HAL (Le Centre pour la Communication Scientifique Directe), Dec 20, 2018
We provide a bare-bones framework that uncovers the circumstances which lead either to the emerge... more We provide a bare-bones framework that uncovers the circumstances which lead either to the emergence of equally-spaced and equally-sized central places or to a hierarchy of central places. We show how these patterns re ‡ect the preferences of agents and the e¢ ciency of transportation and communication technologies. With one population of homogeneous individuals, the economy is characterized by a uniform distribution or by a periodic distribution of central places having the same size. The interaction between two distinct populations may give rise to a hierarchy of central places with one or several primate cities.
We develop a two-sector model of monopolistic competition with a dierentiated intermediate good a... more We develop a two-sector model of monopolistic competition with a dierentiated intermediate good and variable elasticity of technological substitution. This setting proves to be well-suited to studying the nature and origins of external increasing returns. We disentangle two sources of scale economies: specialization and competition. The former depends only on how TFP varies with input diversity, while the latter is fully captured by the behavior of the elasticity of substitution across inputs. This distinction gives rise to a full characterization of the rich array of competition regimes in our model. The necessary and sucient conditions for each regime to occur are expressed in terms of the relationships between TFP and the elasticity of substitution as functions of the input diversity. Moreover, we demonstrate that, despite the folk wisdom resting on CES models, specialization economies are in general neither necessary nor sucient for external increasing returns to emerge. This highlights the profound and non-trivial role of market competition in generating agglomeration economies, endogenous growth, and other phenomena driven by scale economies.
We characterize three classes of demand systems, all of which are defined non-parametrically: hom... more We characterize three classes of demand systems, all of which are defined non-parametrically: homothetic demand systems with a single aggregator (HSA), those with direct implicit additivity (HDIA), and those with indirect implicit additivity (HIIA). In HSA, all the cross-price effects are captured by one price aggregator, while in HDIA and in HIIA, they are captured by two price aggregators. Each of these three classes contains CES as a special case. Yet, they are pairwise disjoint with the sole exception of CES. Thus, these classes of homothetic demand systems offer us three alternative ways of departing from CES.
We develop a model of monopolistic competition with a differentiated intermediate good and variab... more We develop a model of monopolistic competition with a differentiated intermediate good and variable elasticity of technological substitution. The model allows to study the nature and origins of external increasing returns. We single out two sources of scale economies: specialization and competition. The former depends only on how total factor productivity (TFP) varies with input diversity, while the latter is fully captured by the behavior of the elasticity of substitution across inputs. This distinction gives rise to a full characterization of the rich array of competition regimes in our model. The necessary and sufficient conditions for each regime to occur are expressed in terms of the relationships between TFP and the elasticity of substitution as functions of the input diversity. Moreover, we demonstrate that, despite the folk wisdom resting on constant elasticity of substitution models, specialization economies are in general neither necessary nor sufficient for external increasing returns to emerge. This highlights the profound and nontrivial role of market competition in generating agglomeration economies and other phenomena driven by scale economies.
We propose a general model of monopolistic competition which encompasses existing models while be... more We propose a general model of monopolistic competition which encompasses existing models while being exible enough to take into account new demand and competition features. Even though preferences need not be additive and/or homothetic, the market outcome is still driven by the sole variable elasticity of substitution. We impose elementary conditions on this function to guarantee empirically relevant properties of a free-entry equilibrium. Comparative statics with respect to market size and productivity shock are characterized through necessary and sucient conditions. Furthermore, we show that the attention to the constant elasticity of substitution (CES) based on its normative implications was misguided: constant markups , additivity and homotheticity are neither necessary nor sucient for the market to deliver the optimum outcome. Our approach can cope with heterogeneous rms once it is recognized that the elasticity of substitution is rm-specic. Finally, we show how our setup can be extended to cope with multiple sectors.
We develop a product-differentiated model where the product space is a network defined as a set o... more We develop a product-differentiated model where the product space is a network defined as a set of varieties (nodes) linked by their degrees of substituability (edges). We also locate consumers into this network, so that the location of each consumer (node) corresponds to her "ideal" variety. We show that there exists a unique Bertrand-Nash equilibrium where prices are determined by both the firms' sign-alternating Bonacich centralities and the average willingness to pay across consumers. We also investigate how local product differentiation and the spatial discount factor affect the equilibrium prices. We show that these effects non-trivially depend on the network structure. In particular, we find that, in a star-shaped network, the central firm does not always enjoy higher monopoly power than the peripheral firms.
