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Copyright by Xue Li 2020 the Dissertation Committee for Xue Li Certifies That This Is the Approved Version of the Following Dissertation Copyright by Xue Li 2020 The Dissertation Committee for Xue Li certifies that this is the approved version of the following dissertation: Three Essays in Microeconomics Committee: Venkataraman Bhaskar, Co-Supervisor Caroline D. Thomas, Co-Supervisor Thomas E. Wiseman Kishore Gawande Three Essays in Microeconomics by Xue Li DISSERTATION Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY THE UNIVERSITY OF TEXAS AT AUSTIN May 2020 Dedicated to my parents and friends Acknowledgments I am deeply grateful to my advisor, Dr. V. Bhaskar and Dr. Caroline Thomas, for their advice and guidance during my graduate study. They have supported me not only in economic research but also in career development. I would also like to express my appreciation to Dr. Thomas Wiseman and Dr. Kishore Gawande for all their valuable comments and suggestions on this dissertation. My gratitude also goes to all other members of UT Austin Theory fac- ulties: Dr. Svetlana Boyarchenko, Dr. Mark Feldman, Dr. John Hatfield, Dr. Vasiliki Skreta, Dr. Dale Stahl, Dr. Maxwell B. Stinchcombe, and Dr. Rodrigo Velez. I wish to give special thanks to my classmates and friends Sangwoo Choi, Jessica Fears, Vasudha Jain, Shaofei Jiang, Anthony Maxam, Yiman Sun, and Mark Whitmeyer for the valuable feedback they provided. I would like to thank my supportive friends Nir Eilam, Ziwei He, Erica Xuewei Jiang, Cao Jin, Yaran Jin, Lisa Yao Liu, Andres Mendez Ruiz, Yong- hang Wang, Shenshen Yang, Chan Yu, and Jiangang Zeng for their help in the last five years. Finally, I am indebted to my parents for their love, understanding, and support throughout my life. v Three Essays in Microeconomics by Xue Li, Ph.D. The University of Texas at Austin, 2020 Co-Supervisors: Venkataraman Bhaskar Caroline D. Thomas This dissertation consists of two chapters in investigating firms’ pricing strategies in different information settings, and one more empirical chapter exploring the effect of low-skilled immigrants on college-educated women. In the first chapter, I investigate the strategic pricing of firms and the innovation adoption processes of consumers in a forward-looking social learn- ing environment. The equilibrium dynamics will depend on both the market structure and the arrival rate of exogenous signals. I show that in perfect good news, with a low arrival rate of exogenous signals, the monopoly firm will encourage learning to end up with a "free samples" period. In contrast, with a high arrival rate of exogenous signals, the monopoly firm does not sell until there is a good signal. In duopoly under perfect good news, for a low arrival rate of exogenous signals, the market structure will make both firms use "free samples" strategy in the early stage to compete for the arrival of a vi breakthrough. On the other hand, for a high arrival rate of exogenous signals, the firms will wait for the good news and only sell after the realization of the state. The concave adoption curves generated in perfect good news are con- sistent with those in marketing literature. In the second chapter, I investigate the prices and consumer switching when switching costs are consumers' private information, but firms can observe consumers' purchase histories. There are two types of equilibrium: poaching equilibrium and non-poaching equilibrium. In a poaching equilibrium, firms will first offer different prices to separate two types of consumers by pur- chase history and then exploit the two types separately. In a non-poaching equilibrium, firms will keep all their current consumers and charge them low- switching-cost consumers' prices until the end of the game. Compared with myopic consumers, forward-looking high-switching-cost consumers will con- sider future high prices when they choose to stay and thus require better prices. Firms will require a more substantial proportion of high-switching-cost consumers to sustain a poaching equilibrium, which improves the efficiency of equilibrium. When consumers' switching costs can randomly change from period to period, firms will be less willing to pursue poaching equilibrium. In the third chapter, I investigate how the inflow of low-skilled immi- grants affects the household decisions: the divorce decision, the fertility deci- sion, and who marries whom. I firstly specify an equilibrium model of match- ing, fertility decision, and divorce decision over the life cycle. Compared the equilibrium outcomes with and without low-skilled immigrants, I find that with vii low-skilled immigrants providing household production: (1) marriage market is more positive assortative; (2) couples both with high-education are more likely to have children; (3) couples both