uncertainty in the theory of renewable resource markets the natural growth rate of most renewable resource stocks is in part stochastic this paper examines the implications of such ecological uncertainty for competitive equilibrium in a market with property rights we show that stochastic fluctuations add a risk premium to the rate of return required to keep a unit of stock in situ and we examine the effects of fluctuations on resource rent examples are used to show that extraction can increase decrease or be left unchanged as the variance of the fluctuations increases depending on the extent of market self correction regulatory implications are also discussed renewable resource economics has traditionally been concerned with the study of dynamically optimal harvesting policies given a deterministic function for the natural growth of the resource stock issues have included the existence and characteristics of steady state equilibria for the optimally managed resource the need for and design of regulatory policies to prevent over exploitation and conditions under which as a social optimum or otherwise the resource will be exploited to extinction 1 much of this work has been based on the assumption of a fixed and exogenous price for the harvested resource typically resulting in bang bang solutions for the harvesting policy however some recent papers make price endogenous and thereby describe how the extraction rate and the rate of return and asset value of the resource behave in a competitive market with property rights 2

equilibrium valuation of natural resources the purpose of this paper is to provide a theoretical investigation of equilibrium spot and futures price behavior in a nonrenewable commodity market the underlying commodity is nonrenewable in the sense that the reserve level of the commodity is expected to decline over time in the absence of successful discoveries of additional reserves i wish to understand how the nonrenewable nature of the commodity influences the intertemporal extraction of the commodity equilibrium spot price behavior and the prices of derivative assets traded on the nonrenewable commodity there is considerable disagreement among economists whether resources are exhaustible in the sense of resource constraints becoming binding on our society in the foreseeable future some economists have argued that natural resources are being depleted at

the price of innovation new estimates of drug development costs the research and development costs of 68 randomly selected new drugs were obtained from a survey of 10 pharmaceutical firms these data were used to estimate the average pre tax cost of new drug development the costs of compounds abandoned during testing were linked to the costs of compounds that obtained marketing approval the estimated average out of pocket cost per new drug is us 403 million 2000 dollars capitalizing out of pocket costs to the point of marketing approval at a real discount rate of 11 yields a total pre approval cost estimate of us 802 million 2000 dollars when compared to the results of an earlier study with a similar methodology total capitalized costs were shown to have increased at an annual rate of 7 4 above general price inflation 2003 elsevier science b v all rights reserved

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

bundle size pricing as an approximation to mixed bundling multiproduct firms can set separate prices for all possible bundled combinations of its products mixed bundling however this is impractical for firms with more than a few products because the number of prices increases exponentially with the number of products we find that simple pricing strategies are often nearly optimal specifically we show that bundle size pricing setting prices that depend only on the size of bundle purchased tends to be more profitable than offering the individual products priced separately and tends to closely approximate the profits from mixed bundling jel d24 d42 l11 l13 l25

price discrimination by a many product firm determining the optimal selling strategy for a multiproduct firm facing consumers with unknown tastes is a difficult task this paper aims to show how almost optimal nonlinear tariffs can often be found when the number of products becomes large

