one switch utility functions and a measure of risk consider the relative attractiveness to a decision maker of two financial gambles as the wealth of that individual varies it may seem reasonable that either one alternative should be preferred for all wealth levels or that there exists a unique critical wealth level at which the decision maker switches from preferring one alternative to the other decreasing risk aversion is not sufficient for this property to hold we identify the small class of utility functions for which it does we show how the property leads naturally to a measure of risk the results of this paper apply equally well to discounting functions for cash flows one switch discount functions permit at most one change in preference between cash flows as all payoffs are deferred in time

willingness to pay for stochastic improvements of future risk under different risk aversion abstract within a general intertemporal decision making framework this work shows one individual with more k th degree k 2 n ross risk aversion always chooses more current paying to improve his future payoff distribution when such stochastic improvement satisfies the n th degree mean preserving stochastic dominance moreover when stochastic improvement of the future payoff distribution is not mean preserving the notions of linearly quadratically restricted more ross risk aversion proposed by eeckhoudt liu and meyer 2017 can help provide a clear cut comparative statics analysis

additional aspects of rational insurance purchasing the purchase of insurance provides an individual with the ability to shift risk associated with either timeless or temporal uncertain prospects see dreze and modigliani 1972 previous insurance decision analysis can be further divided into cases in which the insurance contract is exogenously specified see mossin 1968 smith 1968 and cases in which the optimal form of contract is to be determined see raviv 1979 brennan and solanki 1981 this note is concerned with extending some of the results for timeless uncertain prospects with the insurance contract exogenously specified many of the properties associated with the purchase of insurance for timeless uncertain prospects are analyzed by mossin 1968 for different forms of contracts see also gould 1969 utilizing the arrow pratt measure of absolute risk aversion the effect of wealth upon the optimal amount of insurance is determined for the different forms of contracts recent work by ross 1981 demonstrates that in situations where individuals face more than one timeless uncertain prospect and they can purchase insurance only for a subset of these prospects then a more risk averse individual in the arrow pratt this paper examines the use of the arrowpratt and ross measures of risk aversion it is shown that in situations where the individual faces more than one uncertain prospect and can purchase insurance only for a subset of these prospects then in many cases the arrow pratt and ross measures of risk aversion are not sufficient to describe the behavior of the individual in purchasing insurance

optimal insurance in incomplete markets this paper examines the theory of optimal insurance purchasing in the presence of uninsurable background risk existing theorems concerning the optimal level of insurance and the optimal form of an insurance contract are shown to hold only under restricted market and risk assumptions in particular conditions sufficient for the optimality of full coverage or sufficient for the optimality of deductible policies depend on the correlation between insurable and uninsurable risks these results may provide a partial explanation why existing theory is often contradicted by observable behavior

risk sharing with competition abstract this paper analyzes noncooperative models in which syndicates form endogenously the analysis differs from that of r wilson 1968 econometrica 36m 119 132 and m machina 1985 the behavior of risk sharers mimeo because an entrepreneur may have to compete with other entrepreneurs to form a syndicate the equilibrium is characterized when there are n entrepreneurs and a single investor the comparative statics results of wilson and machina may not hold when other entrepreneurs are present for example an entrepreneur may not favor a first order stochastic dominating shift of an investment s returns because the shift makes the other entrepreneur more competitive and makes it more costly to form a syndicate journal of economic literature classification number 022

informational implications of interest rate rules this paper compares interest rate and money supply rules the analysisis conducted within a rational expectations macro model that incorporates flexible prices and informational frictions with differential information interest rate targets can affect the information content of market prices and real activity but these realconsequences can always be replicated by an appropriately chosen moneystock rule with feedback to economic activity however when the policyauthority lacks information about the state of the economic system itfaces a discrete choice between an interest rate peg and strict moneystock control copyright 1986 by american economic association

taxation insurance and precautionary labor we examine optimal taxation and social insurance with adverse selection in competitive insurance markets in a previous literature it has been shown that with perfect insurance markets social insurance improves welfare since it is able to redistribute without creating distortions this result has been taken as robust to the introduction of adverse selection as this would only provide additional justifications for social insurance we show however that adverse selection can weaken the case for social insurance compared to a situation with perfect markets whenever social insurance mitigates private underinsurance it also causes welfare reducing effects by decreasing precautionary labor supply and hence tax revenue in addition adverse selection may reduce the redistributive potential of social insurance we illustrate our general results using different equilibrium concepts for the insurance market notably we derive conditions under which a complete renunciation of social insurance is optimal and the government only relies on income taxation to achieve its redistributive objectives

