[pt] O mercado brasileiro de derivados de petróleo está sendo aberto para competição este ano, saindo de um ambiente de preços regulados pelo Governo Federal para um ambiente onde os preços são estabelecidos pelas leis de oferta e demanda. Neste contexto, existe a preocupação de como serão estes preços, e seus impactos sobre os consumidores e sobre os produtores locais. Esta Tese propõe alguns modelos matemáticos para estimar preços, níveis de produção, níveis de consumo (demanda), e importação e exportação de derivados de petróleo nas diversas regiões do mercado brasileiro. O fornecimento de derivados de petróleo não é considerado um mercado competitivo, e sim oligopolizado, principalmente no curto prazo, devido à capacidade instalada de refinarias e aos altos custos envolvidos na construção de novas refinarias. Estes modelos são multi- produto, considerando um fato importante na produção de derivados que é a impossibilidade de produzir apenas um derivado. Assim, existem restrições onde a oferta de um derivado é relacionada a oferta dos outros. O primeiro modelo considera um mercado de oligopólio fechado, com um número fixo de firmas. Tal modelo é formulado como um problema de equilíbrio a Nash. Um segundo modelo é apresentado expandindo o primeiro para o caso em que existem preços teto de demanda definidos politicamente. O terceiro modelo relaxa a suposição do mercado fechado, com número fixo de firmas, e considera a possibilidade de competição de novas firmas no mercado. Um quarto modelo é discutido, onde assume-se que existe uma firma líder no mercado, que consegue definir sua estratégia antes das demais firmas, semelhante ao problema econômico de Stackelberg. Todos os modelos foram formulados como problemas de inequações variacionais, sendo que o último modelo é ainda um problema de programação binível. Algoritmos de solução são propostos para os três primeiros modelos. Simulações sobre o mercado brasileiro de derivados são apresentadas. / [en] The Brazilian petroleum refined products market is being opened to competition this year, leaving an environment of regulated prices to another one where the prices are defined by the supply demand interactions. Considering this new scenario, there is a concern about how high the prices will be, and about their impact on the consumers and on the local producers. This thesis proposes some mathematical models to predict prices, production, consumption, and import and export levels of petroleum-refined products in all the sub-regions of the Brazilian market. Instead of a competitive market, the supply of refined products is considered an oligopoly market, especially in the short term, given the already installed refining capacity and the high costs involved in building new refineries. These models are multi-products, and they consider an important characteristic of the production of refined products, the impossibility of producing only one refined product. Hence, constraints where the production of one refined product is related to the production of the others are considered. The first model considers a closed oligopoly market, with a fixed number of firms. This problem is formulated as a Nash equilibrium problem. A second model is presented generalizing the first one to consider the possibility of ceiling demand prices politically defined. The third model relaxes the assumption of a fixed number of firms in the first model, and considers the possibility of competition by new entrants. A fourth model is discussed, where it is assumed that there is a leader firm in the market, which can define its strategy before the other firms, similar to the economic problem of Stackelberg. All the models are formulated as variational inequalities problems, and the last model is also a bi-level programming problem. Solution algorithms for the three first models are proposed. Some analyses of the Brazilian petroleum refined- products market are presented.

Die Dissertation beschäftigt sich mit den Auswirkungen verschiedener Politikoptionen auf den Weltzuckermarkt. Dazu wird ein räumliches Preisgleichgewichtsmodell wie von Takayama und Judge vorgeschlagen mit hoher Abdeckung von Regionen und Politiken erstellt. Der Vorteil dieses Modelltyps gegenüber den in bisherigen Analysen verwendeten besteht in seiner Fähigkeit, die Annahme der Ursprungshomogenität (im Gegensatz zu Modellen, die auf dem Armington Ansatz basieren) mit der Möglichkeit zu kombinieren, bilaterale Handelsströme explizit abzubilden. Ein wesentlicher Nachteil ist die quasi-normative Natur des Ansatzes. Nach der Einführung wird zunächst in Kapitel zwei der Weltzuckermarkt detailliert beschrieben und von anderen Agrarmärkten abgegrenzt sowie die Anforderungen an ein Gleichgewichtsmodell des Weltzuckermarktes diskutiert. Dann wird im dritten Kapitel eine Übersicht über verschiedene in der Vergangenheit verwendete Modellansätze gegeben und deren Ergebnisse ausgewertet. Im vierten Kapitel wird ein Überblick die theoretische Entwicklung des Modellansatzes gegeben und schließlich das in der Dissertation verwendete Modell beschrieben. Das Modell umfasst 104 Zucker produzierende und 90 Zucker konsumierende Regionen. Nationale Handels- und Agrarpolitiken sowie eine Vielzahl regionaler und präferentieller Handelsabkommen sind im Modell berücksichtigt. Im zweiten Teil von Kapitel vier wird eine Analyse von vier Szenarien mit dem Modell durchgeführt. Diese umfassen eine Fortführung gegenwärtiger Politiken, ein WTO Abkommen, eine einseitige Liberalisierung des Zuckermarktes der EU sowie eine Liberalisierung der Zuckermärkte aller im Modell vertretenen Länder. Im Abschlusskapitel werden einige Kernergebnisse zusammengefasst und eine Weiterentwicklung des Ansatzes diskutiert. Hier wird insbesondere auf das Problem der Quasi-Normativität eingegangen. / The Dissertation at hand investigates the effects of different policy options on the world sugar market. A Spatial Price Equilibrium Model as suggested by Takayama and Judge is established. This model type has one considerable advantage over previously ap-plied types which is its ability to combine the assumption of homogeneous goods regardless of origin (as opposed to Armington-based models) with the possibility to model bilateral trade flows explicitly. One major drawback of the approach is that is behaves in part like a normative model. After the introductory chapter, a detailed description of the world sugar market and how it distinguishes from markets for other agricultural commodities is given. In this frame-work requirements of a valid equilibrium model of the world sugar market are discussed. In the third chapter various studies of the world sugar market based on equilibrium models are surveyed. In the chapter four the development of the approach of spatial equilibrium modeling finally the model applied in this dissertation are described The model covers 104 sugar pro-ducing and 90 sugar consuming regions. National agricultural and trade policies as well as numerous regional and preferential trade agreements are accounted for. In the second part of chapter four, four scenarios are simulated with the model. These are a reference scenario in which current policies are maintained, a WTO agreement, a unilateral liberalization of sugar policies on the part of the EU as well as a multilateral liberalization of the sugar markets of all countries. In the final chapter, some core results are summarized and further development of the applied approach especially possible solutions for the problem of quasi-normativity are dis-cussed.

In the study a class of multisector network models, suitable for simulation of the interaction between production, demand, trade, and infrastructure, is presented. A characteristic feature of the class is a vintage model of the production system. Hence, the rigidities in existing capacities and the temporary monopolies obtainable from investments in new capacity at favourable locations are emphasized.As special cases, the class contains models in the modelling traditions of "interregional computable general equilibriunT, Hspatial price equilibrium**, "interregional input-output" and transportation networks.On the demand side, a multihousehold spatial linear expenditure system is introduced. This allows for an endogenous representation of income effects of skill-differentiated labour.The models are represented by a set of complementarity problems. This facilitates a comparison of model properties and the choice of an appropriate solution algorithm.The study is mainly devoted to single period models. Such equilibrium models are interpreted as adiabatic approximations of processes in continuous time. A separation by the time scale of the processes and an application of the slaving principle should thus govern the choice of endogenous variables in the equilibrium formulation. / digitalisering@umu