Ithaca Apartments are Matching Markets
It is currently leasing season in Ithaca and people are looking to secure places in Collegetown that are cheaper and more desirable before they sell out. Some students even spent an entire evening outside of the leasing office to secure a lease. Honestly, I was quite shocked when I heard that people camped out overnight, but this makes sense if we think about it from a matching markets and perfect matching perspective. Apartments are an example of matching markets. People desire a certain price, number of bedrooms, and number of bathrooms in their apartments and sign leases for apartments that match their specific preferences. However, in reality this is slightly more complicated because people would normally rather pay less if they can and are willing to sacrifice certain preferences in order to do so. Also, signing a lease is “first come, first serve.” To make things easier to explain though, let’s suppose that there are no ordering of preferences, in which people are assigned to an apartment based off of their preferences instead of the order of people who claim the apartments. Also, let’s suppose pricing is not involved.
There are obviously a limited number of apartments and as the article implied, the number of people who want specific apartments in Collegetown is higher than the number of those desired apartments. This article shows that the people who desire a specific apartment are a constricted set and thus there are no perfect matches between people who desire apartments and the desired apartments. We can demonstrate this with a bipartite graph.
Here, S= {A,B,D} is the constricted set of nodes in this example. D only wants a 1 bedroom and 1 bathroom at location A. If D is assigned the 1 bed 1 bathroom, then A and B are both only left with 2 bedroom and 2 bathroom at location A. The set of apartments {2 bed 2 bath location A, 1 bed 1 bath location A} has fewer nodes than the number of nodes in S. When we bring the example back to the article, the number of desired specific apartments are less than the number of people who desire those apartments, thus making the people who desire specific apartments a constricted set. When the demand of an apartment exceeds the number of apartments, there are no perfect matches. So, in the situation highlighted in this article, there are no perfect matches between the desired apartments and the people who desire those apartments. Due to the fact that there are no perfect matches, people are forced to wait in line early, even camp out overnight, in order to sign a lease for their desired apartment.