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Commonly used methods of production function estimation assume that a firm’s output quantity can be observed as data, but typical datasets contain only revenue, not output quantity. We examine the nonparametric identification of production function from revenue data when a firm faces a general nonparametric demand function under imperfect competition. Under standard assumptions, we provide the constructive nonparametric identification of various firm-level objects: gross production function, total factor productivity, price markups over marginal costs, output prices, output quantities, a demand system, and a representative consumer’s utility function.

Nonparametric Identification of Production Function, Total Factor Productivity, and Markup from Revenue Data