We develop a simple partial-equilibrium model of endogenous city structure formation. No producti... more We develop a simple partial-equilibrium model of endogenous city structure formation. No production externalities are at work, the only two forces shaping the spatial configurations of the city being love for variety (on the consumer side) and seeking for a better access to the market (on the firm side). We show that, unlike in existing models of a similar nature, our model generates clustering rather than co-agglomeration. Namely, if there are few firms relative to the urban population size, then firms tend to cluster at the city center, while consumers choose to reside on the outskirts. Otherwise, the opposite holds. Although a continuum of equilibrium city structures may emerge, we show that all spatial equilibria are segregated. In addition, the market outcome features spatial price dispersion, even though our framework does not involve imperfect information and search costs on the consumer side.
We provide a selective survey of what has been accomplished under the heading of monopolistic com... more We provide a selective survey of what has been accomplished under the heading of monopolistic competition in industrial organization and other economic elds. Among other things, we argue that monopolistic competition is a market structure in its own right, which encompasses a much broader setup than the celebrated constant elasticity of substitution (CES) model. Although oligopolistic and monopolistic competition compete for adherents within the economics profession, we show that this dichotomy is, to a large extend, unwarranted.
Agents, embedded in a social network, first decide whether or not to adopt a new costly technolog... more Agents, embedded in a social network, first decide whether or not to adopt a new costly technology, and, then, choose their level of productivity effort. The latter choice is affected by the social norm of each individual so that she loses utility from failing to conform to the average effort of her peers (local-average model). Contrary to the local-aggregate model, we show that, in the second stage, if agents are ex ante identical but have different positions in the network, they all exert the same effort level, which corresponds to the first best. We also demonstrate that multiple equilibria may arise in the two-stage game. We show under which conditions symmetric and asymmetric subgame-perfect Nash equilibria emerge and why they are inefficient. Finally, we propose different subsidy policies that can restore the first-best solutions.
We develop a simple partial-equilibrium model of endogenous city structure formation. No producti... more We develop a simple partial-equilibrium model of endogenous city structure formation. No production externalities are at work, the only two forces shaping the spatial configurations of the city being love for variety (on the consumer side) and seeking for a better access to the market (on the firm side). We show that, unlike in existing models of a similar nature, our model generates clustering rather than co-agglomeration. Namely, if there are few firms relative to the urban population size, then firms tend to cluster at the city center, while consumers choose to reside on the outskirts. Otherwise, the opposite holds. Although a continuum of equilibrium city structures may emerge, we show that all spatial equilibria are segregated. In addition, the market outcome features spatial price dispersion, even though our framework does not involve imperfect information and search costs on the consumer side.
We study the welfare implications of intrasectoral shocks whose direct e ect is welfareimproving ... more We study the welfare implications of intrasectoral shocks whose direct e ect is welfareimproving in two-sectoral general equilibrium models with entry. We develop a dual necessary and su cient condition of welfare losses, which occur when the negative intersectoral e ect dominates the positive intrasectoral e ect. Our approach is exible enough to study (i) losses from trade liberalization in models of intraindustry trade between symmetric countries under constant or variable markups, (ii) welfare losses from sectoral productivity improvements in multisectoral models with Melitz-type heterogeneity across rms. We show that, when goods producrd by the two sectors are gross complements, welfare gains will always take place. For the case of gross substitutes, we develop a systematic procedure of constructing examples of losses. In particular, we show that, for losses from trade to occur, neither any asymmetries across countries, nor variable markups in either sector are essential. The on...
We develop a general equilibrium model of monopolistic competition with a traded and a non-traded... more We develop a general equilibrium model of monopolistic competition with a traded and a non-traded sector. Using a broad class of homothetic preferences—that generate variable markups, display a simple behavior of their elasticity of substitution, and nest the ces as a limiting case—we show that trade liberalization: (i) reduces domestic markups and increases imported markups in the traded sector; (ii) increases markups in the non-traded sector; and (iii) increases firm sizes in both sectors. Thus, while domestic and export markups in the traded sector converge across countries, markups diverge across sectors within countries. The negative welfare effects of higher markups and less consumption diversity in the non-traded sector dampen the positive welfare effects of lower markups and greater diversity in the traded sector.
