This dissertation consists of three empirical studies on nonlinear pricing in energy and environmental markets. The first investigates how consumers respond to multi-tier nonlinear price schedules for residential electricity. Chapter 2 asks a similar research question for residential water pricing. Finally, I examine the effect of nonlinear financial rewards for energy conservation by applying a regression discontinuity design to a large-scale electricity rebate program that was implemented in California. Economic theory generally assumes that consumers respond to marginal prices when making economic decisions, but this assumption may not hold for complex price schedules. The chapter "Do Consumers Respond to Marginal or Average Price? Evidence from Nonlinear Electricity Pricing" provides empirical evidence that consumers respond to average price rather than marginal price when faced with nonlinear electricity price schedules. Nonlinear price schedules, such as progressive income tax rates and multi-tier electricity prices, complicate economic decisions by creating multiple marginal prices for the same good. Evidence from laboratory experiments suggests that consumers facing such price schedules may respond to average price as a heuristic. I empirically test this prediction using field data by exploiting price variation across a spatial discontinuity in electric utility service areas. The territory border of two electric utilities lies within several city boundaries in southern California. As a result, nearly identical households experience substantially different nonlinear electricity price schedules. Using monthly household-level panel data from 1999 to 2008, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. I show that even though this sub-optimizing behavior has a minimal impact on individual welfare, it can critically alter the policy implications of nonlinear pricing. The second chapter " How Do Consumers Respond to Nonlinear Pricing? Evidence from Household Water Demand" provides similar empirical evidence in residential water markets. In this paper, I exploit variation in residential water pricing in Southern California to examine how consumers respond to nonlinear pricing. Contrary to the standard predictions for nonlinear budget sets, I find no bunching of consumers around the kink points of their nonlinear price schedule. I then explore whether consumers respond to marginal price, expected marginal price, or average price when faced with nonlinear water price schedules. The price schedule of one service area was changed from a linear price schedule to a nonlinear price schedule. This policy change lead to an increase in marginal price and expected marginal price but a decrease in average price for many consumers. Using household-level panel data, I find strong evidence that consumers respond to average price rather than marginal or expected marginal price. Estimates of the short-run price elasticity for the summer and winter months are -.127 and -.097, and estimates of the long-run price elasticity for the summer and winter months are -.203 and -.154. I conclude with "The Effect of Cash Rewards on Energy Conservation: Evidence from a Regression Discontinuity Design" to examine the effect of an alternative form of nonlinear pricing that was developed to provide an explicit financial incentive for conservation. In the summer of 2005, California residents received a 20% discount on their summer electricity bills if they could reduce their electricity consumption by 20% relative to 2004. Nearly all households automatically participated in the program, but the eligibility rule required households to have started their electricity service by a certain cutoff date in 2004. This rule generated an essentially random assignment of the program among households that started their service right before and after the cutoff date. Using household-level monthly billing records from the three largest California electric utilities, I find evidence that the rebate incentive reduced consumption by 5% to 10% in the areas where summer temperature is persistently high and income-level is relatively low, but the estimated treatment effects are nearly zero in other areas. To save 1 kWh of electricity, the program cost 2 cents in inland areas, 91 cents in coastal areas, and 14.8 cents for all service areas.

