Second-best pricing for incomplete market segments: Application to electricity pricing

Due to technological, political, or practical considerations, most price mechanisms are not fully differentiated by time, location, and contingency of delivery. Rate or tax designers then face a trade-off between the costs and benefits of using more complex price schedules. This paper studies the second-best problem of designing, for a given market segment, a linear pricing schedule with a limited number of distinct prices while facing exogenous constraints within a large and practically relevant family. Interestingly, we find that second-best prices may be computed using simple machine learning techniques. As an illustration, we apply our framework to retail electricity pricing in California.     

Towards a complete real-time electricity market design

The general design for the real-time electricity market presented in this paper optimizes and prices both real and reactive power simultaneously in an AC setting, where all assets—generation, load and transmission—are allowed to bid and are financially settled at the locational price times energy consumed or produced. The result is that transmission lines are compensated for both capacity and admittance, providing incentives for efficient operation of transmission-related assets such as FACTS devices, if price-taking behavior is assumed. Losses are incorporated into the design and become an operating cost for transmission. The market design is shown to be revenue neutral and, under some assumptions, nonconfiscatory.      

Time-varying pricing may increase total electricity consumption: Evidence from Costa Rica

We study the implementation of a time-varying pricing (TVP) program by a major electricity utility in Costa Rica. Because of particular features of the data, we use recently developed understanding of the two-way fixed effects differences-in-differences estimator along with event-study specifications to interpret our results. Similar to previous research, we find that the program reduces consumption during peak-hours. However, in contrast with previous research, we find that the program increases total consumption. With a stylized economic model, we show how these seemingly conflicted results may not be at odds. The key element of the model is that previous research used data from rich countries, in which the use of heating and cooling devices drives electricity consumption, but we use data from a tropical middle-income country, where very few households have heating or cooling devices. Since there is not much room for technological changes (which might reduce consumption at all times), behavioral changes to reduce consumption during peak hours are not enough to offset the increased consumption during off-peak hours (when electricity is cheaper). Our results serve as a cautionary piece of evidence for policy makers interested in reducing consumption during peak hours—the goal can potentially be achieved with TVP, but the cost is increased total consumption     

Household response to dynamic pricing of electricity: a survey of 15 experiments

Since the energy crisis of 2000–2001 in the western United States, much attention has been given to boosting demand response in electricity markets. One of the best ways to let that happen is to pass through wholesale energy costs to retail customers. This can be accomplished by letting retail prices vary dynamically, either entirely or partly. For the overwhelming majority of customers, that requires a change out of the metering infrastructure, which may cost as much as $40 billion for the US as a whole. While a good portion of this investment can be covered by savings in distribution system costs, about 40% may remain uncovered. This investment gap could be covered by reductions in power generation costs that could be brought about through demand response. Thus, state regulators in many states are investigating whether customers will respond to the higher prices by lowering demand and if so, by how much. To help inform this assessment, this paper surveys the evidence from the 15 most recent pilots, experiments and full-scale implementations of dynamic pricing of electricity. It finds conclusive evidence that households respond to higher prices by lowering usage. The magnitude of price response depends on several factors, such as the magnitude of the price increase, the presence of central air conditioning and the availability of enabling technologies such as two-way programmable communicating thermostats and always-on gateway systems that allow multiple end-uses to be controlled remotely. In addition, the design of the studies, the tools used to analyze the data and the geography of the assessment influence demand response. Across the range of experiments studied, time-of-use rates induce a drop in peak demand that ranges between 3 and 6% and critical-peak pricing (CPP) tariffs induce a drop in peak demand that ranges between 13 and 20%. When accompanied with enabling technologies, the latter set of tariffs lead to a reduction in peak demand in the 27–44% range.     

Nodal pricing of electricity: how much does it cost to get it wrong?

Economists know how to calculate optimal prices for electricity transmission. These are rarely applied in practice. This paper develops a 13-node model of the transmission system in England and Wales, incorporating losses and transmission constraints. It is solved with optimal prices, and with uniform prices for demand and for generation, re-dispatching when needed to take account of transmission constraints. Moving from uniform prices to optimal nodal prices could raise welfare by 1.3% of the generators’ revenues, and would be less vulnerable to market power. It would also send better investment signals, but create politically sensitive regional gains and losses.      

Dynamic pricing of electricity in the mid-Atlantic region: econometric results from the Baltimore gas and electric company experiment

The Baltimore Gas and Electric Company (BGE) undertook a dynamic pricing experiment to test customer price responsiveness to different dynamic pricing options. The pilot ran during the summers of 2008 and 2009 and was called the Smart Energy Pricing (SEP) Pilot. In 2008, it tested two types of dynamic pricing tariffs: critical peak pricing (CPP) and peak time rebate (PTR) tariffs. About a thousand customers were randomly placed on these tariffs and some of them were paired with one of two enabling technologies, a device known as the Energy Orb and a switch for cycling central air conditioners. The usage of a randomly chosen control group of customers was also monitored during the same time period. In 2009, BGE repeated the pilot program with the same customers who participated in the 2008 pilot, but this time it only tested the PTR tariff. In this paper, we estimate a constant elasticity of substitution (CES) model on the SEP pilot’s hourly consumption, pricing and weather data. We derive substitution and daily price elasticities and predictive equations for estimating the magnitude of demand response under a variety of dynamic prices. We also test for the persistence of impacts across the two summers. In addition, we report average peak demand reduction for each of the treatment cells in the SEP pilot and compare the findings with those reported from earlier pilots. These results show conclusively that it is possible to incentivize customers to reduce their peak period loads using price signals. More importantly, these reductions do not wear off when the pricing plans are implemented over two consecutive summers. Our analyses reveal that SEP participants reduced their peak usages in the range of 18 to 33% in the first summer of the SEP pilot and continued these reductions in the second summer.     

