mixed integer programming approaches for index tracking and enhanced indexation we consider the problem of reproducing the performance of a stock market index but without purchasing all of the stocks that make up the index index tracking we also consider the problem of out performing the index enhanced indexation we present mixed integer linear programming formulations of these problems our formulations include transaction costs a constraint limiting the number of stocks that can be purchased and a limit on the total transaction cost that can be incurred as our formulations of these problems are mixed integer linear programs we can use a standard solver cplex numeric results are presented for eight data sets drawn from major markets the largest of these data sets involves over 2000 stocks

frictionless commerce a comparison of internet and conventional retailers there have been many claims that the internet represents a new nearly frictionless market our research empirically analyzes the characteristics of the internet as a channel for two categories of homogeneous products books and cds using a data set of over 8 500 price observations collected over a period of 15 months we compare pricing behavior at 41 internet and conventional retail outlets we find that prices on the internet are 9 16 lower than prices in conventional outlets depending on whether taxes shipping and shopping costs are included in the price additionally we find that internet retailers price adjustments over time are up to 100 times smaller than conventional retailers price adjustments presumably reflecting lower menu costs in internet channels we also find that levels of price dispersion depend importantly on the measures employed when we compare the prices posted by different internet retailers we find substantial dispersion internet retailer prices differ by an average of 33 for books and 25 for cds however when we weight these prices by proxies for market share we find dispersion is lower in internet channels than in conventional channels reflecting the dominance of certain heavily branded retailers we conclude that while there is lower friction in many dimensions of internet competition branding awareness and trust remain important sources of heterogeneity among internet retailers

competition and the number of firms in a market are duopolies more competitive than atomistic markets this paper uses a variant of the standard search model to examine market equilibrium and the consequences for market equilibrium of an increase in the number of firms if marginal search costs increase with the number of searches then the demand curve facing any firm will be kinked with the elasticity of demand with respect to price decreases being less than with respect to price increases prices may not change in response to changes in marginal costs as the number of firms increases the maximum price that is consistent with equilibrium increases to the monopoly price but the minimum price decreases on the other hand if marginal search costs decrease with the number of searches equilibrium if it exists is characterized by a

how do banks respond to shocks a dynamic model of deposit taking institutions abstract this paper proposes a dynamic model of the optimal choices of a bank that benefits from market power and takes into account the impact of the deposit generation process interbank lending borrowing emerges as a buffer that assists the bank in smoothing intertemporal adjustments in interdependent loan and deposit choices the bank smooths the impact of interest rates shocks on its customers to minimize the adjustments over time of the stocks of deposits and loans it does not however provide insurance against negative shocks of real origin that increase its expected default costs the predictions of the model help to shed light on the available empirical evidence and to analyze some recent developments of the banking industry

the optimal selection of small portfolios portfolios that are risk return efficient in the sense of markowitz sometimes contain too many securities to be attractive to the small investor an optimal portfolio subject to a size constraint can be found by an implicit enumeration algorithm that is much faster than a previous approach and moreover allows the inclusion of securities whose coefficient is negative a simple and computationally very efficient heuristic method that almost always produces optimal portfolios is described as well

an equilibrium model of search unemployment this paper develops a simple general equilibrium model with sequential search in which a nondegenerate wage offer distribution is endogenously determined we use this model to analyze the comparati

search unemployment in an overlapping generations setting this paper constructs an overlapping generations model in which the steady state equilibrium is characterized by the existence of search unemployment this dynamic general equilibrium model captures the possible existence of search unemployment in the long run despite the absence of exogenous shocks furthermore it allows for the wage offers distribution to be determined endogenously the effect of partial revelation of information on the existence of search unemployment in the long run is examined it is shown that search unemployment may be eliminated in the long run despite the persistence of the state of imperfect information this paper develops an overlapping generations model in which the steady state equilibrium is characterized by search unemployment 2 unemployment is created via a rational rejection of available wage offers in favor of further search for potentially more attractive offers the proposed dynamic general equilibrium model allows for the existence of long run search unemployment despite the absence of exogenous shocks and permits the presence of an endogenously determined nondegenerate wage offer distribution 3 the paper analyzes the trade off between revelation of information and the level of search unemployment in the long run in the absence of external disturbances the level of search unemployment would be expected to decrease as information becomes available in particular if information is fully revealed search unemployment is naturally eliminated exploring the likelihood of the existence of long run search unemployment in a deterministic world this study provides an example of partial revelation of information which eliminates search unemployment in the long run despite the persistence of the state of imperfect information 4 the proposed model presents a discrete infinite time horizon world where economic activity is conducted under imperfect information in every period a single homogeneous good is produced using two factors capital and labor in the production process the aggregate endowment of labor is exogenously given in

