We study equilibrium investment strategies of rms competing in stochastic dynamic market settings... more We study equilibrium investment strategies of rms competing in stochastic dynamic market settings and facing two types of investment structures: investment with signicant lead time (or time-to-build) and investment without (or minor) lead time. We investigate how investment behavior changes when investment is subject to time-to-build versus when it is not. We characterize equilibrium investment strategies under several information structures and compare results to the social optimum. We oer some new results. The model predicts that, controlling for demand, and production and investment costs, investments and outputs can be higher in progressive industries (which often exhibit time-to-build) than in fast-paced industries (where time-to-build is insignicant). Furthermore, for both investment types (investment with or without time-to-build) we oer a novel equilibrium in which rms incrementally invest. This behavior is driven by demand uncertainty and capacity constraints. Also, expected outputs are lower than Cournot outputs as rms face uncertainty. Moreover, the amount of uncertainty has dierent eects over investment types.
A goal of this paper is to compare results for discriminatory auctions to results for uniform-pri... more A goal of this paper is to compare results for discriminatory auctions to results for uniform-price auctions when suppliers have capacity constraints. We have a pretty good understanding of what equilibrium results look like for the uniform-price auctions. But an unresolved problem is what happens when a discriminative auction is run and suppliers have capacity constraints. We formulate a supply function equilibrium (SFE) model in continuous offer schedules with inelastic, time varying demand and with single step marginal cost function to compare two auction institutions in the presence of capacity constraints. We show that payments made to the suppliers in the unique equilibrium of the discriminatory auction can be less than the payments in the uniform-price auction, depending on which uniform-price auction equilibrium is selected. For the high demand and/or low excess capacity cases we also characterize mixed strategy supply function equilibrium under the discriminatory auction.
This thesis examines several issues that arise in restructured electricity markets. These issues ... more This thesis examines several issues that arise in restructured electricity markets. These issues include production, scheduling and forward contract decision making, capital investment decisions in uncertain environments, and equilibrium bidding in wholesale electricity auctions. In the chapter, "Supply Function Equilibria with Pivotal Suppliers", we study the impact of pivotal suppliers in supply function bidding settings. Observers of these markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that when pivotal suppliers are present, the set of SFE is reduced relative to when no suppliers are pivotal. In the chapter, "Dynamic Oligopolistic Games Under Uncertainty: A Stochastic Programming Approach", we study several stochastic programming formulations of dynamic oligopolistic games under uncertainty. It is well known that if the number of state variables increases, dynamic programming becomes computationally intractable. For such games, we show that under certain symmetry assumptions, players earn greater expected profits as demand volatility increases. The key to our approach is the "scenario formulation" of stochastic programming. The examples presented in this paper illustrate that this approach can address dynamic games that are clearly out of reach for dynamic programming, the common approach in the literature on dynamic games. In the chapter, "Scenario-based Electricity-Gas Forward and Spot Pricing and Load Formulations", we propose load models and price and return formulations in specific energy markets. Existing energy models do not consider inter-relations between the trio: spot price, derivative price and electric load. Also these models, which are in the spirit of the models proposed in financial and commodity markets, ignore special characteristics of electricity, which may make the proposed models useless. In our formulations we consider these characteristics and correlations between these variables. Simulation results that we run support our modeling approaches
The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted how generation capacity constraints may contribute to market power of generation firms. If a generation firm's rivals are capacity constrained then the firm may be pivotal; that is, the firm could substantially raise the market price by unilaterally withholding output. However the SFE literature has not properly analyzed the impact of capacity constraints nor has it considered the impact of pivotal firms on equilibrium predictions. We characterize the set of symmetric supply function equilibria when firms are capacity constrained and show that this set is increasing as capacity per firm rises. We also provide conditions under which asymmetric equilibria exist and characterize these equilibria.
