existence and characterization of optimal growth paths including models with non convexities in utilities and technologies this paper is concerned with the existence and characterization of optimal growth paths in continuous time infinite horizon problems and brings to bear on these issues mathematical techniques presented by the author in chichilnisky 1977 these techniques non linear functional analysis in hilbert weighted l2 and sobolev spaces permit generalization clarification and simplification of existing results in particular the following points are of importance i as hilbert spaces are self dual continuous linear functionals on the commodity space are elements of the space and thus have a totally natural interpretation as prices we therefore obtain that commodity and price paths are in the same spaces a useful property to prove existence in general equilibrium models a failure to meet this condition has led to earlier work on characterization being troubled by the problem that supporting linear functionals are not always interpretable as prices so that one cannot always give a price characterization of optimal and efficient paths in the present framework this problem does not arise ii a natural way to pose the problem of finding an optimal path is as one of maximizing a continuous function on a compact set a major advantage of the techniques we use here is demonstrated by the fact that we are actually able to follow this approach iii because of ii it is possible to establish the existence of an optimal path without the use of any convexity assumptions on either the technology or the preferences this is a major relaxation of earlier conditions and enables existence results to be applied to models with increasing returns in production non convex preferences and endogenous population for instance in lane 1977 both the feasible net production set and the preference ordering are in general non convex due to the endogenous response of population growth to income in ryder and heal 1973 and wan 1970 non convexities appear as well as in environmental and biological problems discussed for example in clark 1976 in this latter case the logistic growth functions of biological populations introduces non convexities in a natural way iv it can be shown that the prices that arise within this framework provide a well defined present value for every feasible program this makes it possible to provide a full characterization of optimal and efficient paths in terms of profit maximization without any reference to transversality conditions this characterization is thus analogous to that

the effects of taxation price control and government contracts in oligopoly and monopolistic competition abstract many government contracts with or policies towards oligopolistic sectors essentially involve private firms selling a given proportion or quantity of output to the government at a fixed price p r with the remainder being sold on the open market often this is combined with consumer rationing examples include cement and sugar in india and health housing and defence in many countries the paper investigates the effects of these schemes including sales and excise taxation on prices output and household welfare under oligopoly and monopolistic competition less government control reduced may raise prices and tax shifting can be above or below 100 percent

differential games with nonconvexities and positive spillovers abstract this paper deals with differential games characterized by nonconvexities and increasing returns the objective function of the players is convex in the control variables and nonconvex in the state variables we employ the open loop nash equilibrium solution concept this framework enables us to handle games characterized by positive spillovers and strategic complementarities e g capital accumulation differential games with learning by doing where the knowledge available to a firm is given by the knowledge accumulated by the economy as a whole

capital accumulation games of infinite duration abstract consider a market in which firms accumulate capital according to the nerlove arrow capital accumulation equation each player chooses a path of investment and thus an induced path of capital to maximize his total discounted profits which depend on his own capital and the capital stocks of his rivals existence is proved for such a nonzero sum infinite horizon differential game and conditions under which the game converges to a particular stationary point regardless of the initial conditions are shown thus the game possesses the property of conditional global asymptotic stability

the price of anarchy in supply chains quantifying the efficiency of price only contracts in this paper we quantify the efficiency of decentralized supply chains that use price only contracts with a price only contract a buyer and a seller agree only on a constant transaction price without specifying the amount that will be transferred it is well known that these contracts do not provide incentives to the parties to coordinate their inventory capacity decisions we measure efficiency with the price of anarchy poa defined as the largest ratio of profits between the integrated supply chain that is fully coordinated and the decentralized supply chain we characterize the efficiency of various supply chain configurations push or pull inventory positioning two or more stages serial or assembly systems single or multiple competing suppliers and single or multiple competing retailers