the determination of spot and futures prices with storable commodities this paper analyzes the effects of futures trading in a market for a storable commodity in which producers and speculators are assumed to be risk averse and specifications of the aggregate supply and inventory demand functions are derived from explicit optimization a critical aspect is how the parameters of these functions change with the introduction of the future market as it is through these induced parameter changes that the futures market exerts its influence on the spot price the effects of the futures market on both the long run average spot price and its variance are analyzed while we are unable to draw any definitive conclusions on this issue we find that in all cases considered the futures market stabilizes the spot price as well as lowering its long run mean for many years now the question of the effects of futures trading on the stability of spot prices has been extensively debated this topic has been discussed at various levels for example farmers and agricultural interest groups have claimed that futures trading destabilizes spot prices thereby imposing welfare losses on the economy in the united states congress has decided that futures trading can cause price destabilization and has subjected futures trading to the regulation of the commodity futures trading commission at a more analytical level economists have been investigating the issue both empirically and more recently theoretically as well

intertemporal pricing and consumer stockpiling we study a dynamic pricing problem for a class of products with stable consumption patterns e g household items staple foods consumers may stock up the product at current prices for future consumption but they incur inventory holding costs we model this situation as a dynamic game over an infinite time horizon in each period the seller sets a price and each consumer chooses how many units to buy we develop a solution methodology based on rational expectations by endowing each player with beliefs we decouple the dynamic game into individual dynamic programs for each player we solve for the rational expectations equilibrium where all players make optimal dynamic decisions given correct beliefs about others behavior in equilibrium the seller may either charge a constant fixed price or offer periodic price promotions at predictable time intervals we show that promotions are useful when frequent shoppers are willing to pay more for the product than are occasional shoppers we also develop several model extensions to study the impact of consumer stockpiling on the seller s inventory production and rationing strategies

measuring the effects of search costs on equilibrium prices and profits abstract this paper assesses the effects of search costs on equilibrium prices and profits using an estimated model of demand and costs in a laundry detergent market i find that some firms profits initially rise and then fall with search costs overall the magnitude and direction of the search costs effects on prices and profits are heterogeneous this is because search costs create conflicting incentives for a firm to reduce prices to attract the attention of searching consumers yet also raise prices to harvest profit from consumers who are unaware of competing products these effects can vary with the relationship between the firms actual prices and the consumers pre search beliefs about prices

beating the market with small portfolios evidence from brazil abstract optimal portfolios with a restriction on the number of assets also referred to as cardinality constrained portfolios have been receiving attention in the literature due to its popularity among market practitioners and retail investors in most cases however the interest is in proposing efficient optimization methods to solve the problem with little or no attention to the characteristics of the resulting portfolio such as risk adjusted performance and turnover we address this question by implementing a tractable reformulation of the cardinality constrained version of the minimum variance portfolio we analyze the out of sample performance of cardinality constrained portfolios according to alternative criteria and check the robustness of the results for portfolios with alternative number of assets and under alternative re balancing frequencies our empirical application for the brazilian equities market shows that cardinality constrained minimum variance portfolios with very few assets e g 3 stocks can deliver statistically lower portfolio risk and higher sharpe ratios in comparison to the market index similar results are obtained for constrained portfolios with 5 and 10 assets and under daily weekly and monthly re balancing frequencies our evidence indicates that it is possible to obtain better risk adjusted performance with fewer securities in the portfolio by using an improved allocation scheme

