| The dissertation explores the increasing block pricing. Building on mechanismdesign and the economics of information, three themes are mainly discussed, i.e., thetheoretical reasons for there existing increasing block schemes, and for not manyblocks in increasing block policy in reality, and the characterization of the optimalincreasing block mechanism. To probe into the theoretical reasons for the introductionof inclining block rate, we have to firstly investigate the existence of increasing pricingschemes, and the relationship between the increasing pricing tariff and inclining blocktariff. In view of the informational and computational costs when pricing mechanismimplemented, the inclining block rate is asymptotic efficient relative to the increasingpricing scheme. Based on the results on equivalency among multi-part tariff andcorresponding menu of two-part tariffs, the problem of optimal increasing blockpricing mechanism can be converted into the one of optimal menu of two-part tariffs.For it is also complicated to search optimal menu of two-part tariffs, for the time beingonly menu of two-part tariffs with two options will be concretely discussed.(1). At the outset we elaborate the existence of increasing pricing scheme fromjustice and semi-welfarist perspectives respectively, paving for further research on thereasons why there exists increasing block pricing tariff in resource industry.At the beginning, from pure justice view and in the presence of asymmetricinformation on consumers' total disposable income, it is researched on how to modifyclassic two-part tariff for making all the consumers afford to pay basic consumptionquantity and for high-income consumers impartially compensating the firm's supplycost. Moreover, it is shown by extensive analysis that the introduction of privateinformation on household scale, negatively related to household's type on income,slows down the marginal price in modified two-part tariff previously.In the domains on rare resources or public utilities, classic Coasian two-part tariffdoes not differentiate diverse consumers by theirs features, letting them pay the sameunit price, which will exclude from market the low-income consumers not affordingmarginal (and/or fixed) cost. In the absence of the information for the regulator onprospective consumers' or households' income, the new two-part tariff derivedreasonably from Coasian two-part tariff, not only can make the regulated operator above deficit line, but also has all the consumers realize the basic life need. Relative toclassic two-part tariff, modified two-part tariff has lower fixed payment component, tothe extent which the consumer with lowest income expends all the money for realizingbasic life need, and clearly has higher marginal price, derived from marginal cost pluscertain makeup. This variable payment component makes consumers with relativelyhigh income exactly remunerate operation cost in the light of "equal liability" principle.Though modified two-part tariff achieves complete market coverage, it impels thesame obligation of cost remuneration undertaken for unit consumption by consumerswith secondarily low income as by those with higher income. The responsibility of costcompensation is out of proportion to the ability to cover relevant cost, violating justicefaith embodying the responsibility balancing with ability. In order to avoid injusticeinflicted by modified two-part tariff to consumers with secondarily low income, theobligations of cost remuneration for those with relatively higher income should bepositively dependent on their income levels. Specifically, the marginal prices ofgeneralized two-part tariff newly modified ought to be inclining with income level,which means the increasing pricing scheme. On the condition that the regulator lacksdetailed information on every prospective consumer's features of income, theincreasing pricing policy by completely screening types can let the affluent consumersequitably undertake the due obligation of cost compensation, while not damaging allthe consumers' abilities to meet basic life needs. If information of household incomeand of other characteristics, such as household scale, composition of family members,both are private and correlative, the results may be different only in the degree. Forinstance, if family income and its scale are negatively correlative, due to partlypalliatory effect of family scale on price progressive level, the newly modified two-parttariff's progressive degree will decrease. Note that for non-essential products, whetheror not to consider family scale is trivial for mechanism pair of modified two-part tariff.Secondly, the efficiency appeal is introduced and the causes and characterization ofincreasing pricing tariff are discussed from semi-welfarist perspective, providingtheoretical basis on the increasing block pricing mechanism. Semi-welfarist appeal isembodied in the concavity of modified welfare with regard to indirect utility. The caseof type continuation with definite upper and lower bounds is initiatorily investigated,and then the upper bound is loosened to be indefinite in an example.So long as the information on prospective consumers' income is complete,regardless of whether justice appeal is considered or not, the regulator's optimal pricing rule still is marginal cost pricing. Apparently, the indirect utility of relevantconsumer is related to justice appeal and the demand of complete market coverage.When information on their incomes is incomplete and the type domain is