intersectoral externalities and indeterminacy abstract we consider a two sector economy with positive intersectoral external effects and nonincreasing social returns we show that if the discount factor is close to 1 then local indeterminacy may be obtained with mild market imperfections moreover with additional conditions when is made smaller the steady state becomes totally unstable and quasi periodic cycles along which equilibrium paths are indeterminate may appear through a hopf bifurcation this will be proved even if the investment good is capital intensive at the private level while this condition guarantees local determinacy in the sector specific case journal of economic literature classification numbers c62 e32 o41

a simple heuristic for joint inventory and pricing models with lead time and backorders we study a joint inventory and pricing problem in a single stage system with a positive lead time we consider both additive and multiplicative demand forms this problem is in general intractable due to its computational complexity we develop a simple heuristic that resolves this issue the heuristic involves a myopic pricing policy that generates each period s price as a function of the initial inventory level and a base stock policy for inventory replenishment in each period the firm monitors its so called price deflated inventory position and places an order to reach a target base stock level the price deflated inventory position weights the on hand and pipeline inventory according to a factor that reflects the sensitivity of price to the net inventory level to assess the effectiveness of our heuristic we construct an upper bound to the exact system the upper bound is based on an information relaxation approach and involves a penalty function derived from the proposed heuristic a numerical s

price discrimination through offers to match price in this paper a firm discriminates between two classes of customer who have a different cost of information by coupling a list price with an offer to match the pr ice of any other shop if the list price elsewhere is lower the firm will be successful in discrimination the list price of each firm is increasing in the number of sellers and the total sales are decreasi ng in the number of sellers furthermore if sellers coordinate they discriminate more efficaciously and increase their profits by increa sing their total sales copyright 1987 by the university of chicago

why do manufacturers issue coupons an empirical analysis of breakfast cereals we explore the relationship between shelf prices and manufacturers coupons for 25 readyto eat breakfast cereals we find that shelf prices are lower during periods when coupons are available this result is inconsistent with static monopoly price discrimination under a broad range of assumptions we present evidence that is inconsistent with both dynamic theories of price discrimination and explanations of couponing based on the vertical relationship between manufacturers and retailers we find support for models of price discrimination in oligopoly settings as well as suggestions that firmwide incentives may induce managers to use coupons and price cuts simultaneously finally lagged coupons have a positive effect on current sales suggesting that coupons are used to induce repurchase

international effects of national regulations external reference pricing and price controls under external reference pricing erp the price that a government permits a firm to charge in its market depends upon the firm s prices in other countries in a two country home and foreign model where demand is asymmetric across countries we show that home s unilaterally optimal erp policy permits the home firm to engage in a threshold level of international price discrimination above which it is just willing to export if the firm faces a price control abroad or bargains over price with the foreign government an erp policy can even yield higher home welfare than a direct price control

technical note a computational approach for optimal joint inventory pricing control in an infinite horizon periodic review system this note considers a joint inventory pricing control problem in an infinite horizon periodic review system demand in a period is random and depends on the posted price besides the holding and shortage costs the system incurs inventory replenishment costs that consist of both variable and fixed components at the beginning of each period a joint inventory and pricing decision is made under the long run average profit criterion we show that an optimal policy exists within the class of so called s s p policies this is established based on our algorithmic development which also results in an algorithm for finding an optimal s s p policy

positively sloping marginal revenue ces utility and subsistence requirements the possibility that marginal revenue may possess a positive slope has long been recognized as important in her classic the economics of imperfect competition joan robinson 14 accorded considerable significance to the possibility and investigated it at length despite robinson s insights upward sloping marginal revenue functions remained largely a curiosity widely regarded as an overly stringent perversity unlikely to occur in reality considerable doubt was cast on this view when in 1980 a a walters 20 reported the presence of positively sloping marginal revenue in the pricing policies of the port of singapore the case for upward sloping marginal revenue was furthered by formby layson and smith s 8 straightforward demonstration that upward sloping marginal revenue schedules are very easily produced and can never be ruled out because simple parallel shifts in strictly convex demand and or rotations always transform demand schedules with downward sloping marginal revenue into ones with positively sloping schedules this strongly suggests that no theoretically reasonable restrictions can be placed on the behavior of marginal revenue because to do so would rule out such simple transformations as parallel shifts or rotations in demand such restrictions would be too stringent to be acceptable upward sloping marginal revenue has found important application in such diverse topics as catastrophe theory 3 third degree price discrimination 13 dual equilibria and monopolistic competition 11 specific taxes and quality 2 and international trade 7 2 the significance of non monotonic marginal revenue functions is further underscored by the fact that the presence of upward sloping marginal revenue significantly affects the sign of comparative static results for example see 18 260 15 16 2 a shortcoming of previous analyses lies in the fact that they draw conclusions from consideration of slope level and curvature of the demand schedule alone the behavior of marginal revenue derived directly from the more fundamental basis of utility theory has not been examined this paper takes up this question employing wold s theorem to analyze marginal revenue

