Given positive integers d and n, there is an integer N such that for every injective map ffrom { 1 ..... N} a into R there is a subset A = A1 x A2 x ... × Ad of { 1 ..... N} a such that (1) each Aj has n elements, (2) the restriction of f to A is monotone in each coordinate, (3) there is an ordering of the coordinates such that f on A is texicographic with respect to that ordering. Because inje...

Public provision of a private goods is justified on efficiency grounds in a modelwith no redistributive preferences. A government’s involvement in the provision of a private good generates information about preferences that facilitatesmore efficient revenue extraction for the provision of public goods. Public provision of the private good improves economic efficiency under a condition that is a...

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