l i t y centres around the fact that a worker always has the al t e r n a t i v e of "producing" l e i s u r e instead of labor. A tax on wages could always bring about the desired pro-p o r t i o n a l i t y between the msr of a worker's labor (the value of the marginal product, which should equal wages including taxes) and i t s msc ( d i s u t i l i t y , which w i l l equal wages net of taxes). But, so i t Is claimed, for the worker's alterna-t i v e product, l e i s u r e , the same proportionality could not be attained. Here, equality between msr and msc must p e r s i s t . For the marginal d i s u t i l i t y of a man's labor w i l l necessarily equal the marginal u t i l i t y of h i s l e i s u r e . As wages (net of taxes) equal the marginal d i s u t i l i t y of labor and constitute the msc of l e i s u r e , t h i s msc of l e i s u r e must equal the msr of l e i s u r e ( i t s marginal u t i l i t y ) . None of the authorities concecned seem to have pursued' "the" argument to i t s f i n a l conclusion. For, as- i t is 1 Professor Frisch's and Professor Hotelling's conclusions that the prop o r t i o n a l i t y of msr and msc i s an adequate deter-minant Of the s o c i a l optimum is shared by Professor" Nordin ("The marginal" cost controversy: a reply", Economica, v o l . 14, pp. 134-149, May, 1947). Professors Bergson ("Socialist econom-i c s " , p; 428). and. Lerner (pp..cit, pp. 100-104) hold that the equality of msr and msc i s necessary. Mr. Coase, while opposing marginal cost p r i c i n g , goes along with Professor Lerner*s arg-ument in t h i s respect (Coase, R.H., "The marginal cost contro- ' versy: some further comments", Economica, v o l . 14, p. 152, May 7 5 possible to tax wages, so is i t possible to tax l e i s u r e . A tax imposed upon a man for each hour of the day w i l l f a l l , equally upon labor and l e i s u r e and w i l l leave the marginal d i s u t i l i t y of labor equali to the marginal u t i l i t y (net of taxes) of l e i s u r e . As was pointed out i n the discussion on income taxes, such a tax has the same effect as a tax on the producers' surplus of a man's labor. The explanation of this paradox l i e s i n the following observation. A l l reduc-tions i n outputs as a r e s u l t of taxation are reductions r e l a t i v e to the outputs of other goods. A tax f a l l i n g equally on labor and l e i s u r e w i l l reduce both r e l a t i v e l y by the same amount. But the outputs of labor and l e i s u r e are uniquely related i n that t h e i r sum must always be the same, for a day always has twenty^.f our hours. An equal r e l a t i v e reduction of labor and le i s u r e w i l l then leave the absolute amount, of labor and the absolute amount of l e i s u r e unchanged. The actual d i v i s i o n between a worker's labor and l e i s u r e could, at the same time, .represent equality and any degree of proportional-i t y between the msr and msc of both labor and l e i s u r e . .It i s immaterial whether a tax f a l l i n g equally on labor and l e i s u r e is regarded as a tax on the producers ' surplus of the worker or as an excise tax on labor and l e i s u r e , or p a r t l y as one and partly as the other. At one and the same time an excise tax of every conceivable magnitude may be regarded to exist. The...diff ere nee. between theActual tax. and the imagined excise 1 Cf. above, p. 66. 76 tax would be a tax on surpluses and should.-the l a t t e r t.urn out to be a negative amount i t could be considered, a bonus to the worker. So long as no tax is imposed which d i s c r i m i -nates between labor and l e i s u r e , t h e i r respective amounts are f i x e d . 1 For seeking to establish a c e r t a i n p r o p o r t i o n a l i t y between msr and msc throughout the entire economy, no special measures need be taken with regard to labor and l e i s u r e . Their unique relationship, which they share with no other products, w i l l - i n the absence of monopolistic r e s t r i c -tions of output or discriminatory taxation - always produce the desired proportionality. Theoretically there seem to be no obstacles, to a propo r t i o n a l i t y of msr and msc which would conform to s o c i a l p r o f i t maximisation. The pr o p o r t i o n a l i t y could be brought about by a system of excise taxes, by monopolistic, r e s t r i c -tions on output, or by a combination of both these methods. In practice, however, the proportionality might be very hard-to achieve. Degrees of monopolistic r e s t r i c t i o n s are hard to estimate and many small scale productive a c t i v i t i e s might escape the attention of an excise tax. The greatest problem would be the avoidance of double taxation of goods which pass through several stages of production. For these reasons, as well as for the presumed t h e o r e t i c a l inadequacy of propor-t i o n a l i t y the. .economists, who. have concerned themselves with T This, of course, is abstracting from changes i n i n -dividuals ' scales of preference* 77 the matter have generally held out for an equality of msr and msc, rather than a proportionality, although the accom-plishment of such an equality, too, is hardly a r e a l i s t i c objective. 78 THE RECORDED CRITICISM OF MARGINAL COST PRICING 1. Apart from general methodological objections to the u t i l i t y analysis, the theory of marginal cost p r i c i n g has encountered l i t t l e written c r i t i c i s m . What c r i t i c i s m i t has been subjected to has been mostly of a p r a c t i c a l nature. 1 Its t h e o r e t i c a l v a l i d i t y as a basic rule for the achievement of s o c i a l l y optimum proportions in production has hardly been challenged. Almost the only theoretic opposition has come from Mr. R.H. Coase. Since the primary purpose of this essay i s to deal with the d e s i r a b i l i t y of marginal cost, pricing, on 1 Wilson, T., "Price and outlay p o l i c y of state enter-'' pri s e " , Economic Journal, v o l . 55, pp. 454-461, December, 1945. Dr. Wilson c r i t i c i s e s marginal cost p r i c i n g as expressed by Professor Lerner 's The economics .of control and Mr." J.E. Meade's and Mr. J.M. Fleming's symposium on "Price and output po l i c y of state enterprise", Economic Journal, v o l . 54, pp. 321-339, December, 1944. Dr. "Wilson's remarks are almost en-t i r e l y of a p r a c t i c a l nature. The p r a c t i c a b i l i t y of both mar-ginal cost p r i c i n g and "multi-part p r i c i n g " , an alternative suggested by Mr. Coase, are disputed i n d e t a i l by Mr. H. Norris i n "State enterprise and output p o l i c y and the problem of cost imputation", Economica, v o l . 14, pp. 54-62,...February, 1947. 2 Mr. Coase's main c r i t i c i s m is contained i n the a r t i c l e "The marginal cost controversy", p r e v i o u s l y referred to. This a r t i c l e provoked comments by Mr. G.F. Thirlby i n "The marginal cost controversy:' a note on Mr. Coase's model", Economica, v o l . 14, pp. #8-53, February, 1947. Professor Nordin i n his a r t i c l e "The marginal cost controversy: a reply", already quoted, disputes the v a l i d i t y of Mr. Coase's arguments on mathematical grounds. An answer by Mr. Coase is given"in "The marginal cost controversy: some further comments", Economica, v o l . 14, pp. 150-153, May, 1947. 79 t h e o r e t i c a l grounds, the discussion w i l l be concerned mainly with Mr. Coase's c r i t i c i s m and the observations on p r a c t i c a l objections w i l l be r e s t r i c t e d to a few short remarks. 1 Preceding his c r i t i c i s m , Mr. Coase introduces what he c a l l s "multi-part pricing"-, as an a l t e r n a t i v e to marginal cost p r i c i n g . Before proceeding with Mr. Coae's main points of c r i t i c i s m t h i s *esuggestion w i l l be analysed. One of the -points of c r i t i c i s m concerns the r e d i s t r i b u t i o n of income which a change to marginal cost p r i c i n g would involve. Mr, Coase also contends that taxation under marginal cost p r i c i n g would have undesirable e f f e c t s . The determination of the s o c i a l l y most p r o f i t a b l e output - i f any p r o f i t , i n a s o c i a l sense, could be made at a l l - i s impossible under marginal cost pricing,according to Mr. Coase. This l a s t argument i s more of a p r a c t i c a l than a t h e o r e t i c a l nature and covers most of the c r i t i c i s m recorded by.other writers. 2. Mr. Coase considers the "marginal cost controversy" as the question of ". . . how prices ought to be determined in conditions of decreasing average costs."^ As i n t h i s essay, the existence of an optimum d i v i s i o n of income i s assumed in Mr. Coase 's article.