APPENDIX TO CHAPTER NINE / Mathematical Analyses of Most Efficient Social Mix with Different Neighborhood Externality Effects

This chapter summarizes the major themes of the book, which has aimed to enhance our understanding of the mutually causal roles in which our neighborhoods and we are intertwined. On the one hand, we make our neighborhoods. We as residential developers and property owners invest the resources to build, maintain and modify dwellings and their supportive infrastructure. Collectively, our neighbors and we tautologically constitute the profile of residents in our neighborhood. Finally, we make our neighborhoods through the local social interactions in which we engage. On the other hand, neighborhoods start to make us once we occupy them. They influence our physical and mental health by shaping our exposures to pollutants and violence and our accessibility to health care services. They influence our attitudes, especially our satisfaction with the quality of our lives. They influence the information we receive about the world, and how we interpret, evaluate and respond to it. They influence when we move and which neighborhood we will move to next. They influence our major life decisions that shape our education, fertility, work, and legal and illegal activities. Unfortunately, the market forces that drive neighborhood dynamics are inefficient and inequitable from a societal perspective.