a model of the firm in time and space abstract we consider a multi plant monopoly that sells to markets which are geographically separated and which stores product over time via an inventory capability it is assumed that plant average production cost is u shaped and that if the output of a plant s production run were sold to a single market at only one point in time the plant would operate on the falling portion of its average cost curve hence it is in the interest of the firm to aggregate markets both spatially and temporally to lower average production cost we develop the optimal joint interplant spacing inventory policy we also consider the effects changes in freight costs storage costs and interest charges have on the firm s optimal policy

skewness preference risk aversion and the precedence relations on stochastic changes this paper provides a general choice theoretic characterization of the trade off between risk and skewness whose importance in understanding risk taking behavior is well documented in empirical studies the condition under which the prudence measure kimball 1990 characterizes the strength of an individual s downside risk aversion against his own risk aversion is identified and interpreted in a unifying framework based on the concept of one stochastic dominant change preceding another and that of the desirability of a stochastic change the framework is also shown to be useful for a better understanding of the arrow pratt measure the stronger ross measure and the coincidence of the characterizations of downside risk aversion and prudence as well as the relationship between stochastic dominances of different degrees

multiplicative background risk although there has been much attention in recent years on the effects of additive background risks the same is not true for its multiplicative counterpart we consider random wealth of the multiplicative form xy where x and y are statistically independent random variables we assume that x is endogenous to the economic agent but that y is an exogenous and nontradable background risk that represents a type of market incompleteness our main focus is on how the presence of the multiplicative background risk y affects risk taking behavior for decisions on the choice of x we extend the results of gollier and pratt 1996 to characterize conditions on preferences that lead to more cautious behavior

managing channel profits a channel of distribution consists of different channel members each having his own decision variables however each channel member s decisions do affect the other channel members profits and as a consequence actions a lack of coordination of these decisions can lead to undesirable consequences for example in the simple manufacturer retailer consumer channel uncoordinated and independent channel members decisions over margins result in a higher price paid by the consumer than if those decisions were coordinated in addition the ensuing suboptimal volume leads to lower profits for both the manufacturer and the retailer this paper explores the problems inherent in channel coordination we address the following questions what is the effect of channel coordination what causes a lack of coordination in the channel how difficult is it to achieve channel coordination what mechanisms exist which can achieve channel coordination what are the strengths and weaknesses of these mechanism what is the role of nonprice variables e g manufacturer advertising retailer shelf space in coordination does the lack of coordination affect normative implications from in store experimentation can quantity discounts be a coordination mechanism are some marketing practices actually disguised quantity discounts we review the literature and present a simple formulation illustrating the roots of the coordination problem we then derive the form of the quantity discount schedule that results in optimum channel profits this article was originally published in marketing science volume 2 issue 3 pages 239 272 in 1983

assortative matching and risk sharing abstract this paper explores the sorting patterns in a two sided matching market where agents facing different risks match to share them when preference belongs to the class of harmonic absolute risk aversion hara the risk premium is perfectly transferable within each partnership thus a stable match minimizes the social cost of risk in the systematic risk model where agents are ranked by their holdings of a common risky asset the convexity of the joint risk premium in joint risk size leads to negative assortative matching nam in the idiosyncratic risk model where agents are ranked by their independent riskiness in the sense of second order stochastic dominance ssd nam arises when preference exhibits decreasing absolute risk aversion dara in the sense of ross and riskier background risk leads to more risk averse behavior however nam may fail to arise when riskier background risk leads to more risk tolerant behavior

comparative statics and non expected utility preferences abstract researchers have shown that many though not all of the basic results of expected utility analysis can be more or less directly generalized to non expected utility preferences this paper describes the essential difference between results which can be extended in this manner and those which cannot and shows that an important family of comparative statics theorems falls into the former class

rational expectations and the effects of government debt abstract this paper incorporates the effects of government debt into a standard rational expectations macroeconomic model due to limited current information even when the most extreme propositions about fiscal neutrality are true there are output and interest rate effects of unanticipated changes in government debt therefore the observation of a positive correlation between government deficits and output or interest rates does not imply that government bonds are net wealth

modeling international investment decisions for financial holding companies abstract this research analyzes the internationalization process model developed by johanson and vahlne and derives two integer programming investment decision models that consider the risk attitudes of investment firms johanson and vahlne s model provides a starting point for building a model that suits the investment approach and decision making process of financial holding companies in practice when firms make an international investment decision there is a need for a model that can generate outputs based on financial measures such as profit investment returns and tolerable levels of risk thus in this paper johanson and vahlne s concepts are studied and financial managers are interviewed to derive models that match the investment decision procedures of the firms the model helps firms manage the risks of their investments and derive accurate investment strategies based on investment objectives and constraints