°" The measurability of u t i l i t y i n terms of a, monetary, unit is implied i n his argument. By elimination 1 A further discussion of the p r a c t i c a l implications of marginal cost p r i c i n g follows. Cf. below, pp. 3 5 - 3 9 . 2 Coase, "The marginal cost controversy", p. 169. 3 Ibid., p. 172. 80 of c e r t a i n complicating factors, Mr. Coase seeks to simplify the problem at hand. In constructing his model he assumes (a) that there are no costs common to more than one consumer, (b) that no quasi-rents for outlays made in the past are demanded, and (e) that a l l factors are i n p e r f e c t l y e l a s t i c supply. Mr. Coase continues: Assume that consumers are situated around a central"mar-ket i n whieh a c e r t a i n product is available at constant prices, Assume that roads run out from the central mar-ket but that each road passes only one consumer of"the product. Assume also that a c a r r i e r can carry on each journey additional units of the product at no additional cost (at least to a point beyond the l i m i t of consump-t i o n of any individual consumer). Assume further that the product i s sold at the point of consumption. It i s clear that the cost of supplying each in d i v i d u a l con-"' sumer would be the cost of the c a r r i e r plus the cost'at the central market of the number of units consumed by that p a r t i c u l a r consumer of the product. The marginal cost would be equal to the cost of a unit of the product at the central market. The average cost would be higher than the marginal cost and would decline as the cost of the c a r r i e r was spread over an increasing number of u n i t s . The Hotelling-Lerner solution would presumably be that the amount which consumers would pay for each unit of the product should be equal only to marginal cost. The effect would be for consumers to pay for the cost of the product at the central market and for the Government, or rather the taxpayer, to bear the costs of carriage. Mr. Coase recognises . . the f a m i l i a r but im-portant conclusion that the amount paid for a product should be equal to i t s c o s t . " 1 This p r i n c i p l e , according to Mr. Coase, has been taken to mean that (a) a price equal to mar-ginal cost should be charged (in which case a loss is made) or that (b) a price equal to average cost should be charged (i n.- wbich_ case no loss i s made), The advantage of the f i r s t 1 Coase, op.cit., p. 173. system would be that a consumer would be allowed the decisio of determining whether i t was worth his while to consume an add i t i o n a l unit of the product or not. The second system would see to i t that the value of the t o t a l product to con-sumers would not be less than i t s cost. Mr. Coase/now claims that the advantages of both systems can be enjoyed by a thir d system, which he c a l l s "multi-part p r i c i n g " . In terms of his model, t h i s p r i c i n g p r i n c i p l e would require a con-sumer to pay the price of the product he buys i n the central market plus the price of the c a r r i e r bringing t h i s product to his home. For additional units he would only have to pay the price i n the central market, as the c a r r i e r would then • already have been paid for. S. Some general observations should be made of Mr. Coase 's argument. F i r s t of a l l , Mr. Coase considers only the question of price determination under conditions of decreasing average cost. Apparently he has no objection to marginal cost p r i c i n g under conditions of increasing average cost. In his reply to Professor Nordin he even states:1 "D do not deny that the output of every product ought to be such that the marginal valuation of the product by the con-sumer i s equal to marginal cost." But neither tide- reasoning for marginal cost p r i c i n g , nor any of i t s q u a l i f i c a t i o n s , distinguished between increasing and decreasing average cost. It would then seem that the argument for marginal 1 Coase, "The marginal cost controversy: some further comments", p. 151. cost p r i c i n g under decreasing average cost could only be defeated by disproving simultaneously the argument for that p r i n c i p l e under conditions of increasing average cost. Mr. Coase also r e f e r s to the usually practiced system of p r i c i n g as "average cost p r i c i n g " . As pointed -i out above, prices seldom conform to average costs. The guiding p r i n c i p l e of private enterprise would appear to be not the equalisation of price and average cost, but rather the maximisation of p r o f i t , which w i l l usually c a l l '. for a price above average cost. The main defects of Mr. Coase 's argument originate i n one of the l i m i t i n g assumptions of his model, v i z . that a l l costs are attributable to i n d i v i d u a l consumers. As was. explained above, 2 and as Mr. Coase admits at one point i n his a r t i c l e , 3 decreasing average costs a r i s e as the r e s u l t of i n d i v i s i b i l i t i e s in the factors of production, gut the cost of an i n d i v i s i b l e factor of production cannot be at-tributed to any in d i v i d u a l consumer. The model- which Mr. Coase proposes to construct for the purpose of analysing price determination i n decreasing average cost industries cannot, from the out set,deal with that type of industry. Yet Mr. Coase does construct his model and does.use i t i n his anal scrutiny of the.-model, w i l l soon, show i t s 1 Cf. above, p. 44. 2 CfV above, pp. 19-20. 3 Coase, "The marginal cost controversy", p. 171, n. 2. 83 defects. In his model Mr. Coase has a r b i t r a r i l y lumped together various products. The product "available at constant prices . . .,at the central market" i s one product. But the various c a r r i e r services are as many d i s t i n c t products. 1 As Mr. Coase.says, "each road passes only one consumer of the^ product". The c a r r i e r service to each consumer may be regar-ded as a d i s t i n c t product of which "only • one item is produced. For this d i s t i n c t product marginal cost and average cost . w i l l then be one and the same thing. Mr. Coase's contention that under marginal cost pricing.the c a r r i e r service would be free of charge i s not j u s t i f i e d . Where only one item of a good i s produced a l l relevant p r i c i n g systems should charge the same.amount - the f u l l cost, which i s average cost and marginal cost at the same time.2 The r e a l p r i c i n g problem to be s e t t l e d , i n Mr. Coase's model is that regarding the product available in-the central market. Mr. Coase quickly passes over t h i s point by 1 Of course, i n actual practice the same corporate body may s e l l both the/original product and the c a r r i e r service, quoting only one p r i c e . If the costs of the various c a r r i e r services are s u f f i c i e n t l y d i s t i n c t , a corporation would.be advised "(both under the marginal cost pricing"and private profitJmaximisatioh'systems) to grade.its price of the com-bined product and c a r r i e r service according to the di f f e r e n t cds;ts of the. l a t t e r . For purposes of economic analysis, however,~such Corporations should be divided into firms pro-ducing homogeneous products. " 2 If if the product had a' greater value to the consumer than i t s cost, the firm, as. a monopoly, could, of course, charge a price "above cost". But, i n any case, the firm would s e l l ' i t s product as long as i t could get a price.equal to cost. 84 r e f e r r i n g to "a c e r t a i n product . . . available at constant p r i c e s " . The v i t a l question i s how these constant prices should be determined. If the "certain product" is produced under conditions of decreasing average costs - the only-case i n which Mr. Coase objects to marginal cost p r i c i n g -then i n d i v i s i b l e factors of production must be considered. But, as appears'from his assumptions, Mr. Coase wishes to exclude problems involving i n d i v i s i b i l i t i e s and i s thus incapable of dealing with the problem of p r i c i n g i n decreasing average cost industries in.the f i r s t place. In his closing remarks, Mr. Coase asks himself the question;! "If there are costs which cannot be at t r i b u t e d to i n d i v i d u a l consumers, does the Hotelling/lrerner solution then come into i t s own . . . ?" Far from being an exceptional case or, at least, a separable category, as Mr. Coase seems to assume, costs common to several consumers (overhead.costs in general) are a feature of p r a c t i c a l l y ' every industry. The question put by Mr, Coase i s indeed the question to be an-swered. But his own analysis has contributed nothing to the argument for or against the a p p l i c a t i o n of marginal cost p r i c i n g under such, or any other circumstances. At i t s very best, multi-part p r i c i n g (as a process of basing prices on the marginal costs of the homogeneous components of a non-homogeneous product) could be considered a special case of marginal cost p r i c i n g . 