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The Job Market: Unemployment and Bipartite Graphs

Ever since the economic crisis that hit the U.S. with full force in 2007 we have been on a road to recovery that still has a long way to go.  The job market is one aspect of the economic downturn that has, and continues to affect millions of Americans.  Although times seem to be improving, unemployment remains an issue that plagues the U.S.  The unemployment rate was around 10% a couple of years ago and now hovers around 9.1%.  The job market is only supposed to become more competitive so it may be even more difficult for people to get jobs, ultimately prolonging the recession that we are in.

http://www.popeconomics.com/2011/01/05/2011s-job-market-the-separation-of-the-haves-and-have-nots/

The link provided is an article titled “2011′s job market: The separation of the haves and have nots.”  The article begins by talking about how there are going to be job openings for the public; however, these occupational spots are for people like software engineers, a job that entails training and specific knowledge.  This is a problem for the majority of Americans, not because they don’t have the intellectual capacity, but rather because most Americans do not have the resources (money) needed to receive the proper training to become qualified in such a position.  The article goes on to say how attending college is essential as it will open up doors to many job opportunities that would have been closed otherwise.  Around 60% of students attend college in order to extend their education and earn a degree while the other 40% is left to enter the job market and often work multiple jobs to make ends meet. Also, many employers choose their employees by seeing if they have a college degree, resulting in a very selective job market and excluding people from the workforce.

The concept of unemployment in the job market is very applicable to bipartite graphs. Bipartite graphs have two categories where matching between the groupings occurs.  An example of a bipartite graph is drawn below:

Screen Shot 2011-09-21 at 6.03.22 PM

The set on the left is of jobs (N(S)) while the set on the right is people (S).  A constricted bipartite graph such as the one above shows that there are more nodes in S than there are in N(S).  The jobs that people can do are indicated by the links between the nodes. The graphs that we are often presented with in class are perfect matching; meaning that each node on the right is assigned to a different node on the left, that it has a link to.  In order for a graph to be perfect matching, everyone would receive the job that they can perform.  However, these do not indicate real world examples.  For example the bipartite graph above has a set of jobs A, B, and C, and a set of people X, Y, and Z. We see that people generally have to compete over jobs because the set is constricted.  The less “skilled” jobs such as an assembly line worker is an occupation that most people are capable of performing.  This job is represented by node A. Both X, Y, and Z are qualified for that position, but only Z is qualified for jobs B and C because these positions require a college degree for employment (which Z has).  Person Z would most likely work at either job B or C because there is no competition and the wage will most likely be higher, while only one of X and Y would receive Job A.  Whoever was not hired out of X and Y would be unemployed.

The bipartite graph with a constricted set is a microcosm of the unemployment in the country that we live in.  Multiple people have to compete for the same job leaving someone without work.  Hopefully as time goes on, more jobs will open up and the unemployment rate will decrease.

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