This paper studies technology choice as a relevant aspect to be considered when analyzing price discrimination and welfare. Our results reinforce the traditional wisdom that an increase in output is a necessary condition for price discrimination to improve social welfare. But we also find that the positive output effect does not need to be as large as previously supposed since, under some conditions, the monopoly will move to a socially preferred technology only if third-degree price discrimination is allowed

Galera, F. (Francisco)

Molero, J.C. (Juan Carlos)

Álvarez, J. L. (José Luis)

Álvarez-Arce, J.L. (José Luis)

Dadun, University of Navarra

       Facultad de Ciencias Económicas y Empresariales          Working Paper nº 15/12       Technology Choice and Third Degree Price Discrimination in a Monopoly    Francisco Galera University of Navarra   José Luis Álvarez  University of Navarra   Juan Carlos Molero University of Navarra   1Technology Choice and Third Degree Price Discrimination in a Monopoly  Francisco Galera, José Luis Álvarez, Juan Carlos Molero  Working Paper No.15/12 October 2012       ABSTRACT  This paper studies technology choice as a relevant aspect to be considered when analyzing price discrimination and welfare. Our results reinforce the traditional wisdom that an increase in output is a necessary condition for price discrimination to improve social welfare. But we also find that the positive output effect does not need to be as large as previously supposed since, under some conditions, the monopoly will move to a socially preferred technology only if third-degree price discrimination is allowed.    Francisco Galera School of Economics and Business Administration University of Navarra fgalera@unav.es   José Luis Álvarez School of Economics and Business Administration University of Navarra jlalvarez@unav.es   Juan Carlos Molero School of Economics and Business Administration University of Navarra jcmolero@unav.es        Technology choice and third degree price discriminationin a monopolyFrancisco Galera1,∗, Jose´ Luis A´lvarez, Juan Carlos MoleroDepartment of Economics, Universidad de Navarra, Campus Universitario, 31080,Pamplona, SpainAbstractThis paper studies technology choice as a relevant aspect to be considered whenanalyzing price discrimination and welfare. Our results reinforce the traditionalwisdom that an increase in output is a necessary condition for price discrim-ination to improve social welfare. But we also find that the positive outputeffect does not need to be as large as previously supposed since, under someconditions, the monopoly will move to a socially preferred technology only ifthird-degree price discrimination is allowed.Keywords:monopoly, technology choice, third degree price discriminationJEL: D42, L12, L13.1. IntroductionPrice discrimination is a common practice. In a regime of third-degree pricediscrimination the producer charges different prices to buyers who belong todifferent markets. For instance, markets can be separated geographically orcustomers may be differentiated by age, employment status (discounts for retiredand unemployed workers), time of purchase (last moment discounts) and manyother variables. The overall effect of third-degree price discrimination on welfareis undetermined. Price discrimination allows firms to increase their profits.Consumers who pay a lower price are also better off. But price discriminationharms consumers in markets with higher prices.The impact of price discrimination on welfare can be rearranged in a dif-ferent way: the misallocation effect and the output effect. The misallocationeffect is always negative for welfare, because a change from uniform pricing to∗Corresponding author. Tel.: +34 948 425600, fax: +34 948 425619Email addresses: fgalera@unav.es (Francisco Galera), jlalvarez@unav.es (Jose´ LuisA´lvarez), jcmolero@unav.es (Juan Carlos Molero)1Financial support from Ministerio de Ciencia e Innovacio´n (ECO2010-18680) is gratefullyacknowledgedPreprint submitted to Economics Letters July 4, 2012price discrimination moves some output from high value buyers to low valueconsumers. However, the output effect can be positive, and it has the potentialto overcome the misallocation effect, but only if the increase in output is bigenough. In consequence, a necessary condition for price discrimination to in-crease welfare is that total output rises (see Schmalensee (1981), Varian (1985)and Schwartz (1990)).Recently Aguirre et al. (2010) presented a general analysis of the two effectson welfare –misallocation and output– in a framework of monopolistic third-degree price discrimination. They establish sufficient conditions under whichdiscrimination has positive effects on output and social welfare.The misallocation effect and the output effect are always present in anymodel of third degree price discrimination. But other variables have to be con-sidered since more effects may appear. For example, Ikeda and Toshimitsu(2010) show that a monopoly, facing linear demands and able to choose thequality of its product, will invest more in quality when price discrimination isallowed, overcoming the misallocation effect in such a way that price discrimi-nation increases social welfare even if the output effect is nil.This paper deals with social welfare and third-degree monopolistic pricediscrimination in the presence of another relevant effect: technology choice.This effect should be taken into account in order to better understand thewelfare effects of monopolistic third-degree price discrimination. In particular,it should be included when studying the conditions that determine the sign ofthese welfare effects.Technology changes can be understood as firms investing to improve theefficiency of their productive processes. These investments can take many forms.Some imply minor modifications (such as small purchases, task reorganizationsor in-the-job training) while others result in significant changes and costs (forexample purchases of new machinery, the building of a new plant, cost reductiontask forces, etc). For the sake of this paper, technology choice means a reductionin variable costs at the expense of some fixed costs.A social inefficiency may exist when a monopoly does not adopt a new tech-nology with lower marginal costs because the associated fixed costs are too high.Here, we find cases where third-degree price discrimination outperforms uniformpricing, since it provides the monopoly with the right incentives for the adoptionof the new technology.First, we prove that if a profit-maximizing monopoly decides to adopt anew technology that increases output, society will also be better off. We thenshow that, in some cases, when society prefers the monopoly to adopt the newtechnology, third-degree price discrimination (but not uniform pricing) can makeit profitable for the firm to do so. Of course, this is not to mean that pricediscrimination is always preferable to uniform pricing. Our point is that anumber of considerations must be made when assessing which price regime wouldmaximize social welfare; and technology choice is a reasonable example. From anormative point of view, our result calls for caution when applying theoreticalresults for policy making.22. Technology choice, price discrimination and social welfareLet’s consider a monopoly facing the possibility of adopting a new technol-ogy, which increases output. The monopoly will only implement this technolog-ical change if it is profitable. If we consider two price regimes and only one ofthem leads the monopoly to adopt the output-increasing technology, this regimewould be more socially desirable.Proposition 1. If the monopoly prefers a technological change that increasesits production level (Qn ≥ Q), so will society.Proof. Let us first consider the case where Qn = Q. If the monopoly prefersthe new technology so will society, since profits increase and consumer surplusremains the same.When Qn > Q, consumers are better off because prices are lower. Again, ifthe monopoly prefers the new technology, so will society since consumers andgovernment are also better off.Note, however, that it is possible for society to prefer a price-lowering tech-nology that the monopoly does not want to adopt. One such example can befound for a monopoly with constant marginal costs of 2, facing a demand givenby p = 6 − Q. Under these conditions, profits are equal to 4, while society’swelfare (consumer surplus plus profits) is 6. If a new technology becomes avail-able with zero marginal costs and a fixed cost of 6, the profits of the monopolywould be lower (3), but welfare would be higher (7.5).Let’s now consider under which price regime a monopoly is more likely toadopt the socially desirable technology.Proposition 2. Suppose a monopolist with constant marginal cost, c, and twopossible regimes: uniform price and third degree price discrimination. Then,in either