optimal supply of a depletable resource with a backstop technology heal s theorem revisited heal s theorem states that if the extraction cost of a depletable resource increases with cumulative extraction and if a backstop technology exists the user cost of the depletable resource declines to zero at the date of exhaustion in this paper we first present a simple method for proving this proposition using a social planning model that determines the optimal rates both of extraction of the depletable resource and of production of the backstop technology we then present two examples that show how this method can be used to solve more difficult problems in the theory of resource economics the first example involves learning by doing in the backstop sector that is backstop costs decline with cumulative production the second example involves uncertainty of backstop costs

equilibrium in hotelling s model of spatial competition we study hotelling s two stage model of spatial competition in which two firms first simultaneously choose locations in the unit interval then simultaneously choose prices under hotelling s assumptions uniform distribution of consumers travel cost proportional to distance inelastic demand of one unit by each consumer the price setting subgames possess equilibria in pure strategies for only a limited set of location pairs because of this problem pointed out independently by vickrey 1964 and d aspremont et al 1979 hotelling s claim that there is an equilibrium of the two stage game in which the firms locate close to each other is incorrect a result of dasgupta and maskin 1986 guarantees that each price setting subgame has an equilibrium in mixed strategies we first study these mixed strategy equilibria we are unable to provide a complete characterization of them although we show that for a subset of location pairs all equilibria are of a certain type we reduce the problem of finding an equilibrium of this type to that of solving three or fewer highly nonlinear equations at each of a large number of location pairs we have computed approximate solutions to the system of equations next we use our analytical results and computations to study the equilibrium location choices of the firms there is a unique up to symmetry subgame perfect equilibrium in which the location choices of the firms are pure in it the firms locate 0 27 from the ends of the market at this equilibrium the support of the subgame equilibrium price strategy is the union of two short intervals most of the probability weight is in the upper interval so that this strategy is reminiscent of occasional sales by the firms we also find a subgame perfect equilibrium in which each firm uses a mixed strategy in locations in fact in the class of strategy pairs in which the firms use the same mixed strategy over locations and this strategy is symmetric about 0 5 there is a single equilibrium in this equilibrium most of the probability weight of the common strategy is between 0 2 and 0 4 and between 0 6 and 0 8 there is a wide range of pure nash as opposed to subgame perfect equilibrium location pairs the subgame strategies in which each firm threatens to charge a price of zero in response to a deviation support all but those location pairs in which the firms are very close

chapter 4 competitive marketing strategies game theoretic models publisher summary this chapter reviews the key developments in the understanding of competitive marketing strategies product price advertising and distribution competition are all addressed while the emphasis is on models the chapter surveys the empirical literature as well there is a significant amount of empirical work to report but the ratio of theoretical to empirical work is nevertheless unpleasantly large much progress has been made in the last ten years or so in the study of competitive marketing strategies most of this chapter has been theoretical using simple models of firm and consumer behavior these models serve the function of demonstrating rigorously the existence of certain effects factors which need to be considered in analyzing real world competition

the induced innovation hypothesis and energy saving technological change we develop a methodology for testing hicks s induced innovation hypothesis by estimating a product characteristics model of energy using consumer durables augmenting the hypothesis to allow for the ine uence of government regulations for the products we explored the evidence suggests that i the rate of overall innovation was independent of energy prices and regulations ii the direction of innovation was responsive to energy price changes for some products but not for others iii energy price changes induced changes in the subset of technically feasible models that were offered for sale iv this responsiveness increased substantially during the period after energy efficiency product labeling was required and v nonetheless a sizable portion of efficiency improvements were autonomous

age effects leverage and firm growth abstract recent theories of firm dynamics emphasize the role of financial variables as determinants of firm growth empirically examining these relationships has been difficult since there is a lack of financial data on the small young and private firms using a unique administrative data set this paper considers the growth of new firms in canadian manufacturing from a financial perspective we find that financial factors such as leverage and initial financial size impact growth rates for new firms further the inclusion of leverage has little impact on the economic significance of the conditional age and size relationships with firm growth

