A Theory of Production, Matching, and Distribution

This paper presents a unified approach to production, matching, and distribution in an environment with labor market frictions. I use competing auctions as both a wage determination mechanism and a microfoundation for an aggregate production and matching technology. For any well-behaved distribution of firm productivities, I show that the aggregate production function exhibits standard neoclassical properties and an elasticity of substitution between capital and labor that is always less than or equal to one. If the distribution is Pareto or power law, this function is particularly tractable. In general, factor income shares vary with the degree of competition between firms to hire workers, the value of non-market activity, and characteristics of the underlying firm productivity distribution. Unlike Diamond-Mortensen-Pissarides style search models with Nash bargaining, production and distribution are endogenously tightly connected: the economy satisfies a generalized version of the Hosios condition