SECTION II THEORY OF MONOPOLY (E) THE PURE THEORY OF MONOPOLY [THIS is a translation of Teoria Pura del Monopolio published the Giornale degli Economisti, 1897; itself a translation from an English original which has been lost. Much of the contents might with equal propriety have appeared in the Sections dealing with Taxation and Mathematical Economics. But it has not seemed advisable to break up the article. The theory of monopoly in the ordinary sense of the term is connected with the theory of two-sided monopoly or "duopoly." duopoly." Cournot had represented the transactions between two parties to be determinate in the same sense as competitive prices. But heavy blows had been dealt on this part of his system by Bertrand in the Journal des Savants, 1883, and by Marshall, in an early edition of his Principles of Economics. Still in 1897 much of Cournot's construction remained standing; the large part which is based on the supposition that the monopolist's expenses of production obey the law of diminishing returns. Now the demolition of Cournot's theory is generally accepted. Professor Amoroso is singular in his fidelity to Cournot (cp. ECONOMIC JOURNAL, September 1922).] CONTENTS SECTION I.-The theory of taxation in the simpler cases of a single monopolist dealing with a group (or groups) of competitive individuals. SECTION II.-Proof of the proposition that in the case of two or more monopolists dealing with competitive groups, economic equilibrium is indeterminate. SECTION III.-On the effects of taxation (and other kinds of governmental regulations) in the more complicated cascs of a single monopolist dealing with groups of competitors-cases of correlation in respect of production or consumption. SECTION IV. Summary in simple language of the theses maintained in the preceding sections. SECTION I.—On the effects of a tax in the simple case of a single monopolist dealing with a group (or groups) of individuals competing against each other. Cournot has fully discussed the typical case in which a commodity of uniform quality is offered at one and the same price by a monopolist producer to consumers who compete against each other. The price is determined by the condition that the net gain of the monopolist should be a maximum. The quantity which is to be maximised may be represented by the expression if p is the price, F(p) the quantity of the article which is demanded at the price p, and (D) the cost of producing the quantity D. This formula remains applicable if we suppose that (D) indicates not merely the money cost, the expenses of the monopolist, but the measure of "real cost," 1 the pecuniary equivalent of the efforts and sacrifices incurred by him in the production. Thus interpreted the formula may be extended, by simply changing the signs, to a monopolist consumer who deals with producers competing against each other. In this case F(p) expresses the quantity of an article offered by competitive producers at the price p; and (D) represents the total utility for the monopolist of the quantity (D).2 The effects on the price and on the quantity of an article which are caused by a tax are represented by the same expression in both the cases. If V is the total net utility of the monopolist, whether he is producer or consumer, then for the increment of price consequent on a small tax, for instance, u per unit of product, we have in both cases which expression is necessarily positive. To investigate the effect 1 Cp. Marshall, Principles of Economics, sub voce "Real Cost." 2 The total utility simpliciter, if the monopoly is enjoyed by an individual; but if the part of monopolist is played by a combination-for instance, a co-operative buyers' association-there should be understood the sum of the total utilities obtained by each member from the portion of commodity assigned to him; a conception which is not necessarily identical with the Gemeinnutzen of Auspitz and Lieben, relating to a regime of Competition. Cournot, Recherches, Art. 38. of the tax on the quantity of the commodity taken at the price, it is convenient to consider the price as a function of the quantity; say p = f(x).1* Then, if the monopolist is the producer, we have which expression is necessarily negative. If the monopolist is the buyer, the signs in the expression for V are changed; while the equation for 4x remains the same. As the tax may very well be imposed not on the monopolist but on the competitive group, especially when the latter act as producers, it may be well to observe that in general it makes no difference theoretically on which of the two parties the tax is imposed.2 Analogous propositions may be proved for an ad valorem tax which is not regressive by inserting in the expression for the tax, instead of u, x as just now, any function of x (or of p) which increases (or diminishes) with the increase (or decrease) of x.3 I hasten to pass on to less beaten ground. An interesting variety of the case in which the monopolist is the buyer occurs when the quantity of the commodity that is on şale is absolutely limited; for instance, when it consists of land offered by competing owners. Here F'(p) is zero, and accordingly Whence, as the price is continually reduced, the net profit of the monopolist continually increases up to the point at which the sellers are beaten down to nothing-theoretically nothing, practically next to nothing. In a case of this kind a tax on rent would not fall on the competing landlords at all, but altogether on the monopolist tenant. There occurs in this case what is erroneously supposed to occur in general, that in the phrase of Mill " the price cannot be further raised to compensate for the tax, and it must be paid from the monopoly profits."4 † 1 Op. cit. Art. 43, p. 89. * x has been substituted for Cournot's D here and in the sequel. 2 Op. cit. Art. 37. 3 Cournot, op. cit. Art. 41. Marshall, Principles, 3rd ed., p. 433, note. 4 Mill, Political Economy, Book V. ch. iv. § 6. He is followed by some eminent writers, but naturally not by any of the mathematical school. See Cournot, Recherches, ch. vi., and Marshall, Principles, Book V. ch. xiii. ed. 3. † It may be recalled, however, that, though the monopolist has an interest VOL. I. I |