Optimal Contract Pricing of Distributed Generation in Distribution Networks

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Optimal contract pricing of distributed generation under a competitive framework

A bilevel programming approach for the optimal contract pricing of distributed generation (DG) in distribution networks is presented. The outer optimization problem corresponds to the owner of the DG who must decide the contract price that would maximize his profits. The inner optimization problem corresponds to the distribution company (DisCo), which procures the minimization of the payments incurred in attending the expected demand while satisfying network constraints. The meet the expected demand the DisCo can purchase energy either form the transmission network through the substations or form the DG units within its network. The inner optimization problem is substituted by its Karush- Kuhn-Tucker optimality conditions, turning the bilevel programming problem into an equivalent single-level nonlinear programming problem which is solved using commercially available software. © 2010 IEEE.

A decision-support system based on particle swarm optimization for multiperiod hedging in electricity markets

This paper proposes a particle swarm optimization (PSO) approach to support electricity producers for multiperiod optimal contract allocation. The producer risk preference is stated by a utility function (U) expressing the tradeoff between the expectation and variance of the return. Variance estimation and expected return are based on a forecasted scenario interval determined by a price range forecasting model developed by the authors. A certain confidence level is associated to each forecasted scenario interval. The proposed model makes use of contracts with physical (spot and forward) and financial (options) settlement. PSO performance was evaluated by comparing it with a genetic algorithm-based approach. This model can be used by producers in deregulated electricity markets but can easily be adapted to load serving entities and retailers. Moreover, it can easily be adapted to the use of other type of contracts.

Licensing in an international triopoly

We study the effects of entry of two foreign firms on domestic welfare in the presence of licensing, when the incumbent is technologically superior to the entrants. We consider two different situations: (i) the cost-reducing innovation is licensed to both entrants; (ii) the cost- reducing innovation is licensed to just one of the entrants. We analyse three kind of license: (lump- sum) fixed-fee; (per-unit) royalty; and two-part tariff, that is a combination of a fixed-fee and a royalty. We prove that a two part tariff is never an optimal licensing scheme for the incumbent. Moreover, (i) when the technology is licensed to the two entrants, the optimal contract consists of a licensing with only output royalty; and (ii) when the technology is licensed to just one of the entrants, the optimal contract consists of a licensing with only a fixed-fee.

Pressure groups and experts in environmental regulation

We study a problem of adverse selection in the context of environmental regulation, where the firm may suffer from a certain degree of ignorance about its own type. In a framework like the construction of a certain infrastructure project, the presence of ignorance about its impact on the environment, can play an important role in the determination of the regulatory policy. First, an optimal contract is constructed for any exogenous level of ignorance. Second, the presence of potentially informed third-parties is studied from the perspective of the regulator, which allows us to analyze the impact on the efficiency of the contract, of the presence of environmentalists and of experts. Then, we obtain some insights on how the problem differs when the degree of ignorance is a choice variable for the firm. We finally use our results to derive policy implications concerning the existing envoronmental regulation, and the potential role of interested parties as information providers.

Business-science research collaboration under moral hazard

I analyze, in the context of business and science research collaboration, how the characteristics of partnership agreements are the result of an optimal contract between partners. The final outcome depends on the structure governing the partnership, and on the informational problems towards the efforts involved. The positive effect that the effort of each party has on the success of the other party, makes collaboration a preferred solution. Divergence in research goals may, however, create conflicts between partners. This paper shows how two different structures of partnership governance (a centralized, and a decentralized ones) may optimally use the type of project to motivate the supply of non-contractible efforts. Decentralized structure, however, always choose a project closer to its own preferences. Incentives may also come from monetary transfers, either from partners sharing each other benefits, or from public funds. I derive conditions under which public interventio

Multi-agent contracting with countervailing incentives and limited liability

We consider a principal who deals with a privately informed agent protected by limited liability in a correlated information setting. The agent's technology is such that the fixed cost declines with the marginal cost (the type), so that countervailing incentives may arise. We show that, with high liability, the first-best outcome can be effected for any type if (1) the fixed cost is non-concave in type, under the contract that yields the smallest feasible loss to the agent; (2) the fixed cost is not very concave in type, under the contract that yields the maximum sustainable loss to the agent. We further show that, with low liability, the first-best outcome is still implemented for a non-degenerate range of types if the fixed cost is less concave in type than some given threshold, which tightens as the liability reduces. The optimal contract entails pooling otherwise.