International Journal of Industrial Organization, Jul 1, 2011
The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted how generation capacity constraints may contribute to market power of generation firms. If a generation firm's rivals are capacity constrained then the firm may be pivotal; that is, the firm could substantially raise the market price by unilaterally withholding output. However the SFE literature has not properly analyzed the impact of capacity constraints and pivotal firms on equilibrium predictions. We characterize the set of symmetric supply function equilibria for uniform price auctions when firms are capacity constrained and show that this set is increasing as capacity per firm rises. We provide conditions under which asymmetric equilibria exist and characterize these equilibria. In addition, we compare results for uniform price auctions to those for discriminatory auctions, and we compare our SFE predictions to equilibrium predictions of models in which bidders are constrained to bid on discrete units of output.
We identify that the United Nations (UN) Sustainable Development Goals (SDGs) of 7, 9, 12 pertain... more We identify that the United Nations (UN) Sustainable Development Goals (SDGs) of 7, 9, 12 pertaining to industry investment, innovation, affordability, clean product, and responsible consumption/production are relevant for the firms operating in closed-loop supply chain (CLSC) structures. We show how these goals can be implemented into a CLSC in which downstream manufacturer serves different types of consumers and engages in vertical relations with a supplier in the upstream. While the supplier invests in a green component, the manufacturer produces the final green product. The manufacturer diversifies its customer base and meet their demands through contracts and a variety of pricing options. Specifically, at the end of the supply chain there are three different customer groups: “contract customers”, “green-conscious customers”, and “wholesale market customers”. While the firms execute sustainability Goals of 7 and 9, the behavioral consumers who are the contract and green-conscious customers are altruistic, consume responsibly, and hence fulfill the Goal 12. We show that green consciousness and altruism play an important role on firm profitability and production. Furthermore, the SDGs proposed by the UN have welfare-improving implications. In particular, when the SDGs are implemented, all parties (firms and consumers) are better off compared to the benchmark case under which no SDGs are applied.
The concept of a supply function equilibrium (SFE) has been widely used to study generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to study generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that the presence of pivotal suppliers reduces the set of supply function equilibria . We show that the size of the equilibrium set depends on observable market characteristics such as the amount of industry excess capacity, the load factor (ratio of minimum demand to maximum demand), the number of suppliers, and the amount of base load capacity. For example, as the amount of industry excess capacity falls and/or the load factor rises, the set of supply function equilibria becomes smaller; the equilibria that are eliminated are the lowest-priced, most competitive equilibria.
We investigate the market implications of ownership of a new low-cost production technology. We r... more We investigate the market implications of ownership of a new low-cost production technology. We relate our theoretical findings to measuring the impact of renewable energy penetration into electricity markets and examine how the ownership of renewable capacity changes market outcomes (prices, outputs, emissions). As the current public policies influence the renewable energy ownership, this research provides useful insights for policy makers. We show that ownership of renewable capacity will matter when there is market power in energy market. We apply our findings to the Ontario wholesale electricity market to analyze the impact of different ownership structures for wind capacity expansions. We show that consumers enjoy better air quality under the largest firm's ownership, but at the expense of higher prices. We find that market structure and the shape of generation cost functions are the key drivers explaining the impact of renewable ownership on market outcomes.
Within a Closed-loop Supply Chain (CLSC) framework we study several consumer return behaviors for... more Within a Closed-loop Supply Chain (CLSC) framework we study several consumer return behaviors for the used products which are based on the product prices and rebates. Consumers evaluate the rebate they receive as well as the price of the new product before deciding whether to dump a return. Therefore, the number of used products returned is examined under two types of rebates: a fixed rebate and a variable rebate. We search for the optimal rebate mechanism and find that the CLSC profits are higher under an variable rebate policy. This finding justifies the industry practices that employ a rebate mechanism based on both the value and the price of used item. We offer two types of solution concepts to the CLSC games: open-loop Stackelberg solution and Markov perfect Stackelberg solution, which are commonly employed in the dynamic games literature. While we mainly employ Markovian equilibrium, we also allow firms to utilize open-loop strategies so as to assess the impact of precommitment on the market outcomes. Therefore, we offer a comprehensive analysis of all possible market equilibrium solutions under different strategic considerations and the commitment deliberations. We show that under the fixed rebate regime open-loop solution coincides with Markov perfect solution. Furthermore, we show how consumer return behavior impacts the dynamic nature of the game. We find that the time frame is irrelevant if firms offer a fixed rebate. In contrast, the game will be fully dynamic when firms offer a variable rebate.