a generalization of pratt arrow measure to nonexpected utility preferences and inseparable probability and utility the pratt arrow measure of local risk aversion is generalized for then dimensional state preference model of choice under uncertainty in which the decision maker may have inseparable subjective probabilities and utilities unobservable stochastic prior wealth and or smooth nonexpected utility preferences local risk aversion is measured by the matrix of derivatives of the decision maker s risk neutral probabilities without reference to true subjective probabilities or riskless wealth positions and comparative risk aversion is measured without requiring agreement on true probabilities risk neutral probabilities and their derivatives are shown to be sufficient statistics for approximately optimal investment and financing decisions in complete markets for contingent claims

putting risk in its proper place this paper examines preferences toward particular classes of lottery pairs we show how such concepts as prudence and temperance can be fully characterized by a preference relation over these lotteries if preferences are defined in an expected utility framework with differentiable utility the direction of preference for a particular class of lottery pairs is equivalent to signing the nth derivative of the utility function what makes our characterization appealing is its simplicity which seems particularly amenable to experimentation

the eclectic paradigm of international production a restatement and some possible extensions this article reviews some of the criticisms directed towards the eclectic paradigm of international production over the past decade and restates its main tenets the second part of the article considers a number of possible extensions of the paradigm and concludes by asserting that it remains a robust general framework for explaining and analysing not only the economic rationale of economic production but many organisational and impact issues in relation to mne activity as well

alternative approaches to comparative nth degree risk aversion this paper extends the three main approaches to comparative risk aversion the risk premium approach and the probability premium approach of pratt 1964 risk aversion in the small and in the large

risk wealth and sectoral choice in rural credit markets we model the role of the informal credit sector in developing countries the informational advantage of informal lenders is portrayed as the ability to monitor borrowers monitoring reduces the incentive problem and allows for contracts with lower collateral this enables informal lenders to serve both individuals who cannot post the collateral required by the formal sector and those who are able but do not want to post collateral the model is consistent with the conventional view of the informal sector as recipient of spillover demand from the formal sector it also shows that the informal sector may provide partial insurance as the lower collateral requirement implies greater consumption smoothing for borrowers

a standard measure of risk and risk value models in this paper we propose a standard measure of risk that is based on the converted expected utility of normalized lotteries with zero expected values this measure of risk has many desirable properties that characterize the notion of risk it is very general and includes many previously proposed measures of risk as special cases moreover our standard measure of risk provides a preference based and unified method for risk studies since the standard measure of risk is compatible with the measure of expected utility it can be used explicitly or implicitly in an expected utility model under a condition called risk independence a decision could be made by explicitly trading off between risk and value which offers an alternative representation of the expected utility model named the standard risk value model finally we discuss some other applications of the standard measure of risk and extensions of our risk value tradeoff framework for descriptive decision making

price level determinacy with an interest rate policy rule and rational expectations abstract this paper reconsiders a result obtained by sargent and wallace namely that price level indeterminacy obtains in their model if the monetary authorities adopt a feedback rule for the interest rate rather than the money stock it is shown that the indeterminacy vanishes if the interest rate rule is chosen so as to have a desired effect on the expected quantity of money demanded this holds even if considerable weight is given in the choice of a rule to the aim of smoothing interest rate fluctuations

modeling quantity discounts under general price sensitive demand functions optimal policies and relationships this paper presents models for determining optimal all unit and incremental quantity discount policies and investigates the effect of quantity discounts on increasing demand and ensuring pareto efficient transactions under general price sensitive demand functions the paper develops optimal quantity discount policies investigates their interrelationships and their benefits to both the supplier and the buyer and gains managerial insights for the scenarios of maximizing the supplier s profit and the joint profit we develop simple and efficient solution approaches for determining the all unit and the incremental optimal decision policies for general price sensitive demand functions we have three main findings first with price sensitive demand there are two incentives in offering quantity discounts increasing demand and ensuring pareto efficient transactions in most cases increasing demand dominates in justifying the offering of quantity discounts second using a single lot size associated with all efficient transactions as with the constant demand case does not hold with the price sensitive demand case third the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in benefiting both the supplier and the buyer

the optimal deductible for an insurance policy when initial wealth is random individual wealth typically includes risky assets often some of these risks are insurable but other risks such as market valuation of stocks inflation and other general economic conditions are usually not insurable a series of recent papers by kihlstrom romer and williams 1981 ross 1981 nachman 1982 and pratt 1982 have shown that the introduction of background risk requires stronger definitions of risk aversion we will use some of these results to examine the choice of the optimal deductible in an insurance contract when initial wealth is random an examination of insurance purchases within a broader portfolio is considered by doherty 1981 and by mayers and smith 1983 these papers use a mean variance framework to examine the separability of the insurance decision in general portfolio relationships have nontrivial implications for insurance buying strategies in particular correlation between insurable and noninsurable risk may affect the optimal level of insurance coverage deductible insurance is considered mainly because of its widespread use by many insurers furthermore deductibles the literature concerning the choice of optimal deductibles for insurance policies assumes that wealth is nonstochastic except for the value being insured however a decision maker s asset portfolio might easily contain other sources of risk some of which might be uninsurable this paper examines the choice of a deductible insurance contract in the presence of uninsurable background risk existing theorems concerning the optimality of full coverage are shown to hold only under restricted conditions concerning the correlation of insurable risk with other risky assets more general propositions are established and the effects of risk aversion are considered