third degree price discrimination with interdependent demands this paper analyzes the price output and welfare effects of third degree price discrimination for a monopolist who sells in two interdependent markets the case where the two goods sold by the monopolist are complements is analyzed as well as the more typical case where the two goods are substitutes the economic effects of price discrimination are shown to depend on the type and strength of demand interdependence the curvature of the demands and the slope of marginal cost the circumstances under which price discrimination causes both market prices to either rise or fall are also analyzed

third degree price discrimination under economies of scale there has long been a controversy in economics about whether or not a firm with monopoly power should be allowed to exploit its monopoly power by engaging in third degree price discrimination the effect of third degree price discrimination on welfare is two fold 1 output under price discrimination is misallocated because different groups are charged different prices but 2 if total output is different under price discrimination than under uniform pricing this will also affect welfare 2 schmalensee 8 varian 11 12 and schwartz 9 have shown that price discrimination must decrease welfare if output under price discrimination is the same or less than output under uniform pricing this fundamental result is quite robust and holds regardless of the number of sub markets or the behavior of marginal cost rising constant or falling it also holds even if the sub market demands are interdependent a necessary but not sufficient condition for price discrimination to be beneficial is that it increase total output perhaps the most common situation in which price discrimination will be beneficial is the case where only one sub market is served under uniform pricing but two or more sub markets are served under price discrimination in this case hausman and mackie mason 3 have pointed out that price discrimination will result in a pareto welfare improvement if marginal cost is constant or falling even when price discrimination does not open up new markets hausman and mackie mason 3 and nahata ostaszewski and sahoo 5 have shown that price discrimination can result in a pareto improvement by lowering prices in all sub markets hausman and mackie mason 3 257 argue that price discrimination is most likely to be beneficial when economies of scale are present 3

competitive price discrimination we model firms as supplying utility directly to consumers the equilibrium outcome of competition in utility space depends on the relationship u between profit and average utility per consumer public policy constraints on the deals firms may offer affect equilibrium outcomes via their effect on u f rom this perspective we examine the profit utility and welfare implications of price discrimination policies in an oligopolistic framework we also show that an equilibrium outcome of competitive nonlinear pricing when consumers have private information about their tastes is for firms to offer efficient two part tariffs

stability global dynamics and markov equilibrium in models of endogenous economic growth abstract this paper studies the local and global dynamics of two sector models of endogenous growth with economy wide external effects and taxes on capital and labor the local analysis classifies the parameter space depending on the number of stationary solutions and local stability of equilibria the global analysis shows that if taxes are within certain bounds and the size of the external effects on the average level of human capital is smaller than the share of physical capital the equilibrium path is monotone and therefore a continuous markov equilibrium can be constructed

technical note joint inventory and pricing control with general additive demand this paper analyzes a periodic review joint inventory and pricing control problem for a firm that faces stochastic price sensitive demand under a nonstationary environment with fixed ordering costs any unsatisfied demand is backlogged the objective is to maximize expected profit over a finite selling horizon by coordinating the inventory and pricing decisions in each period we show that for an additive demand model an s s p policy is optimal when the expected revenue is quasi concave in price the inventory cost of holding and or backlogging is quasi convex and the nonnegative random demand has a polya or uniform density function for the special case with no fixed ordering cost the optimality of a base stock list price policy is demonstrated for more general demand distributions and convex inventory cost these sets of sufficient conditions generalize the existing conditions in the literature that require for example the demand and or revenue functions to be concave or the model parameters to be stationary in time our generalization makes the structural results applicable to models broadly supported by economic theory and empirical data in addition our proof uses a distinct sequential optimization technique for iteratively establishing the quasi k concavity of dynamic optimal value functions

