In the market of higher education, buyers are students who can buy only one unit of the good, a college education, but we change the rules so that sellers have multiple units of their good. Buyers’ valuations on each seller’s good may be modeled as how much each buyer could and would be willing to pay for a unit of each seller’s good. We disregard in this example the probability of being accepted into the school, putting all buyers on the same level, but with individual valuations on the goods. Each person belongs to this network, having at some time been in the position of the buyer.

In this article, Brandeis professor of social and economic policy, Robert Reich, writes about the flaws of higher education in America, and how it is a market changing for the worse. In the past decade, the percentage of students of low-income families that attend college has been decreasing. Financial aid now covers a much smaller percentage of tuition costs compared to earlier generations. Using the market system described before, this fact can account for the reason why buyers today from lower income families will have lower valuations on the goods, because they will not be able to pay as much to go to the university. Performing an auction procedure on the higher education market, it’s clear that students who come from high-income families will receive admission to their choice schools, which are often private, more renowned universities. Assuming that there are enough schools so that every student can potentially have a higher education, there should be a matching in a bipartite graph, and theoretically, a set of market-clearing prices from a perfect matching in a preferred-seller graph. However, because of the wide differences in the buyers’ valuations, which correlate to family income, it is likely that the payoffs for some students will become negative or that there will be an unreasonably large gap in the final prices. In the market-clearing auction procedure, only the goods of the sellers in the neighboring set of the constricted set of buyers is raised. However, prices are increasing for all universities, private or state-funded. As a result, buyers from low-income families often cannot afford to go to college at all.

Reich also observes that the goal of higher education has shifted from public good of society to the advancement of the individual’s ambitions. So it may be that there is social-welfare maximization with regards to the valuations that directly correlate to income, but it should be that valuations should be closer. As it is now, the valuation a higher income buyer may have for a good they might not even want is often still higher than the valuation a low-income buyer has for their first choice of good. The way the system is set up makes it harder and harder for the low-income buyers to have goods they really want. Therefore, in the higher education, there is rarely a baseline-maximizing perfect matching. Many low-income students are left not well off, and while higher education is becoming like an industry catered to specific individuals who are allowed to get more out of what society has to sell, others are made to settle for less.

Of course these flaws in the higher education system extend way beyond that which can be accounted to the changing market and the simple theory behind it. But perhaps in the future, we will be able to see changes in this market that influence social-welfare maximizing on a more human level.