stronger measures of higher order risk attitudes this paper aims to extend the results by ross 1981 15 and by modica and scarsini 2005 13 to stochastic dominance of degree 4 and over specifically it is shown that ross approach can be extended to any order of risk attitude beyond the generalization proposed by modica and scarsini by means of sth degree increase in risk defined by ekern 1980 8 c 2010 elsevier inc all rights reserved

preservation of more risk averse under expectations abstract the preservation of risk aversion properties of utility functions under expectation operations is of interest in the study of derived utility functions in sequential decision problems and in problems with multiple contemporaneous sources of uncertainty the purpose of this note is to present sufficient conditions for the pratt relation more risk averse to be preserved under expectations

the short run shutdown decision when output price and initial wealth are random abstract this paper extends the research of hori 1983 and chavas 1985 by investigating the short run shutdown decision of the competitive firm under output price risk when initial wealth is random central to this endeavor are the results of doherty and schlesinger 1986 and doherty et al 1987 concerning global and local risk premia under multiple sources of risk using a local risk premium two novel and intuitively pleasing results are reported here the reservation price of the shutdown decision varies a according to the diversification of the decision maker s cash flows and b if the decision maker exhibits dara then according to the depth of decision maker s pockets

risk aversion and the propensities for self insurance and self protection for a risk averse individual the methods for reducing the expected financial impact of a loss include reducing the severity of any loss that occurs self insurance and reducing the probability of the occurrence of a loss self protection the literature on this topic has pointed to several anomalies whereby the use of self protection and self insurance yield quite unsimilar results for example ehrlich and becker 5 show that self insurance is always a substitute for market insurance an insurance company s indemnifying a loss whereas self protection and market insurance might be complements dionne and eeckhoudt 4 show that a more risk averse consumer would always invest more in self insurance activities but not necessarily more in self protection activities they argue 4 42 that this result is counterintuitive and provides an exception to the widely accepted result that increased risk aversion reduces risky activities ehrlich and becker 5 639 argue that the incentive to self protect is not so dependent on attitude towards risk both of the above papers seem to take for granted that self protection activities reduce the riskiness of the final wealth distribution however as we argue below this is not the case if riskiness is defined as in rothschild and stiglitz 14 even if we use the variance as our risk measure we do not always reduce risk via self protection dionne and eeckhoudt suggest that these results might not be robust enough to extend to models that incorporate random initial wealth risk and state dependent preferences we show that the model seems to be very robust we also explain why self protection is not at all an exception to the long standing result of arrow 1 whereby more risk averse individuals undertake a lower

diversification exchange risk and corporate international investment all international investments inevitably have some diversification consequences yet the literature on foreign direct investment accords only a limited role to diversification or financial variables this paper develops a theory of corporate international investment from the standpoint of finance in an environment where the segmentation of international capital markets for individuals or the presence of agency costs provide some independence to corporate decisions separate from shareholders the model does not depend on any particular advantage of multinational firms and is specifies the stochastic properties of domestic and foreign output and input prices it is found that real exchange risk and diversification gains affect corporate international investment in a significant way it is also shown that the model embodies several existing explanations based on behavioral and economic variables

the newsvendor problem under multiplicative background risk this note studies the single period newsvendor problem when the newsvendor faces a multiplicative neutral independent background risk in an expected utility framework it is shown that multiplicative risk vulnerability is a sufficient condition to guarantee a decrease in the optimal order a weaker sufficient condition which has more interpretability is also provided and discussed this result sheds light on situations where exchange tax or inflation rates risks which apply multiplicatively to the final wealth are at work

improving buyer seller system cooperation through inventory control abstract much of the literature pertaining to inventory control systems assumes a perfectly competitive market in which increases or decreases in the buyer s purchase costs affect neither the final retail price nor consumer demand this paper attempts to contribute results to the more recent literature characterized by the buyer seller in a monopolistic market the focus is on issues and advantages of improving buyer seller cooperation in an inventory control system two inventory models are structured in a game framework in the first model a noncooperative relationship transaction is assumed in which the seller as the leader makes the first decision and then the buyer as the follower makes its decision the unique equilibrium of the game is obtained and found to coincide with the classical eoq result in the second model the leader follower relationship is relaxed and a scenario is examined in which the seller and the buyer cooperatively maximize their joint system profit comparison of the two models reveals that 1 a the total system profit is higher at cooperation than at noncooperation 2 b the optimal order quantity of the buyer is higher at cooperation than at noncooperation 3 c the wholesale price of the seller to the buyer is lower at cooperation than at noncooperation it is also demonstrated that a quantity discount approach is an effective mechanism for achieving system cooperation

