a minimum wage can be welfare improving and employment enhancing abstract we examine whether minimum wages can fulfill a useful role as part of an optimal tax transfer scheme the government cannot observe household abilities only their incomes and is constrained to ensure that those working are at least as well off as those not working a minimum wage combined with the institutional features of typical welfare systems allows the incentive constraint to be severed at the ability level associated with the minimum wage if such a scheme can be enforced the government can increase the amount of redistribution from those working to those not working and possibly lower the number of unemployed

the ellsberg paradox and risk aversion an anticipated utility approach the paper describes a decision process under which it is rational to prefer a lottery with known probabilities to a similar ambiguous lottery where the decision maker does not know the exact values of the probabilities the ellsberg paradox this is done by modeling ambiguous lotteries as two stage lotteries by assuming the independence axiom without the reduction of compound lotteries axiom and by using the anticipated utility functional this paper also gives conditions under which less ambiguity is preferred and presents some comparative statics analysis as well as some inter personal comparisons finally it proves that within the anticipated utility framework risk and ambiguity are almost identical copyright 1987 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

does the preference reversal phenomenon necessarily contradict the independence axiom one of the most puzzling paradoxes in decision theory is the preference reversal phenomenon this phenomenon seems to contradict the transitivity axiom for a long time one of the cornerstones of utility theory this paradox is established whenever a decision maker prefers lottery x to lottery y but is willing to put a lower selling price on x than on y such experiments first reported by harold lindman 1971 and sarah lichtenstein and paul slovic 1971 were repeated by david grether and charles plott 1979 werner pommerehne et al 1982 and robert reilly 1982 although the later researchers improved the mechanism through which the selling price emerges they all found systematic reversals a new approach to this problem was developed by charles holt 1986 and edi karni and zvi safra 1987 from two different starting points these authors showed that the preference reversal phenomenon does not necessarily prove a violation of the transitivity axiom as it may contradict the independence axiom this implies that people do not maximize expected utility but in that case the preference reversal phenomenon becomes just another evidence against expected utility theory but not against the transitivity axiom these results have their own disadvantages although the independence axiom is not as fundamental as transitivity it is nevertheless very appealing on normative grounds of course the preference reversal phenomenon necessarily contradicts at least one of the assumptions of expected utility theory but empirical evidence shows that despite its normative appeal violations of the reduction of compound lotteries axiom may happen see for example joshua ronen 1971 and doug snowball and clif brown 1979 in this paper i therefore suggest a decision mechanism for the preference reversals lotteries which is transitive and satisfies the independence axiom but not the reduction axiom

decision making in quasi markets a pedagogic analysis abstract the objective of the 1991 nhs reforms was to reduce excessive vertical integration by constructing a quasi market in which incentive structures and increased availability of information would enable decision makers make better use of resources there is however no overall framework in which to consider the welfare gains which result from the introduction of a quasi market or the welfare losses which arise from distortions in a quasi market this paper offers an analysis which can be applied to illustrate the difficulty of estimating the welfare loss from cream skimming and also to consider the impact of local monopoly

taxes redistribution and the minimum wage a theoretical analysis this paper considers a simple general equilibrium model that contains two types of workers with differing levels of ability and a social welfare maximizing government the paper shows that social welfare can sometimes be increased by supplementing an optimal linear income tax with a minimum wage but that social welfare can never be increased by supplementing an optimal nonlinear income tax with a minimum wage

econometric studies in health economics a survey of the british literature this paper provides a survey of british applied econometric work in the field of health economics as well as reviewing the literature it suggests some avenues for future research it covers six main areas the supply of health care the demand for health care non medical influences on health market and non price rationing evaluation of health care systems and planning budgeting and monitoring mechanisms

non cooperative games with prospect theory players and dominated strategies abstract we investigate a framework for non cooperative games in normal form where players have behavioral preferences following prospect theory pt or cumulative prospect theory cpt on theoretical grounds cpt is usually considered to be the superior model since it normally does not violate first order stochastic dominance in lottery choices we find however that cpt when applied to games may select purely dominated strategies while pt does not for both models we also characterize the cases where mixed dominated strategies are preserved and where violations may occur