the principle of minimum differentiation holds under sufficient heterogeneity the so called principle of minimum differentiation stated by hotelling has been challenged by many authors this paper restores the principle by showing that n firms locate at the center of the market and charge prices higher than the marginal cost of production when heterogeneity in consumers tastes is large enough

cycles in nonrenewable resource prices with pollution and learning by doing we study how environmental regulation in the form of a cap on aggregate emissions from a fossil fuel e g coal interacts with the arrival of a clean substitute e g solar energy the cost of the substitute is assumed to decrease with cumulative use because of learning by doing we show that optimal energy prices may initially increase because of pollution regulation but fall due to learning and rise again because of scarcity of the resource finally falling after transition to the clean substitute thus nonrenewable resource prices may exhibit cyclical behavior even in a purely deterministic setting

a location model with preference for variety we propose a new location model where consumers are allowed to make multiple purchases i e one unit from each firm this model may fit many markets e g newspapers credit cards better than existing models a common feature of these markets is that some consumers are loyal to one brand while others consume more than one product our model yields predictions consistent with this observation if firms are allowed to choose their locations on the interval then spatial differentiation may not be maximal and in some cases it may even be minimal thus under certain conditions we restore hotelling s principle of minimum differentiation

hotelling s spatial competition as a model of sales abstract hotelling s spatial competition model is used to explain the existence of sales it is shown that 1 an equilibrium in randomized strategies exists when a pure strategy equilibrium fails to exist 2 with more dissimilarity among brands prices are chosen from a wider interval

spatial competition and price leadership in the stackelberg price leader price follower model each firm is typically better off as a follower than as a leader in this paper we show that introducing the spatial dimension provides a means of endogenising the role of price leadership furthermore the leader follower framework yields existence of a price and location equilibrium in the hotelling spatial model of competition where none exists under the original specification we first analyse the original hotelling model by determining reaction functions for firms this approach allows the model to be fully characterised and affords an intuitive explanation of the non existence of a price equilibrium for certain locations the reaction functions are then used to determine the solution when one firm adopts the stackelberg leadership role contrary to the existing predictions of the simple spatial duopoly model it is found that the outcome is asymmetric in terms of stackelberg equilibrium locations prices and profits with the first firm in the market enjoying higher profits than the subsequent entrant the equilibrium involves one firm locating at the mid point of the market this outcome is also appealing as it corresponds to the entry deterring and monopoly solutions

note competitive price and positioning strategies brand positioning and brand pricing are important strategic decisions for marketing managers such decisions are interrelated and depend upon competitive brand positions and prices however any unilateral decisions may encourage repositioning and price adjustment by competitors thus leading to either new market equilibria or a price positioning war this paper examines such price and positioning decisions in a competitive environment by extending the defender consumer model to more complex equilibria we assume that the brands are already in the market and that positions are sticky in the sense that brands cannot leapfrog one another among the insights for such incumbent brands are if prices are symmetric and held constant firms seek to reposition toward the center of the market but price advantages by central firms can mediate that central tendency such that an equilibrium exists with positive profits if brand positions are held constant the nash equilibria for prices exist and are unique and category profits the sum of brand profits are maximized for maximum brand differentiation for two and three brand markets the subgame perfect nash equilibrium where positioning decisions are made with foresight on the price equilibria causes firms to unilaterally seek maximum brand differentiation but for four or more brands greater foresight and or cooperation appears necessary to reach the point of maximum brand differentiation these results apply where the defender consumer model is an exact description of consumer response and where the competitive reaction assumptions hold in any empirical situation such forces might be softened resulting in differentiated but not maximally differentiated brands