closed andcompact, the pricing rules are greatly diverse and complex, resting on the notion ofequilibrium solution in the consumer maximization problem. Under the concept offully separating equilibrium, even to maintain complete market coverage, marginalcost pricing yet is the optimal pricing rule implemented to the consumers with highest-and lowest-incomes. Even in pursuit of efficiency and complete coverage, marginalcost pricing rule still is optimal in this setting. More generally, type screening isincomplete and market coverage is incomplete. At this time, some consumers withcertain types choose identical consumption level, and parts of consumers with lowincomes have to retreat from the market. If regulator doesn't care about welfare oflow-income consumers, and allows them to quit form market, his optimal pricing ruleis to demand a price above marginal cost for consumers within market except the oneswith highest income, asked for price equating with marginal cost. Differently, if theregulator cares for low-income consumers and thus attempts to meet all the consumers'basic life needs, the optimal price asked by regulator for non-endpoint consumers otherthan those with lowest-and highest-incomes is over marginal cost. Moreover, ifefficiency, justice and complete market coverage are all concerned, the best pricingrule is following: highest-income consumers are requested to pay price exactly equal tomarginal cost, and other consumers are asked for above-marginal-cost prices, which isincreasing and then decreasing with respect to type. Compared with classic literatureon nonlinear pricing, it is shown that the addition of justice appeal to efficiency pursuitindeed can make the increasing pricing scheme be locally optimal applied by theregulator to many consumers locally and continuously distributed in type domain.Whereas, in an analytical case of modified welfare maximization problem, theloosening of the definite upper bound of type continuation toward plus infinity resultsto increasing pricing tariff being globally optimal.(2). Taking the implementation of the increasing pricing mechanism as starting point,we study the theoretical causes of the increasing block pricing policies appearingpervasively in the resources provided by pipeline network, and further interpret thereasons why the number of blocks in these policies is quite small. In particular, wediscuss the effects of high informational and computational cost generated during theprocess of executing the increasing block policy on the implementation of increasing pricing tariff. The relevant findings are embodied as the asymptotic efficiency of theincreasing block scheme relative to the some increasing pricing tariff, and equivalenceproperty among any increasing block tariff and relevant menu of two-part tariffs insupplied-by-network resources.It is found out that, with regard to supplied-by-network resources, the increasingpricing policy, can be approximated by an increasing block pricing mechanism. Anyincreasing pricing structure can be approximated by upper envelope of certain menu ofmodified two-part tariffs satisfying corresponding incentive compatible constraints.There does exist the equivalency between any inclining block tariff with n blocks andcorresponding menu of two-part tariffs with n options. Technically, for any forms oftype distribution and partition, relative to fully increasing pricing mechanism, the lossof modified welfare generated by an increasing block tariff with n blocks isinfinitesimal of the same order as the reciprocal of n squared. In other word, the lossdeclines promptly as the block number n increases. In spite of the rising of blocknumber decreasing welfare loss, on the other hand, this behavior will dramatically raisethe informational and computational requirements needed by the parties in the processof executing more complicated block tariff, thereby expending involuntarily extratransactional cost and corresponding welfare. More importantly, this kind of welfareloss will rapidly increase when the block number increases. So there exists areasonable tradeoff between the depletion of welfares as a result of informational andcomputational complexities and the savings of welfares causing from the increasingblock tariff approximating increasing tariff with full continuity. Besides, the tradeoffrelationship determines that the optimal block number of the proper increasing blockschemes is a small and positive integer. Due to the absence of the features ofmathematically continuity and differentiability and of economic theoreticallyindependence between any two variables for the inclining block mechanism, it is ratherdifficult to design directly optimal increasing block mechanisms. Yet, within pricingproblems of resources provided via networks, the equivalency between increasingblock mechanism and menu of two-part tariffs makes it feasible and valid to convertthe problem of optimal increasing block mechanism design into the one of optimalmenu of two-part tariffs. In a word, the results on equivalency and asymptoticefficiency evidently facilitate the study of increasing block pricing policy.