non additive beliefs and strategic equilibria abstract this paper studies n player games where players beliefs about their opponents behaviour are modelled as non additive probabilities the concept of an equilibrium under uncertainty which is introduced in this paper extends the equilibrium notion of dow and werlang 1994 j econom theory 64 305 324 to n player games in strategic form existence of such an equilibrium is demonstrated under usual conditions for low degrees of ambiguity equilibria under uncertainty approximate nash equilibria at the other extreme with a low degree of confidence maximin equilibria appear finally robustness against a lack of confidence may be viewed as a refinement for nash equilibria journal of economic literature classification numbers c72 d81

minimum wage effects on labor market outcomes under search matching and endogenous contact rates building upon a continuous time model of search with nash bargaining in a stationary environment we analyze the effect of changes in minimum wages on labor market outcomes and welfare although minimum wage increases may or may not lead to increases in unemployment in our model they can be welfare improving to labor market participants on both the supply and demand sides of the labor market we discuss identification of the model using current population survey data on accepted wages and unemployment durations and show that by incorporating a limited amount of information from the demand side of the market it is possible to obtain credible and precise estimates of all primitive parameters we show that the optimal minimum wage in 1996 depends critically on whether or not contact rates can be considered to be exogenous and we note that the limited variation in minimum wages makes testing this assumption problematic

unemployment and the business cycle in a small open economy g m m estimation and testing with french data abstract what is a relevant model for the european business cycle in this paper the empirical performances of three models are compared a canonical walrasian r b c framework its extension to the case of a small open economy and a version of this model with search and wage bargaining on the labor market structural parameters of the models are estimated using g m m and their abilities to reproduce the french business cycle taken as representative of the european business cycle are tested only the small open economy with unemployment is able to generate theoretical moments that match their empirical counterparts

risk sharing on the labour market and second best wage rigidities the starting point of the analysis is that a significant proportion of the labour force is not covered by efficient labour contracts in particular the non existence of forward labour contracts limits the opportunity of efficient risk sharing through private arrangements among young labour suppliers and capital owners in such a context state dependent labour taxes and employment subsidies would be required to achieve ex ante pareto efficiency in the absence of employment subsidies a certain limited degree of downward wage rigidity is in general pareto superior to full wage flexibility at the second best optimum so defined productive efficiency is sacrificed in some states in order to achieve greater efficiency in risk sharing thus the unemployment associated with wage rigidity is inefficient though voluntary due to the levels of benefits and second best efficient a limited degree of wage discrimination by hiring date is typically part of the second best policy

minimum wage legislation and unemployment insurance as instruments for redistribution the use of minimum wages and unemployment insurance as instruments for redistributing income is analyzed the government is assumed to be able to implement an optimal income tax in an economy consisting of two types of individuals who differ in ability the effect of introducing a minimum wage which induces involuntary unemployment will be to improve social welfare under weak conditions circumstances under which combining unemployment insurance with the minimum wage will be welfare improving are also considered

optimal linear income taxation with general equilibrium effects on wages abstract the paper argues that the endogeneity of wages may make a considerable difference to optimal linear tax rates in this case there is not only the usual direct redistribution via the fiscal system but also the general equilibrium redistribution due to the change in wages depending on the elasticity of substitution of the production function and the labour supply elasticities these may be reinforcing or opposing it is shown that the general equilibrium effect may plausibly outweigh the direct effect so that net redistribution to the lower paid involves a wage subsidy financed by a lump sum tax

delayed agreements and nonexpected utility the unexplained occurrence of inefficient delays in reaching agreement is known in the economics literature as the hicks paradox this paper describes a strategic situation in which players may play a simultaneous move game either before or after a move of nature the structure is such that if the players were expected utility maximizers they would be indifferent over the order of play however if at least one of the players is a nonexpected utility maximizer for example if player one has preferences over lotteries which exhibit betweenness and fanning out such a player may strictly prefer to wait before playing the game if both players exhibit fanning out and betweenness then there exist games in which both prefer to delay agreement

correlated equilibrium as an expression of bayesian rationality if it is common knowledge that the players in a game are bayesian utility maximizers who treat uncertainty about other players actions like any other uncertainty then the outcome is necessarily a correlated equilibrium random strategies appear as an expression of each player s uncertainty about what the others will do not as the result of willful randomization use is made of the common prior assumption according to which differences in probability assessments by different individuals are due to the different information that they have where information may be interpreted broadly to include experience upbringing and genetic makeup copyright 1987 by the econometric society

