competition and price variation when consumers are loss averse we modify the salop 1979 model of price competition with differentiated products by assuming that consumers are loss averse relative to a reference point given by their recent expectations about the purchase consumers sensitivity to losses in money increases the price responsiveness of demand and hence the intensity of competition at higher relative to lower market prices reducing or eliminating price variation both within and between products when firms face common stochastic costs in any symmetric equilibrium the markup is strictly decreasing in cost even when firms face different cost distributions we identify conditions under which a focal price equilibrium where firms always charge the same focal price exists and conditions under which any equilibrium is focal

dynamic pricing strategies with reference effects we consider the dynamic pricing problem of a monopolist firm in a market with repeated interactions where demand is sensitive to the firm s pricing history consumers have memory and are prone to human decision making biases and cognitive limitations as the firm manipulates prices consumers form a reference price that adjusts as an anchoring standard based on price perceptions purchase decisions are made by assessing prices as discounts or surcharges relative to the reference price in the spirit of prospect theory we prove that optimal pricing policies induce a perception of monotonic prices whereby consumers always perceive a discount respectively surcharge relative to their expectations the effect is that of a skimming or penetration strategy the firm s optimal pricing path is monotonic on the long run but not necessarily at the introductory stage if consumers are loss averse we show that optimal prices converge to a constant steady state price characterized by a simple implicit equation otherwise the optimal policy cycles the range of steady states is wider the more loss averse consumers are steady state prices decrease with the strength of the reference effect and with customers memory all else equal offering lower prices to frequent customers may be suboptimal however if these are less sensitive to price changes than occasional buyers if managers ignore such long term implications of their pricing strategy the model indicates that they will systematically price too low and lose revenue our results hold under very general reference dependent demand models

are markets with loss averse consumers more sensitive to losses behavioral pricing and revenue management aim to incorporate realistic consumer behavior into firms pricing and inventory models the key input to these models is market demand which is often assumed to inherit the characteristics of consumer behavior as when for example one assumes that a market consisting of loss averse consumers is more responsive to losses than to gains yet market demand and consumer behavior need not be related and so we argue that approach to modeling market demand is misguided this paper proposes an approach that accounts for the heterogeneity in consumer valuation we aggregate the demand of individual loss averse consumers to obtain market demand and show that market demand may be more responsive to gains or losses or it may be equally responsive our results have profound implications not only for how best to characterize the market demand of behaviorally biased consumers but also for determining the firm s optimal pricing policy this paper was accepted by serguei net

tariff structure of japanese electric power companies an empirical analysis using dea this research explores a marginal cost mc based pricing system using data envelopment analysis dea this dea technique is widely applied for performance analysis and efficiency measurement in public and private sectors this article does not follow such a previous research direction rather directing itself towards the new measurement of mc and ramsey prices of multiple electric power services as an important case study this research applies the proposed dea approach to examine how much the current tariffs of japanese electric power services deviate from these mc and ramsey prices this type of research has never been explored in japan even though such a research effort is needed by many policy makers and consumers it is hoped that our empirical findings can serve as a policy making basis for guiding the japanese electric power industry this study believes that this japanese experience is useful for other nations such as asia pacific countries where many public industries are regulated by their governments

social welfare loss due to second best pricing an application to the portuguese telecommunications the telecommunications industry is usually characterized by low marginal costs and significant fixed costs which are the conditions for the inefficiency of marginal cost pricing in such cases theory postulates that optimal pricing is obtained by maximizing welfare subject to a restriction of viability of the firm the second best pricing scheme the possible welfare losses due to second best pricing varies according to the values of marginal costs prices and demand elasticities this paper analyses to what extent the second best pricing has been achieved in the portuguese telecommunications firm ctt over the period 1950 150 1984 as well as the magnitude of the price cost margins and welfare losses created we obtained empirical evidence of the presence of economies of scale a welfare loss estimate of 1 of the telecommunications receipts and a result that price was 40 greater than marginal cost we concluded that price regulation and public ownership of the firm did not seriously affect social welfar