goodwill and market shares in oligopoly economic literature treats price as the traditional competition variable however schmalensee 1976 p 493 argued that prices change infrequently and that firms compete mainly through non price variables the most important non price competition variables are advertising and product variation although there are many works dealing with non price competition they have not devoted much attention to the multi period effect of these variables and the models have been mainly static or a sequence of static models further discussion of this argument can be found in kydland 1977 in which dynamic dominant player models are discussed in an earlier paper arrow and nerlove 1962 pointed out that advertising expenditure should be treated in the same way as investment in a durable good they assumed that there is a stock of goodwill that determines the current demand this stock of goodwill summarizes the advertising in the past and like capital stock depreciates over time arrow and nerlove analysed the optimal advertising strategy for the monopolistic firm in this paper we extend the arrow nerlove model to oligopolistic competition in which the firms compete among themselves via goodwill the game we describe takes place over time and discounted profit is used as a criterion the current advertising of any player affects future demand and therefore the model has an intertemporal dependence structure extending an assumption by schmalensee 1978 in section i we allow market shares to depend on the firm s goodwill and not merely on current advertising using this definition of market share we discuss in section ii the optimal advertising policy for a single firm in section iii we prove the existence of a unique stationary equilibrium point for oligopolistic competition since we allow firms to have different cost functions the equilibrium point is not a symmetric one i e different firms have different market shares and different goodwill at the equilibrium point in section iv we discuss this asymmetric solution by explaining the relation between production cost and market shares the impact of the number of firms on the advertising expenditure is discussed in section v we prove that the firms advertising expenses tend to decline as the number of firms increases however if one of the firms is a leading firm in the industry and has a market share above one half we show that this firm might increase its advertising as other firms enter into the industry as an example we discuss in section vi the duopoly case and offer an explicit statement of the market shares at the equilibrium point in section vii we analyse an industry consisting of identical firms and explore the influence of the interest rate and the depreciation rate on the firms goodwill and advertising policy

a note on closure properties of failure rate distributions increasing generalized failure rate igfr distributions were introduced as a tool in the study of contracting mechanisms in supply chains in this note we compare and contrast the closure and the lack thereof of igfr and increasing failure rate ifr distributions with respect to standard operations on random variables some implications of these results for the use of igfr distributions in supply chain models are noted

optimal investments with increasing returns to scale the author analyzes the firm optimal investment policy assuming a pure increasing returns to scale technology and adjustment costs the existence of an optimal plan is proved by applying a new set of necessary and sufficient conditions for optimality the analysis is carried out in a linear quadratic framework that enables one to study a general nonlinear problem in a neighborhood of the long run equilibrium the investment policy shows a reverse accelerator effect in a general setting he proves that the saddle point characterization is a sufficient condition for a stationary competitive equilibrium to be a finitely optimal trajectory copyright 1998 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

a note on pricing with risk aversion abstract we consider the pricing problem of a risk averse seller facing uncertain demand demand uncertainty stems from buyers valuations being privately observed by imposing very mild restrictions on the distribution of buyers valuations an increasing generalized failure rate distribution and the bernoulli utility function we show that a risk averse seller will unambiguously post a lower price than a risk neutral counterpart

relationships among three assumptions in revenue management this note discusses the relationships among three assumptions that appear frequently in the pricing revenue management literature these assumptions are mostly needed for analytical tractability and they have the common property of ensuring a well behaved revenue function the three assumptions are decreasing marginal revenue with respect to demand decreasing marginal revenue with respect to price and increasing price elasticity of demand we provide proofs and examples to show that none of these conditions implies any other however they can be ordered from strongest to weakest over restricted regions and the ordering depends upon the region

a dns curve in a two state capital accumulation model a numerical analysis abstract in this paper we study a capital accumulation model in an optimal control theoretic framework where the capital stock and the investment rate are modelled as state variables and the change in the investment rate as control adjustment costs are introduced for investment rate and its change moreover we model network externalities by a convex segment in the revenue function which implies the existence of two long run optimal steady states one with a low level and the other with a high level capital stock it depends on the initial capital endowment and initial investment rate to which steady state it is optimal to converge we numerically compute a curve in the state plane for which it holds that when starting from a point on this curve the decision maker is indifferent between going to either one of these steady states and identify this curve as the dns curve the negative slope of the dns curve indicates that there is a trade off between the initial capital endowment and initial investment rate

the impact of the international coffee agreement on producing countries the main objective of this article is to analyze the impact of the international coffee agreement s export system on the world coffee market focusing on increases in real export revenues transfer benefits and reductions in income variability risk benefits in each exporting country over the recent period of operation of the international coffee agreement s export quota system the authors find that the quota system had a stabilizing effect on world coffee prices the quotas reduced real export revenues for most small exporting countries but large producers gained most small countries gained however in terms of risk reduction if a brief suspension of the quota occurs from time to time caused for example by adverse weather which results in a shortfall in world supply the quota system works like a buffer stock scheme on average producing countries as a whole lose transfer benefits but gain risk benefits

