| This thesis consists of three essays. The first one deals with the theory of cost sharing. We study the implications of "Ranking", which is a fairness requirement. The second and third essays are applications of micoreconomic theory to the analysis of issues encountered in the energy market.;The second chapter, "Optimal Management of Strategic Reserves of Nonrenewable Natural Resources", examines the issue of strategic petroleum reserves management. Indeed, due to uncertainty on the supply side, many countries are holding precautionary stocks of oil. Assuming that the evolution of the price of oil is consistent with the Ho-telling rule, we derive the optimal stockpiling policy for a small country which is likely to suffer an embargo, the occurrence and duration of which are stochastic. We show the existence of a decreasing "target path" (for the reserves) that the country wants to attain in order to hedge against these disruptions. We also introduce the possibility for the importing country to invest in research on a backstop technology, which would reduce the dependence on oil. Success in research is random and the date at which the backstop will be discovered is also stochastic. We prove that it is always optimal for the importing country to undertake research in order to free itself from the embargo threat and achieve energy independence. The effort invested in research is shown to decrease with the size of the strategic reserves.;As for the third chapter, 'The Economics of Oil, Biofuel and Food Commodities", it studies within a tractable model the effects on the food market of the introduction of biofuels as a substitute for fossil fuel in the energy market. We consider a world economy with an oil cartel and a competitive fringe of farmers producing energy in the form of biofuels. Farmers also produce food and sell it on the world food market. We determine the resulting relationship between prices in the energy and food markets and characterize the cartel's extraction path and the price path of energy. We then show that the price of food will be growing as long the oil stock is being depleted, whether population is growing or not, and that it will keep growing after the oil stock is exhausted if population is growing.;Keywords: cost sharing method, Ranking, demand profile, flow, symmetry, imports, nonrenewable resource, random embargoes, strategic reserves, biofuel, oil depletion, energy price, food price.;In the first chapter, "The Implications of the Ranking Axiom for Discrete Cost Sharing Methods", we study the Ranking axiom in cost sharing problems. Suppose that a group of agents have to share the cost of a joint project, depending on their respective demands. The Ranking axiom requires the demands and the cost shares to have the same ordering, as long as the cost function is symmetric in these demands. In other words, if the demands of two agents play exactly the same role in raising the cost of the project, then the agent who demands more should pay more. This is a legitimate fairness condition. Dealing with the discrete version of the model, we characterize the set of all methods satisfying Ranking in the case of two agents. We prove that, in order to satisfy our requirement, the flow representing the method must exhibit a specific symmetry condition. With three agents or more, we derive strong necessary conditions. We show, however, that they are not sufficient. We also characterize the elementary fixed-flow methods satisfying the axiom. |