price dispersion in an automobile insurance market from automobile insurance data for alberta over the period 1974 81 we find thatpremiums are highly correlated across driver classes in a given year but that premiums for a given driver class are not correlated over a period of more than 5 years firms relative market shares among drivers over age 25 and married males under 25 are inversely related to their deviations from the mean premiums in these driver classes the variance of real premiums decreases with the numberof firms in the market and increases with the real loss cost per car insured and the number of cars insured from these results we conclude that the price dispersion in automobile insurance in alberta is based on costly consumer search

the effects of unemployment compensation in general equilibrium with search unemployment it is shown that when the effects of an increase in unemployment subsidies are studied in a general equilibrium framework unemployment increases far less than in a partial partial model in fact the result may very well be a decrease in unemployment if the general equilibrium forces are strong enough in the model used in this paper an increase in unemployment compensation unambiguously decreases the rate of unemployment copyright 1990 by the editors of the scandinavian journal of economics

a theory of clearance sales clearance sales are widely used by firms as an intertemporal selling policy in particular in markets where firms face demand uncertainty and need to choose capacity in advance clearance sales consist in charging a high price initially but then lowering the price in the sales period high valuation consumers purchase the good at the high initial price so as to avoid rationing at the low price while low valuation consumers wait for the price to drop we develop a simple model of intertemporal monopoly pricing under demand uncertainty and show that clearance sales may be the optimal intertemporal selling policy

an analysis of the stabilizing and welfare effects of intervention in spot and futures markets this paper analyzes the effects of three alternative rules on the long run distributions of both the spot and futures prices ina single commodity market in which the key behavioral relationships are derived from the optimizing behavior of producers and speculators the rules considered include i leaning against the wind in the spot market ii utility maximizing speculative behavior by the stabilization authority in the futures market iii leaning against the wind in the futures market since the underlying model is sufficiently complex to preclude analytical solutions the analysis makes extensive use of simulation methods as a general proposition we find that intervention in the futures market is not as effective in stabilizing either the spot price of the futures price as is intervention in the spot market indeed rule iii while stabilizing the futures price may actually destabilize the spot price furthermore the analogous type of rule undertaken in the spot market will always stabilize the futures price to a greater degree than it does the spot price the welfare implications of these rules are also discussed our analysis shows how these can generate rather different distributions of welfare gains including the overall benefits this abstract was borrowed from another version of this item

how many stocks make a diversified portfolio we show that a well diversified portfolio of randomly chosen stocks must include at least 30 stocks for a borrowing investor and 40 stocks for a lending investor this contradicts the widely accepted notion that the benefits of diversification are virtually exhausted when a portfolio contains approximately 10 stocks we also contrast our result with the levels of diversification found in studies of individuals portfolios

coupons and everyday low prices price competition with multiple instruments abstract a simple two stage game is examined where firms compete in prices by chosen pricing instruments those considered include a simple uniform pricing technology and a promotional pricing technology like an advertised discount coupon consumers are separated by types informed and uninformed therefore a motive for price competition exists for the purpose of separating the two types of consumers it is shown that the sustainability of an asymmetric choice of pricing instrument between the two firms will prevail in a duopoly market in equilibrium consequently the coexistence of two different pricing schemes is viable even when firms are otherwise symmetric jel classification l1 l13 coupons et bas prix tous les jours concurrence par les prix a l aide de multiples instruments ce memoire examine un simple jeu a deux etapes dans lequel des entreprises se concurrencent par les prix a l aide d un instrument particulier les instruments consideres incluent une simple technologie de prix uniforme et une technologie de prix de promotion sous la forme de l annonce d un coupon d escompte on divise les consommateurs en deux groupes ceux qui sont informes et ceux qui ne le sont pas un des motifs pour ce genre de concurrence est de separer les deux types de consommateurs on montre qu on peut soutenir un choix asymetrique d instrument de tarification entre les deux entreprises dans un marche de duopole en equilibre en consequence la coexistence de deux strategies de prix differentes est viable quand les entreprises sont symetriques sous tous les autres rapports