on limiting the market for status signals abstract in many societies individuals care how others view them in their efforts to impress such individuals engage in consumption signals which attempt to establish higher levels of status than their true status type this leads to an inefficiency which offers the possibility of a pareto improving tax policy the impacts of tax policy and benefits on the signalling equilibrium are considered

non convexities in continuous time investment theory that non convex preferences or technologies cause problems for economic theory is well known in recent years there have been numerous contributions to the nonconvexity problem in the context of models with a finite dimensional commodity space in the capital theory context non convexities have received explicit treatment in a few papers in two distinguishable ways the problem is cast either in a discrete time framework aoki 1971 rothschild 1971 or in a continuous time framework in which there are implicitly unbounded economies of scale in investment the latter formulation leads to jumps in the state variable or lumpy investment the standard problem treated is one of decreasing costs in the installation of new capacity contributions include chenery 1952 dixit mirrlees and stern 1975 hartwick 1976 manne 1967 srinivasan 1967 starrett 1978 and weitzman 1970 these types of analysis unfortunately ignore some of the most interesting problems associated with non convexities in investment theory in a discrete time framework the important distinction between stocks and flows is blurred while the capacity installation problem by admitting unbounded scale economies excludes the smoothing of state variables that follows by allowing for eventually increasing costs of adjustment in this paper we undertake a systematic examination of non convexities or sometimes non concavities in the context of a classic problem in continuous time investment theory the optimal accumulation of capital by a firm maximizing its present value over an infinite horizon while the results obtained are specific to this particular model we feel that they can be qualitatively extended to any capital theory problem which can be cast in a continuous time optimal control theory framework there are various sorts of non2 convexities which can arise in these problems first there can be either stock or flow non convexities that is non convexities which are introduced into the net benefit function the measure of the flow of benefits at each moment through changes in the capital stock state variable on the one hand or changes in the flow of investment control variable on the other if the benefit and transition functions are not concave in both these variables then necessary conditions are no longer sufficient for optimality and conventional marginal analysis fails non convexities can also be introduced into the value functional which has a stock dimension in order to examine these different sorts of non convexity problems we shall now present the basic economic problem a firm is faced with the problem of maximizing the present value of discounted cash flow over an infinite horizon hence it chooses an investment programme i t to maximize 00

dynamic capital structure choice and investment timing abstract the paper considers the problem of an investor that has the option to acquire a firm initially this firm is run as to maximize shareholder value where the shareholders are risk averse to do so it has to decide each time on investment and dividend levels the firm s capital stock can be financed by equity and debt where less solvable firms pay a higher interest rate on debt revenue is stochastic we find that the firm is run such that capital stock and dividends develop in a fixed proportion to the equity in particular it turns out that more dividends are paid if the economic environment is more uncertain we also derive that the relationship between the levels of risk aversion of the current shareholders and the potential investor is a significant determinant in establishing whether the firm is a profitable takeover target for the investor

testing oligopolistic behavior abstract this paper develops an empirical model of short run pricing behavior for firms in a homogeneous product oligopoly it is based on the variable profit function and related output supply and factor demand equations and is used to analyze the behavior of firms in the coffee roasting industry a parametric test of the dominant firm model is developed and applied the hypothesis of dominant firm behavior and cournot behavior are rejected the hypothesis of price taking behavior is rejected for the largest two firms in the industry but is not rejected for all other firms using the estimated pattern of firm behavior an index of overall industry performance is constructed

a simultaneous equations model of coffee brand pricing and advertising this paper explores the relationship between a differentiated brand s market share and its price in the con text of a model that recognizes the endogeneity of the brand s advertising behavior and pricing decisions the empirical analysis suggests that general foods charged higher prices for its regular grind maxwell house coffee in geographic areas where the brand s market share was relatively large available cross sectional time series data and company documents sug gest that this empirical relationship is attributable to the preference grocery retailers have for putting dominant coffee brands on special rather than cross sectional variations in costs market concentration or consumer tastes i introduction r his paper explores the relationship between a differentiated brand s market share and its price in the context of a model that recognizes the endogeneity of the brand s advertising behav ior and pricing decisions by using price as the measure of economic performance rather than accounting profits and by recognizing that adver tising is determined simultaneously with price the empirical tests reported here avoid some of the more serious problems of structure perfor mance studies moreover by focusing on the rela tionship between a single brand s market share and price this study analyzes the unilateral mar ket power of a differentiated brand as well as the effect of market wide concentration on a brand s prices the empirical analysis focuses on the hypothe sis that the general foods corporation charged higher prices for its regular grind maxwell house coffee in geographic areas where the brand s market share was large during the 1970s we identify a statistically significant positive relation ship between maxwell house s wholesale price

