"The objective of this project is to study the proper design of benefit and tax programs that promote employment and reduce inequality when individuals are heterogeneous in several dimensions. To do so, we will develop original mathematical models some of which will relate optimal taxation theory to other strands of economic theory (e.g., modern labor economics) and to the literature about equality of opportunity, which lies between social choice theory and philosophy. The nature of the assumed unobserved heterogeneity between individuals is very important for the predictions derived from optimal taxation models. Optimal income tax problems typically restrict individuals’ heterogeneity to one-dimension: their innate ability.Although incentives problems with multi-dimensional heterogeneity (a.k.a. multidimensional screening problems) are empirically relevant, they are notoriously very hard to treat. The THE project aims at (1) elaborating a toolbox to solve these problems and (2) developing a wide range of applications for this toolbox. To solve multidimensional screening problems, we propose to: (i) develop recent results obtained using a random participation framework, (ii) build up on the type aggregator technique and (iii) extend the techniques used in the literature on optimal transportation.Beside these technical contributions, the project will allow us to address three original applied economic questions. First, what is the tax schedule over the entire earnings distribution that satisfies equality of opportunity? Second, what is the optimal tax schedule when there are both skill heterogeneity and gender-specific responses in terms of labor force participation decisions? Third, should workfare be used when labor supply is simultaneously modeled along the participation margin (decision to enter or not the labor market) and the intensive margin (i.e. people decide on their labor hours)?"