ABSTRACT Abstract: We investigate price responsiveness of wholesale electricity customers in the ... more ABSTRACT Abstract: We investigate price responsiveness of wholesale electricity customers in the hourly Ontario wholesale electricity market. We use detailed generator and market level data to calculate market power measures such as the Lerner Index, Residual Supplier Index, and Pivotal Supplier Index which are combined with the competition model to structurally estimate price elasticity of demand in peak hours of summer and winter seasons. We find that the hourly price elasticities are small and change over the peak hours of seasons and years. For instance, in 2008 the elasticity estimates are in the interval of (0.019, 0.083). Comparing high demand winter hours to summer hours indicates that consumers’ price responsiveness is lower in summer than in winter. We also employ these indices along with the estimated price elasticities to project the likely impacts of interconnection capacity expansions on market prices. Our calibrations show that even small amount of transmission investments (and hence trade activities) can result in substantial market price reductions.
We investigate wholesale demand response to hourly price movements in the Ontario wholesale elect... more We investigate wholesale demand response to hourly price movements in the Ontario wholesale electricity market using detailed generator and market level data. We calculate hourly market power measures such as the Lerner Index and the Residual Supplier Index, which are utilized in a Cournot competition model to structurally estimate price elasticity of demand during peak hours of days, seasons and years. We find that price elasticities are small and statistically significant, and they exhibit large variations over the times of days/seasons and show differences over the years. For instance, while the elasticity estimates fall into the range [-0.021, -0.133] in 2007, they are in the interval of [-0.013, -0.053] in 2008. We also extend the study period to include 2006 (during which extreme weather conditions occurred) and 2009 (when the economic crisis hit and natural gas prices plummeted) to measure the demand responses to irregular price movements and find that price elasticities during the economic crisis were higher than a year earlier. Comparing high demand winter hours to high demand summer hours indicates that consumers' price responsiveness is lower in summer than in winter during 2006-2009. Moreover, we employ these indices along with the estimated price elasticities to project the likely impact of interconnection capacity expansions on market prices. Our calibrations show that even a small amount of transmission investment (and hence trade activity) can result in substantial market price reductions. In addition, we discuss how our approach could be used to estimate price elasticities for other goods such as crude oil and gasoline.
ABSTRACT In the presence of indivisible goods, resource allocation models often result in mixed-i... more ABSTRACT In the presence of indivisible goods, resource allocation models often result in mixed-integer linear programs (MILP). Unlike linear programming duality however, MILP problems present duality gaps and dual variables (as part of the price system) are not unique and not as conveniently interpreted. These issues have been visited for almost fifty years starting with Gomory and Baumol (1960) and subsequently by a number of other authors. However, finding a price system in resource allocation models with indivisibilities that has attributes of shadow prices has remained a long-standing unresolved problem in economic theory. In this paper, we resolve this issue for binary MILP problems. We provide an important step in allocating charges of indivisible goods, and recover the total costs of inputs. Moreover, we characterize unique (two-sided) shadow prices for resources in binary MILP problems. We also provide an economic interpretation of implied constraints in the form of productivity requirements that must be satisfied for integer programming problems.
Abstract We consider behavioral issues in a new dynamic model in which a manufacturer (M) makes p... more Abstract We consider behavioral issues in a new dynamic model in which a manufacturer (M) makes pricing and green investment decisions while facing heterogeneous customers including emotional, conscious, and rational consumers. Emotional consumers base their purchasing decisions on M’s green investments. Their emotions are stochastic, dynamic, and accumulate over time. The investment is made over time and is subject to time-to-build so that there is a time-lag between investment and production. Differently, conscious consumers respond to both green investments and prices and have no memory on the M’s past green initiatives. The rational consumers are not sensitive to environmental issues and base their decisions only on product price. Our findings suggest that M should realize that emotional consumers have the largest impact on investments, prices, and profits. Therefore, firms should first think to satisfy the emotional consumers and then all other segments. When firms have environmental targets or restrictions, all segments must be satisfied independent of their impact on the profits. This finding contributes to the literature by highlighting that the trade-off between economic and environmental performance also exists in presence of consumer segments.