efficiency wages and wage dispersion the efficiency wage hypothesis has normally been used to generate an equilibrium level of unemployment the authors use it instead to generate an equilibrium wage distribution this paper starts by generalizing the previous work of r m solow in this area they then use their results on effort wage elasticities to derive a model of wage dispersion the wage rate is shown to be an increasing function of the damage potential of workers that is workers with the highest damage potential receive the highest wage the analysis of the equilibrium of the wage distribution provides interesting qualitative insights into the nature of actual wage differentials copyright 1991 by the london school of economics and political science

information and economic analysis a perspective ten years ago i delivered a paper before this group with the title information and economic analysis i chose the title deliberately i did not call the subject on which i was speaking the economics of information because to do so would have been to suggest that my topic like the economics of agriculture or the economics of industry or the economics of labour represented another branch of specialisation within economics i wanted to suggest that informational considerations were in fact central to the analysis of a wide variety of phenomena that they constituted a central part of the foundations of economic analysis at the time though economists had long paid lip service to the importance of information there was little formal literature the last decade has seen a burgeoning of the literature it has become to the late 7o s and early 8o s what growth theory was to the early 6o s and it has been greeted with some of the same scepticism there seems to be a myriad ofspecial cases and few general principles the little examples are often contrasted unfavourably with the generality of general equilibrium theory what have we learned have diminishing returns set in are there fruitful directions for future research and if so what are they these are the questions which i wish to address here the work of the past decade has made i think a fundamental and lasting contribution to economic analysis the contributions have been both negative and positive we have learned that much of what we believed before is of only limited validity that the traditional competitive equilibrium analysis though having the superficial appearance of generality in terms of superscripts and subscripts is indeed not very general the theory is not robust to slight alterations in the informational assumptions it is but a special and not very plausible example among the possible set of informational assumptions which can be employed to characterise an economy at the same time the theory has been able to provide insights into phenomena about which the traditional model had nothing to say or which seemed inconsistent or inexplicable within the competitive paradigm it has provided some of the micro foundations for macro economics it has provided the basis of a new theory of the firm of a new new welfare economics and of a theory of economic organisation including a comparison of economic

a simple model of price dispersion abstract this article considers a simple stock flow matching model with fully informed market participants unlike the standard matching literature prices are assumed to be set ex ante when sellers pre commit themselves to sell their products at an advertised price the unique equilibrium is characterized by price dispersion due to the idiosyncratic match payoffs in a marketplace with full information this provides new insights into the price dispersion literature which instead commonly assumes that buyers are not perfectly informed and engage in a costly search

general equilibrium wage and price distributions this paper extends models of search market equilibrium to incorporate general equilibrium considerations the model we treat is one with a single product market and a single labor market an equilibrium distribution of prices and wages is the result of optimal price and wage setting behavior by firms in conjunction with optimal search by individuals we prove the existence of a degenerate equilibrium and of a two point dispersion equilibrium

equilibrium price dispersion in retail markets for prescription drugs this study seeks to establish the empirical importance of price dispersion due to costly consumer search by examining retail prices for prescription drugs posted prices in two geographically distinct markets are shown to vary considerably across pharmacies within the same market even after one controls for variation due to pharmacy differences pharmacy heterogeneity accounts for at most one third of the observed price dispersion the empirical analysis hinges on the observation that consumers incentives to price shop depend on characteristics of the drug therapy cross sectional patterns in price distributions across drugs are consistent with the predictions of a search model prices for repeatedly purchased prescriptions for which the expected benefits of search are highest exhibit significant reductions in both dispersion and price cost margins