the validity of qalys under non expected utility this paper examines applications of non expected utility in the health domain the most widely used utility model in health economics the time linear qaly model assumes i separability of quality of life and life duration and ii linearity of the utility for life duration we perform new tests which are robust to violations of expected utility of these two assumptions the data support separability but show that the utility for life duration is concave rather than linear the finding of concave utility may not be surprising in itself the contribution of this paper is to demonstrate this empirically without being invalidated by violations of expected utility it has by now been widely recognised that expected utility is not valid as a descriptive theory of decision under uncertainty the descriptive violations of expected utility have led to the emergence of several non expected utility theories the increasing importance of non expected utility makes it necessary to reassess applications that were previously based on expected utility examples of such reassessments include karni and safra 1989 crawford 1990 and dekel et al 1991 for game theory machina 1995 and wakker et al 1997 for insurance theory and cubitt and sugden 1998 for the evolution of preferences see starmer 2000 for a review the present paper examines applications of non expected utility in the health domain we focus on the main utility model in health economics the quality adjusted life years qaly model and present new theoretical foundations for and empirical tests of this model under non expected utility qalys provide a simple way to combine the two dimensions of health life duration and health status into a single utility index they are intuitively appealing which facilitates communication to policy makers and analytically tractable which explains their widespread use in practical studies a disadvantage of qalys is that they only represent individual preferences over health under strong assumptions if these assumptions do not hold then the use of qalys may lead to incorrect policy recommendations to gain insight into the validity of qalys it is necessary to assess the restrictiveness of the assumptions that the qaly model imposes in the most common version of the qaly model the time linear qaly model the utility of the health outcome of spending t years in health state q is equal to tv g where v is a utility function over health states that is in the time linear qaly model the utility for duration is linear it is well known that under expected utility linearity of utility implies risk neutrality as it turns out risk neutrality with

on the optimality of a minimum wage new insights from optimal tax theory we build a theoretical model to study whether a minimum wage can be welfare improving if it is implemented in conjunction with an optimized nonlinear income tax we consider this issue in a framework where search frictions on the labor market generate unemployment workers differ in productivity the government does not observe workers productivity but only their wages hence the redistributive policy solves an adverse selection problem we show that a minimum wage is optimal if the bargaining power of the workers is relatively low however if the government controls the bargaining power then it is preferable to set a sufficiently high bargaining power

existence and dynamic consistency of nash equilibrium with non expected utility preferences sufficient conditions for the existence of a nash equilibrium are given when preferences may violate the reduction of compound lotteries assumption rcla without rcla decision makers may not be indifferent between compound lotteries which have the same probabilities of final outcomes therefore the conditions depend on how players perceive the game whether they view themselves as moving first or second we also review conditions under which the equilibria will be dynamically consistent

is a minimum wage an appropriate instrument for redistribution textabstractwe analyze the redistributional dis advantages of a minimum wage over income taxation in competitive labor markets without imposing assumptions on the in efficiency of labor rationing compared to a distributionally equivalent tax change a minimum wage increase raises involuntary unemployment but also raises skill formation as some individuals avoid unemployment a minimum wage is an appropriate instrument for redistribution if and only if the public revenue gains from additional skill formation outweigh both the public revenue losses from additional unemployment and the utility losses of inefficient labor rationing we show that this critically depends on how labor rationing is distributed among workers a necessary condition for the desirability of a minimum wage increase is that the public revenue gains from higher skill formation outweigh the revenue losses from higher unemployment we write this condition in terms of measurable sufficient statistics our empirical analysis suggests that a minimum wage increase is undesirable in nearly all oecd countries a reduction in the minimum wage along with tax adjustments that keep net incomes constant would yield a pareto improvement

dynamic consistency revelations in auctions and the structure of preferences analyzing the optimal bidding behaviour in ascending bid auctions and second price sealed bid auctions with independent private values we show that expected utility maximizing behaviour is equivalent to a dynamically consistent bidding in ascending bid auctions b the equivalence of the optimal bids in ascending bid auctions and in second price sealed bid auctions c bidding the value of the object in second price sealed bid auctions in addition the optimal bid in ascending bid auctions equals the value of the object if and only if the bidder s preferences on lotteries are both quasi concave and quasi convex