This thesis examines several issues that arise in restructured electricity markets. These issues ... more This thesis examines several issues that arise in restructured electricity markets. These issues include production, scheduling and forward contract decision making, capital investment decisions in uncertain environments, and equilibrium bidding in wholesale electricity auctions. In the chapter, "Supply Function Equilibria with Pivotal Suppliers", we study the impact of pivotal suppliers in supply function bidding settings. Observers of these markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that when pivotal suppliers are present, the set of SFE is reduced relative to when no suppliers are pivotal. In the chapter, "Dynamic Oligopolistic Games Under Uncertainty: A Stochastic Programming Approach", we study several stochastic programming formulations of dynamic oligopolistic games under uncertainty. It is well known that if the number of state variables increases, dynamic programming becomes computationally intractable. For such games, we show that under certain symmetry assumptions, players earn greater expected profits as demand volatility increases. The key to our approach is the "scenario formulation" of stochastic programming. The examples presented in this paper illustrate that this approach can address dynamic games that are clearly out of reach for dynamic programming, the common approach in the literature on dynamic games. In the chapter, "Scenario-based Electricity-Gas Forward and Spot Pricing and Load Formulations", we propose load models and price and return formulations in specific energy markets. Existing energy models do not consider inter-relations between the trio: spot price, derivative price and electric load. Also these models, which are in the spirit of the models proposed in financial and commodity markets, ignore special characteristics of electricity, which may make the proposed models useless. In our formulations we consider these characteristics and correlations between these variables. Simulation results that we run support our modeling approaches
We study equilibrium investment strategies of rms competing in stochastic dynamic market settings... more We study equilibrium investment strategies of rms competing in stochastic dynamic market settings and facing two types of investment structures: investment with signicant lead time (or time-to-build) and investment without (or minor) lead time. We investigate how investment behavior changes when investment is subject to time-to-build versus when it is not. We characterize equilibrium investment strategies under several information structures and compare results to the social optimum. We oer some new results. The model predicts that, controlling for demand, and production and investment costs, investments and outputs can be higher in progressive industries (which often exhibit time-to-build) than in fast-paced industries (where time-to-build is insignicant). Furthermore, for both investment types (investment with or without time-to-build) we oer a novel equilibrium in which rms incrementally invest. This behavior is driven by demand uncertainty and capacity constraints. Also, expected outputs are lower than Cournot outputs as rms face uncertainty. Moreover, the amount of uncertainty has dierent eects over investment types.
A goal of this paper is to compare results for discriminatory auctions to results for uniform-pri... more A goal of this paper is to compare results for discriminatory auctions to results for uniform-price auctions when suppliers have capacity constraints. We have a pretty good understanding of what equilibrium results look like for the uniform-price auctions. But an unresolved problem is what happens when a discriminative auction is run and suppliers have capacity constraints. We formulate a supply function equilibrium (SFE) model in continuous offer schedules with inelastic, time varying demand and with single step marginal cost function to compare two auction institutions in the presence of capacity constraints. We show that payments made to the suppliers in the unique equilibrium of the discriminatory auction can be less than the payments in the uniform-price auction, depending on which uniform-price auction equilibrium is selected. For the high demand and/or low excess capacity cases we also characterize mixed strategy supply function equilibrium under the discriminatory auction.