do fair trade and eco labels in coffee wake up the consumer conscience abstract in this study a face to face survey was conducted in order to reveal consumer preferences for ethical and environmentally sound labeling programs in coffee valuation questions regarding the fair trade shade grown and organic coffee labels were asked using a payment card format after consumers were previously informed about each of the labeling programs results suggest that consumers are very receptive toward both fair trade and shade grown coffee labels and consequently are willing to pay higher premiums for these labeling programs than for the organic coffee

capacity investment preemption and commitment in an infinite horizon model the commitment value of capacity is analyzed in an infinite horizon duopoly model the paper focuses on the role of alternative behavioral assumptions about the ability of firms to commit to investment paths each firm s investment strategy in a feedback nash equilibrium is shown to be a decreasing function of its rival s current capacity this creates an incentive for a firm to expand its capacity to preempt subsequent rival investment in a precommitment equilibrium there are no incentives to invest preemptively as a consequence steady state capacity levels are greater in a feedback nash equilibrium than in a precommitment equilibrium copyright 1987 by economics department of the university of pennsylvania and the osaka university institute of social and economic research association

responding to the coffee crisis what can we learn from price dynamics an econometric model of coffee price dynamics is specified and estimated to capture the evolution of coffee prices at the farm wholesale and retail levels it investigates the historical influence of the international coffee agreement ica through its effects on yield and planting decisions in the short run the ica caused brazilian farm prices to become disconnected from international prices the ica helped coffee producers to better incorporate current world price information into planting decisions this created a price cycle that did not exist in non ica periods the low coffee prices experienced since the disintegration of the ica are consistent with low supply response to price information asymmetric price transmission at the retail level helped roasters and retailers benefit from upstream price interventions our results urge caution when considering future coffee price interventions

turnpike properties of capital accumulation games abstract a differential game is considered in which players accumulate capital their payoff functions depend upon the capital stocks of both players and their cost functions are convex previous existence and stability results are relied upon to show that the game under an additional assumption possesses the following properties a every equilibrium of the infinite horizon game converges to the unique stationary equilibrium b for a time horizon long enough the finite horizon equilibrium stays in the neighborhood of the infinite horizon equilibrium except for some final time c for a time horizon long enough the finite horizon equilibrium stays in the neighborhood of the stationary equilibrium except for some initial and final time

a note on probability distributions with increasing generalized failure rates distributions with an increasing generalized failure rate igfr have useful applications in pricing and supply chain contracting problems we provide alternative characterizations of the igfr property that lead to simplify verifying whether the igfr condition holds we also relate the limit of the generalized failure rate and the moments of a distribution

conspicuous consumption snobbism and conformism abstract we develop a model in which consumers purchase a conspicuous good in order to signal high income and thereby achieve greater social status in equilibrium the signalling value of conspicuous consumption depends in an identifiable way on the number of consumers and consumer behaviour is characterized by either snobbism or conformism the market demand curve for the conspicuous good may exhibit a positive slope if consumers are conformist we derive some unconventional policy implications concerning the taxation of luxuries and the voluntary provision of public goods

two state capital accumulation with heterogenous products disruptive vs non disruptive goods the paper considers the problem of a firm that while producing a standard product has the option to introduce an innovative product the innovative product competes with the standard product and will therefore reduce revenues of the standard product a distinction is made between innovative products that do or do not become even more relatively appealing as their market share grows e g because of network externalities it is shown that in the former case which we call a disruptive good history dependent long run equilibria can occur which are in line with recent real life economic examples