making book against oneself the independence axiom and nonlinear utility theory an individual with known preferences over lotteries can be led to accept random wealth distributions different from his initial endowment by a sequential process in which some uncertainty is resolved and he is offered a new lottery in place of the remaining uncertainty this paper examines the restrictions that can be placed on an individual s preferences by axioms that stipulate that such a process not be able to generate a new wealth distribution that is prima facie inferior to the original the relationship of these axioms to the independence axiom of von neumann and morgenstern and to the quasi convexity of preferences in the wealth distribution are explored

product improvement and technological tying in a winner take all market in a winner take all duopoly market for systems in which rms invest to improve their products a vertically integrated monopoly supplier of an essential system component may have an incentive to advantage itself by technological tying that is by designing the component to work better in its own system if the vertically integrated rm is prevented from technologically tying then there is an equilibrium in which the more e cient rm invests and serves the entire market however another equilibrium may exist in which the less e cient rm invests and captures the market technological tying enables a vertically integrated rm to foreclose its rival the welfare implications of technological tying are ambiguous and depend on the asymmetric qualities of the system suppliers and on equilibrium selection

optimal minimum wage policy in competitive labor markets this paper provides a theoretical analysis of optimal minimum wage policy in a perfectly competitive labor market and obtains two key results first we show that a binding minimum wage while leading to unemployment is nevertheless desirable if the government values redistribution toward low wage workers and if unemployment induced by the minimum wage hits the lowest surplus workers first importantly this result remains true in the presence of optimal nonlinear taxes and transfers in that context a binding minimum wage enhances the effectiveness of transfers to low skilled workers as it prevents low skilled wages from falling through incidence effects second when labor supply re sponses are along the extensive margin only the co existence of a minimum wage with a positive tax rate on low skilled work is always second best pareto ineffcient a pareto improving policy consists of reducing the pre tax minimum wage while keeping constant the post tax minimum wage by increasing transfers to low skilled workers and financing this reform by increasing taxes on higher paid workers overall our results imply that the minimum wage and subsidies for low skilled workers are complementary policies pa

risk averse behavior in generalized matching pennies games in experimental studies of behavior in 2 2 games with unique mixed strategy equilibria observed choice frequencies are systematically different from mixed strategy nash predictions this paper examines experimental results for a variety of such games and shows that a structural econometric model which incorporates risk aversion into a quantal response equilibrium explains the data very well moreover risk aversion estimates are stable across the different games and are close to those obtained from laboratory and field auction data as well as from individual lottery choice experiments

optimal income taxation with endogenous participation and search unemployment we characterize optimal redistributive taxation when individuals are heterogeneous in their skills and their values of non market activities search matching frictions on the labor markets create unemployment wages labor demand and participation are endogenous average tax rates are increasing at the optimum this shifts wages below their laissez faire value and distorts labor demand upwards the marginal tax rate is positive at the top of the skill distribution even when the latter is bounded these results are analytically shown under a maximin objective when the elasticity of participation is decreasing in the skill level and are numerically confirmed under a more general objective under the maximin above approximately 20 000 per year our model recommends higher marginal tax rates than a comparable competitive setting

optimal labour taxation and search abstract this paper explores the optimal role of the tax system in alleviating labour market imperfections and raising revenue for this purpose the standard search model of the labour market is extended by introducing scarce entrepreneurial talent and arbitrage between the supply and demand sides of the labour market we study how these extensions affect the following two major implications of the standard model 1 only the ad valorem component of the wage tax should be employed to raise revenue 2 the optimal tax system should not distort labour market tightness

a theory of anticipated utility abstract a new theory of cardinal utility with an associated set of axioms is presented it is a generalization of the von neumann morgenstern expected utility theory which permits the analysis of phenomena associated with the distortion of subjective probability

equilibrium without independence abstract because players whose preferences violate the von neumann morgenstern independence axiom may be unwilling to randomize as mixed strategy nash equilibrium would require a nash equilibrium may not exist without independence this paper generalizes nash s definition of equilibrium retaining its rational expectations spirit but relaxing its requirement that a player must bear as much uncertainty about his own strategy choice as other players do the resulting notion equilibrium in beliefs is equivalent to nash equilibrium when independence is satisfied but exists without independence this makes it possible to study the robustness of equilibrium comparative statics results to violations of independence

