precautionary saving in the small and in the large the theory of precautionary saving is shown to be isomorphic to the arrow pratt theory of risk aversion making possible the application of a large body of knowledge about risk aversion to precautionary saving and more generally to the theory of optimal choice under risk in particular a measure of the strength of the precautionary saving motive analogous to the arrow pratt measure of risk aversion is used to establish a number of new propositions about precautionary saving and to give a new interpretation of the dreze modigliani substitution effect copyright 1990 by the econometric society

standard risk aversion this paper introduces the concept of standard risk aversion a von neumann morgenstern utility function has standard risk aversion if any risk makes a small reduction in wealth more painful in the sense of an increased reduction in expected utility also makes any undesirable independent risk more painful it is shown that given monotonicity and concavity the combination of decreasing absolute risk aversion and decreasing absolute prudence is necessary and sufficient for standard risk aversion standard risk aversion is shown to imply not only pratt and zeckhauser s proper risk aversion individually undesirable independent risks always being jointly undesirable but also that being forced to face an undesirable risk reduces the optimal investment in a risky security with and independent return similar results are established for the effect of broad class of increases in one risk on the desirability of or optimal investment in a second independent risk

missing risk sharing markets and the benefits of cross hedging in developing countries abstract we study the impact of exchange rate risk on an exporting firm in a developing country when there is no forward market in the foreign currency however there exists a forward traded cross hedging asset in this country by cross hedging its foreign exchange exposure the firm can increase its economic welfare export production increases and promotes international trade of the developing country if the spot rate of foreign exchange has some regression relationship to the price of the cross hedging asset we extend our results to the case of price as well as initial wealth uncertainty

optimal international hedging in commodity and currency forward markets abstract this paper derives optimal hedging and production rules for an exporting firm which faces both commodity price and foreign exchange rate uncertainty the size of the commodity hedge is independent of the properties of the foreign exchange market however the optimal foreign exchange hedge depends on the commodity hedge and the properties of the commodity forward market the firm s production decision is independent of its objective function if both forward markets exist but depends on the consumption beta of the unhedgeable risks in the absence of one or both of the markets

multiple currencies and hedging this paper presents a model of a competitive exporting firm confronting multiple currency risks future markets do not exist for the firm s own currency but do exist between currencies of two countries to which the firm exports its entire output we provide analytical insight into optimal cross hedging and its implications on production and on trade flows we show that the unbiasedness of the cross currency futures market does not imply non random profits furthermore the availability of cross hedging opportunities has no effects on production but does have effects on exports

financial complexity and trade what are the implications on trading activity if investors are not sophisticated enough to understand and evaluate trades that have a complex payoff structure can frictions generated by this type of financial complexity be so severe that they lead to a complete market freeze like that of the recent financial crisis starting from an allocation that is not pareto optimal we find that whether complexity impedes trade depends on how investors perceive risk and uncertainty for smooth convex preferences such as subjective expected utility complexity cannot halt trade even in the extreme case where each investor is so unsophisticated that he can only trade up to one arrow debreu security without being able to combine two or more in order to construct a complex trade however for non smooth preferences which allow for kinked indifference curves such as maxmin expected utility complexity can completely shut down trade

optimal hedging by firms with multiple sources of risky revenues abstract we study the hedging behavior of competitive risk averse firms producing under price uncertainty and owning other sources of risky income as well we show that the well known separation property holds when a futures market for the commodity produced is available however unbiased futures market does not imply full hedging by which the firm avoids price risk altogether

currency hedging with options and futures abstract this paper examines the optimal hedging decision of a competitive exporting firm which faces concurrently hedgeable exchange rate risk and non hedgeable price risk we show that the hedging role of currency options is due to two distinct sources of non linearity i the multiplicative nature of the price and exchange rate risk and ii the marginal utility function of the firm in particular we show that a long put option position is optimal when the price risk is negatively correlated with the exchange rate risk and or the firm is prudent