the impact of heterogeneity in purchase timing and price responsiveness on estimates of sticker shock effects the notion that individuals have an internal reference price against which they compare observed prices is well supported by several psychological theories empirically several papers in the marketing literature employing scanner panel data have modeled the impact of reference prices on brand choice via the sticker shock formulation in which consumers evaluate choice alternatives using differences between shelf prices and reference prices most of the studies reported thus far have not accounted for heterogeneity in price response among consumers and have typically imputed reference prices from the shelf prices of brands that a consumer is supposed to have observed on previous purchases in the category since category marketing activity can differentially affect the purchase timing of households we argue that this measure of reference price may follow certain systematic patterns across consumers and when combined with unaccounted for price response heterogeneity may result in a spurious sticker shock effect specifically we show that estimates of sticker shock are biased upward if households that are price sensitive in the brand choice decision are also more responsive to category promotion activity in their purchase timing decision we discuss some general conditions under which the bias occurs and conduct a simulation experiment to confirm our specific hypotheses our simulation results show that changes in purchase timing are a critical determinant of the bias in the sticker shock effect we also show that unaccounted for price response heterogeneity can in itself result in a biased sticker shock parameter however this requires very large differences in price sensitivities across consumers far greater than what is normally observed we develop a hierarchical bayes version of the nested logit model which models heterogeneity via individual level parameters in a continuous random effects framework we estimate the model on scanner panel data from the yogurt and ketchup categories we find in both categories that the 95 probability interval of the posterior distribution of the mean sticker shock coefficient contains the value zero therefore at least for the data used in this study there is no evidence for the sticker shock effect at the aggregate level in contrast the corresponding coefficient from a standard model which ignores this heterogeneity is highly significant and supports the existence of a possibly spurious sticker shock effect consistent with our explanation of the underlying cause of the bias households that are more price sensitive in the choice decision are also found to be more responsive to category promotion activity in their decision to purchase in the category the results highlight the measurement problems associated with imputing reference prices from past prices since the frequency duration and price level of a retailer s promotional program depend on its size and prevalence accurate estimates of the sticker shock effect are essential for formulating optimal promotion strategies an adequate accounting of consumer heterogeneity is critical to this effort

strategic information manipulation in duopolies abstract this paper studies a duopoly market in which firms can draw inferences concerning uncertain market demand from observations of their outputs and market price firms may adjust their outputs away from myopically optimal levels to affect the informativeness of the market price because firms quantities are observed firms can manipulate the extent to which belief revision occurs rather than the direction in which beliefs are revised as in signal jamming models we develop conditions and present examples under which the value of information is positive and negative and under which firms will increase or decrease quantity to manipulate information journal of economic literature classification numbers d80 l13

optimal pricing of the portuguese telephone service a first attempt is made at finding the optimal two part tariff for portugese telephone service a theoretical model of consumer demand is presented and the two part tariff which maximizes social welfare is derived the model is then calibrated using portugese data and previous econometric studies the optimal long run two part tariff consists of an access charge that is close to twice the marginal cost of access and a usage charge 25 above the marginal cost of use the level of the optimal two part tariff depends mainly on the marginal cost of taxation and on an index of aversion to inequality the structure of the optimal two part tariff depends mainly on the ratio between the marginal consumer s usage level and the average usage level although the cost estimates are very tentative the results suggest that the 1986 usage charge was greater than optimum no similar conclusion can be drawn with respect to the acces charge

growth under uncertainty with experimentation abstract we introduce bayesian learning into a stochastic growth model and study the effect of experimentation on the optimal level of the investment decision and on the amount of information gathering when more investment produces more information experimentation can push towards a lower level of investment thus reducing information acquisition symmetrically when more investment reduces information experimentation can increase investment and again decrease information gathering these results run contrary to intuitions generated by the standard literature on experimentation

on the inefficiency of two part tariffs the partial equilibrium literature on two part tariffs suggests that if a commodity is produced under increasing returns efficiency can be achieved through marginal cost pricing and a suitable choice of entry fees fixed charge which may vary from consumer to consumer we show that this partial equilibrium intuition cannot be extended beyond some special cases even with a consumer specific fixed charge it is possible that none of the equilibria yield pareto efficiency furthermore it may be impossible to achieve pareto efficiency through any specification of taxes which are levied solely to cover losses hotelling 1939 and lerner 1944 among others see for example the surveys by ruggles 1949 1950 argued that firms operating under increasing returns to scale should be regulated to equate their marginal cost to the price of the output and the resulting losses financed through lump sum taxes being concerned primarily with efficiency issues the proponents of the marginal cost pricing principle did not advocate any particular distribution of the lump sum taxes among the consumers after the ensuing debate see for example ruggles 1950 there seems to have been a general agreement that marginal cost pricing is necessary for efficiency while admitting this coase 1946 presented an illuminating analysis of the drawbacks of what he called the hotelling lerner solution and also proposed an alternative solution it will be useful to begin by briefly recalling coase s criticism of the hotelling lerner solution apart from the practical problem of collecting lump sum taxes he emphasized two distinct drawbacks of the hotelling lerner scheme he claimed that this solution would not necessarily guarantee efficiency in the sense that it might lead to a marginal cost pricing equilibrium in which a positive amount of the commodity was produced whereas it would be better not to produce the commodity at all this can be restated simply as the argument that in the presence of non convexities marginal conditions need not guarantee global optimality there may be several marginal cost pricing equilibria some efficient and some inefficient as such this phenomenon can hardly be ruled out coase s second objection to the hotelling lerner solution was that it could effectively alter the income distribution if for instance a lump sum tax was imposed on all the consumers but only some of them consumed the commodity produced by the firm operating under increasing returns to scale then there would effectively be a redistribution in favour of those who consumed this subsidized commodity it was natural to keep the issue of efficiency separate from that of equity and coase argued that the hotelling lerner solution

