rational panics and stock market crashes abstract this paper offers an explanation for stock market crashes which focuses on the role of rational but uninformed traders we show that uninformed traders can precipitate a price crash because as prices decline they surmise that informed traders received negative information which leads them to reduce their demand for assets and drive the price of stocks even lower the model yields several implications such as that crashes can occur even when the fundamentals are strong and that the magnitude of the crash depends on the fraction of uninformed investors and the amount of unsophisticated passive investing present in the market

input market price discrimination and the choice of technology recent concerns over the effects of the robinson patman act and so called priceprotection policies such as most favoredcustomer clauses mfc s 2 on market performance have given economists new reasons to examine the welfare effects of third degree price discrimination in order to assess these effects correctly it is imperative that one understand how price discrimination influences market behavior joan robinson s 1933 work launched the formal inquiry into the welfare effects of third degree price discrimination building on the intuition presented by arthur pigou 1932 she showed that if a monopolist faces two independent linear demand curves the use of price discrimination will not affect industry output but will reduce welfare richard schmalensee 1981 extends these results to nonlinear demand curves and shows that an increase in total industry output is a necessary condition for price discrimination to be welfare improving hal varian 1985 broadens these results by deriving upper and lower bounds on the welfare change due to the use of price discrimination he shows that these results can be applied to markets in which there are nonzero cross price effects all of this work examines how the ability of a monopolist to price discriminate will affect the market outcome when all other characteristics of the market are treated as exogenous recently two lines of research have extended this inquiry beyond the case of a monopolist in a market with exogenously fixed parameters the first line considers the case of oligopoly the work of charles holt and david scheffman 1985 and thomas cooper 1986 has shown that restrictions on price discrimination imposed by the use of mfc s can facilitate collusion between oligopolists attempting to restrict output this implies that third degree price discrimination can be welfare improving the second line of research shows that price discrimination by a firm can affect nonprice decisions made by other market participants thus affecting the market outcome michael katz 1987 presents a model in which a large firm s ability to vertically integrate backward into the production of an input allows it to obtain a lower per unit price from the supplier of the input than can be obtained by smaller firms without this ability he shows that third degree price discrimination reduces welfare unless it prevents inefficient backward integration degraba 1987 shows that the use or nonuse of price discrimination by a national firm can affect nonprice decisions made by local firms that compete with the national firm in this situation third degree price discrimination is welfare reducing because it induces local firms to produce a product that is overly differentiated from the product of the national firm in all of the work cited above price discrimination is important when sellers set prices in separate markets or charge different prices to different customers in the same market the following analysis which can be considered a contribution to the second line of research suggests that price discrimination can be important even when a seller faces a single market in which all customers are identical the intuition behind this result is that nonprice decisions made by downstream producers such as the choice of technology can be affected by the use or johnson graduate school of management cornell university ithaca ny 14853 i thank robert frank robert smiley richard thaler and the participants of the jgsm applied microeconomics workshop for their helpful comments see william baldwin 1987 pp 438 40 for a good summary of the debate 2see john kwoka and lawrence white 1989 pp 196 7

security analysis and trading patterns when some investors receive information before others in existing models of information acquisition all informed investors receive their information at the same time this article analyzes trading behavior and equilibrium information acquisition when some investors receive common private information before others the model implies that under some conditions investors will focus only on a subset of securities herding while neglecting other securities with identical exogenous characteristics in addition the model is consistent with empirical correlations that are suggestive of oft cited trading strategies such as profit taking short term position reversal and following the leader mimicking earlier trades in existing models of information acquisition all informed investors receive their information at the same time while these models provide many important insights in reality some investors either fortuitously or owing to superior skill acquire pertinent information before others by being first an investor can exploit this information to great advantage information that is uncovered only slightly later is less valuable even if it has not yet been publicly revealed we show in this article that the sequential nature of information arrival has a significant effect on both the trading decisions and the types of information collected by investors the model we develop describes the investment choices of a set of competitive risk averse investors who investigate the long term prospects of firms lucky or high ability investors uncover the