cross hedging under multiplicative basis risk cross hedging price risk in an incomplete financial market creates basis risk we propose a new way of modeling basis risk where price risk and basis risk are combined in a multiplicative way under this specification positive prudence is a necessary and sufficient condition for underhedging in an unbiased market using the example of cross hedging jet fuel price risk with crude oil futures we show that the new specification is superior in describing the price series and that optimal cross hedges differ significantly from those derived under the traditional additive cross hedging model

risky business multinationals uncertainty and asymmetric insurance a partial equilibrium model is used to examine the international production allocation of a two plant multinational firm that is confronted with uncertainty with respect to foreign sales the firm produces identical products in both plants using firm specific factors the internationally price discriminating multinational has monopoly power in both segmented markets the analysis focuses on how asymmetric insurance facilities between the firm s home and host country influence its international production allocation and level of intra firm trade

hedging with price and output uncertainty abstract this paper extends mckinnon s analysis of hedging with price and output uncertainty to the general case where preferences are not necessarily quadratic and probability distribution not necessarily normal

the gains from differentiated policies to control stock pollution when producers are heterogeneous we derive optimal input taxes to control stock pollution problems generated by heterogeneous agents the taxes vary over time and in response to differences of asset quality and technology choice we also derive second best policies and compare them to the efficient policy and also among themselves different policies will affect the timing for when and the extent to which conservation technologies are adopted a numerical example based on the california drainage problem shows significant efficiency gains from the optimal policy compared to no intervention but much of the gains are lost with second best interventions the gains from optimal policies do not always increase with the degree of heterogeneity copyright 2008 oxford university press

a continuous time equilibrium model of forward prices and futures prices in a multigood economy abstract this paper is a theoretical investigation of equilibrium forward and futures prices we construct a rational expectations model in continuous time of a multigood identical consumer economy with constant stochastic returns to scale production using this model we find three main results first we find formulas for equilibrium forward futures discount bond commodity bond and commodity option prices second we show that a futures price is actually a forward price for the delivery of a random number of units of a good the random number is the return earned from continuous reinvestment in instantaneously riskless bonds until maturity of the futures contract third we find and interpret conditions under which normal backwardation or contango is found in forward or futures prices these conditions reflect the usefulness of forward and futures contracts as consumption hedges

exchange rate uncertainty futures markets and the multinational firm abstract we consider a monopolistic risk averse multinational firm which sells and produces at home and abroad under exchange rate uncertainty first we show that the stochastic exchange rate implies higher production and lower sales in the foreign country then we analyze the impact of currency futures markets a separation result is obtained for a multinational firm i e production and the allocation of sales are independent of the distribution of the random exchange rate and of the firm s attitude towards risk we also examine the effect of currency futures on a multinational firm s foreign direct investments in the absence of futures markets we obtain some comparative statics results when risk aversion increases

forward market and international trade many studies on hedging currency risk and international trade 6 14 18 17 have investigated the simultaneous hedging and production decisions with the nonstochastic home and foreign earnings assumption these studies derived a separation theorem which shows that the production decision made by a multinational firm for international trade is independent of the distribution of the exchange rate and dependent only on the forward price the separation theorem has two different implications first although the production decision is shown to depend on the forward price there is still a missing link connecting the trading activity in the forward markets with international trade second exchange rate uncertainty will not have an impact on the level on trade since the forward price can be used by multinational firms as a guide for the expected future spot rate the first implication seems to contradict results by britto 8 and telser 37 demonstrating that futures price has a real impact on resource allocation and production within an economy the second implication is inconsistent with a number of other empirical studies 2 11 12 22 29 that have shown exchange rate uncertainty has an adverse effect on trade and other studies 5 13 that have found exchange rate volatility to have a positive impact on trade although some studies 7 27 do recognize stochastic foreign income in the foreign hedging they ignore the two kinds of issues discussed above thus this paper attempts to investigate the simultaneous decisions for foreign exchange hedging and production under a stochastic assumption of foreign earnings a simple model is developed here to examine a the interaction of forward markets with international trade and b the impact of exchange risk on trade by endogenizing the forward price in a variety of scenarios this paper derives several interesting results under the stochastic foreign income scenario a new foreign exchange hedging rule which incorporates the covariability of foreign earnings and exchange risk is derived further we find that the separation theorem breaks down under such a situation interestingly we are able to show a positive linkage between trading activity in forward markets and export furthermore

