International Journal of Environmental Research and Public Health
This paper examines horizontally differentiated duopolies à la Hotelling with environmentally con... more This paper examines horizontally differentiated duopolies à la Hotelling with environmentally conscious consumers and a planner promoting a sustainable good with costly awareness campaigns (ACs). The objective is to find the planner’s optimal strategies and their effects on the firms’ behaviour. The analysis is carried out with two approaches, considering a private and a public duopoly. In both, it is shown that the planner chooses the average characteristic supported by a higher intensity campaign. However, with the private one, such an outcome is possible if the planner has minimal resources. Consumer consciousness and ACs have opposite effects on the firms and the planner. It is proven that consumer awareness favours the interests of the duopolies and reduces those of the planner, while the contrary is true for ACs. Finally, it is shown that a public duopoly is the best scenario for sustainability. This study provides an environmental policy to replace or complement traditional i...
In this work we focus on the general quadratic transportation cost function in the linear model c... more In this work we focus on the general quadratic transportation cost function in the linear model considering both the concave and the convex case. From earlier results in the literature it is clear that no pure-strategy price equilibrium exists for whatever firm locations with linear-quadratic costs in the linear model. Therefore, our first objective is to calculate the feasible equilibrium region for a general linear-quadratic cost function, since there is no price equilibrium for the whole market. In order to do this, it is crucial to perform a change of variables that explicitly allows us to calculate, in an easier way, the necessary conditions to obtain the equilibrium regions. Finally, we compare the feasible regions equilibrium with both the concave and the convex cases and we find that the feasible region with convex costs is bigger than with concave costs.
This article considers a model of spatial competition where firms and consumers are located in a ... more This article considers a model of spatial competition where firms and consumers are located in a semicircular space rather than in the whole circle (Salop’s model) or the linear city (Hotelling’s model), under the assumptions of both, convex and concave, transportation costs. The paper tries to generalize the results of the two previous models. We find that for concave transportation costs the existence of a price equilibrium is warranted for every firms’ location when the length of the semicircular space is greater than 3/4. For the convex case, perfect equilibrium is only obtained when the size of the market segment is equivalent to Hotelling's linear model.
Dans les annees recentes, la litterature theorique sur la differenciation des produits a revele l... more Dans les annees recentes, la litterature theorique sur la differenciation des produits a revele le probleme de la non-existence de l'equilibre de Nash en strategies pures. Cette difficulte est due generalement a la discontinuite ou a la non quasi-concavite des fonctions de profit des entreprises et elle est liee en grande partie aux specifications adoptees dans les modeles. L'etude de cette these est centree sur l'analyse de la non-existence de l'equilibre de Nash en prix dans les marches duopolistiques differenciees : nous mettrons en valeur l'importance des specifications choisies dans les modeles ainsi que les eventuelles modifications que l'on peut y apporter pour restaurer l'existence des equilibres en prix. Le theoreme classique d'existence de l'equilibre en strategies mixtes (Glicksberg, 1952) permet la restauration de l'equilibre. Cependant, les solutions presentees recemment par un certain nombre d'auteurs sont obtenues sur des es...
Under quadratic transportation costs, the existence of the sequential first-locate-thenprice equi... more Under quadratic transportation costs, the existence of the sequential first-locate-thenprice equilibrium in spatial competition is well known in the literature. In this paper, we find that the equilibrium may fail to exist under certain restrictions with respect to the location of firms and consumers in the market. This result is valid for both the linear and the circular models
In this paper, we consider the design of optimal environmental policies composed of pollution sta... more In this paper, we consider the design of optimal environmental policies composed of pollution standards and probabilities of inspection, where fines for exceeding the standards depend on the degree of noncompliance and the environmental technology that the firm uses in its production process. We show that the selection of a progressive or a proportional penalty with respect to the degree of noncompliance is crucial: while the optimal standard is zero in the progressive case, we obtain a positive standard in the linear case, with important welfare implications. While firms prefer proportional fines due to the relaxed regulations induced, regulators may prefer the progressive case for sufficiently large monitoring costs. JEL Classification: L51, K32, K42.
Zbornik radova Ekonomskog fakulteta u Rijeci: časopis za ekonomsku teoriju i praksu/Proceedings of Rijeka Faculty of Economics: Journal of Economics and Business
ABSTRACT This paper studies a zoning mechanism that gives the optimal locations of two firms in a... more ABSTRACT This paper studies a zoning mechanism that gives the optimal locations of two firms in a linear city under mill prices. A regulator biased towards consumers allows a central area of the city to be shared by firms and consumers and thus firms are not allowed to locate outside the city limits. A regulator more concerned about firms extends this central zone outside the city limits and the city has a residential use only if the firms so decide. Finally, a regulator highly biased towards firms allows them to locate only beyond a set distance from the city, so there is a strip of land outside the city but close to its boundaries, for alternative uses.