This thesis examines several issues that arise in restructured electricity markets. These issues ... more This thesis examines several issues that arise in restructured electricity markets. These issues include production, scheduling and forward contract decision making, capital investment decisions in uncertain environments, and equilibrium bidding in wholesale electricity auctions. In the chapter, "Supply Function Equilibria with Pivotal Suppliers", we study the impact of pivotal suppliers in supply function bidding settings. Observers of these markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that when pivotal suppliers are present, the set of SFE is reduced relative to when no suppliers are pivotal. In the chapter, "Dynamic Oligopolistic Games Under Uncertainty: A Stochastic Programming Approach", we study several stochastic programming formulations of dynamic oligopolistic games under uncertainty. It is well known that if the number of state variables increases, dynamic programming becomes computationally intractable. For such games, we show that under certain symmetry assumptions, players earn greater expected profits as demand volatility increases. The key to our approach is the "scenario formulation" of stochastic programming. The examples presented in this paper illustrate that this approach can address dynamic games that are clearly out of reach for dynamic programming, the common approach in the literature on dynamic games. In the chapter, "Scenario-based Electricity-Gas Forward and Spot Pricing and Load Formulations", we propose load models and price and return formulations in specific energy markets. Existing energy models do not consider inter-relations between the trio: spot price, derivative price and electric load. Also these models, which are in the spirit of the models proposed in financial and commodity markets, ignore special characteristics of electricity, which may make the proposed models useless. In our formulations we consider these characteristics and correlations between these variables. Simulation results that we run support our modeling approaches
The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted how generation capacity constraints may contribute to market power of generation firms. If a generation firm's rivals are capacity constrained then the firm may be pivotal; that is, the firm could substantially raise the market price by unilaterally withholding output. However the SFE literature has not properly analyzed the impact of capacity constraints nor has it considered the impact of pivotal firms on equilibrium predictions. We characterize the set of symmetric supply function equilibria when firms are capacity constrained and show that this set is increasing as capacity per firm rises. We also provide conditions under which asymmetric equilibria exist and characterize these equilibria.
International Journal of Industrial Organization, Jul 1, 2011
The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to model generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted how generation capacity constraints may contribute to market power of generation firms. If a generation firm's rivals are capacity constrained then the firm may be pivotal; that is, the firm could substantially raise the market price by unilaterally withholding output. However the SFE literature has not properly analyzed the impact of capacity constraints and pivotal firms on equilibrium predictions. We characterize the set of symmetric supply function equilibria for uniform price auctions when firms are capacity constrained and show that this set is increasing as capacity per firm rises. We provide conditions under which asymmetric equilibria exist and characterize these equilibria. In addition, we compare results for uniform price auctions to those for discriminatory auctions, and we compare our SFE predictions to equilibrium predictions of models in which bidders are constrained to bid on discrete units of output.
We identify that the United Nations (UN) Sustainable Development Goals (SDGs) of 7, 9, 12 pertain... more We identify that the United Nations (UN) Sustainable Development Goals (SDGs) of 7, 9, 12 pertaining to industry investment, innovation, affordability, clean product, and responsible consumption/production are relevant for the firms operating in closed-loop supply chain (CLSC) structures. We show how these goals can be implemented into a CLSC in which downstream manufacturer serves different types of consumers and engages in vertical relations with a supplier in the upstream. While the supplier invests in a green component, the manufacturer produces the final green product. The manufacturer diversifies its customer base and meet their demands through contracts and a variety of pricing options. Specifically, at the end of the supply chain there are three different customer groups: “contract customers”, “green-conscious customers”, and “wholesale market customers”. While the firms execute sustainability Goals of 7 and 9, the behavioral consumers who are the contract and green-conscious customers are altruistic, consume responsibly, and hence fulfill the Goal 12. We show that green consciousness and altruism play an important role on firm profitability and production. Furthermore, the SDGs proposed by the UN have welfare-improving implications. In particular, when the SDGs are implemented, all parties (firms and consumers) are better off compared to the benchmark case under which no SDGs are applied.
The concept of a supply function equilibrium (SFE) has been widely used to study generators' bidd... more The concept of a supply function equilibrium (SFE) has been widely used to study generators' bidding behavior and market power issues in wholesale electricity markets. Observers of electricity markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that the presence of pivotal suppliers reduces the set of supply function equilibria . We show that the size of the equilibrium set depends on observable market characteristics such as the amount of industry excess capacity, the load factor (ratio of minimum demand to maximum demand), the number of suppliers, and the amount of base load capacity. For example, as the amount of industry excess capacity falls and/or the load factor rises, the set of supply function equilibria becomes smaller; the equilibria that are eliminated are the lowest-priced, most competitive equilibria.