optimal currency hedge ratios and interest rate risk abstract the objective of this article is to provide a framework for the interpretation of the optimal currency hedge ratios on foreign investments taking into account interest rate risk this is made possible by using a continuous time setting in the spirit of merton 1969 we focus on the importance of the interest rate differential forward basis in setting the optimal currency hedge because of the influence of interest rates on exchange rates more specifically we consider two discount bonds a domestic and a foreign one which follow stochastic processes possibly correlated with the other state variables of the model it is shown that the optimal hedge ratio can be split into five components a a macro economic component which is a function of the volatility of the interest rate differential and its covariance with currency movements this term depends on the currency considered but not on the asset being hedged b an asset specific term which is directly related to the covariance of the foreign currency asset return with exchange and interest rate movements c a speculative term function of the investor s risk preference and of the conditional risk premium on the exchange rate and d two stochastic opportunity set hedging terms the analysis of the optimal hedge ratio is illustrated on the period december 1970 1989 for stock and bond investments in seven countries jel g15 f31

futures market efficiency in the soybean complex 13 1 rev division of agricultural sciences university of ifornla working paper no 139 r i j futures market efficiency in the soybean complex gordon c rausser and colin carter giannini foundation of agricultural economics l ibraili v im california agric u l tural elqieriment station giannini foundation of agricultural economics march 1982

ambiguity models and the machina paradoxes daniel ellsberg 1961 constructed counterexamples to show the limitations of leonard j savage s 1954 subjective expected utility seu ellsberg s examples involved a comparison between objective uncertainty risk in which probabilities are known and subjective uncertainty in which they are not the prevailing prefer ence for objective over subjective uncertainty known as ambiguity aversion raised an important paradox for economic theory since ellsberg s classical work many models have been developed to generalize seu in order to accommodate the pref erence for objective over subjective uncertainty in the same manner as ellsberg mark j machina 2009 proposed two examples that falsify one of the seu generalizations david schmeidler s 1989 choquet expected utility ceu this article shows that the impact of machina s examples is not restricted to the model initially targeted his examples pose difficulties not only for ceu but also for the four other most popular and widely used models of ambiguity averse preferences namely maxmin expected utility itzhak gilboa and schmeidler 1989 variational preferences fabio maccheroni massimo marinacci and aldo rustichini 2006 a maxmin paolo ghirardato maccheroni and marinacci 2004 and the smooth model of ambiguity aversion peter klibanoff marinacci and sujoy mukerji 2005 consequently the implications for economics are more pro found than initially thought we also discuss marciano siniscalchi s 2009 vector expected utility veu model which can account for the typical ambiguity averse preferences in machina s examples finally we examine how our results are related to the uncertainty aver sion axiom which is assumed in virtually all commonly used decision models under ambiguity in particular we argue that machina s examples demonstrate that the uncertainty aversion axiom can be overly restrictive in some circumstances the article proceeds as follows section i presents the four models of ambiguity averse preferences which are alternatives to ceu and which are examined in this paper in section ii and iii the implications of machina s examples for these models are presented section iv discusses alternative models and the uncertainty aversion axiom

forward contracts and futures contracts abstract this paper provides a detailed discussion of the similarities and differences between forward contracts and futures contracts under frictionless markets and continuous trading simple arbitrage arguments are invoked to value forward contracts to relate forward prices and spot prices and to relate forward prices and futures prices we also argue that forward prices need not equal futures prices unless default free interest rates are deterministic