learning experimentation and monetary policy abstract we present a model of monetary policy where the policymaker faces uncertainty about which he is learning in a bayesian fashion a fixed money supply rule is not optimal since the learning leads to adjustments in the monetary action we present cases in which it is optimal to bear some cost in terms of current output performance in order to gain information that can be used in the formulation of future monetary policy experimentation therefore pays we also show that even passive learning without experimentation still leads to an activist monetary policy i e one that is responsive to new information

empirical generalizations from reference price research considerable theoretical justification for consumers use of psychological reference points exists from the research literature from a managerial perspective one of the most important applications of this concept is reference price an internal standard against which observed prices are compared in this paper we propose three empirical generalizations that are well supported in the marketing literature first there is ample evidence that consumers use reference prices in making brand choices second the empirical results on reference pricing also support the generalization that consumers rely on past prices as part of the reference price formation process third consistent with other research on loss aversion consumers have been found to be more sensitive to losses i e observed prices higher than reference prices than gains we also propose topics for further research on reference prices

seigniorage and political instability the importance of seigniorage relative to other sources of government revenue differs markedly across countries this paper tries to explain this regularity by studying a political model of tax reform the model implies that countries with a more unstable and polarized political system will have more inefficient tax structures and thus will rely more heavily on seigniorage this prediction of the model is tested on cross sectional data for seventy countries the authors find that after controlling for other variables political instability is positively associated with seigniorage copyright 1992 by american economic association

inflation variability and gradualist monetary policy this paper considers the optimal approach to reducing inflation when the cost of inflation is its conditional variability inflation is stochastically related to money growth with unobservable time varying autonomous and induced components a sharp reduction in money growth provides information about the responsiveness of inflation to money but also induces variability as the economy heads into unknown territory gradual policy is always optimal and the model explains why moderate inflation countries adopt a much more gradual money growth reduction than high inflation countries additionally the analysis sheds light on the more general problem of learning with two unobservable parameters

income taxation public sector pricing and redistribution income taxation and public sector pricing are considered in an integrated control theory model of the mirrlees tradition it is shown that the often alleged separability between income taxation as a purely distributional instrument and public pricing as a purely allocational instrument usually does not hold rather in our model public prices have to resemble the distributionally modified public prices proposed by feldstein 1972 application of the fiscal policy instrument public pricing restricts the distributional task of income taxation our results differ considerably from the direct indirect taxation controversy because the assumption of constant returns to scale cannot be imposed in a model of public pricing

monetary policy as a process of search monetary policymakers are uncertain about the state of the economy and learn from the economy s reaction to policy private agents however anticipate any systematic attempt to incorporate this information into future policy the authors analyze this feedback in the context of a monetary authority s attempt to stimulate an economy in recession they show that modest stimuli may prove ineffectual if small reductions in interest rates are unlikely to promote a response then they may be followed by further cuts a vicious circle develops in which the expectation that the policy could fail leads investors to delay investment thereby promoting failure copyright 1996 by american economic association

temporary acceleration of inflation what can a central bank learn from it in this article i present a model in which the monetary authority conducts policy by setting money supply in the presence of uncertainty and bayesian learning about the economic environment i find that there exists a set of assumptions under which a temporary acceleration of money growth and thus of inflation increases the government s overall expected utility there also exists a set of assumptions under which a temporary deceleration of money growth and thus of inflation increases the govern ment s overall expected utility

an informational externality in a competitive market abstract consider a new competitive market with unknown demand the market price generated by incumbents conveys information that firms including potential entrants use for future decisions yet the incumbents are not rewarded for their assistance suggesting that an inefficiency can exist it has been argued that greater entry generates more information about a new market and should be subsidized a simple model of partial information and learning is developed finding that an informational externality can exist in competitive markets but there may be excessive entry free entry and a public price conditions for competitive market efficiency are conditions for inefficiency