Portfolio delegation under short-selling constraints

In this paper we study delegated portfolio management when themanager's ability to short-sell is restricted. Contrary to previousresults, we show that under moral hazard, linear performance-adjustedcontracts do provide portfolio managers with incentives to gatherinformation. The risk-averse manager's optimal effort is an increasingfunction of her share in the portfolio's return. This result affectsthe risk-averse investor's optimal contract decision. The first best,purely risk-sharing contract is proved to be suboptimal. Usingnumerical methods we show that the manager's share in the portfolioreturn is higher than the rst best share. Additionally, this deviationis shown to be: (i) increasing in the manager's risk aversion and (ii)larger for tighter short-selling restrictions. When the constraint isrelaxed the optimal contract converges towards the first best risksharing contract.

Failure to collude in the presence of asymmetric information

In this paper, we design the optimal contract when two agents can collude under asymmetric information. They have correlated types, produce complementary inputs and are protected by limited liability. Therefore, a joint manipulation of reports allows them to internalize informational and productive externalities. We show that by taking advantage of the transaction costs created by asymmetric information, even though they collude, the principal can achieve the outcome without collusion regardless of the sign and the degree of correlation. In particular, the principal can implement a non-monotonic quantity schedule in a collusion-proof way while this is impossible if collusion occurs under complete information.

