On the Stochastic Macro-equilibrium and a Microfoundation for the Production Function

We provide a microfoundation for the production function by using the concept of stochastic macro-equilibrium in Yoshikawa ("Stochastic Macro-equilibrium and Microfoundations for Keynesian Economics," RIETI Discussion Paper, 2013). We consider an economy with multiple firms, with each firm possessing Leontief technology. We assume that the allocation of labor is determined by entropy maximization. We show that for selected productivity distribution, aggregate production is described by the popular Cobb-Douglas type.