We investigate the market implications of ownership of a new low-cost production technology. We r... more We investigate the market implications of ownership of a new low-cost production technology. We relate our theoretical findings to measuring the impact of renewable energy penetration into electricity markets and examine how the ownership of renewable capacity changes market outcomes (prices, outputs, emissions). As the current public policies influence the renewable energy ownership, this research provides useful insights for policy makers. We show that ownership of renewable capacity will matter when there is market power in energy market. We apply our findings to the Ontario wholesale electricity market to analyze the impact of different ownership structures for wind capacity expansions. We show that consumers enjoy better air quality under the largest firm's ownership, but at the expense of higher prices. We find that market structure and the shape of generation cost functions are the key drivers explaining the impact of renewable ownership on market outcomes.
Within a Closed-loop Supply Chain (CLSC) framework we study several consumer return behaviors for... more Within a Closed-loop Supply Chain (CLSC) framework we study several consumer return behaviors for the used products which are based on the product prices and rebates. Consumers evaluate the rebate they receive as well as the price of the new product before deciding whether to dump a return. Therefore, the number of used products returned is examined under two types of rebates: a fixed rebate and a variable rebate. We search for the optimal rebate mechanism and find that the CLSC profits are higher under an variable rebate policy. This finding justifies the industry practices that employ a rebate mechanism based on both the value and the price of used item. We offer two types of solution concepts to the CLSC games: open-loop Stackelberg solution and Markov perfect Stackelberg solution, which are commonly employed in the dynamic games literature. While we mainly employ Markovian equilibrium, we also allow firms to utilize open-loop strategies so as to assess the impact of precommitment on the market outcomes. Therefore, we offer a comprehensive analysis of all possible market equilibrium solutions under different strategic considerations and the commitment deliberations. We show that under the fixed rebate regime open-loop solution coincides with Markov perfect solution. Furthermore, we show how consumer return behavior impacts the dynamic nature of the game. We find that the time frame is irrelevant if firms offer a fixed rebate. In contrast, the game will be fully dynamic when firms offer a variable rebate.
ABSTRACT Abstract: We investigate price responsiveness of wholesale electricity customers in the ... more ABSTRACT Abstract: We investigate price responsiveness of wholesale electricity customers in the hourly Ontario wholesale electricity market. We use detailed generator and market level data to calculate market power measures such as the Lerner Index, Residual Supplier Index, and Pivotal Supplier Index which are combined with the competition model to structurally estimate price elasticity of demand in peak hours of summer and winter seasons. We find that the hourly price elasticities are small and change over the peak hours of seasons and years. For instance, in 2008 the elasticity estimates are in the interval of (0.019, 0.083). Comparing high demand winter hours to summer hours indicates that consumers’ price responsiveness is lower in summer than in winter. We also employ these indices along with the estimated price elasticities to project the likely impacts of interconnection capacity expansions on market prices. Our calibrations show that even small amount of transmission investments (and hence trade activities) can result in substantial market price reductions.
We investigate wholesale demand response to hourly price movements in the Ontario wholesale elect... more We investigate wholesale demand response to hourly price movements in the Ontario wholesale electricity market using detailed generator and market level data. We calculate hourly market power measures such as the Lerner Index and the Residual Supplier Index, which are utilized in a Cournot competition model to structurally estimate price elasticity of demand during peak hours of days, seasons and years. We find that price elasticities are small and statistically significant, and they exhibit large variations over the times of days/seasons and show differences over the years. For instance, while the elasticity estimates fall into the range [-0.021, -0.133] in 2007, they are in the interval of [-0.013, -0.053] in 2008. We also extend the study period to include 2006 (during which extreme weather conditions occurred) and 2009 (when the economic crisis hit and natural gas prices plummeted) to measure the demand responses to irregular price movements and find that price elasticities during the economic crisis were higher than a year earlier. Comparing high demand winter hours to high demand summer hours indicates that consumers' price responsiveness is lower in summer than in winter during 2006-2009. Moreover, we employ these indices along with the estimated price elasticities to project the likely impact of interconnection capacity expansions on market prices. Our calibrations show that even a small amount of transmission investment (and hence trade activity) can result in substantial market price reductions. In addition, we discuss how our approach could be used to estimate price elasticities for other goods such as crude oil and gasoline.
