Under which condition does the set of desirable uncertain prospects expand when wealth increases? We show that the decreasing concavity (DC) of the utility function u is necessary and sufficient in the α-maxmin expected utility model. In the smooth ambiguity aversion model with the ambiguity valuation function φ, the DC of u and of φ • u is necessary and sufficient. An alternative classical definition of decreasing aversion is based on the hypothesis that the investment in a risky asset is increasing in wealth. We show that this hypothesis does not hold in general under ambiguity aversion, and that one needs to constrain the structure of ambiguity to obtain unambiguous results.
This paper is aimed at evaluating the net gains and trade-offs at stake in implementing the competition of the rail mode in the long distance passenger market either by means of franchise or by an open access mechanism. We simulate the outcomes of competition in and for the market using a differentiated-products oligopoly model allowing for inter-and intra-modal competition in a long distance passenger market. Specifically we first calibrate the model using data describing high speed lines in France and show that the incumbent railway operator's strategy does not simply boil down to a short-term profit maximization (e.g., because of existing regulation or limitpricing strategy). This yields two important results when simulating competition. First, whether it is for or in the market, the opening to competition does not guarantee a decrease in prices in favor of passengers. Second, the effects of opening up to competition for the market are relatively predictable and potentially positive, while those of opening up to competition in the market remain very uncertain.JEL Codes: L13, L90, R40
When evaluating public and private investment projects, those that contribute more to the collective risk should be more penalized through an upward adjustment of their discount rate. This paper shows how to estimate the risk-adjusted discount rate for different projects, with applications to the electricity sector. Using the standard framework of consumer theory, we express any investment project's beta in terms of the easier-to-measure price and income elasticities of the goods generated by the project. When considering an investment in production capacity, the beta has a flat term structure, and is positive (negative) for normal (inferior) goods. When considering core infrastructures carrying goods or services, such as energy transmission and distribution assets, the beta has a decreasing term structure with very high values at short horizons for infrastructures facing capacity constraints. We provide a real-case example of a cross-border electricity connection with negative beta for the exporting country.
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