This paper proposes an assignment model where sorting occurs on attributes including both skills (Sattinger, 1979) and preferences (Tinbergen, 1956). The key feature of this model is that the wage function admits both jobs' and workers' attributes as arguments. Since this function is generically nonlinear (Ekeland et al., 2004), even under positive assortative matching, the correlation between the contribution of workers' attributes to wages and that of jobs' attributes can vary from -1 to 1 depending on the parameters of the model, i.e. preference, technology and the distribution of both sets of attributes. The paper discusses a closed form solution of the model, presents conditions under which nonadditive marginal utility and production function are nonparametrically identified using observations from a single hedonic market and proposes a nonparametric estimator.