bounding the welfare effects of third degree price discrimination under pigouvian third degree price discrimination a profit maximizing monopolist typically charges different groups of customers different prices resale between groups is assumed to be impossible these differences in price entail a loss of efficiency because marginal valuations of the output are not equal across buyers the net welfare effect of allowing price discrimination is ambiguous though because the total output under discrimination may exceed that under uniform pricing nevertheless under quite general conditions third degree price discrimination by a monopolist can increase static welfare only if total output is greater under discriminatory pricing than under uniform pricing richard schmalensee 1981 hal r varian 1985 marius schwartz 1990 although there has been much analysis of whether price discrimination raises or lowers total output or welfare the size of these effects has remained largely unexplored varian 1985 compares discriminatory pricing to uniform pricing for a monopolist and provides some bounds for the change in welfare in terms of market prices and outputs but these relationships give little sense of the relative size of welfare changes resulting from third degree price discrimination i address this issue by asking what can be said about the ratio wd wu where wd and wu denote welfare under discriminatory and uniform pricing respectively welfare is measured as the sum of producer surplus and marshallian consumer surplus section i provides two examples showing that this ratio can range from zero to infinity in these examples all markets are served under uniform pricing and demand in one of the markets is strictly convex considering a two market model in which a monopolist with constant marginal cost serves two independent markets under uniform pricing i show in section iii that if demands in both markets are concave then wd w is bounded below by 2 the assumptions of constant marginal cost and independent demands allow producer surplus and consumer surplus to be identified separately for each market separability across markets is central to the approach taken in this paper following joan robinson 1933 i call a market strong weak if the discriminatory price in that market is at least as great as no greater than the profit maximizing uniform price surprisingly the key to bounding wd wu is that the demand function in the weak market be concave if one market is strong the other is weak and demand in the weak market is concave then wd w can be bounded above by 2 5 or even 1 75 or 1 6 with additional assumptions on the demand functions these bounds arise for several reasons first the monopolist s profit under uniform pricing must be at least as large as the profit in the weak market under discrimination moreover if at all prices demand in the strong market is as great as in the weak market then profit under uniform pricing must be at least twice as great as profit in the weak market under discrimination otherwise the monopolist could do better by charging the monopoly price for the weak market second this relationship between profits in the two markets is useful in bounding welfare because welfare in each market can be related to profit in that market section ii shows that if demand is con department of economics and a b freeman school of business tulane university new orleans la 70118 i thank marius schwartz and two anonymous referees for their comments on earlier drafts of this paper

the return to capital in ghana we show that the real return to capital in ghana s informal sector is high for farmers we find annual returns ranging from 205 350 in the new technology of pineapple cultivation and 30 50 in well established food crop cultivation we also examine the relative prices of durable goods of varying durability and estimate a lower bound to the opportunity cost of capital of 60 this abstract was borrowed from another version of this item

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

bounding the relative profitability of price discrimination we derive bounds on the ratio of a monopolist s profit from third degree price discrimination to that from uniform pricing if the monopolist serves n independent markets demand is continuous and the cost function is superadditive then the profit ratio is bounded by n a linear demand example is provided coming arbitrarily close to this bound we provide examples showing the profit ratio can be unboundedly large when marginal cost is decreasing demand is discontinuous or fixed cost is positive if the monopolist has access to certain demand rationing strategies under uniform pricing we can bound the profit ratio even for discontinuous demand functions and multiproduct cost functions

on monopoly power in extractive resource markets abstract potential monopoly power in extractive resource markets is reduced by the depletability of reserves this paper examines the dependence of monopoly power on resource rent and on uncertainty over future reserve levels a model is developed that treats reserves as inventories that fluctuate stochastically over time as a result of exploration development and production activities solutions of the model illustrate how output and monopoly power vary with the elasticity of demand rent as a fraction of price and the variance of reserve fluctuations it is shown that uncertainty over future reserves can speed up production and by reducing resource rent restore part of the monopoly power otherwise lost because of depletion antitrust implications are discussed with reference to several resources

opportunism in multilateral vertical contracting nondiscrimination exclusivity and uniformity comment an input supplier selling to competing downstream firms would benefit from publicly committing at the outset to all contracts efficient commitment however would require complete contracts the authors study instead bilateral contracting without commitment regarding others terms each firm then fears that the supplier might opportunistically renegotiate another s contract to increase bilateral profit at the firm s expense the authors show that nondiscrimination clauses generally cannot curb such third party opportunism even with symmetric firms to reassure firms crude forms of commitment may be adopted this could explain the pervasiveness of exclusivity arrangements and the striking uniformity and intertemporal rigidity of franchise contracts copyright 1994 by american economic association

preventives versus treatments preventives are sold ex ante before disease status is realized while treatments are sold ex post even if the mean of the ex ante distribution of consumer values is the same as that ex post the shape of the distributions may differ generating a difference between the surplus each product can extract if for example consumers differ only in ex ante disease risk then a monopolist would have more difficulty extracting surplus with a preventive than with a treatment because treatment consumers having contracted the disease no longer differ in disease risk we show that the ratio of preventive to treatment producer surplus can be arbitrarily small in particular when the distribution of consumer values has a zipf shape and the disease is rare the firm s bias toward treatments can be reversed for example if the source of private information is disease severity learned ex post the difference between the producer surplus earned from the products can result in distorted rd the deadweight loss from this distortion can be as large as the entire producer surplus difference calibrations for hiv and heart attacks based on risk factors in the u s population suggest that the distribution of disease risk is sufficiently zipf similar to generate substantial differences between producer surplus from preventives and treatments empirically we find that proxies for the zipf similarity of the disease risk distribution are associated a significantly lower likelihood of vaccine development but not drug development jel codes o31 l11 i18 d42