Using real-time electricity data to estimate response to time-of-use and flat rates: an application to emissions

Using a generalized McFadden specification, we estimate the determinants of hourly response for the years 2006 through 2010 for all 16 standard retail customers who were on an optional real-time electricity rate offered by Duke Energy as of 2010, and provide a method to estimate how these customers would respond to time-of-use (TOU) and flat rates. We generalize the model to allow for inter-day response, as well as threshold prices, above which individual customer response may increase or decrease. With these inclusions, we find hourly elasticity for the group of customers to be as large as ?0.7, larger than previous studies. We apply the method to examine a recent finding that time-differentiated rates could increase electric utility emissions. However, that result did not differentiate between real-time and TOU rates, and furthermore held energy use constant in comparing flat rates and time-differentiated rates. We perform a case study to examine emissions of SO₂, NOx, Hg, and CO₂ based on predicted energy use changes as well as for an energy-neutral case for real-time, TOU and flat rates. Employing energy use predictions from the model, increased energy use results in increased emissions in almost all cases. For the energy-neutral case, time-differentiated rates increase CO₂ as compared to flat rates, and the TOU rate causes a larger increase than does real-time pricing. But both rates decrease other emissions in the majority of years, particularly SO₂ In addition, time-differentiated rates reduce NOx potency by shifting it to non-daylight hours when conditions for the formation of smog are less favorable. Our application leads to the conclusion that the effect of the rates on emissions must consider total energy use as well as the shift from peak to off-peak. Furthermore, the predictions require consideration of the generating mix at a more detailed level than was contained in previous studies.     

Responsive pricing

We study the efficiency property of responsive pricing, a scheme that proposes to increase prices as a function of the level of capacity utilization in environments where traditional allocation schemes (e.g. competitive markets, non-linear pricing) cannot be implemented in practice. We show that although responsive pricing implements allocations that are arbitrarily close to full capacity utilization (no wasted capacity and no excess demand), these allocations are not always efficient. We identify conditions under which efficiency occurs and discuss implications for the use of responsive pricing. We would like to thank seminar participants at the LSE, Venezia, Toulouse, and Copenhagen as well as Piero Gottardi, Karel Mertens, Marco Ottaviani, Markus Poschke, Karl Schlag, and Sanne Zwart for useful comments.     

软件产品定价的常见问题及定价策略

本篇文章首先对软件产品定价方式进行阐述,从定价模式问题、价格变动问题、定价针对性问题等多个方面,对软件产品定价的常见问题进行分析,并以此为依据,提出软件产品定价策略。     

Average cost pricing versus marginal cost pricing under moral hazard

This paper presents a general framework for analyzing shadow wages in LDCs. We focus on (i) the differences between the domestic and international prices, (ii) the equilibrating mechanisms in the economy, (iii) the endogeneity of earnings in industry and agriculture, (iv) the consequences of industrial employment creation on agriculture, and (v) the nature of migration and unemployment.We identify those reduced form relationships which are central in determining the shadow wage, and use them to obtain general formulae for the shadow wage. These formulae can be specialized to alternative technological, behavioral, and institutional settings. This yields many new results concerning the relationship between the shadow wage and the market wage. Also, earlier results on shadow wages are derived as special cases of our formulae.     

Strategic nonlinear pricing

The objective of this paper is to examine the role of nonlinear strategies in a standard oligopoly framework. We demonstrate that nonlinear pricing may indeed emerge as an equilibrium strategy, but only when firms produce differentiated products, when one firm retains market power due to a cost advantage, or as part of an equilibrium in mixed strategies. In addition, we examine the role of nonlinear pricing in a spatial-competition framework. Our main conclusion is that in highly competitive markets, nonlinear pricing strategies are not likely to emerge as an equilibrium.     

Robust monopoly pricing

We consider a robust version of the classic problem of optimal monopoly pricing with incomplete information. In the robust version, the seller faces model uncertainty and only knows that the true demand distribution is in the neighborhood of a given model distribution. We characterize the pricing policies under two distinct decision criteria with multiple priors: (i) maximin utility and (ii) minimax regret. The equilibrium price under either criterion is lower then in the absence of uncertainty. The concern for robustness leads the seller to concede a larger information rent to all buyers with values below the optimal price without uncertainty.     

Cooperative oligopolistic pricing

The main purpose of the present paper is to show that the equilibrium price in an oligopolistic market with cooperative pricing but noncooperative production as a rule approaches neither the monopoly price (when there are few firms) nor the competitive price (when there are many firms). Instead it is equal to that price which maximizes collective sales revenues if the industry's demand curve is inelastic, while it is “almost” competitive if demand is elastic.