This dissertation contains two self-contained chapters. Although each essay examines a different question and each contributes to several distinct bodies of literatures, the essays are linked by findings and implications related to public economics. The first chapter contributes to dynamic contest theory by examining the effects of a relative performance based-prize scheme on the expected effort and the final results in best-of-N contests. The second chapter investigates the relation between a sitting governor's popularity and the incumbent's tax policy choices. Chapter 1 contributes to existing literature on contest and tournament. It examines the effects of a relative performance prize scheme on participants' efforts and final results in best-of-N contests. In most best-of-N contests the winner-take-all scheme is widely used to allocate prizes. Under this scheme, the prizes are awarded only to the winning individual or group. Each participant's incentive in a round is highly related to outcomes of previous rounds. If a participant losses several early rounds and has little chance of winning the contest, he or she may no longer continue to exert effort in subsequent rounds. Chapter 1 first develops a two-player best-of-N contest model with a relative performance prize scheme under which prizes are distributed based on the participants' relative performance. The essay then contrasts this model's efficiency to the winner-take-all scheme. In a simplified best-of-three contest model it is found that the relative performance prize scheme increases the participants' expected effort level only in certain conditions; furthermore, the relative performance prize scheme lowers the expected total effort of the entire contest relative to the winner-take-all scheme. Moreover, the model suggests that, contrasted with the winner-take-all scheme, the relative performance scheme raises the expected number of sets played in contests. Empirically, the first chapter investigates these theoretical predictions using a volleyball dataset from FIVB (Federation Internationale de Volleyball) World League and FIVB World Grand Prix between 2004 and 2013. The results indicate that the relative performance prize scheme only intensifies effort exerted by the participating teams; however, it does not significantly affect final results in the contest. The second chapter contributes to the literature of political competition and the policy choices of public officials. The chapter discusses whether, and to what degree, a governor's popularity affects his or her tax policies. The model predicts that holding high levels of popularity lead a governor to tend to adopt tax policies arguably contrary to the interests of independent voters. In the empirical analysis, each governor's popularity is measured by an index that was developed for this study and based on the results of presidential and gubernatorial elections. The analysis investigates the impact of a governor's popularity on her or his tax policies between 1970 and 2010. The results support the prediction that high levels of popularity may induce governors to act contrary to the interests of voters. The chapter also finds that popular Democratic governors have more incentives to increase corporate taxes while popular Republican governors are more likely to raise sales taxes. Further analysis suggests that popular term-limited governors are more likely to increase total taxes than their counterparts who are eligible for re-election. In addition to explaining the role of popularity in incumbents' policy choices, these findings improve our understanding of the interaction between voters' behavior and the political attitude of public officials in a representative democracy. In conclusion, this dissertation examines three relevant questions in public economics. The essays not only develop comprehensive theoretical frameworks for these questions but also provide abundant supporting empirical evidence for the theoretical predictions. Addressing these questions both enhances our understanding of several contemporary real-world issues and provides theoretical and practical implications for further work linking social interests and economic policies.