prospect theory in a dynamic game theory and evidence from online pay per bid auctions abundant evidence exists that expected utility theory does not adequately describe decision making under risk although prospect theory is a popular alternative it is rarely applied in strategic situations in which risk arises through individual interactions this study fills this research gap by incorporating prospect theory preferences into a dynamic game theoretic model using a large field data set from multiple online pay per bid auction sites the authors empirically show that their proposed model with prospect theory preferences makes a better out of sample prediction than a corresponding expected utility model prospect theory also provides a unified explanation for two behavioral anomalies average auctioneer revenues above current retail prices and the sunk cost fallacy the empirical results indicate that bidders are loss averse and overweight small probabilities such that the expected revenue of the auction exceeds the current retail price by 25 46 the authors illustrate and empirically confirm a managerial implication for how an auctioneer can increase revenue by changing the details of the auction design

minimum wage legislation as a second best policy mass unemployment is a striking phenomenon of the present economic situation of european market economies although the profession of economists has been criticized for not providing satisfactory cures it has produced a number of different explanations either complementary or contradictory for the occurrence of mass unemployment in this paper we examine the argument that unemployment is the consequence of minimum wage legislation which is socially desirable the observation of current wage legislations suggests that the above argument is broadly at least partly accepted by policy makers curiously enough a defence of this argument meeting the rigorous requirements of modern theory seems to be missing symmetrically attacks against minimum wage legislation often rely upon reasonings of dubious relevance i e the obvious remark that unemployment is a waste with first best efficiency criteria the present paper proposes a second best analysis where second best stems from informational asymmetries which prevent the implementation of lump sum transfers needed for a first best redistribution policy the question under scrutiny can be reformulated in a more precise way as follows does a second best optimal redistribution policy lead to minimum wage legislation and unemployment our elements of answer are gathered in 3 sections in section 2 the principles of the analysis of the desirability of quantity controls and existing results are recalled in section 3 the analysis of section 2 is specified to a simple prototype model for the study of linear income taxation in section 4

optimal redistributive taxation in a search equilibrium model this paper characterizes optimal non linear income taxation in an economy with a continuum of unobservable productivity levels and endogenous involuntary unemployment due to frictions in the labour markets redistributive taxation distorts labour demand and wages compared to their efficient values gross wages unemployment and participation are lower average tax rates are increasing marginal tax rates are positive even at the top finally numerical simulations suggest that redistribution is much more important in our setting than in a comparable mirrlees type setting

national health service waiting lists a discussion of competing explanations and a policy proposal abstract a discussion of the main arguments advanced to explain waiting lists in britain s national health service nhs is presented in a framework which focuses upon demand and supplier induced demand considerations the difficulties associated with determining an optimum waiting list are explicitly emphasised hence it is in the context of an alleged requirement to reduce numbers waiting that the proposal to offer a price subsidy for private medical care is appraised such a policy is compared with that of direct expansion of expenditure on the nhs attention is drawn to the second round effects of supplier induced demand which may be associated with these policies

david vs goliath an analysis of asymmetric mixed strategy games and experimental evidence mixed strategies are widely used to model strategic situations in diverse fields such as economics marketing political science and biology however some of the implications of asymmetric mixed strategy solutions are counterintuitive we develop a stylized model of patent race to examine some of these implications in our model two firms compete to develop a product and obtain a patent however one firm values the patent more because of its market advantages such as brand reputation and distribution network contrary to some intuition we find that the firm that values the patent less is likely to invest more aggressively in developing the product and will also win the patent more often we argue that the reason for these counterintuitive results is inherent in the very concept of mixed strategy solution in a laboratory test we examine whether subjects behavior conforms to the equilibrium predictions we find that the aggregate behavior of our subjects is consistent with the game theoretic predictions with the help of the experience weighted attraction ewa learning model proposed by camerer and ho 1999 we show that adaptive learning can account for the investment behavior of our subjects we find that the ewa learning model tracks the investment decisions of our subjects well whether we hold out trials or an entire group of subjects

elasticity estimates from a dynamic model of interrelated demands for private and public acute health care this paper investigates the private public mix in acute health care provision in the uk it uses an interrelated shares model derived from a translog function combined with dynamic adjustment using prices for public care constructed from nhs waiting lists the insurance cost of private care and the retain price index impact intermediate and long run elasticities of demand for private and public care are obtained the role of hospital consultants and of an aging population are also considered