abatement r d and growth with a pollution ceiling abstract the consequences of the 2 c climate target and the implicitly imposed ceiling on co2 have been analyzed in several studies we use an endogenous growth model with a ceiling and an abatement option to study the effect of the ceiling on the allocation of limited funds for r d abatement and capital accumulation it is found that the advantagenousness of abatement rises with the cost advantage of fossil fuel versus backstop if the cost advantage is sufficiently large at some point in time it outweighs the costs of abatement and the gains of r d and capital accumulation the reallocation of production towards abatement may cause an increase or decrease in long run consumption in the latter case abatement allows an intertemporal consumption trade off which may even justify the disregard of everlasting growth in case of stock dependent fossil fuel costs an abatement induced speed up of technology development may cause an increase in fossil fuel stock left in situ

scarcity growth and r d abstract the limits to economic growth due to resource scarcity can be alleviated only by the development of backstop substitutes this paper combines resource based economic growth with r d to reduce the cost of backstop technologies characterizing the entire dynamics of optimal growth and r d processes we find that an economy s growth prospects depend on its type as determined by its production technology and learning ability and by its knowledge capital endowment a wide variety of growth patterns emerges ranging from cases in which an economy that without r d eventually stagnates converges to a steady state is diverted by r d onto a path of sustained growth to cases in which r d is not warranted resource scarcity is shown to encourage r d due to the increased reliance on the backstop technology

allocation of pollution abatement under learning by doing abstract this paper examines how learning by doing affects the allocation of pollution abatement between heterogeneous technologies over time the optimal policy balances current abatement costs against reductions in future costs and infant technologies may be preferred to mature technologies despite greater initial costs we characterize when a technological winner might emerge and we identify conditions under which optimal abatement is shared across all technologies pigouvian taxes can implement the first best but may need to be differentiated across technologies when technical change is induced an important role of environmental policies is to put abatement on the right technological trajectories

targeted advertising strategies on television the personal video recorder pvr facilitates the use of targeted advertising by allowing companies to monitor television viewing behavior and to build demographic profiles of viewers from the data that are collected our research explores the extent to which an advertiser should allocate resources to increase the quality of its targeting we present a game theoretic model that extends the conventional measurement of targeting quality by exploring the trade off between two measures accuracy and recognition accuracy measures the likelihood that any target segment prediction is correct while recognition conversely measures the likelihood that any member of the target segment is identified we find that the relative resources allocated to improving accuracy and recognition depend upon the size of the population of viewers the propensity of viewers to skip commercials the overall cost of airing commercials and the competitive environment furthermore the incentives to improve accuracy are markedly different from those to improve recognition although improving accuracy does not affect the extent of price competition improving recognition leads to intensified price competition and reduced profitability in the product market thus when facing a competitor that pursues a strategy to improve its recognition of potential customers an advertiser should choose to reduce its investment in recognition and increase its investment in accuracy

climate policy and the optimal extraction of high and low carbon fossil fuels we study how restricting co2 emissions affcts resource prices and depletion over time we use a hotelling style model with two nonrenewable fossil fuels that differ in their carbon content e g coal and natural gas and that are imperfect substitutes in final good production we study both an unexpected constraint and an anticipated constraint both shocks induce intertemporal substitution of resource use when emissions are unexpectedly restricted it is cost effective to use high carbon resources relatively more less intensively on impact if this resource is relatively scarce abundant if the emission constraint is anticipated it is cost effective to use relatively more less of the low carbon input before the constraint becomes binding in order to conserve relatively more less of the high carbon input for the period when climate policy is active in case the high carbon resource is relatively scarce abundant

invention and innovation under alternative market structures the case of natural resources this paper examines the interactions between market structure and resource allocation over time when there is endogenous technical progress the structures considered are a planned economy pure monopoly and competition with patent rights in an efficient allocation the date of invention coincides with the date of innovation the date at which technology is used this is also true with a pure monopoly but monopoly retards technical progress relative to the efficient level competition for patents rights to a new technology results in excessively rapid technical progress if the resource endowment of the economy is sufficiently large also competition may lead to sleeping patents where invention strictly precedes the date of innovation