We combine spatial and monopolistic competition to study market interactions between downtown ret... more We combine spatial and monopolistic competition to study market interactions between downtown retailers and an outlying shopping mall. Consumers shop at either marketplace or at both, and buy each variety in volume. The market solution stems from the interplay between the market expansion eect generated by consumers seeking more opportunities, and the competition eect. Firms' prots increase (decrease) with the entry of local competitors when the former (latter) dominates. Downtown retailers swiftly vanish when the mall is large. A predatory but ecient mall need not be regulated, whereas the regulator must restrict the size of a mall accommodating downtown retailers.
To understand theoretically how competitive pressures affect selection and sorting of firms with ... more To understand theoretically how competitive pressures affect selection and sorting of firms with different productivity, we study the Melitz (2003) model under the H.S.A. (Homothetic with a Single Aggregator) class of demand systems. H.S.A. is tractable due to its homotheticity and to its single aggregator that serves as a sufficient statistic for competitive pressures, which acts as a magnifier of firm heterogeneity. It is also flexible enough to allow for the choke price, the 2nd law of demand--“a higher price leads to a higher price elasticity”--, and the 3rd law of demand--“a higher price leads to a smaller rate of change in the price elasticity.” We show, among others: i) More productive firms have higher profits and revenues; they have higher markup rates under the 2nd law and lower pass-through rates under the 3rd law. Employments are not monotone in firm productivity; they are hump-shaped under the 2nd and 3rd laws. The 2nd law also implies the procompetitive effect and stra...
The Dixit-Stiglitz model of monopolistic competition is widely used as a building block across ma... more The Dixit-Stiglitz model of monopolistic competition is widely used as a building block across many applied general equilibrium fields. Two of its remarkable features are the invariance of the markup rate and the optimality of the free-entry equilibrium. Of course, neither of these two features is robust. Departure from CES makes entry either procompetitive or anticompetitive (i.e., the markup rate either goes down or goes up as more firms enter). Departure from CES also makes entry either excessive or insufficient. But how is the condition for procompetitive vs. anticompetitive entry related to that for excessive vs. insufficient entry? To investigate this question, we extend the Dixit-Stiglitz monopolistic competition model to three classes of homothetic demand systems, which are mutually exclusive except that each of them contains CES as a knifeedge case. In all three classes, we show, among others, that entry is excessive (insufficient) when it is globally procompetitive (anticompetitive) and that, in the presence of the choke price, entry is procompetitive and excessive at least for a sufficiently large market size.
HAL (Le Centre pour la Communication Scientifique Directe), Dec 20, 2018
We provide a bare-bones framework that uncovers the circumstances which lead either to the emerge... more We provide a bare-bones framework that uncovers the circumstances which lead either to the emergence of equally-spaced and equally-sized central places or to a hierarchy of central places. We show how these patterns re ‡ect the preferences of agents and the e¢ ciency of transportation and communication technologies. With one population of homogeneous individuals, the economy is characterized by a uniform distribution or by a periodic distribution of central places having the same size. The interaction between two distinct populations may give rise to a hierarchy of central places with one or several primate cities.
We develop a two-sector model of monopolistic competition with a dierentiated intermediate good a... more We develop a two-sector model of monopolistic competition with a dierentiated intermediate good and variable elasticity of technological substitution. This setting proves to be well-suited to studying the nature and origins of external increasing returns. We disentangle two sources of scale economies: specialization and competition. The former depends only on how TFP varies with input diversity, while the latter is fully captured by the behavior of the elasticity of substitution across inputs. This distinction gives rise to a full characterization of the rich array of competition regimes in our model. The necessary and sucient conditions for each regime to occur are expressed in terms of the relationships between TFP and the elasticity of substitution as functions of the input diversity. Moreover, we demonstrate that, despite the folk wisdom resting on CES models, specialization economies are in general neither necessary nor sucient for external increasing returns to emerge. This highlights the profound and non-trivial role of market competition in generating agglomeration economies, endogenous growth, and other phenomena driven by scale economies.
We characterize three classes of demand systems, all of which are defined non-parametrically: hom... more We characterize three classes of demand systems, all of which are defined non-parametrically: homothetic demand systems with a single aggregator (HSA), those with direct implicit additivity (HDIA), and those with indirect implicit additivity (HIIA). In HSA, all the cross-price effects are captured by one price aggregator, while in HDIA and in HIIA, they are captured by two price aggregators. Each of these three classes contains CES as a special case. Yet, they are pairwise disjoint with the sole exception of CES. Thus, these classes of homothetic demand systems offer us three alternative ways of departing from CES.