wealth effects of open market operations and optimal monetary policy abstract equilibrium models of the business cycle such as those developed by lucas 1973 and barro 1976 barro 1980 are often used to analyze the effects of monetary disturbances on the economy these models typically view monetary injections as arising through lump sum transfer payments that are independent of an agent s holdings of money this paper examines the effects caused by misperceptions about money for the more realistic case when money is injected through open market operations the major result is that unperceived open market operations have a negative wealth effect

technical change and irreversible investment under risk abstract a stochastic dynamic model was constructed to analyze investment decisions of an individual farmer under risk in the presence of irreversibilities embedded technical change and indivisible capital an analytical solution was obtained and its local behavior studied by numerical methods optimal investment is obtained by regulating the difference between the desired and actual capital stocks between two barriers that define an inaction interval while the desired capital drifts between the barriers no action is taken if the desired capital touches the upper barrier the farmer invests pushing the average efficiency of the actual capital stock up this in turn raises the desired capital even higher and contracts the inaction interval if these effects are strong enough the farmer will invest again until the potential gains of the technological package are exhausted if the desired capital falls enough the farmer disinvests pushing down the average productivity and expanding the inaction interval disinvestment continues until it stops either because the inaction interval becomes so wide that it is no longer optimal to disinvest or because the actual capital stock is so small that it is no longer profitable to produce

bargaining power fear of disagreement and wage settlements theory and evidence from u s industry the paper develops and estimates a theoretical model of wage determination and union nonunion wage differentials in order to overcome the institutional ctiticisms of the formal bargaining literature the paper generalizes the nash zeuthen harsanyi model by linking the solution to the institutional concepts of bargaining power and fear or cost of disagreement and by making the outcome depend not only on endogenous but also on exogenous factors an operational specification of bargaining power and fear of disagreement allows the model to be estimated with data covering twelve companies and trade unions during the period from mid 1950 s to the late 1970 s while giving limited support to the nashzeuthen harsanyi solution the empirical analysis indicates that the bargaining outcome usually deviates from the nash zeuthen harsanyi point and in accordance with the institutionalist claim that it varies significantly with exogenous factors contrary to the traditional labor economics view the results do not support the general conclusion that the bargaining solution lies on the marginal revenue product curve of labor instead the relevant coefficients suggest that for many firms and unions the outcome might be better characterized by the efficient contract vertical contract curve

network linkages and location choice in foreign direct investment this paper shows that network linkage is an important determinant of location choice in foreign direct investment fdi network linkages are divided into internal intra firm and external inter firm linkages external linkages are further separated into strategic and relational linkages we found that taiwanese firms are keen on making external linkages but are indifferent to or incapable of making internal linkages through fdi strategic linkages motivate taiwanese fdi in the united states while relational linkages facilitate taiwanese fdi in southeast asia and china small firms are more sensitive to relational linkages than large firms in their choice of fdi location

prudence in bargaining the effect of uncertainty on bargaining outcomes abstract we investigate the outcome of bargaining when a player s pay off from agreement is risky we find that a risk averse player typically increases his equilibrium receipts when his pay off is made risky this is because the presence of risk makes individuals behave more patiently in bargaining strong analogies are drawn to the precautionary saving literature we show that the effect of risk on receipts can be sufficiently strong that a decreasingly risk averse player may be better off receiving a risky pay off than a certain pay off

health and portfolio choices a diffidence approach the effect of health status on portfolio decisions has been extensively studied from an empirical viewpoint in this paper we propose a theoretical model of individuals choice of financial assets under bivariate utility functions depending on wealth and health our approach makes an extensive use of the diffidence theorem we establish the conditions under which the share of wealth held in risky assets falls as 1 individuals health status deteriorates and 2 individuals health status becomes risky these conditions are shown to be related to the behavior of the intensities of correlation aversion and of cross prudence as wealth increases

substituting one risk increase for another a method for measuring risk aversion abstract this paper defines the rate of substitution of one stochastic change to a random variable for another it then focuses on the case where one of these changes is an nth degree risk increase and the other is an mth degree risk increase where n m 1 the paper shows that the rate of substitution for these two risk increases can be used to provide a broader definition and two additional characterizations of the nth degree ross more risk averse partial order the implications for local intensity measures of nth degree risk aversion are also examined the analysis organizes the existing results as well as generates new ones

inventory investment product cycles and the imperfectly competitive firm we consider a profit maximizing imperfectly competitive firm with downward sloping demand functions that can produce multiple products at a single facility we show that if the firm dedicates production to a single product both dynamic production which exploits inventory and static production which does not can be optimal we also consider sharing the production facility by multiple products we evaluate the efficiency of scheduling production using simple rotation cycle scheduling and give a condition for guaranteeing optimality of this scheduling rule we conclude by studying when dedicated production is preferred over shared production

