Before revision:  We extend classical duality results for price-taking firms to a setup with rich heterogeneity, and with limited variation in prices. We characterize the identified set for production sets, and provide conditions that ensure point identification. We present a general computationally-feasible framework for sharp counterfactual bounds, such as bounds on quantities at a counterfactual price. We show that existing convergence results for quantile estimators may be directly converted to convergence results for production sets , which facilitates statistical inference .
After revision:  We extend classical duality results for price-taking firms to a setup with rich heterogeneity, and with limited variation in possibly latent prices. Finally, we show that convergence results for quantile estimators may be directly converted to convergence results for production sets , which facilitates statistical inference .