indeterminacy and sunspots with constant returns recently there has been a renewed interest in the possibility of indeterminacy and sunspots or alternatively put in the existence of a continuum of equilibria that arises in dynamic economies with some market imperfections much of the research in this area has been concerned with the empirical plausibility of indeterminacy in markets with external effects or with monopolistic competition and which exhibit some degree of increasing returns while the early results on indeterminacy relied on relatively large increasing returns and high markups more recently benhabib and farmer 1996a showed that indeterminacy can also occur in two sector models with small sector specific external effects and very mild increasing returns

indeterminacy under constant returns to scale in multisector economies recently there has been a renewed interest in indeterminacy or alternatively put in the existence of a continuum of equilibria in dynamic economies that exhibit some market imperfections one of the primary concerns of this literature has been the empirical plausibility of indeterminacy which arises in markets with external effects or with monopolistic competition often coupled with some degree 10 of increasing returns

third degree price discrimination in the presence of congestion externality this paper analyzes third degree price discrimination of a monopoly airline in the presence of congestion externality when all markets are served the model features the business passenger and leisure passenger markets where business passengers exhibit a higher time valuation and a less price elastic demand than leisure passengers our main result is the identification of the time valuation effect of price discrimination which can work in the opposite direction as the well known output effect on welfare this time valuation effect clearly explains why discriminating prices can improve welfare even when this is associated with a reduction in aggregate output

pareto price discrimination abstract as the collection of consumer data becomes more common online merchants are better equipped to price discriminate now more than ever before while standard first degree price discrimination benefits merchants and harms consumers relative to uniform pricing i derive an alternative first degree pricing strategy that achieves efficiency and pareto improves upon the uniform pricing equilibrium furthermore i show that price ceilings can enforce these pareto price discrimination strategies making pareto price discrimination a viable option for merchants and policy makers

monopoly price discrimination and demand curvature this paper presents a general analysis of the eects of monopolistic third degree price discrimination on welfare and output when all markets are served su cient conditions involving straightforward comparisons of the curvatures of the direct and inverse demand functions in the dierent mar kets are presented for discrimination to have negative or positive eects on

testing static oligopoly models conduct and cost in the sugar industry 1890 1914 we explore the widespread methodology of using demand information to infer market conduct and unobserved cost components under the hypothesis of static oligopoly behavior direct measures of marginal cost and conduct indicating small market power serve as benchmarks the more competitive models yield better cost estimates the best cost estimates occur when conduct is estimated as a free parameter which in turn only slightly underestimates our direct measure it also tracks the decline in market power accompanying the industry s structural changes the methodology is largely validated although partial cost information can improve its predictive power conclusions are robust to demand function

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 law of demand positive sloping marginal revenue and multiple profit equilibria this paper demonstrates that the conditions for a positively sloping marginal revenue curve are much less stringent than is generally recognized simple transformations of any well behaved convex demand function can easily result in a demand for which marginal revenue is positively sloping for this reason positively sloping marginal revenue functions must be considered whenever convex demand functions are analyzed the existence of positively sloping marginal revenue makes multiple profit equilibria for the firm a very real possibility

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

further tests of static oligopoly models whiskey 1882 1898 using data from the turn of the century whiskey industry we conduct tests of the neio methodology similar to those conducted by genesove and mullin 1998 like genesove and mullin we find that the neio methodology appears to perform reasonably well for low levels of market power conduct is somewhat overestimated with estimates ranging from 0 17 to 0 35 as compared to direct estimates of 0 09 cost parameters are generally underestimated estimates of conduct and remaining cost parameters improve significantly however with additional information on cost estimates improve further if conduct is allowed to have two regimes which are identified based on historical evidence

indeterminacy and increasing returns abstract we investigate properties of the one sector growth model with increasing returns under two organizational structures capable of reconciling the existence of aggregate increasing returns with competitive behavior by firms the first involves input externalities the second involves monopolistic competition we show for parameters in close accord with recent literature on real business cycles that the model displays an indeterminate steady state that can be exploited to generate a model of business fluctuations driven by self fulfilling beliefs in our first class of models growth is generated by exogenous increases in factor productivity in the second class the marginal product of capital is large enough for endogenous growth journal of economic literature classification numbers e00 e3 o40