the welfare effects of third degree price discrimination in the author examines third degree price discrimination by an upstream monopolist in an intermediate good market discrimination is motivated by the fact that downstream firms differ in their abilities to integrate backward into supply of the input the author shows that under reasonable specifications of equilibrium price discrimination leads to all buyers facing higher input prices in other cases discrimination raises some prices and lowers others the author derives conditions under which discrimination lowers welfare by reducing total output and shows that in some markets discrimination will raise welfare by preventing socially inefficient backward integration copyright 1987 by american economic association

mean variance portfolio selection of cointegrated assets abstract this paper considers the continuous time mean variance portfolio selection problem in a financial market in which asset prices are cointegrated the asset price dynamics are then postulated as the diffusion limit of the corresponding discrete time error correction model of cointegrated time series the problem is completely solved in the sense that solutions of the continuous time portfolio policy and the efficient frontier are obtained as explicit and closed form formulas the analytical results are applied to pairs trading using cointegration techniques numerical examples show that identifying a cointegrated pair with a high mean reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long term equilibrium we propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean reversion speed based on the mean variance paradigm an empirical example is given to illustrate the use of the theory in practice

public disclosure private information collection and short term trading abstract this paper examines how public disclosure affects private inforamtion acquisition activity in a market economy we analyze a setting where traders with short term investment horizons are allowed to trade on their private information prior to a public disclosure we demonstrate in this setting that public disclosure stimulates investment in private information acquisition this result is shown to have implications for the magnitude of the pre announcement and announcement price reactions to the disclosure

continuous time mean variance asset allocation a time consistent strategy abstract we develop a numerical scheme for determining the optimal asset allocation strategy for time consistent continuous time mean variance optimization any type of constraint can be applied to the investment policy the optimal policies for time consistent and pre commitment strategies are compared when realistic constraints are applied the efficient frontiers for the pre commitment and time consistent strategies are similar but the optimal investment strategies are quite different

insider trading outside search and resource allocation why firms and society may disagree on insider trading restrictions we show that entrepreneurs may prefer to allow insider trading even when it is not socially optimal we examine a model in which an insider manager allocates resources on the basis of his private information and outside information conveyed through the secondary market price of the firm s shares if the manager is allowed to trade he will compete with informed outsiders reducing the equilibrium quality of outside information while the benefits to production of outside information are the same for society and entrepreneurs we show that the social and private costs are different thus entrepreneurs and society may disagree on the conditions under which insider trading restrictions should be imposed article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

imperfect competition in a multi security market with risk neutrality the central purpose of this paper is to develop a model of insider trading i e trading based on private information in the context of an imperfectly competitive multi security market with risk neutral agents imperfect competition allows us to consider strategic behavior and a multi security market lets us study the effect of a correlated environment on equilibrium we employ the informational assumption that market makers can observe all order flows and so portfolio diversification arises in this model for strategic reasons given correlated fundamentals market makers can potentially learn about every security from each order flow this causes even a risk neutral trader who does not face short selling restrictions to refrain from determining the demand for each security independently this contrasts with traditional multi asset models which focus on the incentive to reduce portfolio variance or the effect of short selling restrictions or budget constraints under imperfect competition correlation has two effects one ceteris paribus it allows the uninformed to learn from additional variables since each order flow could potentially have information about all payoffs on the other hand it creates an incentive for informed traders to restrict what others can learn from public information thus our analysis can be viewed as an application to the multi security heterogeneous information model in admati 1985 of the imperfectly competitive equilibrium concept which kyle 1985 first applied to the single security homogeneous information model of grossman and stiglitz 1980 our principal results include an explicit characterization of a linear equilibrium as a function of three general covariance matrices associated with payoffs noise trading and errors in private signals under general covariance structures we show that there always exists an equilibrium in which the relationship between the vector of prices and the vector of order flows is governed by a symmetric positive definite matrix the plan of the paper is as follows in section 2 we introduce our model we derive the equilibrium in section 3 and section 4 comments on the properties of the equilibrium the proofs of the results are in the appendix