risk aversion and the choice between risky prospects the preservation of comparative statics results most results in what can be termed the comparative statics of risk aversion are obtained when there is only one source of uncertainty the primary example which originally motivated the definition of risk aversion is that more risk averse people are willing to pay a higher premium for insuring against risk it is known that the results do not generally carry over when there is another source of uncertainty the paper develops conditions under which comparative statics results are robust against the introduction of additional sources of uncertainty

the information content of the interest rate and optimal monetary policy optimal monetary policy rules are derived in a rational expectations cum contracting framework monetary policy is redundant if wage setters exploit the incomplete current information embodied in today s nominal interest rate however the monetary authorities can save wage setters the costs of indexing to the interest rate a contemporaneous money supply feedback rule is as effective as wage indexation a lagged rule relevant under a regime of money supply targeting is also as effective if investors use the interest rate both rules have the same implications for the real interest rate as poole s combination policy however the two rules have strikingly different implications for the nominal interest rate

demand for risky financial assets a portfolio analysis abstract demand for risky financial assets takes place in portfolio settings the common stochastic orders applied in economics fail to rank demand for assets in such situations even for risk averse investors therefore the evaluation of the relative desirability of risky financial assets requires the establishment of new orders we prove that if returns on risky assets are ordered by the monotone likelihood ratio order then dominating assets will be more desired by all investors with nondecreasing utility functions

some stronger measures of risk aversion in the small and the large with applications the arrow pratt measures of risk aversion for von neumann morgenstern utility functions have become workhorses for analyzing problems in the microeconomics of uncertainty they have been used to characterize the qualitative properties of demand in insurance and asset markets to examine the properties of risk taking in taxation models and to study the interaction between risk and life cycle savings problems to name just a few applications equally importantly they have generated the linear risk tolerance class of utility functions which has provided canonical examples in such diverse areas as portfolio theory and the theory of teams despite these successes there have been a number of areas for which the results have been weaker than hoped it is natural to use the risk aversion measures to compare the behavior of individuals in risky choice situations for example consider the individual portfolio choice problem in a two asset world with a riskless asset and a risky asset if individual a has a uniformly higher arrow pratt coefficient of risk aversion than individual b then b will always choose a portfolio combination with more wealth invested in the risky asset but suppose that both assets are risky now there is no obvious sense in which the more risk averse individual can be said to hold a less risky portfolio but it seems strange that such a simple alteration should destroy the analytics which support the basic intuition similarly consider the basic insurance problem if one individual a is more risk averse than another b in the arrow pratt sense it follows that a will pay a larger premium to insure against a random loss than will b typically though an individual evaluates partial rather than total insurance that is only some gambles can be insured against and others must be retained in this case even when the gambles which are retained are independent from those which are insured it is no longer true that the individual whose arrow pratt measure of risk aversion is higher will pay a larger insurance premium the situation is no better when we consider comparative statics exercises for a single individual decreasing absolute risk aversion in the sense of arrow and

the market for sweepstakes this paper studies the market for monopolistically supplied sweepstakes we derive equilibrium demands for fixed prize and variable prize sweepstakes and determine the profit maximizing prize level and pay out ratio respectively it can be profitable to offer each type of sweepstake when there is a large enough number of weighted utility consumers who have constant absolute risk attitudes are strictly averse to small as well as symmetric risks and display longshot preference behaviour moreover for the variable prize sweepstake the supplier will generally find it profitable to combine sweepstakes targeting two smaller populations and offer a single sweepstake to the combined population this implication is corroborated by the recent spate of mergers of smaller state lotteries into larger ones

is land leasing a solution to unaffordable housing the increase in u s mortgage rates from nine per cent in 1976 to fifteen per cent in 1982 raised monthly mortgage payments by about sixty per cent even before rising house prices in the united states over this period are taken into account not surprisingly attention has been focused on ways and means of counteracting spiralling housing costs one proposed solution is land leasing under such an arrangement the homebuyer purchases the house but leases the land there may be an option to buy the land at some time in the future land leasing reduces the overall purchase price and hence lowers the minimum down payment and the initial monthly mortgage payment in hawaii land leasing has been a readily available alternative to land owning throughout the postwar period the analysis of residential housing prices in hawaii provides some quantitative estimates of the relative prices of leasehold versus fee simple properties the average price differential is surprisingly small one explanation of these small price differentials for which a model is developed and tested here is that borrowing constrained households use high discount rates to calculate the present value of the future land price that they will in effect have to pay at the expiration of the lease these discount rates are estimated in a nonlinear hedonic property price equation the results are then employed to answer the question under what conditions would a leaseholder buy the land outright before the expiration of the lease