We develop a model of monopolistic competition with a differentiated intermediate good and variab... more We develop a model of monopolistic competition with a differentiated intermediate good and variable elasticity of technological substitution. The model allows to study the nature and origins of external increasing returns. We single out two sources of scale economies: specialization and competition. The former depends only on how total factor productivity (TFP) varies with input diversity, while the latter is fully captured by the behavior of the elasticity of substitution across inputs. This distinction gives rise to a full characterization of the rich array of competition regimes in our model. The necessary and sufficient conditions for each regime to occur are expressed in terms of the relationships between TFP and the elasticity of substitution as functions of the input diversity. Moreover, we demonstrate that, despite the folk wisdom resting on constant elasticity of substitution models, specialization economies are in general neither necessary nor sufficient for external increasing returns to emerge. This highlights the profound and nontrivial role of market competition in generating agglomeration economies and other phenomena driven by scale economies.
We propose a general model of monopolistic competition which encompasses existing models while be... more We propose a general model of monopolistic competition which encompasses existing models while being exible enough to take into account new demand and competition features. Even though preferences need not be additive and/or homothetic, the market outcome is still driven by the sole variable elasticity of substitution. We impose elementary conditions on this function to guarantee empirically relevant properties of a free-entry equilibrium. Comparative statics with respect to market size and productivity shock are characterized through necessary and sucient conditions. Furthermore, we show that the attention to the constant elasticity of substitution (CES) based on its normative implications was misguided: constant markups , additivity and homotheticity are neither necessary nor sucient for the market to deliver the optimum outcome. Our approach can cope with heterogeneous rms once it is recognized that the elasticity of substitution is rm-specic. Finally, we show how our setup can be extended to cope with multiple sectors.
We develop a product-differentiated model where the product space is a network defined as a set o... more We develop a product-differentiated model where the product space is a network defined as a set of varieties (nodes) linked by their degrees of substituability (edges). We also locate consumers into this network, so that the location of each consumer (node) corresponds to her "ideal" variety. We show that there exists a unique Bertrand-Nash equilibrium where prices are determined by both the firms' sign-alternating Bonacich centralities and the average willingness to pay across consumers. We also investigate how local product differentiation and the spatial discount factor affect the equilibrium prices. We show that these effects non-trivially depend on the network structure. In particular, we find that, in a star-shaped network, the central firm does not always enjoy higher monopoly power than the peripheral firms.
We develop a simple partial-equilibrium model of endogenous city structure formation. No producti... more We develop a simple partial-equilibrium model of endogenous city structure formation. No production externalities are at work, the only two forces shaping the spatial configurations of the city being love for variety (on the consumer side) and seeking for a better access to the market (on the firm side). We show that, unlike in existing models of a similar nature, our model generates clustering rather than co-agglomeration. Namely, if there are few firms relative to the urban population size, then firms tend to cluster at the city center, while consumers choose to reside on the outskirts. Otherwise, the opposite holds. Although a continuum of equilibrium city structures may emerge, we show that all spatial equilibria are segregated. In addition, the market outcome features spatial price dispersion, even though our framework does not involve imperfect information and search costs on the consumer side.
We provide a selective survey of what has been accomplished under the heading of monopolistic com... more We provide a selective survey of what has been accomplished under the heading of monopolistic competition in industrial organization and other economic elds. Among other things, we argue that monopolistic competition is a market structure in its own right, which encompasses a much broader setup than the celebrated constant elasticity of substitution (CES) model. Although oligopolistic and monopolistic competition compete for adherents within the economics profession, we show that this dichotomy is, to a large extend, unwarranted.
Agents, embedded in a social network, first decide whether or not to adopt a new costly technolog... more Agents, embedded in a social network, first decide whether or not to adopt a new costly technology, and, then, choose their level of productivity effort. The latter choice is affected by the social norm of each individual so that she loses utility from failing to conform to the average effort of her peers (local-average model). Contrary to the local-aggregate model, we show that, in the second stage, if agents are ex ante identical but have different positions in the network, they all exert the same effort level, which corresponds to the first best. We also demonstrate that multiple equilibria may arise in the two-stage game. We show under which conditions symmetric and asymmetric subgame-perfect Nash equilibria emerge and why they are inefficient. Finally, we propose different subsidy policies that can restore the first-best solutions.
