This paper studies optimal bundling of products with non-additive values. Under monotonic preferences and single-peaked profits, I show a monopolist finds pure bundling optimal if and only if the optimal sales volume for the grand bundle is larger than the optimal sales volume for any smaller bundle.

This paper uses both empirical and theoretical methods to answer salient questions about possible geographical distortion of supply from demand: (i) how to empirically infer whether some regions are "under-supplied" relative to others; (ii) howto identify mechanisms that lead to unequal access to supply across regions; and (iii) how to design policies that alleviate geographical supply inequities. If supply in a spatial market (such as rideshare) is geographically distorted from demand, it will lead to disproportionately low demand-fulfillment rates in some regions relative to other regions. However, empirically identifying such spatial distortions is challenging since unfulfilled demand is unobserved. To deal with this issue, we devise an approach, called relative outflows analysis, which has a simple implementation and minimal data requirements. Our method takes advantage of the overlooked fact that individuals do not migrate as often as they take rides, hence for every trip there is a "trip back." Suppose, for example, that Lyft's "relative outflow" in Staten Island (i.e., the number Lyft rides exiting Staten Island divided by those entering it) is consistently around 0.6. Then we conclude that Lyft's supply is distorted away from Staten Island; because the same population that chooses Lyft over other options to enter the borough, is likely to choose other options over Lyft to exit. This conclusion becomes stronger if Uber's relative outflow in Staten Island is consistently close to 1.

How can we control for latent discrimination in predictive models? How can we provably remove it? Such questions are at the heart of algorithmic fairness and its impacts on society. In this paper, we define a new operational fairness criteria, inspired by the well-understood notion of omitted variable-bias in statistics and econometrics. Our notion of fairness effectively controls for sensitive features and provides diagnostics for deviations from fair decision making. We then establish analytical and algorithmic results about the existence of a fair classifier in the context of supervised learning. Our results readily imply a simple, but rather counter-intuitive, strategy for eliminating latent discrimination. In order to prevent other features proxying for sensitive features, we need to include sensitive features in the training phase, but exclude them in the test/evaluation phase while controlling for their effects. We evaluate the performance of our algorithm on several realworld datasets and show how fairness for these datasets can be improved with a very small loss in accuracy.