risk aversion liquidity and endogenous short horizons we analyze a competitive model in which different information signals get reflected in value at different points in time if investors are sufficiently risk averse we obtain an equilibrium in which all investors focus exclusively on the short term in addition we show that increasing the variance of informationless trading increases market depth but causes a greater proportion of investors to focus on the short term signal which decreases the informativeness of prices about the long run finally we also explore parameter spaces under which long term informed agents wish to voluntarily disclose their information article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

crowding out and the informativeness of security prices individual investors trade less agressively on any particular piece of information as more investors observe it the trades of the new investors observing a piece of information crowd out some of the trades of the old investors who observe that same piece of information this paper shows that when traders are risk averse these crowding out effects lead the proportions of traders who choose to observe one signal versus another to differ from the proportions that maximize the informativeness of prices one of the principal functions of security markets is to provide incentives for individuals to collect economically relevant information and then to incorporate this information into pricing this paper shows that the presence of multiple types of information can have a major impact on investors incentives to acquire information and the informativeness of the resulting security price specifically the model studies the case in which there are two factors a and b whose sum is the asset s payoff and a fixed pool of investors each of which is about to choose whether to learn a or to learn b the paper addresses the question will the proportion of investors who choose to learn a in equilibrium maximize the security price s ability to predict terminal value the paper finds that when traders are risk averse the answer is no and that there is a clear economic interpretation for the forces which push the equilibrium allocation of information away from the allocation which maximizes price informativeness the paper also finds strikingly different results for risk neutral and riskaverse investors this suggests that intuitions gained from models with risk neutral strategic traders1 may not be robust to situations with riskaverse investors

the numeraire portfolio abstract a portfolio formed from a given list of assets is defined as a numeraire portfolio for the list if a it is self financing b its value is always positive and c zero is always the best conditional forecast of the numeraire dominated rate of return of every asset on the list the numeraire portfolio exists if and only if there are no profit opportunities from trading assets on the list for a sample list of heterogeneous assets nyse size quintile portfolios corporate bonds and short term bills numeraire dominated returns are similar to market model forecast errors and as abnormal return measures clearly dominate market adjusted returns

ownership structure speculation and shareholder intervention an institution holding shares in a firm can use information about the firm both for trading speculation and for deciding whether to intervene to improve firm performance intervention increases the value of the institution s existing shareholdings but intervention only increases the institution s trading profits if it enhances the precision of the institution s information relative to that of uninformed traders thus the ability to speculate can increase or decrease institutional intervention we examine key factors that affect the intervention decision the usefulness of short swing provisions and restricted shares in encouraging institutional intervention and implications for ownership structure across different firms institutional investors hold an ever greater fraction of corporate america s equity traditionally these institutions were stock pickers who tried to beat the market through trading if a firm whose stock they held seemed headed for trouble these investors headed for the door the wall street rule more recently some of these institutions have been using the ownership rights attached to their shares to pressure firms to act in the shareholders interest some have even argued that there is a synergy between gathering information for use in trading shares speculation and intelligently pressuring firms to improve performance intervention we argue that these motives can also conflict analyzing these motives allows us to predict which firms are most likely to attract institutional intervention which in turn has crosssectional implications for firm ownership structure recent examples suggest that institutional investors with large stakes sometimes intervene and sometimes follow the wall street rule so that there is indeed a choice to be studied in the early 1990s there was a wave of activism by a variety of large institutional investors among them calpers the california public employees pension fund putnam management a mutual fund manager and j p morgan a bank holding company these institu

distinguishing panics and information based bank runs welfare and policy implications in this paper we contrast panics and information based bank runs in an effort to provide a robust and empirically plausible model of how bank runs are triggered the model of information based runs is characterized by two sided asymmetric information the bank cannot observe the true liquidity needs of the depositors while depositors are asymmetrically informed about bank asset quality we also examine the relative degrees of risk sharing provided by bank deposit contracts and traded equity contracts we show that the choice of deposit or equity depends on the attributes of and information about the underlying investment returns