explicit solutions of optimization models and differential games with nonsmooth asymmetric reference price effects models in marketing with asymmetric reference effects lead to nonsmooth optimization problems and differential games which cannot be solved using standard methods in this study we introduce a new method for calculating explicitly optimal strategies open loop equilibria and closed loop equilibria of such nonsmooth problems application of this method to the case of asymmetric reference price effects with loss aversive consumers leads to the following conclusions 1 when the planning horizon is infinite after an introductory stage the optimal price stabilizes at a steady state price which is slightly below the optimal price in the absence of reference price effects 2 the optimal strategy is the same as in the symmetric case but with the loss parameter determined by the initial reference price 3 competition does not change the qualitative behavior of the optimal strategy 4 adopting an appropriate constant price strategy results in a minute decline in profits

the impact of reference price effects on the profitability of price promotions this paper investigates the impact of reference price effects on retailer price promotions and describes why these effects can make promoting profitable first we analyze the profit impact of reference price effects generated by a single period of promotion the promotion can increase profit if the gain that these effects create in the promotion period outweighs the loss they create in future periods we then describe how retailers can estimate the optimal strategy of recurring promotions that maximizes profits from reference price effects over a time horizon examples of such strategies are presented for a retailer selling a national brand of peanut butter we obtain insights into how promotion prices timing and profits are affected by changes in costs interest rates consumers reactions to reference price effects and error in estimates used in the model the retailer s optimal reaction to a trade deal is also examined this strategy involves a phase of increased promotion activity sandwiched between phases of decreased activity we explain these results using the effects described in the single period model

recurrent hyperinflations and learning we use a model of boundedly rational learning to account for the observations of recurrent hyperinflations in the 1980 s in a standard monetary model we replace the assumption of full rational expectations by a formal definition of quasi rational learning the model under learning matches some crucial stylized facts observed during the recurrent hyperinflations experienced by several countries in the 1980 s remarkably well we argue that despite being a small departure from rational expectations quasi rational learning does not preclude falsifiability of the model it does not violate reasonable rationality requirements and it can be used for policy evaluation

optimal pricing of local telephone service although payment for nearly all other goods and services including toll long distance telephone calls increases with greater consumption nearly 90 percent of the residential telephone subscribers and more than half the business subscribers in the united states now pay a flat monthly rate for local calls see larry garfinkel recently however the telephone companies and regulatory commissions have been moving cautiously toward imposing usage charges for local telephone calls there is renewed interest in what is currently termed usage sensitive pricing t usp it is due to the combined forces of inflation increased local usage and competition from independent firms that sell telephone terminal equipment and supply private toll lines to business customers under usp the pricing of such services as telephone installation directory assistance and minutes of calling is based on incremental rather than average costs since world war ii technological advances have benefited long distance far more than local telephone calling development in microwave communications coaxial cable satellites and waveguides have dramatically lowered the costs of long distance transmission in contrast the costs of local service have moved upward since the late 1960 s at a rate not far below the general price index see at t 1975 faced with a continuing stream of requests for local telephone rate increases state regulatory commissions are finding the concept of tying prices to usage increasingly attractive at t and some of the independent telephone carriers are beginning to test usp plans in several cities with flat rate tariffs increases in local calling add to carrier costs but not to their revenues the local calling rate per subscriber has increased by an average of 2 percent for the past seven years at t s chairman has stated we are moving more and more in the direction of usage sensitive pricing see washington star news p a12 and according to newspaper accounts of at t management documents the bell system plans to phase out flat rate telephone service and begin charging for each local call in major metropolitan areas in 1978 80 see seattle postintelligencer pp 1 10 still regulatory commissions consumer groups and the carriers themselves remain cautious about requiring usage sensitive tariffs for all subscribers the prospective gains from prices more closely related to costs are at least partially offset by the added costs of metering equipment and billing most telephone subscribers prefer flat rates according to bell system marketing surveys see garfinkel p 28 and it is by no means clear which groups of subscribers will be helped and which harmed by such revisions in local tariff structures will the poor end up paying more because they use their phones more should different prices be charged for calls at different times of day on what bases should the monthly and per call rates be determined the purpose of this paper is to sort out some of the questions of economic efficiency and equity that arise when changes are considered in the methods of pricing local telephone services in section i i construct a department of economics the rand corporation and the international institute of management berlin this study was supported under a grant from the john and mary r markle foundation i am indebted to walter s baer for numerous contributions to this paper to s c littlechild and patricia munch and to the managing editor and a referee of this review for critical and constructive review of a draft i have benefited as well from the comments and suggestions of james h alleman stanley m besen william s comanor john m drew leland l johnson john a kay edward d lowry carl pavarini john rolph ralph turvey and chris witze bryant mori assisted with the computer programming see my 1976 paper for a more extensive version of this paper which also discusses optimal flat rate and optimal peak load tariffs