on the theory of the competitive firm under uncertainty when initial wealth is random since sandmo s seminal paper on the theory of the competitive firm under output price uncertainty there has been considerable research on this topic 2 5 6 10 11 14 in all these studies it is assumed that in the absence of complete contingent markets output price risk is the only source of uncertainty for the firm however this may not be a realistic assumption in particular as argued by kihlstrom et al 7 it appears reasonable to consider the case where some of the initial wealth of the firm is held in risky assets in that case initial wealth is uncertain and should be modelled as a random variable the objective of this paper is to investigate the introduction of random initial wealth in sandmo s theory of the firm under price uncertainty in sandmo s model a number of important comparative static results e g the conditions under which the supply function is upward sloping 14 69 or under which increased price uncertainty reduces supply 5 depends critically on the sign of a particular expression stated in lemma 2 in ishii 5 while sandmo 14 69 shows this expression is non negative under arrow pratt decreasing absolute risk aversion it can be verified that his proof no longer holds when initial wealth is random therefore the comparative static analysis conducted by sandmo 14 batra and ullah 2 and ishii 5 is no longer valid and gives ambiguous results under initial wealth uncertainty the reason is that the arrow pratt measures of risk aversion 1 12 are too weak for making comparisons in situations where there is more than one source of uncertainty 13 then what can be deduced from the theory of the competitive firm in the realistic case where both initial wealth and output price are uncertain we will show here that meaningful results on the behavior of the competitiv firm under uncertainty can be obtained provided that the arrow pratt measures of risk aversion 1 12 are replaced by the ross measures of risk aversion 13 in particular a comparative static analysis of the production decisions using ross characterization of risk behavior is presented a number of new results are derived on the properties of risk responsive supply and input demand functions under both price and initial wealth uncertainty

arrow pratt measures of risk aversion the multivariate case arrow pratt measures of risk aversion have been defined for the univariate case for utility functions having the same ordinal preferences the authors extend k j arrow s probability premium index to the multivariate case and obtain a unique solution that can be employed to risk aversion comparison analysis they also extend g t duncan s definition of the risk premium vector and show that it can be employed in comparative risk aversion once they confine themselves to the same preference ordering hence the authors end up with two multivariate risk indexes that are parallel to the arrow and pratt univariate indexes copyright 1991 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

multivariate risk aversion and consumer choice this paper analyzes the effect of increases in risk aversion on a general consumer choice model with multiple sources of risk sufficient and in the two commodity case necessary conditions for a given demand function to increase or decrease with increased risk aversion are derived these general results are illustrated with a two period consumption savings model copyright 1990 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

a normalized value for information purchases consider agents who are heterogeneous in their preferences and wealth levels these agents may acquire information prior to choosing an investment that has a property of no arbitrage and each piece of information bears a corresponding cost we associate a numeric index to each information purchase information cost pair this index describes the normalized value of the information purchase it is the risk aversion level of the unique cara agent who is indifferent between accepting and rejecting the purchase and it is characterized by a duality principle that states that agents with a stronger preference for information should engage more often in information purchases no agent more risk averse than the index finds it profitable to acquire the information whereas all agents less risk averse than the index do given an empirically measured range of degrees of risk aversion in a competitive economy with no arbitrage investments our model therefore comes close to describing an inverse demand for information by predicting what pieces of information are acquired by agents and which ones are not among several desirable properties the normalized value formula induces a complete ranking of information structures that extends blackwell s classic ordering

monetary instruments and policy rules in a rational expectations environment abstract this paper explores the implications of rational expectations and the aggregate supply theory advanced by lucas 1973 and barro 1976 for analysis of optimal monetary policy under uncertainty along the lines of poole 1970 returning to a topic initially treated by sargent and wallace 1975 not surprisingly these two classical concepts alter both the menu of feasible policy choice and the desirability of certain policy actions in our setup unlike that of sargent and wallace 1975 the systematic component of monetary policy is a relevant determinant of the magnitude of business fluctuations that arise from shocks to the system central bank behavior both the selection of monetary instruments and the framing of overall policy response to economic conditions can work to diminish or increase the magnitude of business fluctuations however the activist policies stressed by the present discussion bear little if any relationship to the policy options rationalized by the conventional analysis of monetary policy under uncertainty in particular in contrast to poole s analysis money supply responses to the nominal interest rate are not important determinants of real economic activity rather the central bank should focus on policies that make movements in the general price level readily identifiable by economic agents

choosing between risky prospects the characterization of comparative statics results and location independent risk we consider expected utility maximizers choosing from a family of risky prospects and examine how choice is influenced by the decision makers attitude to risk if the family of risky prospects can be ordered so that as decision makers are more risk tolerant they choose a gamble higher in the ordering then it is natural to say that the family of risky prospects admit a comparative static result the paper characterizes when comparative static results of this sort exist an application is to propose a criterion of location independent riskiness