endogenous market thinness and stock price volatility thin equity markets cannot accommodate temporary bulges of buy or sell orders without large price movements the resulting volatility can induce risk averse transactors who face transaction costs to desert these markets thus thinness and the related price volatility may become joint self perpetuating features of an equity market irrespective of the volatility of asset fundamentals if however appropriate incentive schemes are adopted to encourage entry by additional investors this vicious circle can be broken eventually shifting the market to a selfsustaining superior equilibrium characterized by a higher number of transactors lower price volatility and larger supply of the asset a number of empirical studies cohen et al 1976 telser and higimbotham 1977 pagano 1986 tauchen and pitts 1983 have found that thin speculative markets are ceteris paribus more volatile than deep ones a plausible explanation for this finding is that thin markets are generally characterized by small numbers of transactors per unit time and thus their prices are more sensitive to the impact of individual traders demand shocks conversely in deep markets transactors are so many that the uncorrelated demand shocks experienced by individual traders tend to offset each other and leave market prices largely unaffected while this suggests a rationale for the observed relationship between market size and price volatility it does so by taking market size as the exogenous factor however the volatility of a speculative market may feed back on its size in the sense that the high liquidation risk implied by very volatile prices can induce potential entrants to keep out of the market this paper shows that in a stock market with transaction costs this interaction between thinness and volatility can produce multiple steady state equilibria some characterized by low trade and high volatility and others by high trade and low volatility whether the market will settle in one equilibrium or another depends entirely on the expectations held by economic agents sections 2 and 3 the existence of these multiple bootstrap equilibria can be explained heuristically as follows each additional trader generates a positive externality for other actual or potential traders by decreasing the riskiness of the stock lower risk in turn tends to attract more investors with the effect of raising stock prices and inducing corporations to issue additional equity we thus have a feedback loop between market size and price volatility where market size is measured both along the dimension of the number of traders and along that of the total stock of equities if however investors face transactions costs in the stock market this positive feedback may fail to be operative if the volume of trade is expected to be small investors with relatively high transaction costs will abstain from trading thus the market

price discrimination and social welfare studies the effect of price discrimination on social welfare using methods from duality theory features of the reservation model presented quasi linear utility and consumers surplus upper and lower bounds on welfare change bounds on welfare change with optimal price discrimination from ebsco

should speculators be taxed a number of economists have supported the taxation of speculation in financial markets we examine the welfare economics of such a tax in a model of a financial market where some agents have superior information and others have a hedging motive we show that a tax on speculators may actually increase speculative profits this occurs if the speculators benefit from less informative prices offsets the cost of the tax the effect on the welfare of other agents depends on how information revelation changes risk sharing opportunities it is possible for the introduction of a tax to cause a pareto improvement copyright 2000 by university of chicago press

optimal consumption and portfolio policies when asset prices follow a diffusion process abstract we consider a consumption portfolio problem in continuous time under uncertainty a martingale technique is employed to characterize optimal consumption portfolio policies when there exist nonnegativity constraints on consumption and on final wealth we also provide a way to compute and verify optimal policies our verification theorem for optimal policies involves a linear partial differential equation unlike the nonlinear partial differential equation of dynamic programming the relationship between our approach and dynamic programming is discussed we demonstrate our technique by explicitly computing optimal policies in a series of examples in particular we solve the optimal consumption portfolio problem for hyperbolic absolute risk aversion utility functions when the asset prices follow a geometric brownian motion the optimal policies in this case are no longer linear when nonnegativity constraints on consumption and on final wealth are included by these examples one can see that our approach is much easier than the dynamic programming approach

the effect of public information and competition on trading volume and price volatility in a one period model of market making with many exogenously informed traders we first show that the variance of prices and expected trading volume depend on the public information released at the start of trading this is accomplished by representing beliefs with elliptically countoured distributions for which the form of optimal decision rules does not depend on the specific distribution used second if the model is altered so that the decision to become informed is made endogenous then the decision rules of the market maker and infomed traders depend on the public information third in a multiperiod model with many informed traders and long lived private information recursion formulas similar to those of kyle 1985 hold for all elliptically contoured distributions trading volume is autocorrelated and unless per period liquidity trading is bounded away from zero as new trading periods are added informed traders profits vanish article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