optimal firm growth under the threat of entry the paper studies the incumbent entrant problem in a fully dynamic setting we find that under an open loop information structure the incumbent anticipates entry by overinvesting whereas in the markov perfect equilibrium the incumbent slightly underinvests in the period before the entry the entry cost level where entry accommodation passes into entry deterrence is lower in the markov perfect equilibrium further we find that the incumbent s capital stock level needed to deter entry is hump shaped as a function of the entry time whereas the corresponding entry cost where the entrant is indifferent between entry and non entry is u shaped

demand for coffee in sweden the role of prices preferences and market power there is a widespread belief that consumer coffee prices are high relative to bean prices and that lower consumer prices would lead to substantial increases in bean exports from third world countries this issue is evaluated by analysing how retail prices preferences and market power influence coffee demand in sweden a demand function is estimated for the period 1968 2002 and used together with information on import prices of coffee beans to simulate an oligopoly model this approach gives estimates of the maximum average degree of market power and shows how coffee demand would react to reductions in marginal cost to its minimum level the maximum level of market power is found to be low but it generates large spreads between consumer and bean prices because the price elasticity has low absolute values moreover the impact of a price decrease would be small because long run coffee demand is dominated by changes in the population structure in combination with different preferences across age groups hence a change to perfect competition would only have a negligible effect on bean imports

existence and properties of equilibria for a dynamic game on productive assets abstract we consider a model in which two agents share access to the same stock of a productive asset and study the implications of non cooperative consumption behavior over time under standard assumptions on the production function we construct infinitely many nash equilibria all of which consist of stationary markovian strategies these equilibria result in overconsumption so that the uniquely determined long run asset stock is too low as compared to the cooperative solution however in the limit as the discount rate becomes sufficiently small the stead states generated by the markovian nash equilibria converge to the efficient steady state journal of economic literatureclassification numbers c73 o41 q22

veblen effects in a theory of conspicuous consumption the authors examine conditions under which veblen effects arise from the desire to achieve social status by signaling wealth through conspicuous consumption while veblen effects cannot ordinarily arise when preferences satisfy a single crossing property they may emerge when this property fails in that case budget brands are priced at marginal cost while luxury brands though not intrinsically superior are sold at higher prices to consumers seeking to advertise wealth luxury brands earn strictly positive profits under conditions that would with standard formulations of preferences yield marginal cost pricing the authors explore factors that induce veblen effects and they investigate policy implications copyright 1996 by american economic association

oligopoly extraction of a common property natural resource the importance of the period of commitment in dynamic games the theory of noncooperative dynamic games has provided an extremely powerful framework for studying many of the classic questions in industrial organization for example questions about resource extraction advertising research and development investment in new capacity and barriers to entry where interactions over time among few firms are involved however an important methodological issue arises when economic competition over time is modeled as a dynamic game the issue is the appropriate formulation of the players strategy spaces

competition in the swedish coffee market 1978 2002 abstract are multinationals exploiting their market power in national coffee markets by keeping consumer prices too high and thereby limiting demand for imports of coffee beans the purpose of this study is to address this issue by testing if there is market power in the swedish market for roasted coffee the market structure is typical of many consumer markets for coffee with four very large roasting companies two of which are multinationals plus many small ones to analyze the degree of market power an oligopoly model is estimated using market time series data the econometric approach is to first test for long run relationships between the variables with cointegration analysis and then to estimate a system of equations for demand and pricing behavior our key finding is that there is evidence of some market power in the short run but none in the long run

do gasoline prices respond asymmetrically to crude oil price changes the authors test and confirm that retail gasoline prices respond more quickly to increases than to decreases in crude oil prices among the possible sources of this asymmetry are production inventory adjustment lags and market power of some sellers by analyzing price transmission at different points in the distribution chain the authors attempt to shed light on these theories spot prices for generic gasoline show asymmetry in responding to crude oil price changes which may reflect inventory adjustment effects asymmetry also appears in the response of retail prices to wholesale price changes possibly indicating short run market power among retailers

do coffee roasters benefit from high prices of green coffee abstract the german coffee industry has repeatedly made the puzzling statement that it would prefer higher prices of green coffee its main input likewise it supported the maintenance of the coffee tax in this paper an oligopoly model with differentiated products is used to illustrate the possibility of profit raising cost increases the relationship between prices and costs of roasted coffee in germany is estimated and the hypothesis of overshifting is tested in addition the demand for coffee is studied however the empirical analysis does not confirm that increasing costs lead to higher profits alternative explanations for the coffee industry s statements based on long term considerations are also discussed