ABSTRACT In the presence of indivisible goods, resource allocation models often result in mixed-i... more ABSTRACT In the presence of indivisible goods, resource allocation models often result in mixed-integer linear programs (MILP). Unlike linear programming duality however, MILP problems present duality gaps and dual variables (as part of the price system) are not unique and not as conveniently interpreted. These issues have been visited for almost fifty years starting with Gomory and Baumol (1960) and subsequently by a number of other authors. However, finding a price system in resource allocation models with indivisibilities that has attributes of shadow prices has remained a long-standing unresolved problem in economic theory. In this paper, we resolve this issue for binary MILP problems. We provide an important step in allocating charges of indivisible goods, and recover the total costs of inputs. Moreover, we characterize unique (two-sided) shadow prices for resources in binary MILP problems. We also provide an economic interpretation of implied constraints in the form of productivity requirements that must be satisfied for integer programming problems.
Abstract We consider behavioral issues in a new dynamic model in which a manufacturer (M) makes p... more Abstract We consider behavioral issues in a new dynamic model in which a manufacturer (M) makes pricing and green investment decisions while facing heterogeneous customers including emotional, conscious, and rational consumers. Emotional consumers base their purchasing decisions on M’s green investments. Their emotions are stochastic, dynamic, and accumulate over time. The investment is made over time and is subject to time-to-build so that there is a time-lag between investment and production. Differently, conscious consumers respond to both green investments and prices and have no memory on the M’s past green initiatives. The rational consumers are not sensitive to environmental issues and base their decisions only on product price. Our findings suggest that M should realize that emotional consumers have the largest impact on investments, prices, and profits. Therefore, firms should first think to satisfy the emotional consumers and then all other segments. When firms have environmental targets or restrictions, all segments must be satisfied independent of their impact on the profits. This finding contributes to the literature by highlighting that the trade-off between economic and environmental performance also exists in presence of consumer segments.
This thesis examines several issues that arise in restructured electricity markets. These issues ... more This thesis examines several issues that arise in restructured electricity markets. These issues include production, scheduling and forward contract decision making, capital investment decisions in uncertain environments, and equilibrium bidding in wholesale electricity auctions. In the chapter, "Supply Function Equilibria with Pivotal Suppliers", we study the impact of pivotal suppliers in supply function bidding settings. Observers of these markets have noted the important role that pivotal suppliers, those who can substantially raise the market price by unilaterally withholding generation output, sometimes play. However the literature on SFE has not considered the potential impact of pivotal suppliers on equilibrium predictions. This is a potentially important deficiency of applications of SFE to electricity markets, given the large role that pivotal suppliers sometimes play in these markets. We formulate a model in which generation capacity constraints can cause some suppliers to be pivotal. In symmetric and asymmetric versions of the model we show that when pivotal suppliers are present, the set of SFE is reduced relative to when no suppliers are pivotal. In the chapter, "Dynamic Oligopolistic Games Under Uncertainty: A Stochastic Programming Approach", we study several stochastic programming formulations of dynamic oligopolistic games under uncertainty. It is well known that if the number of state variables increases, dynamic programming becomes computationally intractable. For such games, we show that under certain symmetry assumptions, players earn greater expected profits as demand volatility increases. The key to our approach is the "scenario formulation" of stochastic programming. The examples presented in this paper illustrate that this approach can address dynamic games that are clearly out of reach for dynamic programming, the common approach in the literature on dynamic games. In the chapter, "Scenario-based Electricity-Gas Forward and Spot Pricing and Load Formulations", we propose load models and price and return formulations in specific energy markets. Existing energy models do not consider inter-relations between the trio: spot price, derivative price and electric load. Also these models, which are in the spirit of the models proposed in financial and commodity markets, ignore special characteristics of electricity, which may make the proposed models useless. In our formulations we consider these characteristics and correlations between these variables. Simulation results that we run support our modeling approaches
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