mineral depletion with cost as the extraction limit a model applied to the behavior of prices in the nickel industry abstract this article follows papers by pindyck and heal and barrow in applying a hotelling type depletion model to a particular resource industry in this case that of nickel by means of the model the resource rent per ton of nickel is calculated as the proper index of extractive resource scarcity the time path of this resource rent indicates that the model explains industry behavior well and that as in the two previous studies depletion has been an important determinant of prices and rents in this industry

optimal pricing use and exploration of uncertain natural resource stocks abstract units of natural resources to be called mines are assumed distributed over an unexplored territory according to a poisson process in space at any moment total reserves and unexplored land are given society can determine the rate of consumption and the rate of exploration reserves are drawn down by consumption and increased by discoveries made during exploration the amount of unexplored land is decreased by exploration at any moment the payoff of society is a concave function of consumption less a linear function of exploration with future payoffs discounted optimal policies are considered and in particular it is shown for a large amount of unexplored land the shadow prices of reserves and of unexplored land move in random cycles but show only a slight upward tread thereby casting some light on the failure of mineral prices to rise at the market rate of interest

the measurement of monopoly power in dynamic markets importance in the design and application of antitrust policy much of the recent literature has focused on the structural and behavioral determinants of monopoly and monopsony power including the characteristics of costs and demand and the ways in which firms in the market interact with each other there has been less concern however with the development of a measure of monopoly or monopsony power instead the lerner index first introduced in 1934 has for years been accepted as the standard measure of monopoly power and is often used as a summary statistic in antitrust applications 1 the lerner index is just the margin between price and marginal cost l p mc p in a static market d i1 where rfis the elasticity of demand facing the firm so that the firm s elasticity of demand completely determines its monopoly power 2 however this need not be the case in a

third degree price discrimination in input markets output and welfare if price discrimination is realized the economy shifts from one equilibrium to another it clearly involves welfare effects the price discriminator clearly gains some consumers may also gain from the price cut but others may lose faced with higher prices etc traditionally the change in social welfare is known to be closely related to the change in total output in the case of third degree price discrimination it is well known that an increase in total output is a necessary condition for welfare improvement richard schmalensee 1981 proves this fact in a model in which the monopolist with constant marginal cost can perfectly separate markets further hal r varian 1985 extends this result to the case of interdependent markets permnitting increasing marginal cost of the monopolist and finally the assumption of nondecreasing marginal cost is eliminated by marius schwartz 1990 roughly speaking this proposition says that if there is a welfare gain from price discrimination there has to be some gain to offset the distortion involved on the other hand the vast majority of legal and other policy disputes over the price discrimination concern input markets not final good markets thus it seems important to investigate the situation in which a discriminating monopolist is not a final good supplier but an input supplier and the buyers of the input are downstream producers of a final good as is assumed in this paper if the downstream firms have different technologies their input demand functions will be different and thus the monopolist has an incentive to price discriminate in this scenario michael l katz 1987 and patrick degraba 1990 study the effect of inputmarket price discrimination and show that price discrimination always lowers welfare because it involves the distortion that a lower cost downstream firm is assigned a higher price unfortunately in their simple settings on the technology of downstream industry price discrimination can never change total output of the input or of the final good 1 thus we must say that welfare effect of input market price discrimination remains open to question if it has some effect on total output in particular we are curious as to whether we can obtain some close relationship between the changes in welfare and total output as we have obtained in the final good market settings with this motivation we will construct a model which involves change in total output of the final good in the next section the model and assumptions are provided in section ii after we extend the result of katz 1987 and degraba 1990 we find a relationship between the changes in welfare and total output strikingly it states that an increase in the total output of the final good is a sufficient condition for welfare deterioration this result contrasts with that obtained by schmalensee 1981 varian 1985 and schwartz 1990 from usual models of price discrimination in a final good market section iii concludes the analysis

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

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