price and trading volume reaction surrounding earnings announcements a closer examination the process of information dissemination and interpretation in securities markets is very complex and mostly unobservable while changes in prices and the amount of trading that takes place at the market level provide evidence of information processing verrecchia 1981 demonstrated that these are not sufficient to describe completely the dissemination of information and its interpretation by investors a descriptive study of price changes and trading volume however may still provide some insights into how investors react to information this paper is an empirical investigation of price changes and trading volume during the days surrounding the announcement of quarterly and annual earnings in the wall street journal wsj in the original paper investigating trading volume and price changes surrounding earnings announcements beaver 1968 was primarily concerned with whether the annual earnings announcement had information content i e led to changes in investors assessments of the probability distribution of future returns if there were any significant price changes and or trading volume during the week of the announcement then the annual earnings announcement was assumed to have had

dynamic asset allocation with mean variance preferences and a solvency constraint abstract the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed and a solvency constraint wealth positiveness is imposed at each point in time under very general assumptions ito processes for the security price dynamics those efficient strategies are identified as synthetic put options on the particular inefficient portfolio yielding the return with minimal second moment this general characterization allows us to derive a closed form formula for the optimal portfolio weights when the investment opportunity set is constant the optimal weights are explicit functions of the current market index the formula is then used to simulate dynamically efficient strategies for different horizons and targets and to describe the time pattern of the allocation to stocks versus bonds

information sales and insider trading with long lived information fundamental information resembles in many respects a durable good hence the eects of its incorporation into stock prices depend on who is the agent controlling its flow similarly to a durable goods monopolist a monopolistic analyst selling information intertemporally competes against herself this forces her to partially relinquish control over the information flow to traders conversely an insider solves the intertemporal competition problem through vertical integration thus exerting a tighter control over the flow of information comparing market patterns i show that a dynamic market where information is provided by an analyst is thicker and more informative than one where an insider trades

dynamic asset allocation in a mean variance framework the aim of this article is to analyze the portfolio strategies that are mean variance efficient when continuous rebalancing is allowed between the current date 0 and the horizon t under very general assumptions when a zero coupon bond of maturity t exists the dynamic efficient frontier is a straight line the slope of which is explicitly characterized every dynamic mean variance efficient strategy can be viewed as buy and hold combinations of two funds the zero coupon bond of maturity t and a continuously rebalanced portfolio an appropriate dynamic strategy defining the latter is explicitly derived for two particular price processes and comparisons of the efficient frontiers static versus dynamic are provided in these cases

price discrimination and efficient distribution this paper focuses on third degree price discrimination by an upstream firm with some degree of monopoly power downstream firms fall into two categories efficient and inefficient according to their relative costs of transforming a unit of the upstream good into a unit of final product under ordinary static conditions price discrimination favors the inefficient firms which have more elastic demands we consider however the possibility that discrimination in the opposite direction can alter the downstream market structure toward greater efficiency discriminatory pricing then involves charging a higher price to the less efficient firms such pricing is shown to be both potentially profitable for the upstream firm and welfare improving as average consumer prices fall

stock price manipulation it is generally agreed that speculators can make profits from insider trading or from the release of false information both forms of stock price manipulation have now been made illegal in this article the authors ask whether it is possible to make profits from a different kind of manipulation in which an uninformed speculator simply buys and sells shares they show that in a rational expectations framework where all agents maximize expected utility it is possible for an uninformed manipulator to make a profit provided investors attach a positive probability to the manipulator being an informed trader article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

