  Commonly used methods of production function and markup 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 and markup from revenue data when a firm
faces a general nonparametri 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.