regime, the derivative with respect to c of the profit function is thequantity produced. In consequence, the monopoly is more likely to adopt a costreducing technology under the price regime with higher output.Proof. A monopolist facing constant marginal cost, c, sells its product in twomarkets, A and B. Let the demand of the monopolist be Q = A(p) + B(p),where A(p) and B(p) represent the demand in these two different markets. Themonopolist can reduce variable costs at the expense of some fixed costs.Under a uniform pricing regime, the monopolist’ profit, net of fixed cost, isgiven byΠU (p) = (p− c) (A(p) +B(p)) .The monopolist will choose an optimal price p∗U . Applying the envelope theoremwe getdΠU (p∗U )dc=∂ΠU (p)∂c∣∣∣p∗U= −(A(p∗U ) +B(p∗U )).3Alternatively, under third degree price discrimination, the monopolist’ profitis given byΠD(pA, pB) = (pA − c)A(pA) + (pB − c)B(pB).The monopolist will choose two optimal prices: p∗A and p∗B . Again, by theenvelope theorem, we getdΠD(p∗A, p∗B)dc=∂ΠD(pA, pB)∂c∣∣∣p∗A,p∗B= − (A(p∗A) +B(p∗B)) .Suppose now that there are two possible technologies, L and H, such thattheir variable costs are cL < cH ; and there is a fixed cost, F , associated to thisreduction in marginal cost. It is clear thatΠD(cL)−ΠD(cH) =∫ cLcHdΠD(p∗A, p∗B)dcdc,andΠU (cL)−ΠU (cH) =∫ cLcHdΠU (p∗U )dcdc.When ΠD(cL) − ΠD(cH) > ΠU (cL) − ΠU (cH), some F can be found suchthat ΠD(cL) − ΠD(cH) > F > ΠU (cL) − ΠU (cH). In that case, the monopolyhas incentives to move to the lower cost technology only under the price dis-crimination regime, but not with uniform pricing. This result would alwayshold if, for every c ∈ [cL, cH ], the output under uniform price is lower than theoutput under price discrimination. More generally, when facing a technologychoice that would lower variable costs, the monopoly will be more likely to actaccording to the interest of society under the price regime with higher output.This result reinforces the well-known criterion in price discrimination: wel-fare cannot improve with price discrimination when total output falls. Otherwisestated, an output increase is a necessary but not sufficient condition for pricediscrimination to improve welfare. But if we take into account the possibilityof the monopoly adopting a lower cost technology, price discrimination can leadto higher welfare even if the positive output effect is small.In order to illustrate our result, we provide an example related to Aguirreet al. (2010), who in proposition 6, state that: “When demand functions haveconstant elasticities: (i) total output is higher with discrimination, and (ii) socialwelfare is lower with discrimination if the difference between the elasticities isat most 1.”This proposition holds if we keep everything else constant. However, it canbe reversed in some cases if technological change is taken into consideration.We illustrate this possibility with a numerical example.2.1. Numerical exampleLet the demands be given by A(p) = αAp−A and B(p) = αBp−B , withA, B > 1. Technological change can reduce marginal costs from cH to cL.4Under price discrimination, the two prices can be calculated with the ex-pression p−cp =1i, i = A,B; that is, with k = L, H, prices arepi(ck) =ckii − 1 . (1)The welfare in market i = A, B, with marginal cost ck, isWi(pi) =∫ αip−ii0((αiQ) 1i − ck)dQ =αipii(ipii − 1 − ck). (2)To obtain the prices for the uniform price regime, we derive the profit func-tionΠU (ck) =(αApA+αBpB)(p− ck) , (3)with respect to p, to obtain∂ΠU (ck)∂p=αBpA+1 + αApB+1 − (p− ck)(αAApB + αBBpA)pA+B+1= 0. (4)Expresion 3, with A, B > 1 and |A − B | < 1 is indeed very complicated tosolve analytically. So, we will use a numeric example to ilustrate our point. Letus suppose that αA = αB = 100, A = 1.1, B = 2, cH = 2 and cL = 1.The first order condition, equation 4, holds for price values pU (cH) = 13.04and pU (cL) = 4.52. With price discrimination regime, from equation 1 priceschange from pA(cH) = 22 and pB(cH) = 4 to pA(cL) = 11 and pB(cL) = 2.Table 1 shows the levels of output, profits and welfare for all combinationsof technology and price regimes. The welfare levels can be calculated withequation 2. The profit with uniform price is in equation 3, while the profit withprice discrimination isΠD(ck) =αApAA(pA − ck) + αBpBB(pB − ck) .Uniform price Price discriminationQU ΠU WU QD ΠD WDcL = 1 6.52 84.20 966.3 9.59 96.53 933.3cH = 2 23.92 71.98 853.2 32.15 79.24 838.3Table 1: Output, Profits and