the dartboard column second hand information and price pressure this study analyzes the effect of second hand information on the behavior of security prices and volume using analysts recommendations published in the monthly dartboard column of the wall street journal for the two days following the publication of the recommendations average positive abnormal returns of 4 percent nearly twice the level of abnormal returns documented in previous research on analyst recommendations and average volume double normal volume levels on the two days following publication of the recommendations are documented the positive abnormal return on announcement is partially reversed within 25 trading days the authors conclude that the positive abnormal return on announcement of the recommendations is a result of naive buying pressure as well as the information content of the analysts recommendations

market response to financial reports abstract a two date rational expectations model is analyzed at the first date traders can privately acquire a costly signal that provides imperfect information about a public report that will be issued at the second date equilibrium characterizations are provided for the fraction of traders that become informed and the informativeness of the first date price as well as the price change variance and the expected trading volume at the second date comparative statics identify how the above variables are influenced by changes in the information content of the public report and in particular how market phenomena at the public release date are influenced by endogenous prior information acquisition and trading in response to the forthcoming public release

short term investment and equilibrium multiplicity abstract i study the effects of the heterogeneity of traders horizons in a 2 period nree model where all traders are risk averse owing to risk premia short termism generates multiple equilibria in particular two distinct patterns arise along the low trading intensity equilibrium short termists anticipate a thinner second period market and owing to risk aversion scale back their trades this reduces both risk sharing and information impounding into prices enforcing a high returns volatility low price informativeness equilibrium along the high trading intensity equilibrium the opposite happens and a low volatility high price informativeness equilibrium arises thus in the presence of short term behavior and traders risk aversion periods of high volatility are a signal of poor price informativeness

dynamic asset allocation for stocks bonds and cash closed form solutions for hara optimal portfolios are obtained in a dynamic portfolio optimization model in three assets stocks bonds and cash in a vasicek type model of stochastic interest rates with correlated stock prices the hara is a buy and hold combination of a zero coupon bond with maturity matching the investor s horizon and a crra mutual fund this simple characterization facilitates insights about investor behavior over time and provides explanations on the rational use of convex versus concave investment strategies the model illuminates clearly the role of the different market parameters and relative risk aversion in portfolio strategies

labor supply flexibility and portfolio choice in a life cycle model abstract this paper examines the effect of the labor leisure choice on portfolio and consumption decisions over an individual s life cycle the model incorporates the fact that individuals may have considerable flexibility in varying their work effort including their choice of when to retire given this flexibility the individual simultaneously determines optimal levels of current consumption labor effort and an optimal financial investment strategy at each point in his life cycle we show that labor and investment choices are intimately related the ability to vary labor supply ex post induces the individual to assume greater risks in his investment portfolio ex ante

differential information and dynamic behavior of stock trading volume this article develops a multiperiod rational expectations model of stock trading in which investors have differential information concerning the underlying value of the stock investors trade competitively in the stock market based on their private information and the information revealed by the market clearing prices as well as other public news we examine how trading volume is related to the information flow in the market and how investors trading reveals their private information article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

optimal hedging in a dynamic futures market with a nonnegativity constraint on wealth abstract this paper examines the issue of optimal hedging demands for futures contracts from an investor who cannot freely trade his portfolio of primitive assets in the context of lognormal rather than normal returns and of a constant absolute risk aversion utility function in this context the nonnegativity constraint on wealth is binding and the optimal hedging demands are not identical with those encountered in the bulk of the literature which has largely overlooked this problem negative results concerning the derivation of equilibrium in the futures markets and the computation of the open interests then follow

a minimum variance result in continuous trading portfolio optimization the problem of minimizing the variance of discounted wealth at the end of a fixed period is solved when the expectation of terminal wealth is constrained to a specified investment goal the results are obtained in a continuous trading framework under the assumption that the funds can be exchanged between a riskless bond and a stock whose discounted price is described by a geometric brownian motion transaction costs are ignored i e the market is frictionless and unlimited borrowing is permitted at the same rate as the return on the bond typically the optimal trading policy under the above assumptions involves a highly leveraged investment in the stock in the early stages followed by an accumulation of the bond in the later stages numerical results are provided as an illustration of the theory