with high-education are less likely to get divorced. In the empirical part, I construct an instrumental variable by exploiting the variation in the immigrants' country of origin. I find that the inflow of low-skilled immigrants does not have a significant effect on women's marriage rate, fertility rate, and working decision in general. Still, it increases college-educated women's marriage rate, fertility rate, and labor participation and, at the same time, decreases college-educated women's divorce rate. viii Table of Contents Acknowledgmentsv Abstract vi List of Tables xii List of Figures xiii Chapter 1. Strategic Pricing and Forward-Looking Social Learn- ing1 1.1 Introduction............................1 1.2 Model...............................8 1.2.1 Players and Payoffs....................8 1.2.2 Learning..........................9 1.2.3 Equilibrium......................... 11 1.3 Equilibrium Analysis....................... 14 1.3.1 Perfect Good News Scenario............... 14 1.4 Extensions............................. 24 1.4.1 Duopoly in Perfect Good News Scenario......... 24 1.4.1.1 Duopoly Pricing Model.............. 25 1.4.1.2 Duopoly Equilibrium Analysis.......... 28 1.5 Conclusion............................. 34 Chapter 2. Strategic Pricing and Switching in Subscription Mar- kets 36 2.1 Introduction............................ 36 2.2 Model............................... 41 2.2.1 Firms............................ 41 2.2.2 Consumers......................... 42 ix 2.2.3 Equilibrium......................... 43 2.3 Equilibrium Analysis....................... 45 2.3.1 Myopic Consumers..................... 45 2.3.2 Forward-looking Consumers................ 49 2.3.3 Equilibrium Efficiency................... 52 2.3.4 Changing Switching Costs................. 55 2.4 Conclusion............................. 58 Chapter 3. The Impact of Low-skilled Immigration onCollege- educated Women 60 3.1 Introduction............................ 60 3.2 Model............................... 64 3.2.1 Divorce Decision Stage.................. 66 3.2.2 Fertility Stage....................... 68 3.2.3 Matching Stage....................... 69 3.3 Model Predictions......................... 71 3.3.1 Without Low-income Immigrants............. 72 3.3.2 With Low-income Immigrants............... 75 3.4 Reduced-form Evidence...................... 77 3.4.1 Constructing Instruments................. 77 3.4.2 First Stage......................... 78 3.4.3 General Effects on Women................ 79 3.4.4 Effects on College-Educated Women........... 82 3.5 Conclusion............................. 85 Appendices 87 Appendix A. Appendix for Chapter 1 88 A.1 Proof of Lemma 1......................... 88 A.2 Proof of Lemma 2......................... 91 A.3 Proof of Lemma 3......................... 92 x Appendix B. Appendix for Chapter 2 97 B.1 Proof of Proposition 1....................... 97 B.2 Proof of Proposition 2....................... 99 B.3 Proof of Proposition 6....................... 101 Appendix C. Appendix for Chapter 3 104 C.1 Calculation of the Model..................... 104 C.1.1 T=2............................. 104 C.1.2 T=1............................. 107 C.1.3 T=0............................. 109 C.2 Equilibrium Without Low-skilled Immigrants.......... 110 C.3 Equilibrium With Low-skilled Immigrants............ 113 Bibliography 120 xi List of Tables 2.1 Equilibrium Path with Myopic Consumers........ 47 2.2 Equilibrium Path with Forward-looking Consumers.... 51 3.1 The Effect of Predicted Actual Low-skilled Immigration Flows on Women................... 80 3.2 The Effect of Predicted Actual Low-skilled Immigrants on College-educated Women................ 83 C.1 List of Cities Included in the Sample.......... 116 C.2 Predicted Low-skilled Immigration In Selected Cities... 117 xii List of Figures 1.1 Belief, Price and Adoption Curve under PGN With Large " . 17 1.2 Belief and Price under PGN Without Signal.......... 18 1.3 Adoption Curves under PGN With Small " ........... 22 1.4 Beliefs and Price in Duopoly under PGN With Small " .... 32 2.1 Comparison of Myopic and Forward-looking Consumers.... 53 3.1 The life cycle of individuals................... 65 C.1 Divorce Rate of Couples Without Low-skilled Immigrants... 112 C.2 Fertility Rate of Couples Without Low-skilled Immigrants.. 112 C.3 Expected Utility of Men Without Low-skilled Immigrants... 112 C.4 Expected Utility of Women Without Low-skilled Immigrants. 113 C.5 Divorce Rate of Couples With Low-skilled Immigrants.... 115 C.6 Fertility Rate of Couples With Low-skilled Immigrants.... 115 C.7 Expected Utility of Men With Low-skilled Immigrants.... 115 C.8 Expected Utility of Women With Low-skilled Immigrants... 116 C.9 Predicted Low-skilled Immigrants................ 118 C.10 The Relationship of Predicted and Actual Numbers
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