Tag: Vector Calculus

Has the number of business establishments in Minneapolis increased since 2006?

Analyzing data always provides interesting insights. For example, a simple analysis of establishment (business) data from the Minnesota Department of Employment and Economic Development (DEED) reveals some fascinating insights into the systems dynamics – a system changing over time – of the Minneapolis marketplace with respect to business firms.

As the data, Graph 1, reveals, the number of establishments, or businesses, in Minneapolis has been decreasing for at least the past 10 years. Why is this so? This blog will not venture into such speculation. This is because the system’s perspective is limited to only establishment data. A multivariate perspective (multiple perspectives) is needed to find such possible reasons.

 

Graph 1

As Graph 1 illustrates, the number of firms per quarter has been decreasing since at least 2006. And although this rate has been variable, which is to be expected because the marketplace is probabilistic, the overall trend has been negative.

Furthermore, this overall negative trend can be shown in a couple of different ways. First, it can be illustrated via linearization. As Graph 2 shows, the overall trend is negative. That is, the Minneapolis marketplace decreased in the total number of establishments between the 1st Quarter of 2006 and the 3rd Quarter of 2016.

Graph 2

It should be noted that the linearization seen here is not the same linearization as in dynamical systems. In dynamical systems, linearization is an approximation “to a function at a given point.” Obviously this is not the case here.

Again, the main idea to take away from linearization, in the way it is used here, is the overall trend of the graph – did the marketplace gain businesses over the period stated in Graph 2, did the marketplace lose businesses over the period stated in Graph 2, or did the marketplace remain about the same over the period stated in Graph 2?

And finally, the marketplace behavior of business establishments in Minneapolis can be illustrated through Vector Algebra. Yes! That’s right – Vector Algebra. In this case, there will be no math included, just an illustration of direction via Graph 3, so there is no reason to be alarmed.

Graph 3

As Graph 3 shows, the overall dynamics, or vector, of the marketplace is negative in regards to the number of establishments from the 1st Quarter of 2006 through the 3rd Quarter of 2016. And the vectors, those letter “a’s” with the hats over them, further illustrate a greater decrease in total establishment between the 1st Quarter of 2006 and the 3rd Quarter of 2010 than between the 3rd Quarter of 2010 and the 3rd Quarter of 2016.

Of course, these vectors could further be broken into smaller vectors. But the way the algebra works, each vector that is computed in this system should add up to the overall vector, which is negative. Thus, this decomposition of the system behavior provides a more conclusive way of viewing the dynamics of this particular system than how linearization is being used here. And the vector idea, along with the math, supports the initial observation. That is, the total number of establishments in the Minneapolis marketplace has decreased since at least the 1st Quarter of 2006.

So how does this market behavior compare to the county or state level? How does Minneapolis compare to the zip codes that reside within it?

And another interesting question to ask one’s self is, has employment increased, decreased, or stayed the same in Minneapolis? And what does this mean for the number of employees per establishment?

 

Matt Johnson is a writer for the Urban Dynamics blog; and is a mathematical scientist. He has also contributed to the Iowa State Daily and Our Black News.

You can connect with him directly in the comments section, and follow him on LinkedIn or Facebook

Photo credit: The Systems Scientist

 

 

 

 

 

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