international trade with forward futures markets under exchange rate and price uncertainty abstract the paper examines a risk averse firm s decisions on the level of trade when the exchange rate and the commodity price are uncertain and the extent of forward exchange and commodity futures commitments first we verify the separation theorem and the full double hedging theorem second we investigate the implications of the existence of both forward foreign exchange and commodity futures markets in comparison to the case where only one or no market is available to the firm the second exercise enables us to focus on conditions under which establishing forward futures arrangements promotes international trade

efficient allocations under ambiguity abstract important implications of the expected utility hypothesis and risk aversion are that if agents have the same probability belief then consumption plans in every efficient allocation of resources under uncertainty are comonotone with the aggregate endowment and if their beliefs are concordant then the consumption plans are measurable with respect to the aggregate endowment we study these two properties of efficient allocations for models of preferences that exhibit ambiguity aversion using the concept of conditional beliefs which we introduce in this paper we provide characterizations of such conditional beliefs for the standard models of preferences used in applications

hedging price risk when real wealth matters abstract this paper analyzes optimal hedging of a tradable risk e g price risk or exchange rate risk with forward contracts in the presence of untradable inflation risk utility is defined over real wealth optimal forward positions are derived relative to a given initial exposure in the tradable risk a nominally unbiased forward market usually implies a non zero real risk premium and hence some risk taking if untradable inflation risk is a monotone function of the tradable risk plus noise cross hedging and speculating on the real risk premium are conflicting objectives the level of relative risk aversion determines which objective is dominant in a nominally unbiased forward market

risk ambiguity and the rank dependence axioms choice problems in the spirit of ellsberg 1961 suggest that rank dependent choquet expected utility preferences over subjective gambles might be subject to the same difficulties that ellsberg s earlier examples posed for subjective expected utility these difficulties stem from event separability properties that rank dependent preferences partially retain from expected utility and suggest that nonseparable models of preferences might be better at capturing features of behavior that lead to these paradoxes

asset demands without the independence axiom an important application of the theory of choice under uncertainty is to asset markets and an important property in these markets is a preference for portfolio diversification if an investor is an expected utility maximizer then s he is risk averse if and only if s he exhibits a preference for diversification this paper examines the relationship between risk aversion and portfolio diversification when preferences over probability distributions of wealth do not have an expected utility representation

exporting firm and forward markets the multiperiod case abstract we consider a model with a competitive risk averse exporting firm who faces uncertain exchanges rates in a multiperiod analysis the capital stock or fixed input has to be determined at the outset while the variable input labor is chosen optimally at the beginning of each period but before the realization of the exchange rate we show that introducing unbiased currency forward markets decreases the capital labor ratio in all periods we also show that such a firm tends to overhedge compared to the one period cases in some cases the introduction of unbiased forward markets results in higher investments and production in all dates

the rich domain of uncertainty source functions and their experimental implementation we often deal with uncertain events for which no probabilities are known several normative models have been proposed descriptive studies have usually been qualitative or they estimated ambiguity aversion through one single number this paper introduces the source method a tractable method for quantitatively analyzing uncertainty empirically the theoretical key is the distinction between different sources of uncertainty within which subjective choice based probabilities can still be defined source functions convert those subjective probabilities into willingness to bet we apply our method in an experiment where we do not commit to particular ambiguity attitudes but let the data speak

indirect hedging of exchange rate risk abstract the purpose of this study is to investigate the impact of exchange rate risk upon export production when the firm cannot engage in a direct forward hedge in the exchange rate however there exists a forward market for a domestic financial asset correlated with the exchange rate in question exporting firms using such an indirect hedging device to reduce foreign exchange risk do not necessarily increase their output when such unbiased hedging market becomes available this contrasts with the well known result in the case of direct hedging

a more robust definition of subjective probability the goal of choice theoretic derivations of subjective probability is to separate a decisionmaker s underlying beliefs subjective probabilities of events from their preferences attitudes toward risk classical derivations have all relied upon some form of the marschak samuelson independence axiom or the savage sure thing principle which imply that preferences over lotteries conform to the expected utility hypothesis this paper presents a choice theoretic derivation of subjective probability in a savage type setting of purely subjective uncertainty which neither assumes nor implies that the decisionmaker s preferences over lotteries necessarily conform to the expected utility hypothesis copyright 1992 by the econometric society