1 Coase, op.cit., p. 182. 85 4. It i s true, as Mr. Coase remarks, that under mar-g i n a l cost p r i c i n g "Consumers who buy products which are produced under conditions of decreasing average costs w i l l . . . obtain products for any given expenditure embodying a greater value of factors than those who do not." By this process what i s the equivalent of a r e d i s t r i b u t i o n of income undoubtedly takes place. This r e d i s t r i b u t i o n may indeed seem objectionable to Mr. Coase who believes to have found in multi-part p r i c i n g a system where no:more and no less than the f u l l cost'of each item of a product w i l l be charged to the consumer. Firms producing at constant marginal cost would indeed be able to charge a price which, for each item of output, would exactly cover cost. Such firms, i f they exist at a l l , are few and far between. Ordinarily, far any length of an output series, firms produce either under conditions of increasing marginal cost or under conditions of decreasing marginal cost. If these firms were to charge a price equal to (marginal) cost' for each item of output, the i d e n t i c a l ' i t ems of the same product would have to be quoted at a variety of prices, depending on their.respective ranks i n thecoutput series, M t h i s rank could be determined at a l l . This would pose an impossible sales problem; people would queue for the cheap items, while the expensive ones would remain unsold and bring production to a s t a n d s t i l l . Whenever a uniform price i s charged, most items w i l l be sold either at. a price below t h e i r 1 Coase, op.cit., p. 176. 86 cost or at a price above t h e i r cost. In either case the re s u l t w i l l be something equivalent to a r e d i s t r i b u t i o n of income. The objection, i f i t i s one, to such a r e d i s t r i b u -t i o n of income has no s p e c i f i c bearing on marginal cost p r i c i n g , however. It applies equally (to any pricing system which charges uniform prices for homogeneous products or, more accurately, to any system which does not follow the impossible procedure of charging cost prices depending on the p a r t i c u l a r rank an item has i n an output s e r i e s . It i s well nigh impossible to detect which of the consumers receive the cheap and which the expensive items of a homogeneous product, nor would i t be f a i r to a t t r i b u t e a greater value received to the individual buying the more expensive item than to the individual purchasing the cheap one. Of course, i t i s possible to say that, for any firm operating at a f i n a n c i a l loss, the consumers of i t s product receive in value, on the average, more than the cost of the factors. S i m i l a r l y , the consumers of a product, manufactured by a firm enjoying a p r o f i t , w i l l receive i n value, on the aver- age . less than the cost of the factors. There is no reason why the former type of r e d i s t r i b u t i o n of wealth should be any more objectionable than the l a t t e r . In any case, some r e d i s t r i b u t i o n of either one or both of these types would seem unavoidable i n any r a t i o n a l economic system. Mr. Coase assumes . . that the d i s t r i b u t i o n of income and wealth can be taken to be the- optimum. 1 , 1 He com-1 Coase, op. c i t . , p.. 172. 87 plains that the r e d i s t r i b u t i o n of income brought about by marginal cost p r i c i n g w i l l cause a divergence from the optimum d i s t r i b u t i o n of income.'*" As -has been pointed out, any other r a t i o n a l p r i c i n g system would also cause a redis-t r i b u t i o n in the above sense. Any actual d i s t r i b u t i o n of money income which is taken to correspond to an optimum d i s t r i b u t i o n of real-income i s but an approximation based on p o l i t i c a l and other compro-mises. This approximation w i l l have to be based on the ex i s t i n g p r i c i n g system with i t s inherent pattern of di s -t r i b u t i o n and r e d i s t r i b u t i o n of income existing before the f i n a l ( p o l i t i c a l ) adjustments are made. A p a r t i c u l a r d i s -t r i b u t i o n of money income can then only be an optimum di s -t r i b u t i o n with respect toa* a p a r t i c u l a r p r i c i n g • system. An.' optimum d i s t r i b u t i o n of money income for a private p r o f i t economy w i l l most l i k e l y not be an optimum d i s t r i b u t i o n for a s o c i a l p r o f i t economy, and vice versa. The patterns of-inherent r e d i s t r i b u t i o n s are different i n the diff e r e n t economies and, therefore, a given money income to a p a r t i c -ular person w i l l r e a l i s e d i f f e r e n t r e a l incomes. Whenever an optimum d i s t r i b u t i o n of income is assumed i t i s only right that t h i s optimum should be assumed to exist with respect to whatever p r i c i n g system is under discussion. When the argument moves to another p r i c i n g system objectiv-ity- .requires, .a. change, to. be assumed i n the/6.ctual d i s t r i b u t i o n 1 Coase, op.cit., pp. 176-178. 88 of money income which w i l l make i t an optimum d i s t r i b u t i o n with respect to the other p r i c i n g system. Whenever mention i s made of an optimum d i s t r i b u t i o n of income, without further q u a l i f i c a t i o n s , i t should be assumed that the government, or some other agency, i s constantly adjusting incomes so as to offset any new r e d i s t r i b u t i o n s which changes i n the economic system might bring with them. 1 5. Many of Mr. Coase's remarks on taxation are argu-ments against various kinds of taxation as such and not . r e a l l y arguments against marginal cost p r i c i n g . For instance t h i s i s the case with the fam i l i a r argument against the 2 income tax as "an excise tax on e f f o r t " , which was dealt with above. 3 No objection i s raised to other taxes suggested by Professor Hotelling, v i z . "rents of land and other scarce goods, inheritance and w i n d f a l l taxes, and taxes designed to reduce s o c i a l l y harmful consumption." But Mr. Coase doubts that these taxes would be s u f f i c i e n t to finance the various a c t i v i t i e s of government as well as the d e f i c i t s of decreasing average cost firms. The almost unlimited revenue which pro-portional excise taxes could bring are not considered by Mr. Coase. In his. second a r t i c l e , 4 he refers, to. Professor 1 Cf. above, pp. 53-54. 2 Coase, op.cit., p. 179. 3 Of.' above, pp. 64-67. " 4 " Coase, ''The marginal cost controversy: some further comments", p. 152. 89 Lerner's argument against proportionality, which was.dis-cussed. above. 2 Another objection raised by Mr. Coase i s that the a d d i t i o n a l taxation necessitated by marginal cost p r i c i n g would, l i k e l y upset the optimum d i s t r i b u t i o n of income. He i s working on the assumption that an optimum d i s t r i b u t i o n of income exists before marginal cost p r i c i n g and i t s attendant taxation i s introduced. As explained above, any optimum d i s t r i b u t i o n should be established with regard to the effects of marginal cost p r i c i n g . Implementation of the optimum d i s t r i b u t i o n should take place largely by the d i r e c t i o n of the attendant taxation. 6. That marginal cost p r i c i n g would lead to a mal-d i s t r i b u t i o n of the factors of production is also claimed by Mr. Coase. He acknowledges that the p r i n c i p l e of mar-ginal cost p r i c i n g i s to operate an industry only where consumers would be w i l l i n g to pay the t o t a l cost of supply-ing the product.°" (The actual c o l l e c t i o n of such an amount could, i n a decreasing average cost industry producing at the s o c i a l l y most p r o f i t a b l e output, be effected only by a system of price discrimination. Most often t h i s would be unfeasible...). The. c r i t i c i s m i s of. a p r a c t i c a l nature, v i z . 1 Lerner, The economics- of control, pp. 102-104. 2 CfV^ above, pp. 71-77. 