We develop a simple partial-equilibrium model of endogenous city structure formation. No producti... more We develop a simple partial-equilibrium model of endogenous city structure formation. No production externalities are at work, the only two forces shaping the spatial configurations of the city being love for variety (on the consumer side) and seeking for a better access to the market (on the firm side). We show that, unlike in existing models of a similar nature, our model generates clustering rather than co-agglomeration. Namely, if there are few firms relative to the urban population size, then firms tend to cluster at the city center, while consumers choose to reside on the outskirts. Otherwise, the opposite holds. Although a continuum of equilibrium city structures may emerge, we show that all spatial equilibria are segregated. In addition, the market outcome features spatial price dispersion, even though our framework does not involve imperfect information and search costs on the consumer side.
We study the welfare implications of intrasectoral shocks whose direct e ect is welfareimproving ... more We study the welfare implications of intrasectoral shocks whose direct e ect is welfareimproving in two-sectoral general equilibrium models with entry. We develop a dual necessary and su cient condition of welfare losses, which occur when the negative intersectoral e ect dominates the positive intrasectoral e ect. Our approach is exible enough to study (i) losses from trade liberalization in models of intraindustry trade between symmetric countries under constant or variable markups, (ii) welfare losses from sectoral productivity improvements in multisectoral models with Melitz-type heterogeneity across rms. We show that, when goods producrd by the two sectors are gross complements, welfare gains will always take place. For the case of gross substitutes, we develop a systematic procedure of constructing examples of losses. In particular, we show that, for losses from trade to occur, neither any asymmetries across countries, nor variable markups in either sector are essential. The on...
We develop a general equilibrium model of monopolistic competition with a traded and a non-traded... more We develop a general equilibrium model of monopolistic competition with a traded and a non-traded sector. Using a broad class of homothetic preferences—that generate variable markups, display a simple behavior of their elasticity of substitution, and nest the ces as a limiting case—we show that trade liberalization: (i) reduces domestic markups and increases imported markups in the traded sector; (ii) increases markups in the non-traded sector; and (iii) increases firm sizes in both sectors. Thus, while domestic and export markups in the traded sector converge across countries, markups diverge across sectors within countries. The negative welfare effects of higher markups and less consumption diversity in the non-traded sector dampen the positive welfare effects of lower markups and greater diversity in the traded sector.
We combine spatial and monopolistic competition to study market interactions between downtown ret... more We combine spatial and monopolistic competition to study market interactions between downtown retailers and an outlying shopping mall. Consumers shop at either marketplace or at both, and buy each variety in volume. The market solution stems from the interplay between the market expansion eect generated by consumers seeking more opportunities, and the competition eect. Firms' prots increase (decrease) with the entry of local competitors when the former (latter) dominates. Downtown retailers swiftly vanish when the mall is large. A predatory but ecient mall need not be regulated, whereas the regulator must restrict the size of a mall accommodating downtown retailers.
To understand theoretically how competitive pressures affect selection and sorting of firms with ... more To understand theoretically how competitive pressures affect selection and sorting of firms with different productivity, we study the Melitz (2003) model under the H.S.A. (Homothetic with a Single Aggregator) class of demand systems. H.S.A. is tractable due to its homotheticity and to its single aggregator that serves as a sufficient statistic for competitive pressures, which acts as a magnifier of firm heterogeneity. It is also flexible enough to allow for the choke price, the 2nd law of demand--“a higher price leads to a higher price elasticity”--, and the 3rd law of demand--“a higher price leads to a smaller rate of change in the price elasticity.” We show, among others: i) More productive firms have higher profits and revenues; they have higher markup rates under the 2nd law and lower pass-through rates under the 3rd law. Employments are not monotone in firm productivity; they are hump-shaped under the 2nd and 3rd laws. The 2nd law also implies the procompetitive effect and stra...
The Dixit-Stiglitz model of monopolistic competition is widely used as a building block across ma... more The Dixit-Stiglitz model of monopolistic competition is widely used as a building block across many applied general equilibrium fields. Two of its remarkable features are the invariance of the markup rate and the optimality of the free-entry equilibrium. Of course, neither of these two features is robust. Departure from CES makes entry either procompetitive or anticompetitive (i.e., the markup rate either goes down or goes up as more firms enter). Departure from CES also makes entry either excessive or insufficient. But how is the condition for procompetitive vs. anticompetitive entry related to that for excessive vs. insufficient entry? To investigate this question, we extend the Dixit-Stiglitz monopolistic competition model to three classes of homothetic demand systems, which are mutually exclusive except that each of them contains CES as a knifeedge case. In all three classes, we show, among others, that entry is excessive (insufficient) when it is globally procompetitive (anticompetitive) and that, in the presence of the choke price, entry is procompetitive and excessive at least for a sufficiently large market size.
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Papers by Philip Ushchev