exchange rate volatility and exports a firm level analysis the relationship between real exports and exchange rate volatility is investigated using panel data analysis at the firm level results indicate that there is no negative or positive relationship between volatility and real exports in addition firm size and level of international activity do not influence the size and significance of the volatility effect on exports however there is some evidence that firms use import revenue to lower their exchange rate exposure

export and hedging decisions under revenue and exchange rate risk a note abstract this note analyzes optimal export and hedging decisions taken by a risk averse exporting firm which simultaneously faces hedgeable exchange rate risk and non hedgeable revenue risk abroad the separation property does not hold exports depend on preferences and expectations revenue uncertainty causes the firm to export less the optimal currency forward position can be divided into three components an expected revenue component a speculative component and a revenue uncertainty component

risk sharing in the small and in the large abstract this paper analyzes risk sharing in economies with no aggregate uncertainty when agents have non convex preferences in particular agents need not be globally risk averse or uncertainty averse in the sense of schmeidler 1989 we identify a behavioral condition under which betting is inefficient i e every pareto efficient allocation provides full insurance and conversely if and only if agents supporting probabilities defined as in rigotti et al 2008 have a non empty intersection our condition is consistent with empirical and experimental evidence documenting violations of convexity in either outcomes or utilities our results show that the connection between speculative betting and inconsistent beliefs does not depend upon global notions of risk or ambiguity aversion

hedging size risk theory and application to the us gas market abstract many corporate commitments exhibit a combined financial exposure to both market prices and idiosyncratic size components e g volume load or business turnover we design a customized contract to optimally mitigate the risk of joint fluctuations in price and size terms the hedge is sought out among contingent claims written on price and any quoted index that is statistically dependent on commitment size closed form solutions are derived for the optimal custom hedge pay off and for the asset holdings of two market strategies one based on price linked forwards the other based on price linked and index linked forwards analytical hedges are obtained using a stylized lognormal market model detailed comparative statics provide a thorough analysis of optimal hedging pay off functions performance assessment is conducted in the context of the us gas market and a prototypical urban region results suggest that hedging through suitable custom claims written on price and an additional index significantly outperforms standard price based as well as mixed price index forward hedging alternatives our optimal custom hedge could be adopted as a benchmark for the relative assessment of any risk management solution

subjective beliefs and ex ante trade we study a definition of subjective beliefs applicable to preferences that allow for the perception of ambiguity and provide a characterization of such beliefs in terms of market behavior using this definition we derive necessary and sufficient conditions for the efficiency of ex ante trade and show that these conditions follow from the fundamental welfare theorems when aggregate uncertainty is absent our results show that full insurance is efficient if and only if agents share some common subjective beliefs our results hold for a general class of convex preferences which contains many functional forms used in applications involving ambiguity and ambiguity aversion we show how our results can be articulated in the language of these functional forms confirming results existing in the literature generating new results and providing a useful tool for applications

the relation between forward prices and futures prices abstract this paper consolidates the results of some recent work on the relation between forward prices and futures prices it develops a number of propositions characterizing the two prices these propositions contain several testable implications about the difference between forward and futures prices many of the propositions show that equilibrium forward and futures prices are equal to the values of particular assets even though they are not in themselves asset prices the paper then illustrates these results in the context of two valuation models and discusses the effects of taxes and other institutional factors

a definition of uncertainty aversion a definition of uncertainty or ambiguity aversion is proposed it is argued that the definition is well suited to modelling within the savage as opposed to anscombe and aumann domain of acts the defined property of uncertainty aversion has intuitive empirical content behaves well in specific models of preference multiple priors and choquet expected utility and is tractable tractability is established through use of a novel notion of differentiability for utility functions called eventwise differentiability

