VIII Some Problems of Discriminating Monopoly

§ 26. Consider an industry in which conditions of decreasing supply price prevail, but in which the supply curve lies wholly above the demand curve, so that neither under simple competition nor under simple monopoly can any output take place. Draw the demand curve DD1 and the supply curve SS1 as in Fig. 10. Through S draw a curve SS2 such that, if a perpendicular be drawn from any point P on SS1, to cut SS2 in Q, and the figure be completed as drawn, the area SQMO is equal, for all positions of P and Q, to the rectangle KPMO. If DD1 lies throughout below both SS1 and SS2, it is obvious that no output can occur under monopoly plus discrimination of the first degree, just as none can occur under simple competition. It may happen, however, in some industries of decreasing supply price, that DD1, while lying below SS1 cuts SS2. If it cuts it once it must obviously cut it a second time. Let it cut it in R and Q. Then, under conditions of simple competition, no output can occur. But under conditions of monopoly plus discrimination of the first degree, provided that the area RQ is greater than the area DRS, an output OM will yield aggregate receipts in excess of aggregate costs, and will, therefore, be forthcoming. This result is more likely to be achieved, the more steeply the curve SS1 slopes downward (that is to say, the more strongly the law of decreasing supply price works); because, the steeper is SS1, the larger, when the distance OM is given, is the area PQS, and, therefore, the greater is the range of demand curves that will make the area

RQ greater than the area DRS. Given the inclination of SS1, it is also more likely to be achieved, if the demand curve does not slope downward steeply in its earlier stages (that is to say, if the demand is elastic till fairly low price levels have been reached).

§ 27. Monopoly plus discrimination of the second degree, as defined on p. 279, approximates in its effects towards monopoly plus discrimination of the first degree, as the number of different prices which it is possible for the monopolist to charge increases. This result, which is obvious in general, can be worked out exactly in a particular case. Let the output proper to discrimination of the first degree be a, and let n be the number of different price-groups. On the hypothesis that the demand and supply curves are straight lines, it can be shown that, when the commodity obeys the law of constant supply price, the output will be equal to for all values of n. That is to say, if one price only can be selected, the output will be ½ a: if two prices can be selected, 2/3 a, and so on. When the commodity obeys the law of decreasing supply price, the output, if n is equal to 1, will still be equal to , but, if n is greater than 1, it will be somewhat less than this.

§ 28. Our next problem has to do with the relative outputs under discriminating monopoly of the third degree—as defined on p. 279—and of simple monopoly respectively. Let conditions of constant supply price prevail, and let there be two markets only. Then if the curves of demand in both markets are straight lines, precise results can be obtained. Let D1D2 and D'1D'2 represent the demand curves of the two markets, and let SS' be drawn at a vertical distance OR above the base line, where OR measures the constant cost of production. Through D'1 draw D'1H parallel to SS', and, through H, draw a straight line HT, such that PT is equal to RP'. Then under discriminating monopoly the output for the two markets will be respectively ½RP' and ½RP. Under simple monopoly, if PH is greater than HD1, the output will be ½RT. But, since

PT is equal to RP', ½RT = ½RP' + ½RP. Therefore, subject to the condition italicised above, the outputs under simple monopoly and under discriminating monopoly will be the same. If PH is less than HD1, the output under simple monopoly will, in some conditions, be ½RP, and there will be no consumption in the less favourable market. When these conditions prevail, so that under simple monopoly nothing would be consumed in one of the two markets, the substitution of discriminating for simple monopoly increases the output; but except in these conditions the output is not changed. When the assumption of constant supply price is removed and it is allowed that increasing or decreasing supply price prevails, the results reached above are not modified, since it is only through a change in the quantity of output that increasing or decreasing supply price can be called into play. Decreasing supply price, however, opens up a possibility referred to in Part II. Chapter XVII. § 13, and analogous to that examined in § 26 above, to which the preceding discussion has no relevance. This is that, in some conditions under which neither simple monopoly nor simple competition would have led to any output, discriminating monopoly may lead to some output.