third degree price discrimination consumption externalities and social welfare this paper analyses monopolistic third degree price discrimination in the presence of consumption externalities within two separate markets assuming linear inverse demands we investigate an associated change in social welfare the sum of the consumers surpluses and the producer s profit with the regime change from uniform pricing to price discrimination when both markets are open under either regime it is shown that social welfare can improve even if total output is unaffected by the regime change moreover it is possible that the sum of the consumers surpluses also increases

the benefits of integrating european electricity markets this paper builds on and extends work under contract ener b1 491 1 2012 published as newbery et al 2013

taxation and the output and welfare of third degree price discrimination the literature on third degree price discrimination dates back to the work by pigou 14 and joan robinson 15 over half a century ago the subsequent works on the output effect can be seen in edwards 3 silberberg 19 battalio and ekelund 1 greenhut and ohta 7 finn 4 smith and formby 20 formby et al 6 and shih mai and liu 18 the welfare effect by yamey 26 was expanded and generalized by schmalensee 16 varian 24 and schwartz 17 in addition nahata ostaszewski and sahoo 12 demonstrate a sufficient condition for price changes that guarantees a welfare increase with the twice differentiable and monotonically decreasing demand functions previous work on third degree price discrimination has not addressed the issue of taxation governments often levy excise taxes on firm s sales under conditions of third degree price discrimination such taxes can have depending upon the form of the tax quite different output and welfare effects this paper investigates the joint effects of third degree price discrimination and excise taxation in several different ways first in a fashion analogous to suits and musgrave s analysis of simple non discriminating monopoly 22 we consider the effects of ad valorem and unit specific excise taxes at a constant level of output but in a third degree price discrimination environment second in a similar manner we compare cost and demand ad valorem taxes and the so called musgravian transformation 11 27 under discriminatory conditions finally we compare the output and welfare effects of a specific cost ad valorem and demand ad valorem excise tax that generate the same level of revenues in a third degree price discrimination environment

a model of search with price discrimination abstract we introduce observable heterogeneity across buyers into a model of simultaneous search buyers differences are informative about their willingness to search giving rise to price discrimination even if they all have the same willingness to pay we analyze and compare equilibrium outcomes when price discrimination is allowed and when it is not we find that the price comparison across consumers as well as the effects of banning price discrimination critically depend on the elasticity of the search cost distribution interestingly for normally distributed search costs there is an inverted u shape relationship between prices and buyers size similarly a ban on price discrimination hurts small and large buyers to the benefit of the medium size ones

a note on the effect of cost changes on prices in a recent article in this journal sumner 1981 took an ingenious approach to estimating the level of monopoly power in the cigarette industry he noted that differences in marginal costs exist in the industry due to varying levels of state taxes the sales prices established will satisfy the equation p i liq l mr mc where p price and q the elasticity of demand for the product in question if elasticity is a constant observing the change in marginal cost and the change in price enables one to infer the elasticity of demand perceived by the firm elasticity could then be used as a proxy for the firm s market power this technique turns out to be of very limited applicability however because it is extremely sensitive to the functional form assumed for the demand curve consider the general problem of a firm facing constant marginal costs of c in maximizing profits the firm solves

differential pricing when costs differ a welfare analysis this article analyzes the welfare effects of monopoly differential pricing in the important but largely neglected case where costs of service differ across consumer groups cost based differential pricing is shown to increase total welfare and consumer welfare relative to uniform pricing for broad classes of demand functions even when total output falls or the output allocation between consumers worsens we discuss why cost based differential pricing tends to be more beneficial for consumers than its demand based counterpart third degree price discrimination we also provide sufficient conditions for welfare improving differential pricing when costs and demands differ across consumer groups

cost pass through and inverse demand curvature in vertical relationships with upstream and downstream competition this paper provides two characterizations of the retailer s markup relative to the manufacturer s markup in vertical relationships with homogeneous manufacturers and homogeneous retailers we first show that retailer s relative markup is equal to the ratio of the retail pass through to the wholesale pass through multiplied by the number of manufacturers relative to the number of retailers we then provide its expression in terms of the inverse demand curvature

