A Microfoundation for Production Functions: Assignment of Heterogeneous Workers to Heterogeneous Jobs

This paper develops an assignment model of heterogeneous workers to heterogeneous tasks that provides a microeconomic foundation for aggregate production functions. The shape of the production function is shown to depend crucially on the distribution of tasks. Necessary and sufficient conditions are provided for the production function to be of the constant ratio of elasticities of substitution form, which nests the widely used constant elasticity of substitution (CES) form. For the CES production function, the elasticity of substitution between skill groups of workers is shown to depend only on the variance of tasks in the economy.