(3). At last, we explore the problem of optimal increasing block pricing mechanism inconsideration of enormously transactional cost stemmed from the two kinds of complexities. In view of the asymmetry of information on potential consumers'incomes, and the restrictions on the regulator's spaces on information (and/or behavior)because of transactional cost, the problem of optimal increasing block pricingmechanism can be regarded as a new-style mechanism design problem withunilaterally informational asymmetry and restrictions on informational and behaviorspaces. The analysis on this problem is complex and immature contemporarily.Building upon the equivalency between multi-part tariff with inclining prices and menuof two-part tariffs, we can merely focus on seeking for the optimal menus of two-parttariffs, solved through classic mechanism design theory.Theoretically, the problem of design of optimal menu of two-part tariffs is applied tothe screening models. However, the co-determinacy between consumption and pricegiven some menu of two-part tariffs leads to the difficulties in representing incentivecompatible constraints. Therefore it is invalid to analyze it through classic screeningmodels and other ways should be employed, such as repeated modifications andapproximation adopted here. That is, to step by step add newly modified two-part tariffinto the generalized two-part tariff optimized within global type region, and to continuethis by n-1times, lastly generating a menu of two-part tariffs with n options consistingof a generalized two-part tariff and n-1modified two-part tariffs. When the type regionwhere the generalized two-part tariff is still applied become enough small withrepeated additions of modified two-part tariffs, the generalized two-part tariff appliedcan be viewed approximately as a modified two-part tariff. Thus an optimal menu oftwo-part tariffs with n options is designed. Clearly, to design optimal menu of two-parttariffs, we can start from the simplest case of generalized two-part tariff, modifiedtwo-part tariff and menu of two-part tariffs with two options. In light of the fact thatthe block number of increasing block tariff (accordingly column number of menu oftwo-part tariffs) is small, we can only add modified two-part tariffs by a few times,which make it very feasible.In fact, the generalized two-part tariff based on global region also within the scopeof the increasing pricing schedules, still made up with fixed and variable payments. Tomaximize modified welfare, the mechanism designer has to choose optimal one(s)within the feasible set of generalized two-part tariffs defined by relevant consumers'incentive compatibility and individual rationality constraints and the regulatedmonopolist' budget constraint. Just as classic pricing literature, the generalizedtwo-part tariffs satisfying incentive constraint meet continuity and monotonicity conditions. When the regulator applies the generalized two-part tariff to a sub-domain,the characterization of optimal consumption decision is intricate and its economicapplication is ambiguous. Of course, if the modified welfare function specifies a linearone with respect to indirect utility, the formulation of optimal consumption on thewhole represents one in classic nonlinear pricing literature. But in this setting theoptimal deviation of price from marginal cost is not only influenced on the form oftype distribution function, but also affected by the coefficient of linear function onwelfare, and intensity of budget constraint. The status above is analogous when thegeneralized two-part tariff is adopted in global domain instead of any sub-domain. Inaddition, on the condition of linear welfare function, both optimal consumption andindirect utility will increase as the upper bound of relevant sub-region reduces, whichis in favor of consumers with informational advantage achieving information rents.The menu of two-part tariff with two columns is achieved approximatively byadding a newly modified two-part tariff into optimal generalized two-part tariffobtained previously. The mechanism designer's behavior of sort is rather likely toinfluence consumers' consumption decisions. On some regular assumptions, if fixedpayment of two-part tariff added is negative, then all the consumers will convert tochoose modified two-part tariff added; otherwise, any consumers within twosub-regions located in the two end points of global domain have incentive to choosemodified two-part tariff while others located intermediately want to insist of usingprevious pricing scheme. So long as the transactional cost in the course of carrying outpricing policy is high enough, modified welfare will be pareto improved when theregulator adds a new modified two-part tariff into generalized two-part tariff. It meansthat it is the existence of informational and computational requirements that make theregulator have incentive to add new tariffs. Because the generalized two-part tariffoptimized in any sub-domain is not still optimal in global region, it is fairly necessaryto design menu of two-part tariffs with two columns optimized in global domain.Particularly, when welfare function is linear, structural coefficients in optimal menu oftwo-part tariffs with two columns have to satisfy some characterization conditions. Forinstance, pricing parameters in first and second options such as fixed payment andmarginal prices are mutually and closely related. And the correlations between pricingparameters and kinks, among pricing parameters or kinks may be more complicated.Here just optimal block pricing mechanisms with two blocks has be exploredincompletely and roughly, and the optimal block tariff with multiple blocks is not studied. To some extent, the exploration of optimal solution to the increasing blockmechanism is better a computational problem, than an economic theoretical one.
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