3 Coase, "The marginal cost controversy", p. 175. that no government would, be able to estimate with accuracy whether consumers would be w i l l i n g to pay at least as much as the t o t a l cost of operation (on the basis of perfect price discrimination) or not. Mr. Coase claims that govern-ments would be in c l i n e d to err on the side of over-expansion of industries, a.s a result of the pleas of pressure groups urging subsidisation of enterprises for which the benefits received by consumers (measured by the maximum amount they would pay under a system of perfect price discrimination), i n r e a l i t y , would be less than the costs of production. Mr. Coase goes so far as to suggest that leaving the decision of which industries should operate to the gov-ernment would lead to the a b o l i t i o n of the p r i c i n g system. 1 This conclusion i s u n j u s t i f i e d . A l l the government would have to decide would be whether cert a i n marginal enterprises should be considered p r o f i t a b l e or not. A l l firms which could make a private p r o f i t by the use of monopolistic practices, or otherwise, would, ipso facto, make a s o c i a l p r o f i t . ^ The (marginal cost) p r i c i n g system would, be f u l l y maintained and would serve the purpose of determining the exact outputs of a l l firms which were proven or considered p r o f i t a b l e . It i s , of course, true that no government would be i n f a l l i b l e in i t s determination of the demarcation between p r o f i t a b l e and unprofitable enterprises. But there would seem l i t t l e logic i n the argument that because of the possible 1 Coase, .op.cit., p.. 175. -- 2 Por the maximum private" p r o f i t of a firm i s always equal to or smaller than the maximum s o c i a l p r o f i t . 91 losses which would be incurred by government errors of estim-ate with respect to some industries on the margin of p r o f i t a -b i l i t y under marginal cost p r i c i n g , a system of private p r o f i t maximisation should be embraced which gives the cer- t a i n t y that s o c i a l losses w i l l be incurred. THE SIGNIFICANCE OF THE MARGINAL COST PRICING THEORY 1. The aim of marginal cost p r i c i n g , as a phenomene.n of Welfare Economics, is to describe a system of price determination which is held to be desirable though i t may never have been put into actual p r a c t i c e . As a matter of fact, i t i s claimed to be the l o g i c a l p r i c i n g system i f a conventional assumption of the aims and objects of the economic a c t i v i t i e s of society i s accepted. That assumption i s the desire to maximise the u t i l i t y of s a t i s f a c t i o n s gained by individuals from the consumption of economic goods over the d i s u t i l i t y incurred i n the process of pro-ducing those goods. The reasoning which leads to the formulajf^of mar-ginal cost p r i c i n g i s quite simple. Wherever the productive machinery of society can produce an additional item of any product - or an e n t i r e l y new product, for that matter - at a cost which i s less than the value which anysmember of society would be w i l l i n g to surrender for the possession of that item, i t should be produced. I f / the argument for marginal cost p r i c i n g sub-s t a n t i a l l y i s considered v a l i d , there are some important conclusions which may be drawn - conclusions which may require the reconsideration of some widely accepted and deep-rooted b e l i e f s as to the proper c r i t e r i a to be applied to productive processes. The marginal cost p r i c i n g theory throws a new l i g h t upon the frequently expressed but usually poorly substantiated claim that there is a d i s t i n c t d i f f -erence between "production for use" and "production for p r o f i t " . The contention that a f i n a n c i a l p r o f i t i s no c r i -t e r i o n of the s o c i a l ' d e s i r a b i l i t y of an enterprise - with the stated welfare objective i n mind - has been j u s t i f i e d by an analysis based on conventional economic theory. The deep-rooted conviction of so many that an enterprise must be f i n a n c i a l l y solvent i n order to j u s t i f y i t s existence s o c i a l l y i s most emphatically rejected. 2. Like almost any other economic analysis, the one employed here has d e f i n i t e l i m i t a t i o n s . The si m p l i f i e d model used can but imperfectly represent the r e a l economic mech-anism of society. Of necessity an attempt was made to deal' with a problem i n i s o l a t i o n , v i z . that of price determina-t i o n i n i t s r e l a t i o n to the maximisation of the general wel-fare. It was cut loose from many other related problems,, the mechanics of which were not brought out by the model. Thus l i t t l e discussion could be undertaken concerning the possible connection between the various methods of price determination and such phenomena as e f f i c i e n c y , incentives of production, f u l l employment of resources, etc. Even the ' chosen f i e l d was not completely covered, since the discussion concentrated on the microeconomic and s t a t i c a nalysis. Gen-eral" e q u i l i b r i a were investigated only s u p e r f i c i a l l y and l i t t l e attention was paid to the emergence of complications 94 in time analysis, such as quasi-rents.. But t h i s i s a short-coming of the present thesis rather than of the marginal cost p r i c i n g theory as such. 3 . Accepting the stated welfare objective, to what extent may the t h e o r e t i c a l v a l i d i t y of the marginal cost p r i c i n g p r i n c i p l e be considered as. established within the l i m i t s of the f i e l d of investigation? The t h e o r e t i c a l con-clusions w i l l be l i m i t e d by the l o g i c a l consistency of the assumptions. . , As indifference theorists are anxious to point out, constant marginal, u t i l i t y of money, though often a close approximation of r e a l i t y , inevitably leads to contradictions when t h e o r e t i c a l analysis i s carried to i t s ultimate l i m i t s . As noted i n Professor Lerner's work, however, the assumption of the constant m a r g i n a l . u t i l i t y .of money, as well as the -entire u t i l i t y analysis, is superfluous when determining the optimum output of most firms. Only i n those borderline cases, where i t has to be decided whether a firm can earn a so c i a l p r o f i t or not, must resort be made to the u t i l i t y analysis i n order to compare the value of the t o t a l product with i t s cost. Apart from th i s one imperfection, the argument for marginal cost .pricing as a welfare objective appears to be t h e o r e t i c a l l y sound. C r i t i c i s m expressed so fa r -has not been able to shake i t s basic l o g i c . 4.. The discussions w i l l appear to have had l i t t l e 95 more than academic value i f the rules of marginal cost p r i c i n g , devised for a s i m p l i f i e d model, are found to have no bearing on economic conditions i n r e a l l i f e o.#> to have f a i l e d to take account of complicating factors which might more than offset the benTicent influence of an improved p r i c i n g system. The p r a c t i c a l l i m i t a t i o n s of marginal cost p r i c i n g are many indeed. A few of these objections based on the less important diverg-ences of the model from p r a c t i c a l conditions are the following; (1) Marginal cost p r i c i n g requires the existence of an op-timum d i s t r i b u t i o n of income. 1 If any standards at a l l exist to determine such a d i s t r i b u t i o n , they would most l i k e l y c o n f l i c t with standards necessary to provide s u f f i c i e n t productive incentives. Alternative ley, the incentives would have to form part of the e t h i c a l c r i -t e r i o n on which the optimum d i s t r i b u t i o n was based. (2) Prices are assumed to r e f l e c t only the u t i l i t y c alcula-tions of the persons involved i n the transactions con-cerned. ^  Sometimes, however, the use of a good by i t s owner w i l l benefit others and thus the good w i l l have a s o c i a l value i n excess of that measured, by the owner's - estimated u t i l i t y . In other cases, the use of a good may.:. j~'"~ 1' The theory of marginal cost p r i c i n g may be sub s t a n t i a l l y v a l i d even with respect" to a d i s t r i b u t i o n of income which i s hot ah optimum. As the argument erf presented above bn pp. 53-54 indicates", a change i n the d i r e c t i o n of marginal cost p r i c i n g may"increase"the s a t i s f a c t i o n s enjoyed by an i n d i v i d u a l , i r r e -spective of the d i s t r i b u t i o n of income, without a f f e c t i n g anv-one else. ...... 2 Cf.above, pp. 31-32. constitute a public nuisance and the good w i l l be worth -' l e s s , s o c i a l l y , than the value placed upon i t by the owner. In practice i t would most often be impossible to take account of such s o c i a l appreciations or deprecia-tions i n value, (3) As indicated before, many items of cost from a s o c i a l standpoint do not appear on the books of firms operating i n the actual world. 