Concavity and Estimation

Concavity of Utility, Concavity of Welfare, and Redistribution of Income

The marginal social value of income redistribution is understood to depend on both the concavity of individuals’ utility functions and the concavity of the social welfare function. In the pertinent literatures, notably on optimal income taxation and on normative inequality measurement, it seems to be accepted that the role of these two sources of concavity is symmetric with regard to the social...

Concavity and B-concavity of Solutions of Quasilinear Filtration Equations

Matroids and log-concavity

We show that f -vectors of matroid complexes of realizable matroids are strictly log-concave. This was conjectured by Mason in 1972. Our proof uses the recent result by Huh and Katz who showed that the coefficients of the characteristic polynomial of a realizable matroid form a log-concave sequence. We also prove a statement on log-concavity of h-vectors which strengthens a result by Brown and ...

Optimal Design and -Concavity

Tools from advanced real analysis and the Prékopa-Borell Theorem are combined to derive a tight sufficient condition for regularity (R. Myerson, Optimal auction design, Mathematics of Operations Research 6, 1981, pp. 58-73). The conventional log-concavity condition arises as a special case. The approach allows various generalizations, for instance to multidimensional types. Regularity is verifi...

Inductive concavity

Sagan, B.E., Inductive proofs of q-log concavity, Discrete Mathematics 99 (1992) 289-306. We give inductive proofs of q-log concavity for the Gaussian polynomials and the q-Stirling numbers of both kinds. Similar techniques are applied to show that certain sequences of elementary and complete symmetric functions are q-log concave.