In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.Martínez-Legaz's research was supported in part by the Ministerio de Ciencia y Tecnología, project BEC2002-00642, and by the Comissionat per Universitats i Recerca de la Generalitat de Catalunya, grant SGR2001-00162.