introduction to a general equilibrium approach to economic growth abstract endogenous growth theory has had some success in explaining the observed data related to the process of economic growth however the results of the models in this literature are typically very sensitive to their micro economic structure it is therefore important to understand how the growth process behaves under more general specifications of such features as the number of commodities the number and preferences of consumers the factors of production and the financial and information structures in other words valuable insights can be gained by integrating growth theory into the framework of general equilibrium theory the summary of the papers in this volume focuses on seven issues that are crucial to this integration and highlights the contributions of the papers to the resolution of these issues journal of economic literature classification numbers c61 d50 d90 f43 o30 o41

coordinating price reductions and coupon events abstract in this article the authors use an economic model to show that it may be optimal to lower the retail price during a coupon event when marginal consumers have moderate hassle costs of coupon redemption results from the model offer predictions on the relationships among coupon redemptions shelf price and coupon face value the authors test these predictions on a large data set of hundreds of coupon events across six packaged goods categories the data show that when a small coupon face value is offered the shelf price is likely to be reduced they also find that coupon efficiency increases when there is a lower retail price the results are of interest to managers planning a promotion calendar and deciding whether to coordinate price promotions with coupon events and they contribute to economic theory when a firm moves from uniform pricing e g no coupons to second degree price discrimination e g coupons all consumers may face a lower price this finding has public policy implication

direct welfare analysis of relative price regulation abstract the paper synthesizes and develops the welfare analysis of regulating relative prices for example price differences of which banning price discrimination is a special case welfare results are derived directly by convexity arguments using functions of welfare levels the method is also used to obtain results about e ects on consumer surplus

double marginalization and cost pass through weyl fabinger and cowan meet spengler and bresnahan reiss consider the classical double marginalization problem of single product successive monopolies we show that the ratio of the cost pass through at the final sale relative to that at the wholesale level is characterized by the curvature of inverse demand in the final market we also apply cowan s 2012 method which utilizes the idea of pass through in an analysis of third degree price discrimination to compare consumer surplus under vertical integration and separation

progressive pricing the ethical case for price personalization price discrimination is widely considered unethical unfair by consumers as has been borne out by decades of psychological research and mainstream press reporting however little academic work has been done to investigate the ethics of price discrimination the work that has been done to date concludes that while price discrimination is not unethical despite widespread lay perceptions it is at best morally neutral we argue price discrimination is more ethical than unitary pricing when done progressively meaning firms charge customers as a function of their willingness to pay we introduce this specific kind of price discrimination as progressive pricing and demonstrate it ethically outperforms a unitary pricing scheme where everyone pays the same price regardless of their willingness to pay at least within a broadly consequentialist framework we do this by comparing a unitary pricing scheme to a progressive one analyzing them through the lenses of four different consequentialist social welfare functions utilitarian egalitarian prioritarian and leximin which are used by welfare economists and philosophers to rank the distributions of different social outcomes concluding that progressive pricing is preferred regardless of which social welfare function s one finds most plausible

competitive equilibrium cycles recently there has been a surge of interest in endogenous business cycles that arise in competitive laissez faire economies in the context of standard overlapping generations economies conditions for the existence of equilibrium cycles have been given by grandmont 1983 and by benhabib and day 1982 models of the economy with extrinsic uncertainty or sunspots that have been developed by shell 1977 and by cass and shell 1983 see also balasko 1983 can also lead to equilibrium cycles

intersectoral external effects multiplicities indeterminacies abstract this contribution focuses on the scope for indeterminacies that originate from global capital stock externalities in a reference two sector growth model a set of sufficient conditions for local indeterminacies and oscillations is established and builds upon a new class of intersectoral dependency in competitive economies the uniqueness of the steady state is also questioned and conditions for global indeterminacies are delimited the underlying features of preferences and sectoral production technologies are assessed in this paper it is shown that the principal attribute of a two sector environment i e a non linear production possibility frontier directly underlies indeterminacies it is the influence of external effects on the relative price of the investment good that leads to these phenomena a key role being detected in this perspective for external effects in the consumption good sector

indeterminacy and endogenous fluctuations in two sector growth models with externalities abstract this paper discusses the influence of technological externalities on the dynamic properties of accumulation paths in a two sector growth model in discrete time following the recent paper of boldrin and rustichini 1994 in which the authors study indeterminacy in a particular case we first provide some necessary and or sufficient conditions for the indeterminacy of equilibria in the general two sector model we also provide some conditions for the existence of period two cycles when equilibria are indeterminate we prove finally that depending on the nature of externality indeterminacy may lead to the existence of quasi periodic paths