strategic pricing consumer search and the number of firms discover prices there are three distinct price dispersed equilibria characterized by low moderate and high search intensity the effects of an increase in the number of firms on search behaviour expected prices price dispersion and welfare are sensitive i to the equilibrium consumers search intensity and ii to the status quo number of firms for instance when consumers search with low intensity an increase in the number of firms reduces search does not affect expected price leads to greater price dispersion and reduces welfare in contrast when consumers search with high intensity increased competition results in more search and lower prices when the number of competitors in the market is low to begin with but in less search and higher prices when the number of competitors is large duopoly yields identical expected price and price dispersion but higher welfare than an infinite number of firms a question that has received much attention in economic theory is how the number of competitors and market outcomes are related despite the existence of work showing the contrary see e g satterthwaite 1979 rosenthal 1980 the prediction that emerges from a market where firms interact in a cournot fashion has come to dominate economic thought namely that an increase in the number of competitors leads to larger aggregate production lower market price and improved market performance measured in terms of some social welfare criterion ruffin 1971 this paper challenges the generality of this belief by presenting an oligopoly model with consumer search where the equilibrium expected price may be constant increasing or nonmonotonic in the number of firms we present an economy with two types of consumers consumers who search for prices at no cost fully informed and consumers who must pay a fixed search cost for each price quotation they observe less informed 1 all buyers have the same willingness to pay for the good and buy either a single unit or nothing at all on the supply side of the market there are n firms producing a homogeneous good at constant marginal cost we analyse a one shot simultaneous move game firms set prices and consumers decide how many prices to search for at the same moment in time our model is essentially an oligopolistic version of burdett and judd 1983 where some consumers search costlessly in this model consumers search using a fixed sample size search strategy i e they choose the number of prices to observe before receiving any offer nonsequential search is appealing when consumers find it more advantageous to gather price information quickly morgan and manning 1985 this occurs when the search outcome is observed with delay and delay is costly for instance an mba graduate looking for a job 1 the presence in the model of consumers who search costlessly captures the fact that some people have a

participation in farm commodity programs a stochastic dominance analysis grube correctly argues that mini max and maximax criteria can help analysts determine the interval in which for a given set of preferences there will be changes in the preferred distribution the criteria is of less value when simulations are used to generate distributions without exact a priori knowledge of the random draw of order statistics we will argue that in most cases one can go even further and solve for the specific break even level of risk aversion this should simplify the procedures commonly used to rank risky prospects the author calculates that for the data presented the mini max critical value is 0 000003 for risk preferrers and 0 000002 for risk avoiders he concludes that these are low values when compared to the range originally considered 0 04 to 0 03 since his numbers fall within our range this suggests that our range could have been narrower than it was but clearly our range did contain the values he calculated it is noteworthy that when the smaller coefficients were used the relative rankings of choices remained unchanged grube concludes that kp s results are correct in the sense that they give a correct ranking of the order in which alternatives would be chosen by decision makers with varying absolute risk aversion coefficients since ultimately risk analysts are interested in the relative ranking of risky prospects this would suggest that our results are more robust than the author implies in his remarks while grube has suggested a means of identifying the interval of interest we would argue that in many cases one could go further and solve for the break even level of risk preference the break even level would be that value at which there is a switching in the dominance of one distribution over another using results developed by hammond it should be possible to simplify both the calculation and presentation of stochastic dominance results by solving for the break even level two conditions must be satisfied in order to apply hammond s results first constant risk aversion must be assumed while the use of utility functions exhibiting decreasing risk aversion has been advocated in the theoretical literature and supported somewhat by empirical studies which have assessed utility functions in most applications constant risk aversion is assumed this is largely because wealth data is frequently unavailable or of questionable accuracy thus risk analysts typically assume that a decision maker s utility function can be approximated over the relevant range by a constant risk aversion function such as the negative exponential function u x 1 e ax

collusion with intertemporal price dispersion we develop a theory of optimal collusive intertemporal price dispersion dispersion clouds consumer price awareness encouraging firms to coordinate on dispersed prices our theory generates a collusive rationale for price cycles and sales patient firms can support optimal collusion at the monopoly price for less patient firms monopoly prices must be punctuated with fleeting sales the most robust structure involves price cycles that resemble edgeworth cycles low consumer attentiveness enhances the effectiveness of price dispersion by reducing the payoff to deviations involving price reductions however for sufficiently low attentiveness price rises are also a concern

intertemporal substitution and storable products storable products allow consumers to time their purchases to exploit price fluctuations it has been documented that during promotions consumers buy more the additional purchases are potentially intended not only for current use but to be stockpiled for future consumption this paper discusses the predictions of a consumer inventory model and reviews the available evidence we then discuss the implications for demand estimation and present estimates of jel lo l4 dl d4 the economic magnitude of the dynamic effect of storability jel lo l4 dl d4 jel lo l4 dl d4

