Supply Function Equilibria with Capacity Constraints and Pivotal Suppliers

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.supply function equilibrium, pivotal firm, wholesale electricity market

Equilibrium Predictions in Wholesale Electricity Markets

We review supply function equilibrium models and their predictions on market outcomes in the wholesale electricity auctions. We discuss how observable market characteristics such as capacity constraints, number of power suppliers, load distribution and auction format affect the behavior of suppliers and performance of the market. We specifically focus on the possible market power exerted by pivotal suppliers and the comparison between discriminatory and uniform-price auctions. We also describe capacity investment behavior of electricity producers in the restructured industry.Electricity markets; Supply function equilibrium; Markov perfect equilibrium; electricity auctions; pivotal suppliers; capacity investment.

Cournot Versus Supply Functions: What does the Data Tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium;Cournot competition;electricity markets

Cournot versus supply functions: what does the data tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium, Cournot competition, electricity markets

Cournot versus Supply Functions: What Does the Data tell us?

The liberalization of the electricity sector increases the need for realistic and robust models of the oligopolistic interaction of electricity firms. This paper compares the two most popular models: Cournot and the Supply Function Equilibrium (SFE), and tests which model describes the observed market data best. Using identical demand and supply specifications, both models are calibrated to the German electricity market by varying the contract cover of firms. Our results show that each model explains an identical fraction of the observed price variation. We therefore suggest using Cournot models for short term analysis, as more market details, such as network constraints, can be accommodated. As the SFE model is less sensitive to the choice of the calibration parameters, it might be more appropriate for long term analysis, such as the study of a merger.supply function equilibrium;Cournot competition;electricity markets

Receiprocity and Downward Wage Rigidity

The employment relationship is to a large extent characterized by incomplete contracts, in which workers have a considerable degree of discretion over the choice of their work effort. This discretion at work kicks in the potential importance of “gift exchange” or reciprocity between workers and employers in their employment relationship. Built on the seminal work of Akerlof (1980), this paper adopts a social norm approach to model reciprocity in labor markets and theoretically derives two versions of downward wage rigidity. The first version explains why employers may adopt a high wage policy far above the competitive level. This version is not a novel finding in the existing literature and is mainly served as a benchmark for later comparison in the current paper. Our main contribution lies in the second version in which not nly may employers adopt a high wage policy far above the competitive level, but one can also account for the asymmetric behavior of wages and explain why employers are hesitant about wage cuts in the presence of negative shocks. We argue that this second and stronger version of downward wage rigidity has moved the efficiency wage theory a step forward.Reciprocity, Downward Wage Rigidity, Social Norm, Efficiency Wage

Misallocation, Education Expansion and Wage Inequality

This study offers a unified explanation for the perplexing fact that the education premium rises more for low-experienced workers, while the experience premium increases mainly for low-educated labor. The interaction of signaling, employer learning and credit constraints resolves this puzzle. When higher education expands, talented individuals acquire skills and abandon the uneducated pool. This decreases unskilled-inexperienced wages and boosts inequality, highlighting that talent misallocation compresses wage dispersion. This explanation fits US data, indicating that for three decades the rise in the education and the experience premium coincided with falling unskilled-inexperienced wages, while skilled or experienced wages remained relatively flat

Employer behavior when workers can unionize

Unionization imposes substantial costs on employers. This paper develops a model that recognizes that, as a result, employers will set wages and employment taking into account the effect of their decisions on workers' incentives to organize. This model of employer behavior allows us to address two questions jointly: What determines which firms become unionized? And what are the consequences of unionization for employment and wages in nonunion firms? The implications of the model depart significantly from those of previous work, which either ignored employers' strategic behavior, or treated these questions in isolation

A Short-term Intervention for Long-term Fairness in the Labor Market

The persistence of racial inequality in the U.S. labor market against a general backdrop of formal equality of opportunity is a troubling phenomenon that has significant ramifications on the design of hiring policies. In this paper, we show that current group disparate outcomes may be immovable even when hiring decisions are bound by an input-output notion of "individual fairness." Instead, we construct a dynamic reputational model of the labor market that illustrates the reinforcing nature of asymmetric outcomes resulting from groups' divergent accesses to resources and as a result, investment choices. To address these disparities, we adopt a dual labor market composed of a Temporary Labor Market (TLM), in which firms' hiring strategies are constrained to ensure statistical parity of workers granted entry into the pipeline, and a Permanent Labor Market (PLM), in which firms hire top performers as desired. Individual worker reputations produce externalities for their group; the corresponding feedback loop raises the collective reputation of the initially disadvantaged group via a TLM fairness intervention that need not be permanent. We show that such a restriction on hiring practices induces an equilibrium that, under particular market conditions, Pareto-dominates those arising from strategies that statistically discriminate or employ a "group-blind" criterion. The enduring nature of equilibria that are both inequitable and Pareto suboptimal suggests that fairness interventions beyond procedural checks of hiring decisions will be of critical importance in a world where machines play a greater role in the employment process.Comment: 10 page