issues in price discrimination a comment on and addendum to teaching price discrimination by carroll and coates there is a large variety of treatments of the topic of price discrimination in the most widely used undergraduate principles and intermediate microeconomic textbooks as well as industrial organization texts in a recent southern economic journal article carroll and coates 1999 set out to bring into focus the issues that ought to be discussed and made clear when teaching price discrimination to undergraduates their paper concludes with a list of six points that instructors should follow to spark students interest and create as little confusion as possible when covering the topic while in several ways their article is an improvement over many a textbook discussion i think their contribution can also be improved upon as it contains some misconceptions and mistakes specifically there are two concerns regarding the coverage of price discrimination in general and both of these affect the paper by carroll and coates in particular the first is mostly technical but has led to widespread misconceptions about the relationship between the price elasticity of demand and third degree price discrimination the other is mainly pedagogical and concerns what can or should actually be taken away from the classroom after a discussion of price discrimination especially regarding implications of price discrimination on economic efficiency

a note on third degree price discrimination with interdependent demands by incorporating symmetric interdependency into linear demands this note shows that monopolistic third degree price discrimination can improve social welfare even if total output remains the same a result that counters one of the main results presented in layson this journal 1998 it is also shown that this positive change in social welfare benefits the monopoly side but that consumers surplus decreases as a whole

timing of investments and third degree price discrimination in intermediate good markets abstract this paper studies the discriminatory pricing of an intermediate good and compares two models with a different timing of investments undertaken by the downstream firms before or after the upstream monopolist sets the input prices when the more efficient downstream firm is charged a higher price than the less efficient firm in the first model in the second model when investments are made after input prices are set it may be charged a lower price due to the additional indirect effect of input prices on derived demands via the change of investment incentives it is illustrated that with linear market demand and quadratic investment cost whether a lower or higher price is charged to the more efficient firm depends on the ratio of the linear and quadratic coefficients in the cost function

s s optimality in joint inventory pricing control an alternate approach we study a stationary single stage inventory system under periodic review with fixed ordering costs and multiple sales levers such as pricing advertising etc we show the optimality of s s type policies in these settings under both the backordering and lost sales assumptions our analysis is constructive and is based on a condition that we identify as being key to proving the s s structure this condition is entirely based on the single period profit function and the demand model our optimality results complement the existing results in this area

procompetitive gains from trade and comparative advantage having made the concepts of pro or anticompetitive output changes precise necessary and sufficient conditions for trade gains are derived under conditions of increasing returns to scale and imperfect competition in a general equilibrium model with any finite number of goods and factors these conditions yield generalizations of the theorems of comparative advantage in goods and implicit factor trade the factor content version of the h o theorem other generalizations can be obtained if one assumes quasihomothetic preferences and that welfare effects are dominated by price rather than income effects copyright 1996 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

welfare increasing third degree price discrimination when demand functions in different markets are derived from distributions of reservation prices that differ only in their means conditions exist such that third degree price discrimination leads to greater total output and greater total welfare welfare is higher with discrimination than with a uniform price when demand functions are derived from logistic distributions with different means welfare and consumer surplus are higher with discrimination for demands derived from a distribution related to the pareto in general whether discrimination increases total output depends on demand being more convex in markets in which prices fall with discrimination than in those in which prices rise

technical note optimal dynamic joint inventory pricing control for multiplicative demand with fixed order costs and lost sales this note studies the optimal dynamic decision making problem for a retailer in a price sensitive multiplicative demand framework our model incorporates lost sales holding cost fixed and variable procurement costs as well as salvage value we characterize the structure of the retailer s discounted expected profit maximizing dynamic inventory policy for both finite and infinite selling horizon problems

the properties of product line prices abstract we study multi product cournot suppliers a monopoly is a special case who offer menus of differentiated qualities under conditions that include linear and constant elasticity demand specifications the equilibrium price for each quality is equal to its price in a single product cournot market a corollary is this a monopolist who naively ignores the substitutability of her products by choosing the standalone monopoly price for each quality successfully implements the optimal discriminatory scheme under other reasonable specifications the equilibrium prices are close to the single product prices we also evaluate the impact of minimum quality standards