impact of spatial differentiation of nitrogen taxes on french farms compliance costs the spatial differentiation of input based pollution fees should in theory decrease compliance costs in the case of nitrate pollution of water bodies from agriculture because both the damage and the compliance costs vary over space however the empirical evidence in the literature does not agree on the extent of the potential savings from differentiation we address this issue in the case of france using a mathematical programming model of agricultural supply aropaj the modeling approach used accounts for the spatial diversity of nitrate pollution and the heterogeneity of farming systems our results reveal the efficiency gains from differentiating pollution fees among polluters and water bodies for instance firm specific and water body specific taxes represent respectively 5 8 and 32 5 of farmers gross margin in terms of compliance costs whereas a uniform policy at the river basin district or national level leads to major economic losses and abandonment of the agricultural activity these results stem from the lower tax rates faced by farmers in less polluted areas for scenarios based on spatial differentiation our estimates suggest that realistic regulation via input based pollution fees should be differentiated in order to significantly reduce the financial burden on farmers of conforming to predefined pollution levels some potential adverse effects related to input based taxation and land use change call for additional fine scale nitrogen pollution regulation e g limitations on crop switching

uniform and non uniform second best input taxes we investigate second best input based taxes foragricultural nonpoint pollution control when marketprices are endogenous and production isheterogeneous theoretically we derive the optimalforms of taxes which take account of heterogeneity non uniform taxes and a tax which does not auniform tax empirically we use a multi factor market equilibrium simulation model to determineoptimal tax rates and associated equity effects particularly differences in landowner gains lossesacross a heterogeneous region when market prices areendogenous second best tax policies result inpecuniary externalities that affect existingenvironmental externalities in particular thepecuniary externalities amplify the effect of producerheterogeneity on determination of sub regionaldifferences in tax rates and returns to land particularly for the uniform policy with endogenousprices the uniform tax rate is considerably higherthan any of the non uniform rates and ironically thenon uniform taxes result in less dispersion oflandowner gains across sub regions than the uniformtax

ambiguity made precise a comparative foundation the theory of subjective expected utility has been recently extended to allow ambiguity to matter for choice we propose a notion of absolute ambiguity aversion by building on a notion of comparative ambiguity aversion we characterize it for a preference model which encompasses some of the most popular models in the literature we next build on these ideas to provide a definition of unambiguous act and event and show the characterization of the latter as an illustration we consider the classical ellsberg 3 color urn problem and find that the notions developed in the paper provide intuitive answers journal of economic literature classification number d81

forward and futures prices evidence from the foreign exchange markets empirical studies of the treasury bill markets have revealed substantial differences between the futures price and the implied forward price these differences have been attributed to taxes transaction costs and the settling up procedure employed in the futures market this paper examines the forward and futures prices in foreign exchange in an attempt to distinguish between the competing explanations empirical studies of the treasury bill market have revealed differences between the futures price or rate and the implicit forward price derived from the term structure of interest rates 1 these differences have generally been attributed to market imperfections such as taxes and transaction costs see for example arak 1 capozza and cornell 2 and rendelman and carabini 6 recently however cox ingersoll and ross 3 henceforth cir derived a model in which forward and futures prices need not be equal even in perfect markets without taxes as long as interest rates are stochastic the significance of the cir effect may be hard to investigate using only data from the bill market because of the potentially complicating effects of taxes and transaction costs unique to this market by using data from the foreign exchange market we are able to eliminate the tax effect and reduce the impact of transaction costs the question we address is whether the discrepancies observed in the treasury bill market are also observed in the foreign exchange market if they are then we have evidence that the differences are due to a combination of the cir effect and the transaction costs common to both markets if they are not then either the magnitude of the cir effect is much less in the foreign exchange market or the treasury bill results are due to the unique tax treatment and transaction costs of that market this paper is organized as follows in section i the trading mechanics of the forward and futures markets in foreign exchange are discussed section ii reviews the explanations for the discrepancies between the forward and futures prices for treasury bills the institutional differences between the foreign exchange and bill markets are also summarized to show which of these explanations cannot apply to the foreign exchange market in section iii the data are decribed and the empirical results are presented the conclusions are summarized in the final section