the private and public economics of renewable electricity generation generating electricity from renewable sources is more expensive than conventional approaches but reduces pollution externalities analyzing the tradeoff is much more challenging than often presumed because the value of electricity is extremely dependent on the time and location at which it is produced which is not very controllable with some renewables such as wind and solar likewise the pollution benefits from renewable generation depend on what type of generation it displaces which also depends on time and location without incorporating these factors cost benefit analyses of alternatives are likely to be misleading other common arguments for subsidizing renewable power green jobs energy security and driving down fossil energy prices are unlikely to substantially alter the analysis the role of intellectual property spillovers is a strong argument for subsidizing energy science research but less persuasive as an enhancement to the value of installing current renewable energy technologies

competitive promotional strategies this article analyzes the equilibrium pricing strategies of brands engaged in a pricing game each brand has a monopoly market loyal consumers and competes with others in a common market called brand switchers in the case of a duopoly it is shown that the behavior of the brand switchers characterizes the equilibrium behavior of the duopolists this article focuses on two key comparative statics namely the depth of discounts away from a regular high price and the probability of giving a deal or the frequency of deals how these properties vary with the size of the loyal markets and the behavior of the brand switching population is discussed copyright 1988 by the university of chicago

characterization of the support of the mixed strategy price equilibria in oligopolies with heterogeneous consumers abstract this paper revisits the theory of oligopoly pricing and shows that for a large class of demand and cost functions a mixed strategy equilibrium necessarily implies that each firm s equilibrium strategy is a discrete distribution over a finite number of prices

price dispersion in duopolies with heterogeneous consumers abstract in this paper i modify varian s varian h r 1980 a model of sales american economic review 70 4 651 659 model of sales to allow for heterogeneity in consumer preferences i show that in mixed strategy equilibria each firm charges a finite number of prices using this characterization i examine the effect of consumer heterogeneity on firms optimal pricing strategies

fossil fuels stock externalities and backstop technology the hotelling exhaustible resource model is extended to include stock pollution and nonpolluting backstop technology it is shown that an optimal energy consumption strategy typically includes a regime in which the two energy sources are consumed simultaneously along this regime fossil fuel consumption decreases and backstop consumption increases together fossil fuel and backstop consumption may form eleven optimal regime combinations a decrease in the backstop price decreases the initial level of optimal emission tax

strategic pigouvian taxation stock externalities and polluting non renewable resources este trabajo propone una extension del modelo de wirl y dockner 1995 disenado para analizar la interdependencia bilateral a largo plazo entre un cartel exportador de un recurso y una coalicion de paises importadores en primer lugar se incorporan los efectos agotamiento al analisis de las propiedades intertemporales de un impuesto pigouviano en segundo lugar se calculan los equilibrios feedback de stackelberg los resultados muestran que la dinamica del impuesto depende criticamente del nivel del dano medioambiental marginal ademas tambien demuestran que el impuesto definido por el equilibrio de nash perfecto de markov es un impuesto pigouviano neutral en el sentido que solo corrige la ineficiencia causada por la externalidad del stock sin embargo para el equilibrio feedback de stackelberg el impuesto es ventajoso para los paises importadores ya que la imposicion pigouviana estrategica reduce el poder de mercado del cartel

trends in natural resource commodity prices an analysis of the time domain abstract this paper attempts to reconcile the theoretical predictions of increasing real prices for nonrenewable natural resource commodities obtained from hotelling style models with the empirical findings of falling prices for these commodities a theoretical model for relative price movements is derived for the case of exogenous technical change and endogenous change in the grade of ores mined the model suggests a u shaped time path for relative prices the implied price movements are tested for all the major metals and fuels and the model parameters are found to be statistically significant for 11 out of the 12 commodities tested