WelfareWe can see that the proposition of Aguirre et al. (2010) holds: total outputrises with price discrimination, but social welfare is always higher under uniformpricing. But we also need to consider the incentives of the monopoly to adopt thenew technology and the effects on welfare. Under both price regimes, profitsincrease if the new technology is adopted but –as Proposition 2 states– the5increase is greater under price discrimination (17.29) than under uniform prices(12.22). Then, (i) if the cost of adopting the new technology is less than 12.22,the technology will be adopted under both regimes; (ii) if the cost is higher than17.29, the new technology will never be adopted; but (iii) if the cost is between12.22 and 17.29, the new technology will be adopted only under third degreeprice discrimination.As we can see from Table 1, society has different threshold values for thecost of adopting the new technology. Under the price discrimination regime, thechange would be desirable for consumers for any cost below 933.3− 838.3 = 95.Under the uniform price schedule, the threshold is 966.3− 853.2 = 113.1.Therefore, if the costs of adopting the new technology are between 12.22and 17.29, that is, clearly below 95 and 113.1, society would prefer that thefirm adopts the new technology, but the monopoly would do so only underthird degree price discrimination. Then, we can conclude that in some casestechnology choice makes third degree price discrimination welfare-superior touniform pricing even with a small output effect.Cowan (2012) shows that discrimination can be good for consumers in aggre-gate cuando se dan ciertas condiciones en las demandas. Como la discriminacionde precios es siempre buena para el monopolista, esto implica que el efecto out-put debe superar al efecto misallocation, y por lo tanto debe ser positivo. Portanto como el efecto output es positivo, siempre hay mas incentivos a bajar loscostes con precio diferenciado que con precio uniforme, como establece nuestraproposicion 2.En nuestro ejemplo se ve que la discriminacion de precios es buena para losconsumidores porque el precio baja de 15.04 con regimen uniforme a unos preciosde 11 y 2, con regimen diferenciado. Pero nuestras demandas no cumplen lascondiciones de Cowan (2012).Por tanto vemos que esas condiciones pueden ser demasiado estrictas cuandose tiene en cuenta que las empresas pueden disminuir sus costes marginales acambio de incrementos en los costes fijos.3. Final remarksThis paper deals with the well-known problem of monopolistic third-degreeprice discrimination and social welfare when all markets are served. A classicalresult in the literature is that the effect of price discrimination can be positive ornegative for welfare depending on the direction and magnitude of the quantityor output effect. Third degree price discrimination reduces welfare when theoutput effect cannot overcome the misallocation effect.However, our paper provides additional conditions under which monopolisticthird-degree price discrimination may increase social welfare. The main resultis that, under some assumptions, the profit-maximizing monopolist will chooseto adopt a socially preferred technology if and only if third-degree price dis-crimination is allowed. Thus, a ban on third-degree price discrimination, even ifseemingly beneficial, may prove detrimental by preventing the monopolist fromadopting a socially superior technology.6ReferencesAguirre, I., Cowan, S., Vickers, J., September 2010. Monopoly price discrimi-nation and demand curvature. American Economic Review 100 (4), 1601–15.Cowan, S., 2012. Third-degree price discrimination and consumer surplus. TheJournal of Industrial Economics 60 (2), 333–345.Ikeda, T., Toshimitsu, T., 2010. Third-degree price discrimination, qualitychoice, and welfare. Economics Letters 106 (1), 54 – 56.Schmalensee, R., 1981. Output and welfare implications of monopolistic third-degree price discrimination. American Economic Review 71, 242–7.Schwartz, M., 1990. Third-degree price discrimination and output: Generalizinga welfare result. American Economic Review 80, 1259–62.Varian, H. R., 1985. Price discrimination and social welfare. American EconomicReview 75, 870–5.7

Technology Choice and Third Degree Price Discrimination in a Monopoly

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Technology Choice and Third Degree Price Discrimination in a Monopoly

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