No 5863, Working Paper from Department of Economics, University of Pittsburgh
The extension of set functions (or capacities) in a concave fashion, namely aconcavi cation, is an important issue in decision theory and combinatorics. It turns out thatsome set-functions cannot be properly extended if the domain is restricted to be bounded.This paper examines the structure of those capacities that can be extended over a boundeddomain in a concave manner. We present a property termed the sandwich property that isnecessary and sufficient for a capacity to be concavfi able over a bounded domain. We showthat when a capacity is interpreted as the product of any sub group of workers per a unit oftime, the sandwich property provides a linkage between optimality of time allocations andefficiency.
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