coordinating inventory control and pricing strategies with random demand and fixed ordering cost the finite horizon case we analyze a finite horizon single product periodic review model in which pricing and production inventory decisions are made simultaneously demands in different periods are random variables that are independent of each other and their distributions depend on the product price pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged ordering cost includes both a fixed cost and a variable cost proportional to the amount ordered the objective is to find an inventory policy and a pricing strategy maximizing expected profit over the finite horizon we show that when the demand model is additive the profit to go functions arek concave and hence an s s p policy is optimal in such a policy the period inventory is managed based on the classical s s policy and price is determined based on the inventory position at the beginning of each period for more general demand functions i e multiplicative plus additive functions we demonstrate that the profit to go function is not necessarilyk concave and an s s p policy is not necessarily optimal we introduce a new concept the symmetrick concave functions and apply it to provide a characterization of the optimal policy

the limits of price discrimination we analyze the welfare consequences of a monopolist having additional information about consumers tastes beyond the prior distribution the additional information can be used to charge dierent prices to dierent segments of the market i e carry out third degree price discrimination we show that the segmentation and pricing induced by the additional information can achieve every combi nation of consumer and producer surplus such that i consumer surplus is non negative ii producer surplus is at least as high as pro ts under the uniform monopoly price and iii total surplus does not exceed the e cient gains from trade as well as characterizing the welfare impact of price discrimination we examine the limits of how prices and quantities can change under price discrimination we also examine the limits of price discrimination in richer environments with quantity discrimination and limited ability to segment the market

third degree price discrimination and consumer surplus this paper considers the effects of monopoly third degree price discrimination on aggregate consumer surplus discrimination is likely to reduce surplus relative to that obtained with a uniform price but surplus can rise under reasonable conditions if the ratio of the pass through coefficient to the price elasticity at the uniform price is higher in the market with the higher price elasticity then surplus is larger with discrimination for a large set of demand functions the relatively high pass through coefficient implies a large price reduction in this market with logit demand functions surplus is higher with discrimination if pass through is above 0 5

on the welfare effects of regulating price discrimination in a model with linear demands and constant variable costs it is shown that a welfare gain is made by restricting the relative rather than absolute prices that a monopolist can charge for a range of products the nature of this class of restrictions is considered one application might occur if cost levels are unknown to the regulatory authority but costs are known to be linear functions of product characteristics copyright 1992 by blackwell publishing ltd

prices and living standards evidence for rwanda abstract we review the explanations of the statistical relationship between spatial price indices and real living standards then using data from several seasons in rural rwanda we show that these variables are negatively associated hinting at price discrimination against the poor in that case policies permanently improving of market functioning may simultaneously improve efficiency and equity moreover under a hypothesis of weak association of nominal living standards and price indices we derive simplified formulae for social welfare indicators these formulae depend only on a small number of sample statistics obtainable from separate publications for prices and living standards

welfare effects of price discrimination by a regulated monopolist should a multiproduct monopolist whose average price is capped by regulation be allowed to engage in third degree price discrimination if the cap applies to a price index with weights proportional to demands at uniform prices then price discrimination benefits consumers as well as the firm but if perhaps more realistically it is the firm s average revenue that is capped then consumers prefer uniform pricing in this case total output is higher when discrimination is allowed which increases welfare but marginal utilities differ across markets which is inefficient and the overall effect is ambiguous a small amount of discrimination is desirable however it is better not to allow price discrimination if the price cap is close to the level of marginal cost the consequences of tightening the price cap when discrimination is allowed are also examined

