Equality of opportunity and optimal effort decision under uncertainty

We analyze a society that cares about inequality of opportunity. We propose adynamic setting in which effort is a decision variable that individuals adopt as asolution of an explicit utility maximization program. Effort determines themonetary outcome and it depends on the individual¿s preferences andcircumstances. The planner designs an incentive scheme so as to foster higherincomes, reducing the opportunity cost of effort and productivity for the lessfavoured agents. Income is assumed to be random, and contrary to the generalneutral assumption, we obtain that luck does have a biased and persistent effect onincome distribution that may be regarded as unfair. We also study the planner¿soptimal policy when she cannot infer perfectly the individuals¿ responsibilityfeature.Equality of opportunity, effort decision, policy design, luck

Education, Utilitarianism, and Equality of Opportunity

We analyze in this paper the impact of different policies on the investment of the families in the education of their children. Families make decisions on the level of human capital of their offsprings regarding the future income that this capital entails (under the assumption that higher education levels yield higher expected income). The families' optimal investment in education depends on their preferences (summarized by their time discount and risk aversion parameters) and their circumstances (initial wealth, parents' education, and children' natural abilities). The public authority designs a balanced tax/subsidy scheme in order to maximize aggregate welfare. We compare the case of a purely utilitarian planner with one that cares about the equality of opportunity.Equality of Opportunity, Investment in Education, Policy design

Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in \cite{ge09_1} where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high and low conductivity inclusions