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A recent empirical literature models search and matching frictions by means of a reduced-form matching function. An alternative approach is to simulate the matching process directly. In this paper, we follow the latter approach to model matching in ride-hailing. We compute the matching function implied by the matching process. It exhibits increasing returns to scale, and it does not resemble the commonly used Cobb-Douglas functional form. We then use this matching function to quantify network externalities. A subsidy on the order of $2 per trip is needed to correct for these externalities and induce the market to operate efficiently.

Vaccinating the world's population quickly in a pandemic has enormous health and economic benefits. We analyze the problem faced by governments in determining the scale and structure of procurement for vaccines. We analyze alternative approaches to procurement, arguing that buyers should directly fund manufacturing capacity and shoulder most of the risk of failure while maintaining some direct incentives for speed. We analyzed the optimal portfolio of vaccine investments for countries with different characteristics as well as the implications for international cooperation. Our analysis, considered in light of the experience of 2020, suggests lessons for future pandemics.