1 However, some of these costs, such as those of education, health care and other s o c i a l ser-vices, could be defrayed by "charging them to the firms u t i l i s i n g the labor force which i s maintained by these services. A great number of countries already apply t h i s p r i n c i p l e i n the f i e l d of i n d u s t r i a l accidents 'and there i s no reason why i t could not be extended consid-erably, A complete i d e n t i t y of s o c i a l cost and the* cost items appearing on the books of firms would be hard to achieve, however. (4) In the process of taxation i t might be d i f f i c u l t to avoid, i n a l l instances, v i o l a t i o n of the taxation p r i n c i p l e s c a l l e d for by marginal cost p r i c i n g . This wil'^be e s p e c i a l l y d i f f i c u l t as the financing of def-icjLts. of decreasing average, cost, firms, will., re.quire. 1 Cf. above, p. 40, n. 1. 97 great government revenues i n a s o c i a l p r o f i t economy.x The only unlimited source of taxation which marginal cost p r i c i n g allows i s that of a proportional excise tax. It would be impossible to apply t h i s tax to every productive process i n the economy and i t would be extremely d i f f i c u l t to avoid duplications. Income taxes would probably have to provide most of the rev-enue. But here again there are dangers of duplication and, i n some instances, objections to progressive taxes. Any government would have a d i f f i c u l t time using i t s taxation p o l i c y to raise s u f f i c i e n t revenue as well as to establish an optimum d i s t r i b u t i o n of income while, at the same time, obeying a l l the rules of the marginal cost p r i c i n g p r i n c i p l e . There are p r a c t i c a l objections to marginal cost p r i c i n g of much greater significance than those mentioned so f a r . For instance, the determination of the s o c i a l l y most pr o f i t a b l e output, with even the s l i g h t e s t degree of accuracy, i s held to be impossible i n p r a c t i c e . Marginal cost and mar-ginal revenue curves are i n t e r e s t i n g t h e o r e t i c a l devices but no ways have been found to determine them i n p r a c t i c e . In the private p r o f i t economy, a manager does not f i x h i s output-by 1 To some extent t h i s heed for taxes may be offset by charging the costs "of a great number of s o c i a l services d i r e c t l y td~firms, as indicated above. The administration of the services would most l i k e l y s t i l l be run by public bodies. The charge to firms would, however,' not be a tax i n the sense i n which t/he word has been used here. 98 i n t e r s e c t i n g a mpr with a mpc curve on a graph i n order to. f i n d where h i s private p r o f i t i s maximised. As a rule a system of t r i a l and error is used i n finding the maximum private p r o f i t output. And the f i n a n c i a l p r o f i t shown i n the books of the firm always provides a c r i t e r i o n by which to judge progress i n the process of private p r o f i t maximisation. In a way i t s t i l l might be easier for the manager of a firm-to calculate the output corresponding to s o c i a l p r o f i t maximisation than that corresponding to private p r o f i t maximisation.1 It i s conceivable that, with p r a c t i c e , a reasonable degree of accuracy could be secured i n the actual construction of the marginal cost curve of a firm. It would then not.be d i f f i c u l t at a l l to determine the point of s o c i a l p r o f i t maximisation. For by charging a price equal to marginal cost and simply regulating output according to the demand (which equals msr), s o c i a l p r o f i t would.be maximised. The manager seeking to maximise the private p r o f i t of his firm would be helped l i t t l e by the knowledge of his marginal cost schedule. For he would have to f i n d the point of equation of his marginal cost, not with the e a s i l y determined demand of the market, but with marginal demand (mpr), and no market tests are available to determine the l a t t e r . Even i f a way were found to determine marginal cost, .schedules, reasonably accurately, there would remain a 1.Meade.,. J.E.,/"Price and output p o l i c y of state enter-p r i s e " , Ec onomi c Jour nal. v o l . 54, p. 324,'December, 1944. 99 p r a c t i c a l d i f f i c u l t y o f ..considerable importance i n the s o c i a l p r o f i t economy. Hxw could managers of firms be given an i n -centive to maintain or improve technical and administrative e f f i c i e n c y by finding means of lowering costs and how could they be induced to produce at the maximum s o c i a l p r o f i t output? Both e f f i c i e n c y and the determination of the proper output under private p r o f i t maximisation are usually reflected i n the f i n a n c i a l surplus shown i n the books of a firm. By giving the manager a share of that surplus he w i l l f i n d i t to his advantage to,maximise i t . But there i s no such mag-nitude -in the books which shows. maintenance of e f f i c i e n c y or^the proper determination of output by a manager i n oper-ating a firm for purposes of s o c i a l .profit maximisation. There i s thus no ready way for a lay authority to judge the merits of the manager of such a firm and to reward him. accordingly. 5. While the serious d i f f i c u l t i e s mentioned, above seem to preclude the application of the marginal cost p r i c i n g p r i n c i p l e , there are equally compelling reasons of a p r a c t i c a l nature why the p r i n c i p l e must be practiced, to some degree, i n some instances. There are industries which are of v i t a l importance to society, yet which cannot be operated by private enterprise at a f i n a n c i a l p r o f i t , .In other cases, monopolistic practices necessary to make such a p r o f i t are obviously ex-tremely detrimental to society. Urban roads are a good example. To l e t private 100 companies operate streets as p r o f i t making enterprises, erecting t o l l gates at every corner, i s so obviously r i d i c -ulous that even i n the most "free enterprise" conscious community the task of providing roads i s gladly l e f t to a public body. Under private enterprise side streets would never pay for themselves and the t o l l s on other streets would be such that many people, to avoid them, would have to trudge through muddy back a l l e y s . Once a road has been . b u i l t , i t costs society no more to l e t everyone use i t f r e e l y . For the marginal cost of allowing one man to cross the s t r e e t - the wear and tear he i n f l i c t s upon the street by his crossing - i s p r a c t i c a l l y zero. In allowing people -to pass f r e e l y along the streets, a municipal government i s then p r a c t i c i n g marginal'cost p r i c i n g i n i t s "road industry". Unconscious of the a p p l i c a b i l i t y of the marginal cost p r i c i n g principle, to productive processes i n general, most people seem to regard industries where t h i s p r i n c i p l e as an e n t i r e l y separate category known.as "public services". There are other cases where p r a c t i c a l considerations of a compelling nature have brought industries closer to mar-ginal cost p r i c i n g . Most examples are to be found i n the f i e l d of transportation, where often the s o c i a l benefits to be gained from new or. expanded f a c i l i t i e s have been obvious despite the i n a b i l i t y of private enterprise to provide such f a c i l i t i e s on a pr o f i t a b l e basis f i n a n c i a l l y . Often t h i s i s the case with the provision and maintenance of canals and locks by the government, free or at a nominal service charge. Subsidisation of railway freight carriage may bring the price of transportation services closer to the marginal cost and thus enable a larger section of the economy of a country to make use of railway services, which i n turn might aid con-siderably i n developing the e conomy of that country. Though i t may seem hard to envisage a society where a l l prices are determined by marginal costs, the prin-c i p l e of marginal cost p r i c i n g does seem to have been estab-lis h e d (perhaps unwittingly) in a small sector of economic l i f e and i t s a p p l i c a t i o n may very well spread. As indicated before, 1 the advantages of marginal cost p r i c i n g may be secured by degrees. If the p r i n c i p l e is introduced gradually,, beginning with industries where the divergence between msc and msr i s r e - l i t i v e l y large, a steady flow of increased benefits to society may r e s u l t . With the tendency of increased government control over growing monopolistic enterprises, t h i s may be very well the.course which the future w i l l take. 6. There are various methods by which marginal cost p r i c i n g could conceivably be further introduced into present day economic l i f e . ,One would be to foster perfect competition, e.g. by a n t i - t r u s t l e g i s l a t i o n . Under pe r f e c t l y competitive conditions, of course, marginal cost p r i c i n g would be auto-matically adhered to. But the return to a more perfect form of competition would, be feasible in only a few cas.es. Present 1 Cf. above, pp. 45-46 and 72-74. 