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 conditions that 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 that are nonadditive in the unobservable random terms, using observations from a single hedonic equilibrium market. These methods are important when statistical tests reject additive specifications or when prior information suggests that consumer or firm heterogeneity in the curvature of utility or production functions is likely to be significant. We provide conditions under which these types of utility and production functions are nonparametrically identified, and we propose nonparametric estimators for them. The estimators are shown to be consistent and asymptotically normal. When the assumptions required to use single market methods are unjustified, we show how multimarket data can be used to estimate the structural functions.