a hotelling model with a ceiling on the stock of pollution abstract environmental agreements such as the kyoto protocol aim to stabilize the amount of carbon in the atmosphere which is mainly caused by the burning of nonrenewable resources such as coal we characterize the solution to the textbook hotelling model when there is a ceiling on the stock of emissions we consider both increasing and decreasing demand for energy we show that when the ceiling is binding both the low cost nonrenewable resource and the high cost renewable resource may be used jointly a key implication is that if energy demand were to decline in the long run we may supplement energy supply through clean renewables to meet the environmental standard but then revert back to using only dirty fossil fuels in the future when the ceiling has become non binding that is the much heralded societal transition to clean energy resources may be short lived

energy transition under irreversibility a two sector approach in this paper we analyze the optimal energy transition of a two sector economy energy and final goods with exhaustible oil reserves a renewable source of energy and a pollution threat the latter corresponds to a pollution threshold above which a part of the capital is lost following flooding for instance we show that the optimal energy transition path may correspond to a corner regime in which the economy starts using both resources then crosses the pollution threshold and therefore loses a part of its capital at the end the sole adoption of the renewable energy is optimal only in the long run this result is in line with the asymptotic energy transition arguments stating that the transition to clean energy may happen only in the long run we also show that economy reduces the use of energy resource as long as the productivity of capital and energy services is high therefore public policies should promote investments in energy innovation that targets productive sector home appliances and buildings and helps to save both money and energy we extend the present model to allow for additional investment in energy saving technologies our main results show that this additional investment favours the energy transition in the sense that it increases the time within which the economy may experience the catastrophe and the welfare of the society for policy implications economic instruments such as taxes on dirty energy subsidies on clean energy or incentives for energy saving technologies need to be implemented in order to promote the energy transition this is particularly important for developing countries that mostly rely on polluting energy resources and are the most vulnerable to climate change but those economic instruments should be carefully designed in line with the asymptotic energy transition result

energy backstop endogeneity and the optimal use of groundwater to meet the growing demand for freshwater many regions have increased groundwater pumping in recent years resulting in declining groundwater levels worldwide a promising development to address these declines is technical change regarding groundwater substitutes such as desalination and wastewater recycling however because these technologies are energy intensive optimal implementation also depends on future energy price trends we provide an operational model for the case of reverse osmosis seawater desalination in an application to the pearl harbor aquifer in hawaii we find that allowing the cost of desalination to increase at an average annual rate of 2 4 over the next century results in a substantially steeper efficiency price path for water the higher prices decrease optimal groundwater extraction and induce a slower head drawdown over a longer period of time thereby delaying the transition to desalination by over 30 years because the rise in energy costs exacerbates efficiency losses from under pricing any delay in implementing efficiency pricing will cause either a greater future increase in prices or the need for rationing reforming prices sooner rather than later may be more politically feasible given that consumers may be more amenable to a gradual rise in prices today than a sudden doubling or tripling of prices ten years from now using this as a foundation we outline a research agenda for extending the framework to other groundwater substitutes and for adapting to climate change

economic growth and transitions between renewable and nonrenewable energy resources abstract we study transitions between nonrenewable and renewable energy forms at different development stages of an economy it is shown that in the historical context the emphasis on energy production may evolve from renewables to nonrenewables and back to renewables typically both energy forms are used simultaneously along the equilibrium path nonrenewable resource consumption may increase and their price decrease an inverted u relation between carbon emissions and income level may follow even without environmental policy

optimal timing of carbon capture policies under learning by doing abstract using a standard hotelling model of resource exploitation we determine the optimal energy consumption paths from three options dirty coal which is non renewable and carbon emitting clean coal which is also non renewable but carbon free thanks to carbon capture and storage ccs and solar energy which is renewable and carbon free we assume that the atmospheric carbon stock cannot exceed an exogenously given ceiling taking into account learning by doing in ccs technology we show the following results i clean coal exploitation cannot begin before the outset of the carbon constrained phase and must stop strictly before the end of this phase ii the energy price path can evolve non monotonically over time and iii when the solar cost is low enough an unusual energy consumption sequence along with solar energy is interrupted for some time and replacement by clean coal may exist