Essais sur la gestion des ressources forestières

Cette thèse est composée de trois essais en économie forestière. Les deux premiers s'intéressent à la fixation de la redevance optimale à laquelle fait face le propriétaire d'une ressource forestière dans un contexte d'information asymétrique. Le troisième analyse l'impact à long terme du recyclage sur la surface de terre affectée à la forêt. La gestion des ressources forestières implique souvent la délégation des droits de coupe par le propriétaire forestier à une entreprise exploitante. Cette délégation prend la forme d'un contrat de concession par lequel le propriétaire forestier octroie les droits d'exploitation aux compagnies forestières, en contrepartie d'une redevance (transfert monétaire). L'octroie des droits d'exploitation s'effectue généralement sous plusieurs modes, dont les plus répandus sont les appels d'offres publics et les contrats de gré à gré, où le propriétaire forestier et la firme exploitante spécifient entre autres la redevance dans les clauses d'exploitation de la forêt. Pour déterminer le mécanisme optimal (choix de la firme, âge de coupe et redevance), le propriétaire forestier a idéalement besoin de connaître les coûts de coupe et de reboisement. Or en réalité, les firmes sont mieux informées sur leurs coûts que le propriétaire forestier. Dans ce contexte d'information asymétrique, le mécanisme optimal doit donc prendre en considération des contraintes informationnelles. Les deux premiers essais caractérisent, sous ces conditions, l'âge de coupe optimal (la rotation optimale) et la redevance optimale. Le premier essai examine le contrat optimal quand le propriétaire forestier cède les droits de coupes à une firme par un accord de gré à gré ou par une procédure d'appel d'offre public au second prix. L'analyse du problème est menée premièrement dans un contexte statique, dans le sens que les coûts de coupe sont parfaitement corrélés dans le temps, puis dans un contexte dynamique, où les coûts sont indépendants dans le temps. L'examen en statique et en dynamique montre que la rotation optimale va satisfaire une version modifiée de la règle de Faustmann qui prévaudrait en information symétrique. Cette modification est nécessaire afin d'inciter la firme à révéler ses vrais coûts. Dans le cas statique, il en résulte que la rotation optimale est plus élevée en information asymétrique qu'en situation de pleine information. Nous montrons également comment le seuil maximal de coût de coupe peut être endogénéisé, afin de permettre au propriétaire d'accroître son profit espéré en s'assurant que les forêts non profitables ne seront pas exploitées. Nous comparons ensuite la redevance optimale en information asymétrique et symétrique. Les redevances forestières dans un arrangement de gré à gré étant généralement, en pratique, une fonction linéaire du volume de bois, nous dérivons le contrat optimal en imposant une telle forme de redevance et nous caractérisons la perte en terme de profit espéré qui résulte de l'utilisation de ce type de contrat plutôt que du contrat non linéaire plus général. Finalement, toujours dans le contexte statique, nous montrons à travers un mécanisme optimal d'enchère au second prix qu'en introduisant ainsi la compétition entre les firmes le propriétaire forestier augmente son profit espéré. Les résultats obtenus dans le contexte dynamique diffèrent pour la plupart de ceux obtenus dans le cas statique. Nous montrons que le contrat optimal prévoit alors que chaque type de firme, incluant celle ayant le coût le plus élevé, obtient une rente strictement positive, laquelle augmente dans le temps. Ceci est nécessaire pour obtenir la révélation à moindre coût à la période courante du véritable type de la firme. Comme implication, la rotation optimale s'accroît aussi dans le temps. Finalement, nous montrons qu'il y a distorsion en asymétrique d'information par rapport à l'optimum de pleine information même pour le coût le plus bas (la réalisation la plus favorable). La concurrence introduite dans le premier essai sous forme d'enchère au second prix suppose que chaque firme connaît exactement son propre coût de coupe. Dans le deuxième essai nous relâchons cette hypothèse. En réalité, ni le propriétaire forestier ni les firmes ne connaissent avec précision les coûts de coupe. Chaque firme observe de manière privée un signal sur son coût. Par exemple chaque firme est autorisée à visiter un lot pour avoir une estimation (signal) de son coût de coupe. Cependant cette évaluation est approximative. Ainsi, le coût de chaque firme va dépendre des estimations (signaux) d'autres firmes participantes. Nous sommes en présence d'un mécanisme à valeurs interdépendantes. Dans ce contexte, la valeur d'une allocation dépend des signaux de toutes les firmes. Le mécanisme optimal (attribution des droits d'exploitation, redevance et âge de coupe) est exploré. Nous déterminons les conditions sous lesquelles le mécanisme optimal peut être implémenté par une enchère au second prix et dérivons la rotation optimale et le prix de réserve dans le contexte de ce type d'enchère. Le troisième essai de la thèse analyse l'impact à long terme du recyclage sur la surface de terre affectée à la forêt. L'un des principaux arguments qui milite en faveur du recours au recyclage est que cela entraînerait une réduction de la coupe de bois, épargnant ainsi des arbres. L'objectif est donc d'aboutir à un nombre d'arbres plus important qu'en l'absence de recyclage. L'idée d'accroître le stock d'arbre tient au fait que les forêts génèrent des externalités: elles créent un flux de services récréatifs, freinent l'érosion des sols et des rives des cours d'eau et absorbent du dioxyde de carbone présent dans l'atmosphère. Étant donné la présence d'externalités, l'équilibre des marchés résulterait en un nombre d'arbre insuffisant, justifiant donc la mise en oeuvre de politiques visant à l'accroître. Le but de ce troisième essai est de voir dans quelle mesure la promotion du recyclage est un instrument approprié pour atteindre un tel objectif. En d'autres mots, comment le recyclage affecte-t-il à long terme la surface de terre en forêt et l'âge de coupe? Nous étudions cette question en spécifiant un modèle dynamique d'allocation d'un terrain donné, par un propriétaire forestier privé, entre la forêt et une utilisation alternative du terrain, comme l'agriculture. Une fois les arbres coupés, il décide d'une nouvelle allocation du terrain. Il le fait indéfiniment comme dans le cadre du modèle de Faustmann. Le bois coupé est transformé en produit final qui est en partie recyclé comme substitut du bois original. Ainsi, les outputs passés affectent le prix courant. Nous montrons que, paradoxalement, un accroissement du taux de recyclage réduira à long terme la surface forestière et donc diminuera le nombre d'arbres plantés. Par contre l'âge de coupe optimal va s'accroître. L'effet net sur le volume de bois offert sur le marché est ambigu. Le principal message cependant est qu'à long terme le recyclage va résulter en une surface en forêt plus petite et non plus grande. Donc, si le but est d'accroître la surface en forêt, il pourrait être préférable de faire appel à d'autres types d'instruments de politique que celui d'encourager le recyclage.