the welfare effects of third degree price discrimination in a differentiated oligopoly this article examines the welfare effects of third degree price discrimination under oligopolistic competition with horizontal product differentiation we derive a necessary and sufficient condition for price discrimination to improve social welfare the degree of substitution must be sufficiently greater in the strong market where the discriminatory price is higher than the uniform price than in the weak market where it is lower it is verified however that consumer surplus is never improved social welfare improves solely owing to an increase in the firms profits in the case of linear demands jel d43 l11 l13 i introduction this article examines the welfare effects of oligopolistic third degree price discrimination explicitly considering product differentiation as a source of market power and strategic interaction product differentiation is one of the main reasons why firms can enjoy market power it enables them to sell products that are no longer perfect substitutes for example coca cola and pepsico sell similar types of soda although it is arguable that they differ in taste each firm thereby attracts some consumers over another as a form of price discrimination coca cola was once reported to be testing a vending machine that would automatically raise prices in hot weather 1 although the plan triggered nationwide controversy and coca cola had to abandon the project as a result it could have changed the regime of uniform pricing to one of price discrimination in the soda market how would the resulting change affect consumer welfare and firms profits in other words is third degree price discrimination good or bad answering this question is important because it helps us to evaluate price discrimination under oligopoly in this article we focus on horizontal product differentiation to consider substitutability as well as complementarity 2 by assuming a linear quadratic utility function of a representative consumer and focusing on the symmetric equilibrium of a pricing game we characterize the conditions relating to such demand properties as substitutability and complementarity required for price discrimination to improve social welfare more specifically we derive a necessary and sufficient condition for price discrimination to improve social welfare the degree of substitution must be sufficiently greater in the strong market where the discriminatory price is higher than the uniform price than in the weak market where it is lower it is also shown that aggregate output must increase for price discrimination to improve social welfare we verify however that consumer surplus is never improved by price discrimination welfare improvement from price discrimination is solely owing to an increase in firms profits in the example above the degree of substitution would be higher in the strong market i e when the temperature is high because consumers care less about which brand when it is hot weather our analysis below implies that social welfare might improve in this case the degree of substitution can vary across markets even if consumers in each market face exactly the same products because consumers taste depends on various market specific factors such as geographical and natural conditions if the strong market is where consumers demand a product more eagerly caring less about which brand in the above example individuals demand soda more eagerly in hot weather then our results suggest that price discrimination has large potential to improve social welfare 3 why does allowing price discrimination improve social welfare notice that there are two forces that determine equilibrium prices in price setting oligopoly a larger market size raises the price whereas a larger substitutability parameter lowers the price for price discrimination to raise social welfare it is necessary that a high degree of substitutability mitigates an increase in the discriminatory price in the larger market

monopolistic third degree price discrimination under vertical product differentiation this paper shows in a vertical product differentiation model with variable costs of quality that monopolistic third degree price discrimination always reduces welfare regardless of whether the quality is fixed or is endogenous the results provide rich implications for antitrust policy

automobile prices in market equilibrium with unobserved price discrimination in markets where sellers are able to price discriminate or the buyers to bargain individuals receive discounts over the posted prices that are usually not observed by the econometrician this paper considers the structural estimation of a demand and supply model a la berry et al 1995 when only posted prices are observed we consider that heterogeneous discounts occur due to price discrimination by firms on observable characteristics of consumers within this framework identification is achieved by assuming that the marginal costs of producing and selling the goods do not depend on the characteristics of the buyers we also require a condition relating the posted prices to the prices actually paid for instance we can assume that at least one group of individuals pays the posted prices under these two conditions the demand and supply parameters as well as the exact discounts corresponding to each type of consumers can be identified we apply our methodology to estimate the demand and supply in the new automobile market in france results suggest that discounting arising from price discrimination is important the average discount is estimated to be 10 5 with large variation depending on the buyers characteristics and cars specifications our results are in line with discounts generally observed in european and american automobile markets

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

on the stability of the two sector neoclassical growth model with externalities we study a class of two sector growth models with sector specific externalities in which one sector produces consumption and the other sector produces investment the novelty is that investment allocated to the consumption sector is an imperfect substitute for investment allocated to the investment sector we show analytically that in this case local indeterminacy near the steady state is impossible for every empirically plausible specification of the model parameters more specifically we show that a necessary condition for local indeterminacy is an upward sloping aggregate labor demand curve in the investment sector which requires a counterfactual strength of the externality we show numerically that an elasticity of substitution of plausible size implies determinacy near the steady state these findings differ sharply from the standard result for two sector models that if the investments allocated to the two sectors are perfect substitutes then local indeterminacy occurs for a wide range of plausible parameter values

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

multi dimensional price discrimination we examine the profitability and welfare implications of price discrimination in a multi dimensional model first when firms price discriminate on one and the same dimension uniform price lies in between discriminatory prices and price discrimination raises profits relative to uniform pricing this is in contrast to common findings in existing one dimensional models featuring best response asymmetry suggesting that price discrimination can have qualitatively different implications in one and multi dimensional models second price discrimination on one and the same dimension is the likely outcome when price discrimination decisions are endogenized using a two stage discrimination then pricing game correspondingly an observation of one dimensional price discrimination in practice does not necessarily indicate that the underlying model should be one dimensional