long lived private information and imperfect competition we develop a multi period auction model in which multiple privately informed agents strategically exploit their long lived information we show that such traders compete aggressively and cause most of their common private information to be revealed very rapidly in the limit as the interval between auctions approaches zero market depth becomes infinite and all private information is revealed immediately these results are in contrast to those of kyle 1985 in which the monopolistic informed trader causes his information to be incorporated into prices gradually and when the interval between auctions is vanishingly small market depth is constant over time fama 1970 defines a strong form efficient market as one in which security prices fully reflect all available information including both publicly and privately held information in a pioneering and influential article kyle 1985 develops a model in which a single privately informed trader with long lived information optimally exploits his monopoly power over time kyle s 1985 main results are i the informed trader trades in a gradual manner so that his information is incorporated into prices at a slow almost linear rate and ii when auctions are held continuously the depth of the market is constant over time however kyle s 1985 assumption of a single informed trader is strong in the sense that in actual financial markets it is reasonable to expect that at least a few players will have access to private information and will trade in the knowledge that they will face competition with other informed agents in the market 1 we develop a multi period auction model in which multiple strategic informed traders optimally exploit their long lived informational advantage we thus explore the restrictiveness of kyle s assumption of a single informed trader and also examine

third degree price discrimination in linear demand markets effects on number of markets served and social welfare author affiliation victor kaftal department of mathematical sciences 839 c old chemistry building university of cincinnati cincinnati oh 45221 usa victor kaftal uc edudebashis pal department of economics 1204 crosley tower university of cincinnati cincinnati oh 45221 debashis pal uc edu corresponding author acknowledgment we are grateful to rick harbaugh laura razzolini david sappington and two anonymous reviewers debashis pal is also grateful to taft research center for financial support 1 introductiondoes monopolistic third degree price discrimination reduce social welfare the question has continued to intrigue economists and policy makers for more than half a century the seminal work of robinson 1933 shows that if a monopolist with a constant marginal cost sells in two distinct and independent markets having linear demands then welfare falls with third degree price discrimination almost half a century later schmalensee 1981 reexamines robinson s result and demonstrates that for any number of markets with linear demands third degree price discrimination lowers welfare schmalensee 1981 also establishes more generally that price discrimination increases welfare only if it increases aggregate output subsequently using ingenious duality approaches varian 1985 and schwartz 1990 generalize the results for correlated demands and nonlinear marginal costs 1it is therefore well known that for linear market demands and constant marginal costs monopolistic third degree price discrimination indeed lowers welfare it is important to note however that the welfare reducing effect of third degree price discrimination is derived under a crucial assumption it is assumed that if the monopolist is forced to charge the same price in all markets uniform pricing the monopolist would sell a positive quantity in each market in a recent article cowan 2007 considers various forms of nonlinear demands and presents the necessary and sufficient and or sufficient conditions for price discrimination to reduce welfare cowan 2007 however also assumes that all markets are served under uniform pricing yet when this assumption does not hold the welfare effects of monopolistic third degree price discrimination turn out to be significantly more intricate observe that when all markets are not served under uniform pricing price discrimination may increase welfare because price discrimination may serve markets that would not be served under uniform pricing thus relative to uniform pricing price discrimination has two countervailing effects on welfare aggregate welfare goes down in those markets that are originally served under uniform pricing whereas welfare goes up in those markets that are not served under uniform pricing therefore the additional welfare from the new markets under price discrimination may offset any loss of welfare in the markets that are originally served under uniform pricing the point is strongly emphasized in schmalensee s 1981 seminal work in the context of prescription drugs an identical sentiment is recently echoed in varian 2000 in the context of two markets the possibility of price discrimination opening up new markets is first analyzed graphically by battalio and ekelund 1972 layson 1994 also considers two markets but includes nonlinear demands and presents conditions for opening of new markets based on endogenous features such as elasticities in the context of patent policy opening of new markets by price discrimination is explicitly incorporated by hausman and mackie mason 1988 using two markets they show that price discrimination by a patent holder is socially desirable in many cases because it allows the patent holder to open new markets there is a related literature in spatial economics beginning with greenhut and ohta 1972 and holahan 1975 that deals with spatial price discrimination and market opening with linear demand

