We introduce a notion of money-metric social welfare for discrete choice under unrestricted heterogeneity and income effects. It is the maximized indirect utility under normalization of the outside option. It also equals the amount of income necessary to achieve a given level of utility, while certain choices are prohibited. We show that the distribution of this quantity is nonparametrically identified as a closed-form functional of average structural demand for the outside option, making it useful for cost-benefit analysis and optimal targeting. An illustration with private tuition subsidies in India shows that the income path of usage-maximizing subsidies differs significantly from welfare-maximizing ones.

Motivated by the prevalence of simultaneous bidding across a wide range of auction markets, we develop and estimate a model of strategic interaction in simultaneous first-price auctions when objects are heterogeneous and bidders have non-additive preferences over combinations. We establish non-parametric identification of primitives in this model under standard exclusion restrictions, providing a basis for both estimation and testing of preferences over combinations. We then apply our model to data on Michigan Department of Transportation (MDOT) highway procurement auctions, quantifying the magnitude of cost synergies and evaluating the performance of the simultaneous first-price mechanism in the MDOT marketplace.