Contracting for innovation under knightian uncertainty

At any given point in time, the collection of assets existing in the economy is observable. Each asset is a function of a set of contingencies. The union taken over all assets of these contingencies is what we call the set of publicly known states. An innovation is a set of states that are not publicly known along with an asset (in a broad sense) that pays contingent on those states. The creator of an innovation is an entrepreneur. He is represented by a probability measure on the set of new states. All other agents perceive the innovation as ambiguous: each of them is represented by a set of probabilities on the new states. The agents in the economy are classified with respect to their attitude towards this Ambiguity: the financiers are (locally) Ambiguity-seeking while the consumers are Ambiguity-averse. An entrepreneur and a financier come together when the former seeks funds to implement his project and the latter seeks new profit opportunities. The resulting contracting problem does not fall within the standard theory due to the presence of Ambiguity (on the financier’s side) and to the heterogeneity in the parties’ beliefs. We prove existence and monotonicity (i.e., truthful revelation) of an optimal contract. We characterize such a contract under the additional assumption that the financiers are globally Ambiguity-seeking. Finally, we re-formulate our results in an insurance framework and extend the classical result of Arrow [4] and the more recent one of Ghossoub. In the case of an Ambiguity-averse insurer, we also show that an optimal contract has the form of a generalized deductible.

The trade-off between incentives and endogenous risk

Standard models of moral hazard predict a negative relationship between risk and incentives, but the empirical work has not confirmed this prediction. In this paper, we propose a model with adverse selection followed by moral hazard, where effort and the degree of risk aversion are private information of an agent who can control the mean and the variance of profits. For a given contract, more risk-averse agents suppIy more effort in risk reduction. If the marginal utility of incentives decreases with risk aversion, more risk-averse agents prefer lower-incentive contractsj thus, in the optimal contract, incentives are positively correlated with endogenous risk. In contrast, if risk aversion is high enough, the possibility of reduction in risk makes the marginal utility of incentives increasing in risk aversion and, in this case, risk and incentives are negatively related.

Essays on asymmetric information problems without the single-crossing property: applications to corporate finance

The objective of this dissertation is to re-examine classical issues in corporate finance, applying a new analytical tool. The single-crossing property, also called Spence-irrlees condition, is not required in the models developed here. This property has been a standard assumption in adverse selection and signaling models developed so far. The classical papers by Guesnerie and Laffont (1984) and Riley (1979) assume it. In the simplest case, for a consumer with a privately known taste, the single-crossing property states that the marginal utility of a good is monotone with respect to the taste. This assumption has an important consequence to the result of the model: the relationship between the private parameter and the quantity of the good assigned to the agent is monotone. While single crossing is a reasonable property for the utility of an ordinary consumer, this property is frequently absent in the objective function of the agents for more elaborate models. The lack of a characterization for the non-single crossing context has hindered the exploration of models that generate objective functions without this property. The first work that characterizes the optimal contract without the single-crossing property is Araújo and Moreira (2001a) and, for the competitive case, Araújo and Moreira (2001b). The main implication is that a partial separation of types may be observed. Two sets of disconnected types of agents may choose the same contract, in adverse selection problems, or signal with the same levei of signal, in signaling models.

Unitização de jazidas de petróleo: uma aplicação do modelo de Green e Porter

Neste trabalho abordamos a unitização como uma reinterpretação de cartel, partindo do modelo clássico de Green e Porter. A incerteza geológica é representada por um componente estocástico no custo marginal. Caracterizamos o contrato ótimo e, a partir da estática comparativa, avaliamos a eficiência e a viabilidade da cooperação. O preço e o grau da externalidade afetam positivamente o nível de eficiência do contrato ótimo. Mas enquanto preços elevados viabilizam os acordos, o grau de externalidade elevado pode conduzir a equilíbrios ineficientes ou mesmo inviabilizar a produção. O mesmo resultado ocorre com os custos fixos. Adicionalmente, quanto maior for o número de firmas envolvidas no acordo, menor será a chance de existir um contrato mais eficiente que a regra da captura.

Contratos de performance sob risco e na ausência de incentivo

Este trabalho mostra que a solução ótima do contrato de remuneração do empregado não é de salário fixo quando sua utilidade reserva é uma função de um fator que pode variar. A remuneração ótima do empregado incluirá um bônus que será também uma função do mesmo fator que modifica sua utilidade reserva, mesmo que tal fator não dependa do seu esforço e que o agente seja avesso ao risco. Esse resultado contrasta com a teoria clássica segundo a qual só se deveria alocar risco ao funcionário quando tal contrato fosse necessário para prover os incentivos para um esforço maior do agente. Outra conclusão desse trabalho é que existe um limite para o tamanho do risco que o funcionário assume no contrato ótimo, ou seja, o valor do bônus é uma função crescente da diferença dos valores da utilidade reserva nos diferentes cenários possíveis até certo ponto apenas e a partir de determinado valor para essa diferença, a magnitude do bônus se mantém estável.