an index of loss aversion to a considerable extent risk aversion as it is commonly observed is caused by loss aversion several indexes of loss aversion have been proposed in the literature the one proposed in this paper leads to a clear decomposition of risk attitude into three distinct components basic utility probability weighting and loss aversion the index is independent of the unit of payment the main theorem shows how the indexes of different decision makers can be compared through observed choices

asymmetric reference price effects and dynamic pricing policies we consider a group of frequently purchased consumer brands which are partial substitutes and examine two situations the first where the group of brands is managed by a retailer and second where the brands compete in an oligopoly we assume that demand is a function of actual prices and reference prices and develop optimal dynamic pricing policies for each situation in addition to researchers studying pricing strategy our results may interest retailers choosing between hi lo pricing and an everyday low price and manufacturers assessing whether to follow procter gamble s lead and replace a policy of funding consumer price reductions through trade deals with a constant wholesale price a reference price is an anchoring level formed by customers based on the pricing environment the literature suggests that demand for a brand depends not only on the brand price but also whether the brand price is greater than the reference price a perceived loss or is less than it a perceived gain the responses to gains and losses are asymmetric broadly speaking we find that when enough consumers weigh gains more than losses the optimal pricing policy is cyclical likewise when they weigh losses more than gains a constant price is optimal thus we provide a rationale for dynamic pricing which is quite distinct from the three explanations previously offered 1 decreasing unit variable costs due to learning effects 2 the transfer of inventory to consumers who face lower inventory holding costs than do retailers and 3 competitive effects our explanations apply even when the other explanations do not i e in mature product categories where learning effects are minimal when retailer inventories are minimized through the use of just in time policies and when competitive effects do not exist as in a monopoly greenleaf 1995 has shown numerically that in the presence of reference price effects the optimal pricing policy for a monopolist can be cyclical we first analytically extend greenleaf s result to a monopolist with a constant cost of goods facing a homogeneous market where all customers either weigh gains more than losses or vice versa using this building block we examine a monopolist retailer managing multiple brands we assume that demand is a linear function of prices of multiple brands and together with an expression which reflects the reference price effect further we assume that the retailer maximizes average profit per period next we analyze a duopoly and extend the results to an oligopoly we assume that the manufacturers are able to set the retail prices as in an integrated channel here we retain the same demand function as for the retailer and derive markov perfect nash equilibria we use two alternative processes of reference price formation the exponential smoothed es past price process which is frequently used in the literature and for the multi brand situations the recently proposed reference brand rb process hardie johnson and fader 1993 in the latter the reference price is the current price of the last brand bought the reference brand we adapt the individual level rb formulation in hardie et al to an aggregate demand specification for the es process we obtain most results analytically for the rb process we use simulation finally we extend our results to a population with two customer segments segment 1 which weighs gains more than losses and segment 2 which does the opposite i e is loss averse when the market consists exclusively of segment 1 customers and es is the reference price process we find that prices are cyclical in all cases analyzed i e for a monopoly a monopolist retailer managing multiple brands a duopoly and an oligopoly if the rb formulation is the underlying process a monopolist retailer managing two brands uses cyclical prices but in a duopoly the equilibrium solution is for the brands to maintain constant prices when all customers belong to segment 2 i e they are loss averse constant prices are optimal in all cases for both reference price formulations when the population consists of both segment 1 and segment 2 and the es process applies we develop a sufficient condition for cyclical pricing policies to be optimal the condition is expressed in terms of the proportion of the two segment sizes the absolute difference between the gain and loss parameters of each segment and their respective exponential smoothing constants interestingly for reasonable values of the latter two factors cyclical policies are optimal even when the proportion of segment 1 is quite small similar magnitudes are obtained numerically for the rb case

loss aversion under prospect theory a parameter free measurement agrowing body of qualitative evidence shows that loss aversion a phenomenon formalized in prospect theory can explain a variety of field and experimental data quantifications of loss aversion are however hindered by the absence of a general preference based method to elicit the utility for gains and losses simultaneously this paper proposes such a method and uses it to measure loss aversion in an experimental study without making any parametric assumptions thus it is the first to obtain a parameter free elicitation of prospect theory s utility function on the whole domain our method also provides an efficient way to elicit utility midpoints which are important in axiomatizations of utility several definitions of loss aversion have been put forward in the literature according to most definitions we find strong evidence of loss aversion at both the aggregate and the individual level the degree of loss aversion varies with the definition used which underlines the need for a commonly accepted definition of loss aversion