stochastic choice in insurance and risk sharing a reply yoram kroll s comment arises from an ambiguity in my paper which i think leads him to misinterpret the purpose of the analysis fortunately the comment does generate an additional result that is of value unfortunately in pursuing the wrong side of this ambiguity kroll concludes that stochastic dominance rules are quite ineffective in ranking insurance strategies such as full coverage and excess policies this conclusion does not hold and my main result is still valid much of the economic analysis of insurance buying strategies has been undertaken on the assumption that the premium to be paid is proportional to the actuarial value of the policy in other words there is a constant percentage loading given these conditions full insurance is never optimal for a risk averter smith 9 mossin 7 why then do so many people routinely purchase full insurance to illuminate this issue consider the problem what premium reduction is necessary to induce a risk averter to select a policy containing an excess deductible over a policy offering full cover the answer given in my paper is that the premium reduction must exceed the mathematical value of the uninsured risk this being a necessary condition but not a sufficient condition this result is robust in the face of kroll s comment but what is at issue is whether the premium example outlined in my paper satisfies this condition using the same notation as kroll the condition for second degree stochastic dominance of the full cover over the excess deductible policy is

constrained choices under risk there has recently been a revival of interest in the implications of rationing for economic theory extending the work of samuelson 21 tobin and houthakker 24 and pollak 16 recent papers by bruno 3 howard 8 latham 13 and neary and roberts 15 have explored the theory of producer and consumer behavior under quantity rationing these developments have provided useful hypotheses in the investigation of economic behavior for example they have stimulated a reexamination of macroeconomic disequilibrium however previous work seems to have focused on economic models in the absence of uncertainty yet given that production decisions are often made before output prices are known and in the absence of complete contingent markets sandmo 22 batra and ullah 2 and others have developed the theory of the competitive firm under price uncertainty under the expected utility maximization hypothesis such a theory provides useful information about the influence of changing economic conditions or of risk behavior on production decisions but because of the presence of short run adjustment costs leading to short run input fixity or because of regulatory or institutional constraints quantity rationing often influences production decisions in order to evaluate how rationing influences such decisions there is a need to develop a conceptual model of constrained choices of the firm under risk the objective of this paper is to explore the implications of quantity rationing in the context of production theory under price uncertainty by introducing risk and risk behavior it extends the classical analysis of quantity constrained production decisions 3 21 the implications of quantity constraints for risk responsive choice functions are derived using the concepts of compensated choice functions and virtual prices it is shown that expected price effects can be decomposed into substitution effects and wealth effects the substitution effects measure the effects of a change in expected price on the compensated choice functions the compensation being made through a change in initial wealth holding expected utility constant the wealth effects characterize risk preferences since a non zero wealth effect reflects a departure from an arrow pratt constant absolute risk aversion utility function the influence of rationing on the properties of ordinary as well as compensated choice functions is analyzed in details by deriving the implications of quantity constraints for firm behavior under uncertainty the paper presents a number of useful results concerning the influence of risk or technology on economic behavior under rationing for example a

risky choices and correlated background risk the analysis of a risky project should take into account not only uncertainties about the return from that project project risk but also uncertainties associated with other ongoing projects and with exogenous factors that can impact final wealth background risk the presence of background risk can change the optimal course of action with respect to a project and ignoring such risk might lead to a poor decision most work on background risk assumes that project risk and background risk are independent and are additive in their impact on wealth however independence is often unrealistic and background risk operates in a multiplicative manner in many situations we relax the independence assumption and consider a model with both additive and multiplicative background risk the optimal decisions in the correlated setting can be very different than those that would appear optimal if the correlation were ignored the impact of correlation differs in the additive and multiplicative cases with positive correlation being beneficial in some cases and negative correlation in others the analytical and numerical results indicate that in analyzing decision making problems it is very important to understand the direction and degree of dependence between project risk and background risks

channel coordination and quantity discounts this paper presents a model for analyzing the impact of joint decision policies on channel coordination in a system consisting of a supplier and a group of homogeneous buyers the joint decision policy characterized by the unit selling price and the order quantity is coordinated through quantity discounts and franchise fees both the annual demand rate and the operating cost including the purchase ordering and inventory holding costs depend on the joint decision policy employed this paper contributes by integrating work addressing quantity discounts on inventory and ordering policies and work focusing on the control mechanism provided by quantity discounts in channel coordination it is shown that the optimal all unit quantity discount policy is equivalent to the optimal incremental quantity discount policy in achieving channel coordination furthermore it is shown that quantity discounts alone are not sufficient to guarantee joint profit maximization the analyses of the general models are illustrated by specific analytical results obtained for a given demand function