We analyze equilibria in hedonic economies and study conditions that lead to identification of structural preference parameters in hedonic economies with both additive and nonadditive marginal utility and marginal product functions. The latter class is more general,allows for heterogeneity in the curvature of consumer utility, and can result in conditionsthat lead to bunching. Such bunching has been largely ignored in the previous literature.We then present methods to estimate marginal utility and marginal product functions thatare nonadditive in the unobservable random terms, using observations from a single hedonicequilibrium market. These methods are important when statistical tests reject additivespecifications or when prior information suggests that consumer or firm heterogeneity inthe curvature of utility or production functions is likely to be significant. We provide conditionsunder which these types of utility and production functions are nonparametricallyidentified, and we propose nonparametric estimators for them. The estimators are shownto be consistent and asymptotically normal. When the assumptions required to use singlemarket methods are unjustified, we show how multimarket data can be used to estimate thestructural functions.