Essays in Market Design

This dissertation consists of three essays in market design. The first essay studies a dynamic allocation problem. The second presents a new model for many-to-one matching markets where colleges are matched to a large number of students. The third analyzes the effect of the minimum wage on training in internships.;In many assignment problems items arrive stochastically over time, and must therefore be assigned dynamically. The first essay studies the social planers ability to dynamically match agents with heterogenous preferences to their preferred items. Impatient agents may misreport their preferences to receive an earlier assignment, causing welfare loss. The first essay presents a tractable model of the problem and mechanisms that minimize the welfare loss.;The second essay, which is joint work with Eduardo Azevedo, considers the classical many-to-one matching problem when many students are assigned to a few large colleges. We show that stable matchings have a simple characterization. Any stable matching is equivalent to market clearing cutoffs---admission thresholds for each college. The essay presents a model where a continuum of students is to be matched to a finite number of schools. Using the cutoff representation we show that under broad conditions there is a unique stable matching, and that it varies continuously with respect to the underlying economy.;The third essay, which is joint work with Michael Schwarz, looks at on the job training in firms. The firm recovers the cost of training by gradually training the worker over time, paying a wage below the worker's marginal product and providing the remaining compensation in the form of training. When the worker's productivity is close to the minimum wage the firm finds it profitable to front-load training, making the worker more productive and the training faster. A decrease in the minimal wage reduces the firm's incentive to front-load training, and can make training less efficient.