102 technological developments usually require more rather than less concentration of industry. There are, of course, many staun/ch supporters of n a t i o n a l i s a t i o n of industry and operation " i n the public i n t e r e s t " . This, according to the interpretation i n t h i s essay, would mean adherence to marginal cost p r i c i n g , For c e r t a i n types of enterprise, such as the postal service, government operation has been accepted not only as a feasible manner of operation, but also as a desirable one. Apart from the determined p o l i t i c a l opposition from vested interests which the suggestion of n a t i o n a l i s a t i o n encounters, there remain the p r a c t i c a l d i f f l e n i t i e s of determining marginal cost and of maintaining managerial e f f i c i e n c y . For some large-scale highly monopolistic enterprises, the operations of which could be closely checked by the government, the advantages of public enterprise at marginal cost, rather than private enterpise at maximum private p r o f i t , might out-weigh the disadvantages. It seems highly improbable, however, that a multitude of small enterprises could be operated pub-l i c l y at marginal cost other than at a p r o h i b i t i v e loss i n e f f i c i e n c y . It i s possible, t h e o r e t i c a l l y , to achieve marginal cost p r i c i n g while maintaining monopolistic private enter-prise with i t s mechanism of private p r o f i t maximisation. A subsidy per unit of output w i l l induce a monopoly to expand production and reduce p r i c e . 1 If the subsidy i s of the proper ~ 1 This suggestion was made, but not worked out, by Pro-fessor K.E Boulding i n Economic Analysis. New York, Harper, }l !' . . d e t a i l e d description of the process follows i n Appendix i i , pp. 111-112. U i i 0 s 103 magnitude, the new equilibrium in. output and price would be made to"coincide with that of marginal cost p r i c i n g . The p r o f i t s of. the firm, which might already be exorbitant, would be increased, of course. However, excessive p r o f i t s could be e a s i l y removed by corporate income taxes. The p r a c t i c a b i l i t y of t h i s scheme may well be questioned. It would be impossible for the government to determine the proper subsidy with any degree of accuracy. This apart from the unlikelihood of a government convincing the public that subsidisation of monop-ol i e s should be undertaken i n the public i n t e r e s t . Price f i x i n g i s another device by which marginal cost p r i c i n g might be accomplished. 1 A governmentally enforced price would make the revenue curvet of a firm horizontal, as i n the case of perfect competition^ If the price wMve fixed at a l e v e l where i t would equal marginal cost at the s o c i a l l y optimum output, i t would be most ad-vantageous to a monopolistic firm to produce at exactly that output. A decreasing average cost firm would, of course, i n -cur a loss with a price fixed at that l e v e l and would have to be subsidised. The shortcomings of a system of price con-t r o l l i e i n the d i f f i c u l t y for a government to determine the appropriate price l e v e l and to maintain f l e x i b i l i t y i n ad-justment to changes i n cost and demand schedules. Much, remains to be done i n the perfection of/the 1 An analysis of"price control as an a i d to marginal' cost p r i c i n g is contained in Appendix i i i , pp. 113-118. 104 theory of marginal cost p r i c i n g . Its complete adaption to the indifference analysis - i f such i s possible - and the further development of the dynamic and. macroeconomic aspects of the theory are tasks which l i e ahead. There i s no indica-t i o n , however, that further investigations w i l l lead to more than a modification i n the formulation of the marginal cost p r i c i n g p r i n c i p l e . With conventional welfare p r i n c i p l e s i n mind and assuming the necessity of uniform prices for homogeneous products, i t s basic" l o g i c seems unassailable. If the problem of price determination could be treated i n i s o l a t i o n , the introduction of marginal cost p r i c i n g would appear of great advantage to society. Unfor-tunately, i n s t i t u t i o n a l complications make the r e a l i s a t i o n of a universal application of this p r i c i n g p r i n c i p l e not appear fe a s i b l e . It i s also doubtful whether i t would be desirable to attempt the universal a p p l i c a t i o n of t h i s p r i n c i p l e , with a view to#r the detrimental effects i t would l i k e l y have i n connection with other aspects-of economic l i f e , e s p e c i a l l y those of managerial e f f i c i e n c y and incentive to production. Nevertheless, the inescapable l o g i c of marginal cost p r i c i n g has led to i t s adoption or approximation i n a few cases where the losses to society r e s u l t i n g from other p r i c i n g systems have become too obvious. Oddly enough, the p r i n c i p l e seems to have been applied where i t has been r i d i c u l e d most severely, v i z . i n decreasing average cost industries, where the a p p l i c a t i o n of the p r i n c i p l e leads 105 to f i n a n c i a l losses. To avoid the admission of the inadequacy of the usually practiced method of price.determination, the public has been conditioned to regard such industries as a separable category, v i z , that of "public services". Even as a p r a c t i c a l guide to economic progress marginal cost p r i c i n g then appears to have some value. A further search for methods by which i t s application in society could be widened would seem well worth while. APPENDIX i SOME NOTES ON THE ANALYSIS OF SOCIAL COST Most of the factors of a firm are but products of previous'sprocesses. In a s o c i a l p r o f i t economy the i r prices would equal the respective marginal costs of t h e i r produc-t i o n . If, of a l l firms using the same factors, only one firm were to acquire additional units, these, obviously, would be marginal units of outputs of the firms producing them. Under marginal cost p r i c i n g the s o c i a l costs of these factors would equal t h e i r p r i c e s . The use of these prices as the s o c i a l costs of the factors of the o r i g i n a l firm i s j u s t i f i e d since the purpose of the msc curiae is to indicate whether in a firm, c e t e r i s paribus, a marginal unit of the factor i s to be added or not. When a l l firms i n society using a certain factor are considered together, i t can be noted that a l l units of that factor are acquired by these firms at the mar-ginal cost of producing that factor. Yet the i n d i v i d u a l units of that factor have been produced at costs varying widely from the cost of the l a s t unit. The s o c i a l cost of most units of a factor w i l l then diverge from the amount by which they are indicated en the msc curve of the firm to which they are a factor of production. For the msc curve r e f l e c t s only the market price - the cost of the marginal unit of a factor. . The costs at which firms acquire t h e i r factors of 1.07 production may diverge from the/actual s o c i a l costs of pro-ducing those factors. Besides the cost of production of the factor, the msc curve of a firm using the factor includes what might be ca l l e d a f a c t o r s ' surplus. 