the behavior of an open economy firm under flexible exchange rates most proponents and opponents of floating believe that greater variability of foreign exchange rates will increase uncertainty in international transactions and hence that the volume of international trade and financial flows will be curtailed without well developed facilities for hedging against exchange uncertainty the effects of exchange risk on merchant exporters and importers have been studied by some authors under the assumption of fixed production ethier 1973 clark 1973 hodder 1977 etc others have investigated the production behaviour of an export firm in a static context see for example baron 1976a b however the impact of the greater volatility of exchange rates upon domestic employment and capital accumulation on the one hand and upon international financial transactions on the other has received scant attention in the literature this paper establishes a dynamic model of a small competitive firm which is engaged in domestic production foreign trade through exports of its products and or imports of its inputs and financial transactions in domestic and foreign currencies since the firm faces uncertainty about future exchange rates and future prices of outputs and inputs it attempts to hedge against the risk if it is risk averse a forward foreign exchange market is assumed to exist the firm s decisions on production investment forward contracting and financing which are closely related in the model are based on exogenously given probability distributions of exchange rates and prices the paper is planned as follows section i presents a model of the firm and formulates its objective function and constraints section ii solves its maximization problem and interprets the first order conditions for short run equilibrium in particular three different roles of the firm in the forward exchange or financial market are emphasized pure hedging speculative hedging and pure speculation section iii analyses the dynamic behaviour of a typical open economy firm section iv conducts comparative dynamic exercises of the firm in a long run steady state equilibrium and discusses how exchange rate uncertainty affects the firm s optimal decisions the implications of the purchasing power parity condition are also developed section v summarizes our conclusions

export flexibility and currency hedging this article studies the behavior of an export flexible firm under exchange rate uncertainty we show that the separation theorem holds if selling exclusively in the domestic market is suboptimal even under the most unfavorable spot exchange rate otherwise the firm s optimal output depends on its preferences and on the underlying uncertainty we further show that the full hedging theorem holds only when the firm always finds it optimal to sell its entire output in the foreign market otherwise export flexibility introduces a convexity into the firm s foreign exchange risk exposure which calls for the use of currency options for hedging purposes

discriminating monopoly forward markets and international trade recent empirical studies see e g kravis and lipsev 1977 1978 isard 1977 aspe and giavazi 1982 demonstrate that there are notable divergencies between domestic and export prices this empirical evidence suggests that the law of one price is systematically violated kravis and lipsey 1977 p 155 argue that many firms involved in international trade particularly manufacturers are in the position of a discriminating monopolist faced with separate markets each characterized by a different demand elasticity a model which explicitly allows for price discrimination has been used by several authors see for example aspe and giavazi 1982 ethier 1982 katz paroush and kahana 1982 and tarr 1979 katz paroush and kahana 1982 hereafter kpk used a model of a price discriminating firm which operates under price uncertainty to investigate its optimal level of output and sales in the two markets the main assumption made in kpk 1982 is that the firm determines its level of output and the allocation of sales between the two markets before the resolution of uncertainty furthermore no forward markets were available to this firm in this paper we analyze a price discriminating firm which sells its produce both in the domestic and on world markets under either exchange rate uncertainty or foreign price uncertainty this firm is a monopoly in the domestic market but a price taker on the world market our model differs substantially from the kpk model and in some cases conforms better with reality due to the following two assumptions first the firm determines its level of output before the resolution of uncertainty but decides about the optimal allocation of sales only after it observes the foreign price denominated in domestic currency secondly forward markets to share the exchange rate risk or the uncertain foreign commodity price are available and their impact on the firm s policy is analyzed hence this work integrates two strands of literature it combines studies on price discriminating firms some were mentioned above and studies on firm behavior when forward markets are available danthine 1978 holthausen 1979 katz and paroush 1979 feder just and schmitz 1980 in this paper we are mainly concerned with a firm which always exports this includes large