This dissertation addresses several open issues in the economics surrounding the use of nonlinear pricing. The first chapter empirically examines the impact of the use of nonlinear pricing by wholesalers. The second chapter evaluates how firm profit depends on the number of prices offered in a nonlinear price schedule. Finally, the third chapter investigates the use of all-unit discounts as a price discrimination instrument. The first chapter exploits a unique data set of price schedules to provide the first empirical estimate of the welfare impact of second degree price discrimination in a market with double marginalization. Theoretical predictions in such a context are ambiguous. Quantity discounts at the wholesale level reduce costs for larger retailers, increasing efficiency. However, quantity discounts raise input costs for smaller retailers, increasing prices consumers may pay. The combined welfare effects on consumers umers depends on how much of input cost discounts are passed through to consumers and the distribution of retailer size. I develop and estimate a model of the New York State retail liquor market where wholesalers offer a multi-part nonlinear tariff for each product. The structural model is then used to estimate the welfare impact of restricting wholesale pricing to be linear. I find that banning quantity discounts reduces total welfare by approximately 14% on average. Consumer surplus and wholesaler profit decline by approximately 26% on average. Average retailer profit increases by a similar magnitude, though effects for a particular retailer are heterogeneous across retailer size. The second chapter examines the shape of observed price schedules more directly. Sellers often offer price schedules with relatively few segments rather than completely nonlinear price schedules which offer a unique price for each unit sold. By not offering a completely nonlinear, sellers are foregoing some additional profit in favor of a simpler pricing strategy. I find that the scale of these foregone profits is relatively small and only loosely related to product characteristics. When considered in percentage terms, foregone profits are very similar across a large number of products. This suggests that simple pricing strategies obtain almost all the profits available and this is a common property of nonlinear pricing strategies. The final chapter compares price discrimination through two different quantity discount mechanisms: all-unit discounts and incremental discounts. All-unit-discounts give consumers a lower marginal price on all units purchased once total purchase size crosses a threshold. Incremental discounts only provide discounts on units above the threshold. Relative to incremental discounts, all-unit-discounts imply higher marginal prices and bunching of purchase sizes in equilibrium. The equilibrium bunching may present a challenge for estimating the model empirically.

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What do phone rates, frequent flyer programs, and railroad tariffs all have in common? They are all examples of nonlinear pricing. Pricing is nonlinear when it is not strictly proportional to the quantity purchased. The Electric Power Research Institute has commissioned Robert Wilson to review the various facets of nonlinear pricing. The work starts with a general non-mathematical discussion, followed by a more technical presentation intended for readers with a fairly advanced background. Thorough and detailed, this study has ample examples of case studies from a variety of industries.

Die Chaostheorie erfreut sich in der Investmentbranche zwar großer Beliebtheit, aber bislang konnte niemand so recht sagen, wie man mit ihrer Hilfe Aktienkurse und Gewinne prognostizieren kann. Dieses Buch zeigt auf der Basis praktischer Methoden, daß Aktienkurse mit Hilfe der nichtlinearen Theorie zumindest teilweise vorhersehbar sind. Es wird anschaulich erläutert, wie verschiedene nichtlineare Techniken wie z.B. genetische Algorithmen, Fuzzy Logic und nichtlineare Dynamik anzuwenden sind. Hierbei läßt der Autor, der diese Methoden selbst gewinnbringend einsetzt, seine eigenen Erfahrungen mit einfließen. Das erste Buch zu diesem Thema, das reale, praxisnahe Anwendungen bietet. (01/99)

This dissertation addresses optimal linear and nonlinear pricing policy design for a monopolistic network service provider with various types of public and private information on user types. In the communication network pricing literature, it is the linear pricing schemes that have been largely adopted, and here we investigate both linear and nonlinear pricing within the framework of a hierarchical Stackelberg (leader-follower) game, where the service provider sets prices for the resources (bandwidth) he offers as the leader, and the users respond by their choices of the amount of bandwidth (flow) they are willing to pay for. At the lower level, the presence of congestion cost (negative network effect) in the net utility functions of users leads to a noncooperative game among themselves, with Nash or Bayesian equilibrium being natural candidates for a solution. In the nonlinear pricing case, the approach is to view the problem as a reverse Stackelberg game, which is also an incentive-design problem. We also consider, for both linear and nonlinear pricing, three different scenarios based on the information sharing structure for all parties on the users' true types, namely complete information, partially incomplete information, and totally incomplete information. For each case, we obtain the optimal, or near-optimal, pricing policy that maximizes the service provider's profit given the noncooperative price-taking behavior of the users, generally for the asymptotic case regarding the number of users, since our focus is on communication networks with a large user population. Comparative studies between linear and nonlinear pricing, as well as between the three classes of informational scenarios, are carried out to evaluate profit improvement by adoption of nonlinear pricing and the service provider's game preferences.