a complete solution to a class of principal agent problems with an application to the control of a self managed firm this paper considers a class of principal agent problems which have the following features 1 there is adverse selection because the principal ignores the value of one parameter of the agent s true characteristics 2 leaving aside the information parameter the principal s welfare as well as the agent s welfare depend on two types of variables observable to both of them the first ones possibly multidimensional are called action variable s and the second one which is one dimensional has in general the meaning of a money transfer 3 the principal is a stackelberg leader of the two person game he can commit himself to decision rules which are admissible on informational grounds he optimizes within the adequate class taking into account besides the agent s reaction one constraint which has generally the meaning of an individual rationality constraint and sometimes of a feasibility constraint the optimization is limited to the class of non stochastic mechanisms 4 the problem can also receive an alternative interpretation the principal faces a continuum of agents of unknown characteristics the distribution being known however stylized principal agent problems of this type have often been considered in the economic literature in particular the reader will later be able to recognize that the standard income tax model a la mirrlees 1971 the quality or quantity choice model of the monopolist a la mussa and rosen 1978 or maskin and riley 1982 and the model of government regulation of the private monopolist of baron and myerson 1982 all belong to

mixed strategy nash equilibrium based upon expected utility and quadratic utility abstract the notion of a mixed strategy nash equilibrium suffers from three inherent difficulties first given the equilibrium strategies of other players there are many best replies second the equilibrium is unstable third comparative statics results are counterintuitive we demonstrate that these difficulties all have their origin in von neumann and morgenstern s expected utility in contrast players with quadratic utility have unique best replies and the nash equilibrium appears to yield intuitive comparative statics results journal of economic literature classification number c72

tax subsidy and capacity decisions in a two tier health system with welfare redistributive objective service delay and patient choice endogenized in the queueing equilibrium through game theoretical approach subsidy policy does not always improve income redistribution the more the lower income patients is concerned the less unlikely is providing subsidy to private care under equal weights the larger the capacity of public sector the lower tax or higher subsidy to private care under unequal weights subsidize only when the capacity exceeds a threshold

choice under uncertainty problems solved and unsolved ffifteen years ago the theory of choice under uncertainty could be considered one of the success stories of economic analysis it rested on solid axiomatic foundations it had seen important breakthroughs in the analytics of risk risk aversion and their applications to economic issues and it stood ready to provide the theoretical underpinnings for the newly emerging information revolution in economics 1 today choice under uncertainty is a field in flux the standard theory is being challenged on several grounds from both within and outside economics the nature of these challenges and of our profession s responses to them is the topic of this paper

minimum wage policy with optimal taxes and unemployment abstract using a search model i derive a formula that links the welfare gains from the minimum wage to its effect on low skilled labor force participation and employment this formula shows that the minimum wage is welfare improving if pushing the low skilled labor market tightness downwards brings it closer to its efficient level i estimate the causal effect of the minimum wage on low skilled labor force participation and employment using federal and state minimum wage variation i discuss the policy implications of my estimates when viewed through the lens of the marginal welfare gain formula

a pareto improving minimum wage this paper shows that a graduated minimum wage in contrast to a constant minimum wage can provide a strict pareto improvement over what can be achieved with an optimal income tax the reason is that a graduated minimum wage requires high productivity workers to work more to earn the same income as low productivity workers which makes it more difficult for the former to mimic the latter in effect a graduated minimum wage allows the low productivity workers to benefit from second degree price discrimination which increases their income

self selection and pareto efficient taxation abstract this paper analyses the set of pareto efficient tax structures the formulation of the problem as one of self selection not only shows more clearly the similarity between this problem and a number of other problems such as the optimal pricing of a monopolist which have recently been the subject of extensive research but also allows the derivation of a number of new results we establish i under fairly weak conditions randomization of tax structures is desirable ii if different individuals are not perfect substitutes for one another in production then the general equilibrium effects until now largely ignored in the literature of changes in the tax structure may be dominant in determining the optimal tax structure in particular if the relative wage of high ability and low ability individuals depends on the relative supplies of labor the optimal tax structure entails a negative marginal tax rate on the high ability individuals and a positive marginal tax rate on the low ability individuals the marnitude of which depends on the elasticity of substitution iii if individuals differ in their preferences pareto efficient taxation may entail negative marginal tax rates for high incomes while iv if wage income is stochastic the marginal tax rate at the upper end may be 100 our analysis thus makes clear that the main qualitative properties of the optimal tax structure to which earlier studies called attention are not robust to these attempts to make the theory more realistic