International Journal of Environmental Research and Public Health
This paper examines horizontally differentiated duopolies à la Hotelling with environmentally con... more This paper examines horizontally differentiated duopolies à la Hotelling with environmentally conscious consumers and a planner promoting a sustainable good with costly awareness campaigns (ACs). The objective is to find the planner’s optimal strategies and their effects on the firms’ behaviour. The analysis is carried out with two approaches, considering a private and a public duopoly. In both, it is shown that the planner chooses the average characteristic supported by a higher intensity campaign. However, with the private one, such an outcome is possible if the planner has minimal resources. Consumer consciousness and ACs have opposite effects on the firms and the planner. It is proven that consumer awareness favours the interests of the duopolies and reduces those of the planner, while the contrary is true for ACs. Finally, it is shown that a public duopoly is the best scenario for sustainability. This study provides an environmental policy to replace or complement traditional i...
In this work we focus on the general quadratic transportation cost function in the linear model c... more In this work we focus on the general quadratic transportation cost function in the linear model considering both the concave and the convex case. From earlier results in the literature it is clear that no pure-strategy price equilibrium exists for whatever firm locations with linear-quadratic costs in the linear model. Therefore, our first objective is to calculate the feasible equilibrium region for a general linear-quadratic cost function, since there is no price equilibrium for the whole market. In order to do this, it is crucial to perform a change of variables that explicitly allows us to calculate, in an easier way, the necessary conditions to obtain the equilibrium regions. Finally, we compare the feasible regions equilibrium with both the concave and the convex cases and we find that the feasible region with convex costs is bigger than with concave costs.
This article considers a model of spatial competition where firms and consumers are located in a ... more This article considers a model of spatial competition where firms and consumers are located in a semicircular space rather than in the whole circle (Salop’s model) or the linear city (Hotelling’s model), under the assumptions of both, convex and concave, transportation costs. The paper tries to generalize the results of the two previous models. We find that for concave transportation costs the existence of a price equilibrium is warranted for every firms’ location when the length of the semicircular space is greater than 3/4. For the convex case, perfect equilibrium is only obtained when the size of the market segment is equivalent to Hotelling's linear model.
Dans les annees recentes, la litterature theorique sur la differenciation des produits a revele l... more Dans les annees recentes, la litterature theorique sur la differenciation des produits a revele le probleme de la non-existence de l'equilibre de Nash en strategies pures. Cette difficulte est due generalement a la discontinuite ou a la non quasi-concavite des fonctions de profit des entreprises et elle est liee en grande partie aux specifications adoptees dans les modeles. L'etude de cette these est centree sur l'analyse de la non-existence de l'equilibre de Nash en prix dans les marches duopolistiques differenciees : nous mettrons en valeur l'importance des specifications choisies dans les modeles ainsi que les eventuelles modifications que l'on peut y apporter pour restaurer l'existence des equilibres en prix. Le theoreme classique d'existence de l'equilibre en strategies mixtes (Glicksberg, 1952) permet la restauration de l'equilibre. Cependant, les solutions presentees recemment par un certain nombre d'auteurs sont obtenues sur des es...
Under quadratic transportation costs, the existence of the sequential first-locate-thenprice equi... more Under quadratic transportation costs, the existence of the sequential first-locate-thenprice equilibrium in spatial competition is well known in the literature. In this paper, we find that the equilibrium may fail to exist under certain restrictions with respect to the location of firms and consumers in the market. This result is valid for both the linear and the circular models
In this paper, we consider the design of optimal environmental policies composed of pollution sta... more In this paper, we consider the design of optimal environmental policies composed of pollution standards and probabilities of inspection, where fines for exceeding the standards depend on the degree of noncompliance and the environmental technology that the firm uses in its production process. We show that the selection of a progressive or a proportional penalty with respect to the degree of noncompliance is crucial: while the optimal standard is zero in the progressive case, we obtain a positive standard in the linear case, with important welfare implications. While firms prefer proportional fines due to the relaxed regulations induced, regulators may prefer the progressive case for sufficiently large monitoring costs. JEL Classification: L51, K32, K42.
Zbornik radova Ekonomskog fakulteta u Rijeci: časopis za ekonomsku teoriju i praksu/Proceedings of Rijeka Faculty of Economics: Journal of Economics and Business
ABSTRACT This paper studies a zoning mechanism that gives the optimal locations of two firms in a... more ABSTRACT This paper studies a zoning mechanism that gives the optimal locations of two firms in a linear city under mill prices. A regulator biased towards consumers allows a central area of the city to be shared by firms and consumers and thus firms are not allowed to locate outside the city limits. A regulator more concerned about firms extends this central zone outside the city limits and the city has a residential use only if the firms so decide. Finally, a regulator highly biased towards firms allows them to locate only beyond a set distance from the city, so there is a strip of land outside the city but close to its boundaries, for alternative uses.
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Papers by Hamid Hamoudi