Housing in Ithaca
I am currently looking for housing for next year, which means I am a part of the bipartite graph between renters and apartments in Ithaca. In theory, there is a perfect matching in this graph, because we can keep expanding our set of apartments by increasing the acceptable distance from the school (since the global housing market is much bigger than the number of Cornell students looking for housing) until there is a place for every student to live. If we assume that every student is willing to take any apartment because it is better than being homeless, then a perfect matching is any set of edges where every node has 1 edge. In reality, though, students do not want a tiny, dingy, expensive, far apartment. This results in a struggle for affordable housing. As the article explains, the pursuit of maximized income by the buyers results in a struggle for affordable housing and a wide disparity between buyers.
Unfortunately, Cornell students in this market are at a disadvantage because there are so many of us, and most of us need to be within walking distance to classes, which severely limits our options. Sellers know this and therefore charge incredibly high prices, going up to $2500/person. If everyone refused to take an apartment more than 10 minutes from classes, we would have a constricted set, simply because the amount of students outnumbers the amount of apartments. As the article says, high demand and low supply leads to increased prices. Additionally, people hold different values for each apartment, making finding a preferred seller graph much harder. If every apartment was $1, there would definitely be a constricted set between many buyers and the nicest, closest apartment. To fix this problem, the apartments in constricted sets raise their rent. While this isn’t an auction, apartments do raise their rent every year for the same reasons an auctioneer does: they want more money and they know there will still be someone willing to pay.
Since the real situation involves buyers with different valuations for each apartment (some might prioritize location over size and vice versa), we need to consider what would be a “good” outcome. Is the goal to maximize social welfare, maximize the baseline, or minimize the disparity? If the market was left alone, it would naturally cater to the rich, because they have so much more money to spend. Because the disparity between the rich and poor is so large, this results in increased social welfare but also a large disparity, with some people getting a baseline close to 0. Programs mentioned in the article, like the Federal Low Income Housing Tax Credit and the, provide subsidies to decrease disparity, while infill housing maximizes the baseline by providing more housing options, which resolves some constricted sets. At the end of the day, most students will find somewhere to live, but interventions like these are necessary so that the market doesn’t continue to excessively cater to the rich.
https://www.ithaca.com/news/ithaca/the-struggle-of-affordable-housing-in-ithaca/article_5e2fb1cc-6b2d-11eb-b9fd-73f8a4787ba9.html