1 The exact mag-nitude of the factors ' surplus i n any firm would be d i f f i -cult to assess. For every unit of factor i t would depend on the exact rank .that that unit had i n the output sequence of the firm which produced i t . There i s no need to fear, however, that the factors*"' surplus w i l l not be taken into account. The f a c t o r s ' surplus of one firm is i d e n t i c a l with part of the producers' surplus>of the firm producing, the _ factor and w i l l thus appear on the l a t t e r 's production graph. . • It might also be noted that the consumers' surplus r e s u l t i n g from the sale of a good which i s used as a factor i n a higher process of production i s part of the^f'producers » surpluses of the firms using the good as a factor. The pro-ducers ' surplus, a f t e r a l l , consists of the difference-between the cost of factors to a firm and the value received for t h e i r oupufe-.'This i s the amount, in addition to the p r i c e , which a firm would be w i l l i n g to s a c r i f i c e , i f i t had to, i n order to obtain i t s factors, and so constitutes a consumers ' surplus. If, i n search for "real cost" (the o r i g i n a l s o c i a l cost, of production), factors are traced to previous processes, 1" The surplus of a p a r t i c u l a r unit of a, factor may be p o s i t i v e or'"negative,"depending on whether that unit was produced below or above the cost of the marginal unit. and the surpluses isolated, the search w i l l end with the -primary factors of pr.oduction: labor (including entrepreneur ship) and land. Labor, i n e f f e c t , i s nothing but the product of a small firm - the worker. The costs of the worker - d i s u t i l -i t i e s - consist, of his s a c r i f i c e s through the exertion, drudgery, or danger of his work. A l t e r n a t i v e l y , these disu-t i l i t i e s could be expressed as. negative u t i l i t i e s r e s u l t i n g from the loss of l e i s u r e , pleasure, and security. The work-er 's output consists of his labor, sold i n the labor market. According to orthodox economic theory the supply of labor i s determined by marginal d i s u t i l i t y . A worker w i l l cease o f f e r i n g additional units of labor.at the point where his cost ( d i s u t i l i t y ) equates with his revenue (the established wage). 1 The';.'.mpr curve for labor w i l l coincide with the msr curve i n the case of perfect competition on the labor market Only where a worker i s i n a monopoly pos i t i o n i n s e l l i n g his labor (e.g. i n case he possesses special t a l e n t s ) , can the mpr and msr curves diverge and necessitate a readjustment when moving from the private p r o f i t economy to the s o c i a l p r o f i t economy. In general, workers w i l l make a producers/ surplus i n that every unit of labor, save the la s t one, pro-vided., by. the. worker w i l l cost less - i n d i s u t i l i t y . - than 1 To avoid a dispute with Lord Keynes on the v a l i d i t y of this'argument," the absence of Vinvoluntary unemployment" would have to be assumed. See The general theory of employ- ment, interest and money, Macmillan, London, 1949, pp. 8-22. 2 Cf". above, p. 37. 109 the wage i t earns. . . Nature can be conceived as being a firm producing land. For a proper analysis land would have to be c l a s s i f i e d on the basis of f e r t i l i t y , , location, mineral resources, etc. There would be a l i m i t e d supply of each type or grade of land, but whatever was supplied would be a free g i f t q.f na-ture. If nature would "produce" ON units of a cert a i n type of land (figure. 14), the msc curve would follow the X-axis from 0 to | (zero cost), and at that point r i s e to i n f i n i t y . As nature charges no price for i t s output, the ent i r e u t i l i t y . value of the land (the area MPNO under the msr curve.) would consist of consumers ' surpluses r e a l i s e d by various owners (past or present) of that land. TV; ce Figure 14 msc /r/S t~ Output The phenomenen of in t e r e s t , involving the complica-tions of economic dynamics, i s perhaps the most d i f f i c u l t to 110 analyse.in terms of cost and surplus. Prom the point of view of l i q u i d i t y preference or other r i s k theories, i t might be considered that the loss of security i s the balancing cost factor. Prom the point of view of time preference, i t might, be claimed that postponement of consumption constitutes the s a c r i f i c e to be. reckoned as a cost item. Some economists agree with Professor Pigou that i n d i v i d u a l sentiments are. incapable of properly recording the cost involved i n saving for investment. This i s the result of a"telescopic f a c u l t y " -the tendency to undervalue future compared with present sat-i s f a c t i o n s . Mr. Dobb, elaborating t h i s argument, claims that saving and investment are proper f i e l d s for c o l l e c t i v e evalua-tions of costs and benefits involved. 1 The agio i n production, earned as a res u l t . o f investment, would have to be balanced with the diminished u t i l i t y of a marginal d o l l a r r e s u l t i n g from increased income. As the main argument i s not dependent upon any p a r t i c u l a r p r i n c i p l e decided upon i n the evaluation of interest, t h i s controversial issue w i l l not be pursued in any d e t a i l . In summary, i t can be seen that while a firm's t o t a l cost may include surpluses, the marginal cost item can be traced to the o r i g i n a l human s a c r i f i c e s which, i n the f i n a l analysis, make up the re a l cost of production in society. 1" Dobb-, M. , Pol i t i c a l economy and capitalism, pp. 298-299 and 311-312, c i t e d i n Bergson, " S o c i a l i s t economics" p. 415. . ' I l l APPENDIX i i MARGINAL COST PRICING THROUGH SUBSIDISATION Subsidisation may induce a monopoly to produce at marginal cost. The monopoly i n figure 15 enjoys a subsidy per unit of output equal to PR, covering the difference between msr and mpr at 'the maximum s o c i a l p r o f i t output ON. To the purpose© of the monopoly the mpc curve w i l l be lowered by PR and w i l l thus be replaced by tb;e mc_ curve. The firm w i l l no longer maximise i t s p r o f i t s at Q^, the inters e c t i o n of the mpc and mpr curves with output ON', but at R, the inters e c t i o n of the mc_ and mpr curves, c a l l i n g for an output ON. The output which has now become most p r o f i t a b l e to the monopoly i s at N' N Output Figure 15 the same time the maximum s o c i a l p r o f i t output. The price which w i l l clear the market for t h i s output i s , of course, PJT. In e f f e c t , marginal cost p r i c i n g has thus been estab-l i s h e d . 113 APPENDIX i i i • . MARGINAL COST PRICING THROUGH PRICE FIXING Price control by the government could be used as an enforcement of marginal cost p r i c i n g . If the government fixe s a maximum pri c e , PN (figure 16), equal to marginal cost at the maximum so c i a l p r o f i t output,.the mpr curve of the firm w i l l be replaced by a horizontal curve. This curve w i l l indicate both marginal revenue (mr_) and average revenue (ar) to the firm, as i n the case of perfect competition. The curve w i l l be horizontal only to point P. For beyond t h i s point consumers w i l l not be w i l l i n g to pay as much as the maximum price set by the government. Beyond point P the ar A/" A/' A/ S Output Figure 16 1-14 curve w i l l f o l l o w the o r i g i n a l apr curve and the mr curve w i l l drop v e r t i c a l l y to j o i n the o l d mpr curve. .As P i s the i n t e r -s e c t i o n of the mpc and mr curves, as w e l l as the i n t e r s e c t i o n of the msc and msr curves, the optimum output from a s o c i a l p r o f i t standpoint, ON, w i l l be achieved at the marginal cost of t h a t output, PN. It i s very l i k e l y that the government w i l l make e r r o r s i n i t s estimate of the co r r e c t • marginal cost at the s o c i a l l y optimum output. I f too low a p r i c e i s s e t j e.g. P'N'f the marginal (and average) revenue curve of t h e - f i r m (m-Jr' = a'r') w i l l i n t e r s e c t with the mpc curve.at P', c a l l i n g f o r t h an output ON', somewhat short of the maximum s o c i a l p r o f i t o u t p u t . 1 But the demand f o r the product w i l l be determined by the p o i n t on the msr curve c o r r e s p o n d i n g t o ' t h e p r i c e P'N 1. Th i s w i l l be p o i n t R, a s s o c i a t e d with an output OS. However, the f i r m w i l l f i n d i t p r o f i t a b l e to produce only ON'. The r e s u l t w i l l be a shortage c h a r a c t e r i s e d by queues and the encouragement of a b l a c k market. A n o v e r e s t i m a t i o n of the marginal cost at the maximum s o c i a l p r o f i t output, such as the p r i c e P"N", w i l l e s t a b l i s h m"r" as the marginal revenue curve and a " r " as the average revenue curve of the f i r m . The m"r" curve, dropping v e r t i c a l l y at i t s c o n t a c t , P", with the apr curve, w i l l i n t e r -sect w i t h the mpc curve at Output w i l l be e s t a b l i s h e d at 1 It i s , of course, p o s s i b l e f o r the maximum p r i c e set by the government to be so low that the f i r m w i l l not be a b l e t o make a p r o f i t a t a l l and w i l l be d r i v e n out of b u s i n e s s . 