disagreements among shareholders over a firm s disclosure policy this paper examines the issue of voluntary disclosure of information by firms with heterogeneous shareholders it shows that in a rational expectations setting better iniformed shareholders prefer less disclosure than less well informed shareholders this is due to differences in the adverse risk sharing effect and the beneficial cost saving effect of disclosure among shareholders with differenit risk tolerances aild information acquisition cost functions the presence of individual liquidity shocks is shown to reduce shareholder disagreements regarding a firm s disclosure policy many firms voluntarily disclose information beyond l evels mandated by financial and accounting regulations still other firms seem to disclose as little information as they can the paper seeks to explain this difference prior studies dealing with disclosure typically are concerned with whether firms would disclose too little or too much information in the absence of mandatory rules 1 results differ across models depending on whether positive or negative externalities are considered for example in a model where disclosure only adversely affects shareholders risk sharing opportunities the optimal level of disclosure is zero and mandatory disclosure rules make all shareholders worse off 2 in contrast mandatory disclosure rules are viewed in this paper as a result of conflicts among firms shareholders with different risk attitudes and different access to inside information in general there is no optimal disclosure policy that is best for all shareholders 3 this paper is based on the model of diamond 1985 diamond considers two opposing effects a positive externality and a negative externality of disclosure to explain the existence of voluntary disclosure when acquiring private information is costly first disclosure adversely affects risk sharing

market liquidity hedging and crashes in the absence of significant news hedging strategies were blamed for the stock market crash of october 1987 but traditional models cannot explain how a relatively small amount of selling could cause so large a price drop the authors develop a rational expectations model in which prices play an important role in shaping expectations markets are much less liquid in their model than in traditional models discontinuities or crashes can occur even with relatively little hedging the model is consistent with theories as disparate as keynes beauty contest insights and thom s catastrophe analysis and suggests means to reduce volatility copyright 1990 by american economic association

using privileged information to manipulate markets insiders gurus and credibility access to private information is shown to generate both the incentives and the ability to manipulate asset markets through strategically distorted announcements the fact that privileged information is noisy interferes with the public s attempts to learn whether such announcements are honest it allows opportunistic individuals to manipulate prices repeatedly without ever being fully found out this leads us to extend sobel s 1985 model of strategic communication to the case of noisy private signals our results show that when truthfulness is not easily verifiable restrictions on trading by insiders may be needed to preserve the integrity of information embodied in prices

a comparison of stock market mechanisms i analyze a multi asset market under two trading mechanisms in the first the unrestricted system traders demand for each asset depends on all equilibrium prices and prices reflect the information contained in all order flows in the second the restricted system traders demand depends on the traded asset price and prices reflect single order flow information i show that informed traders use of multidimensional private information depends on the number of prices they observe and on the price formation process i then give conditions rendering the restricted system more efficient than the unrestricted system

risk aversion market liquidity and price efficiency a model of a noncompetitive speculative market is analyzed in which privately informed traders and market makers are risk averse market liquidity is found to be nonmonotonic in the number of informed traders their degree of risk aversion and the precision of their information it is also shown that increased liquidity trading leads to reduced price efficiency and that under endogenous information acquisition market liquidity may also be nonmonotonic in the variance of liquidity trades article published by oxford university press on behalf of the society for financial studies in its journal the review of financial studies

informed trading investment and welfare this article studies the welfare economics of informed stock market trading we analyze the effect of more informative prices on investment given that this dependence will itself be reflected in equilibrium prices while a higher incidence of informed speculation always increases firm value through a more informative trading process the effect on agents welfare depends on how revelation of information changes risk sharing opportunities in the market greater revelation of information that agents wish to insure against reduces their hedging opportunities on the other hand early revelation of information that is uncorrelated with hedging needs allows agents to construct better hedges