the impact of collusion on price behavior empirical results from two recent cases abstract we use extended arch and garch models to examine the differences in the behavior of the first two moments of the price distribution during collusive and competitive phases of two recently discovered conspiracies citric acid and lysine according to our results the conspirators managed to raise prices by 9 and 25 cents per pound in the short run relative to non collusive periods also the variance of prices during the lysine conspiracy was lower and the variance of prices during the citric acid conspiracy was higher than during more competitive periods the proposed methodology may be used for antitrust screening and prosecution purposes

government target price intervention in economies with incomplete markets the target price deficiency payment program is among economists favorite examples of costly government intervention in competitive markets dubbed the brannan plan after president truman s secretary of agriculture this program pays producers any positive difference between a given target price and the prevailing market price for their output in a world of certainty and perfect competition such an intervention benefits producers hurts consumers as taxpayers and causes a net harberger triangle welfare loss these implications are not only standard fare in economics lecture halls they have become conventional wisdom in contemporary policy discussions for example the 1986 economic report of the president states income support programs by inhibiting the efficient operation of agricultural markets can impose extra costs on consumers and taxpayers that exceed the amount of income transferred to farmers when such losses occur the programs are doing more than redistributing income they are wasting valuable economic resources that could be used to make everyone better off the object of this paper is to show that these conclusions do not extend to a stochastic production economy with incomplete contingent claim markets in the latter setting the distributional and welfare implications of a brannan plan can be reversed producers can be made worse off consumers can be made better off and with nonstochastic compensation all agents can be made better off the conditions under which these outcomes occur include producer risk aversion and low price and income elasticities of demand all well known characteristics of staple food markets in which target price programs are actually employed e g markets for wheat corn and rice like many other equilibrium analyses of resource allocation

the timing of sales this paper presents a model of intertemporal price discrimination a fixed number of sellers produce a homogeneous good consumers with different preferences enter the market in each period and leave when they make a purchase the sellers typically vary their prices over time charging a high price in most periods but occasionally cutting the price to sell to a large group of customers with a low reservation price in some equilibria all stores lower their price at the same time and to the same level

consumer stockpiling and competitive promotional strategies an examination of brand prices in several categories reveals that the distribution of prices is multimodal with firms offering shallow and deep discounts another interesting feature of these distributions is that they may have holes in the interior of the support these pricing distributions do not occur in extant theoretical models of price promotions we develop a dynamic model of competition in which some price sensitive consumers stockpile during periods of deep discounts a game theoretic analysis of our model generates a multimodal pricing distribution with a hole in the interior of the support consumer stockpiling in our model also gives rise to negative serial correlation in prices this is consistent with our empirical observation of the pricing distribution of several brands across multiple categories in the iri marketing data set we generate several interesting insights into firms optimal promotional strategies and their interplay with the clientele mix market structure and other market factors we find that in equilibrium stockpiling by price sensitive consumers neither harms nor benefits firms when they adopt equilibrium strategies interestingly when price sensitive consumers stockpile even increased consumption as a result of stockpiling does not lead to higher profits for firms

general equilibrium with real time search in labor and product markets the paper is concerned with economies in which agents find sellers and employers in a time consuming search process while they simultaneously trade with their current partners a symmetric steady state equilibrium does not exist but asymmetric steady state equilibria exist and are such that larger firms offer higher wages and charge lower prices than smaller firms but still make more profits these profits can be seen as rents from a superior market position

storable good monopoly the role of commitment we study dynamic monopoly pricing of storable goods in an environment where demand changes over time the literature on durables has focused on incentives to delay purchases our analysis focuses on a different intertemporal demand incentive for consumers the key force on the consumer side is advance purchases or stockpiling this stockpiling motive can be present in the case of standard durables as well in environments unmodeled in the prior literature we show that if the monopolist cannot commit then prices are higher in all periods and social welfare is lower than in the case in which the monopolist can commit this is in contrast with the durable goods analysis in the literature on the coase conjecture