115 ON", again short of the s o c i a l l y optimum output. The point P" being situated v e r t i c a l l y above the,price at output ON'.? w i l l be the maximum price set by the government.1 Price f i x i n g i s indeed applied i n practice - at times quite extensively - to curb excessive p r o f i t s . Theo-r e t i c a l l y i t might.be used to achieve marginal cost p r i c i n g i n increasing average cost industries by a system of t r i a l and error. The maximum price w i l l then have to be lowered continuously u n t i l the point i s reached where the output of a firm w i l l just commence to f a l l short of demand at the fixed price, ^or that w i l l be the sign that the marginal cost price, of.the s o c i a l l y optimum output has been reached. In practice, however, i t w i l l be impossible to regulate prices by the minute adjustments necessary to maintain the precarious balance where i t would be pr o f i t a b l e to,a fi r m to just meet demand. For when a firm changes Its output i t does such by a substantial amount and a serious shortage w i l l have to ar i s e before the government w i l l r e a l i s e that the proper maximum price was reached. Government price f i x a t i o n at the marginal cost corresponding to maximum s o c i a l p r o f i t output can, of course, not be applied to private firms working under decreasing average posts, without, d r i v i n g them into bankruptcy. If. p r o f i t s 1 If the maximum price i s set above the price the firm would have demanded on i t s own accord, as a monopoly, the m"r_" curve w i l l j o i n the mpr curve before i t s in t e r s e c t i o n with. 'the - mpc curve. In'that case the monopoly w i l l determine price and output as "before'and the maximum price set by the govern-ment w i l l be ir r e l e v a n t . 116 are .made by the decreasing average cost firm i t <will be poss-i b l e , however, to f i x a maximum price somewhat below the price o r i g i n a l l y demanded by the firm. Prices can be fixed at the marginal cost of the s o c i a l l y optimum output of a decreasing marginal cost firm i f the .government undertakes to finance i t s d e f i c i t s . 1 In a nationalised firm the government can then encourage e f f i c i e n c y (cost reduction) and the attainment of the s o c i a l l y optimum output by rewarding managers according to t h e i r success i n minimising losses per unit of output. The maximum price which the decreasing marginal cost firm i n figure 17 may ask i s set at PN, equalling mpc at the point (.p) where i t coincides with msr, The marginal revenue curve to the firm w i l l become the horizontal curve mr which drops v e r t i c a l l y at P to join.the o r i g i n a l mpr curve. With decreasing marginal cost and constant marginal revenue to .the firm, the- loss per unit of. output wilL be constantly decreasing up to the point where the mr_ curve reaches the msr curve and further sales at the maximum price become i m p o s s i b l e B u t t h i s occurs at point P, where the -1 In t h i s case the analysis concerns a decreasing marginal cost firm. For those decreasing average cost firms which have increasing marginal costs over the l a s t part of t h e i r output • series, the analysis w i l l follow more closely that'previously discussed. The losses of "firms i n the l a t t e r category "over the f i r s t part of t h e i r output series (where cost exceeds revenue) w i l l , of course, be i n excess of the p r o f i t enjoyed on the" l a s t part "of th e i r output "(where revenue exceeds cost) i f they are producing at the s o c i a l l y most p r o f i t a b l e output. 2'It i s just possible that for some range beyond' output ON the loss per"unit of output (distance between the mpc and mr curves) would" be less than the average" loss over the range~ON "(the average"""distance between the mpc and mr curves over that range). By making the maximum price a minimum price as well, a firm "could'be~prevented from expanding beyond the s o c i a l l y optimum output ON. J 117 s o c i a l l y optimum output ON is attained, and where the price equals marginal cost (PN). Too high an estimate of marginal cost at maximum s o c i a l p r o f i t output w i l l give the fixed price P"N". Marginal revenue to the firm w i l l be indicated by the m"r" curve, horizontal to point P". Up to that point the loss per unit of output (excess of mpc over mr) decreases s t e a d i l y and even becomes a p r o f i t over the la s t part of that range. The average loss w i l l be minimised, therefore, at point P", where the demand at the maximum price ceases. This w i l l be for an output ON", somewhat short of the s o c i a l l y optimum output. P r i c e 0 A/" A/ A/' Outpu.t Figure 17 With a maximum price, P'N', lower than marginal cost at the maximum s o c i a l p r o f i t output, the marginal revenue to the firm (m 'r') w i l l again be horizontal t i l l i t meets the msr curve at point p \ The average loss w i l l 1-18 decrease up to point P w h e r e demand at the maximum price ceases (but even for. the la s t item of output cost w i l l exceed revenue). Output w i l l be ON', a l i t t l e over the maximum s o c i a l p r o f i t output. • . The p r a c t i c a b i l i t y of price f i x i n g as a government instrument, to achieve marginal cost p r i c i n g i s limited by the government's accuracy i n estimating marginal cost at the s o c i a l l y optimum output. With decreasing marginal cost .firms there i s no indication wlfther the price has been fixed above, below,.aor at the appropriate l e v e l . Moreover, with prices fixed, firms would: not be able to react to changes in-the— cost schedules of t h e i r product. 119 BIBLIOGRAPHY Bergson, Abram, " S o c i a l i s t economics", i n E l l i s , Howard S"., ed., A survey of contemporary economics, Philadelphia and Toronto, Blakiston, 1948, pp. 412-448. Boulding, Kenneth E., Economic analysis, New York, Harper, 1948. Chamberlin, E.H., The theory of monopolistic competition, Cambridge, Harvard University Press, 1933. Clark, J. Maurice, Studies in the economics of overhead  costs, Chicago, 1923. Coase, R.H., "The marginal cost controversy", Economica,. v o l . 13, pp. 169-182, August, 1946.. Coase, R.H.,- "The marginal cost controversy.- some further comments", Economica. v o l . 14, pp. 150-153, May, 1947. Dickinson, H.D., Economics of socialism, Oxford, 1939. Dobb, M.,. "Economic theory and the problems of a s o c i a l i s t economy", Economic Journal, v o l . 43, pp. 588-598, December, 1933. Dobb, M., P o l i t i c a l economy and capitalism, New York, 1940. Dupuit, Jules, "De 1 ' u t i l i t e ' et de sa mesure", c o l l e c t e d and reprinted by d i Bernardi, Mario, and Einaudi, L u i g i , La, riforma soziale . Turin, 1932. Fleming, J.M.,, and Meade, J.E. , "Price and output p o l i c y of' ' state enterprise", Economic Journal, v o l . 54, pp. 321-339, December, 1944. Frisch, Ragnar, "The' Dupuit taxation theorem", Econometrica. v o l . 7, pp. 145-150, A p r i l , 1939. Fris c h , Ragnar, "A. further note on the Dupuit taxation theorem", Econometrica. v o l . 7, pp. 156-157, A p r i l , 1939. • Hicks, J.R., Value and c a p i t a l , Oxford, Clarendon, 1948. Hotelling, Harold, "The genera,l welfare i n r e l a t i o n to prob-lems "of" taxation and of railway and u t i l i t y rates", Econometrica, v o l . 6, pp. 242-269, July, 1938. 1 H o t e l l i n g , Harold, "The r e l a t i o n of prices to marginal costs i n an optimum system", Econometrica, v o l . 7, pp. 151-155, A p r i l , 1939. Hotelling, Harold, "A f i n a l note", Econometrica, v o l . 7, pp. 158-160, A p r i l , 1939. Hutt, W.H.,. "The concept of consumers' sovereignty", Economic  Journal, v o l . 50, 'pp. 66-77, March, 1940. Keynes, J.M., The general theory of employment, interest and  money, London, Macmillan, 1949. Lange, Oskarj "On the economic theory of socialism", i n Lippincott, Benjamin E., ed., On the economic theory of  socialism, Minneapolis, University of Minnesota Press, 1948, v o l . 2, pp. 55-143. Lerner, Abba P., The economics of control, New York, Macmillan 1944. Marshall, Alfred, P r i n c i p l e s of economics. London, Macmillan, 1938. Meade", J.E., and Fleming, J.M., "Price and output p o l i c y of state enterprise", Economic Journal, v o l . 54, pp. 321-339, December, 1944. Nord.in, J . A » » "The marginal cost controversy: a reply", Economica, v o l . 14, pp. 134-149, May, 1947. Norris, Harry, "State enterprise and output p o l i c y and the • problem of cost imputation", Economica, v o l . 14, pp. 54-62, February, 1947. Pigou, A.C., The economics of welfare. London, Macmillan, 1929. Robinson, Joan V., The economics of imperfect competition. London, Macmillan, 1933. Thirlby, "G. F., "The marginal cost controversy: a note on Mr. Coase's model", Economica. v o l . -14, pp. 48-53, February, 1947. Wilson, T., "Price, and outlay policy of- state enterprise", Economic Journal, v o l . 55, pp. 454-461, December, 1945. 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0106875/manifest

Comment

Related Items