Tag: Economic Systems

Distinguishing between sets and systems through mathematics, economics, and chemistry

A set with objects

So far, we’ve presented the (3) systems’ axioms and the notions of system’s behavior and system’s boundary. We have also explored these ideas via different examples. And we’ve touched on the idea of a set. However, we now want to differentiate between what a set is and what a system is. Once we show the difference between the two, then we will be able to demonstrate the difference between a subset and a subsystem. And most importantly, we will be able to better observe, analyze, and make sense of different kinds of systems, albeit economic systems, political systems, or political systems.

So how can we differentiate between a set and a system? First, we can address this question by referencing back to the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.
Set A is a subset of set B

The difference between a set and a system is that a set satisfies the first axiom; whereas, a system satisfies all three axioms. More specifically, a set B is a collection of well-defined objects (we will use Naive Set Theory for now), for instance B = {2,4,6,8,10}. Further more, the elements in this set interact with each other. For example, the element ‘2’ interacts with element ‘8,’ or element ‘4’ interacts with element ’10,’ or some combination of possible interaction. And finally, there is a function that is produced, or purpose, via the interactions.

As we can see, a set satisfies the first axiom; whereas, a system satisfies all three axioms. Now we have the tools to delve into the subsets and subsystems. We will see that subsets satisfy the first axiom while subsystems satisfy all three axioms.

As stated before, a set B is a collection of well-defined objects, for instance B = {2,4,6,8,10}. However, a subset of B can be partitioned and observed. For instance, a subset A is a subset of set B if all of the elements in the set A are contained in the set B. That is, A = {2,4,6} so since all of the elements in the set A are contained in  the set B, the set A = {2,4,6} is a subset of set B = {2,4,6,8,10}.

Thus, this subset or any combination of subsets with any of the five elements – 2,4,6,8,10 – satisfies the first system’s axiom.

To illustrate the second axiom with respect to a subsystem, we want to show that if elements interact in a subsystem, then they interact in a parent system. There are a few ways we can do this. For this article, we can do this by observing the interactions in set A = {2,4,6}. Thus if ‘2’ interacts with ‘4’ and ‘6,’ and ‘4’ interacts with ‘6’ in set A, then these elements also interact in set B because set A = {2, 4, 6} is a subset of set B = {2, 4, 6, 8, 10} because set A is contained in set B.

The final step is to show that a subsystem has a function, or purpose. It could be the case that a subsystem has the same function as its parent system, or it could be the case that it has a function different from its parent system. But either way, it ought to have a function no matter if it is the same or different from its parent system. So how can this be illustrated?

Example 1

As Donella Meadows conveyed in her book Thinking in Systems: A Primer identifying the function of a system can sometimes be difficult. Indeed, there are instances where the function or a system is fairly obvious.

One way this can be done is by mapping the elements in set B to the elements in set A. In other words, the elements in set B will go to the elements in set A.

The sketch in Example 1 illustrates this point. For instance, 1 goes to 3, and 2 also goes to 3; 4 goes to 7; and 5 goes to 8.

And so something is imputed through 1, 2, 4, and 5, and something is outputted through 3, 7, and 8. This means the elements in set B = {1, 2, 4, 5} would be the inputs of the system and the elements in set A = {3, 7, 8} would be the outputs.

To illustrate this point further, one could view a system that includes labor and wages as the elements. That is, a person exchanges their labor, hours worked, for a wage. If, for example, the wage was set at $30 per hour, then a person would obviously make more for every hour worked as Graph 1 shows.

That is, if 5 hours are imputed into the system, then $150 will be outputted from the system; if 6 hours are imputed into the system, then $180 will be outputted from the system; and if 7 hours are imputed into the system, then $210 will be outputted from the system. And of course this game could be played over and over again. Thus, as the number of hours imputed into the system increases, the number of dollars outputted from the system increases.

Example 1

Another demonstration of a function can be illustrated through an interaction between an oxygen molecule, O2, and two hydrogen molecules, 2H2. If a gaseous oxygen molecule interacts with two gaseous hydrogen molecules at a high temperature, these molecules are known as the reactants in chemistry, then two gaseous H2O molecules, known as the products in chemistry, will be produced. In other words, if one gaseous oxygen molecule and a two gaseous hydrogen molecules are imputed into a system, then the system will output two gaseous H2O molecules as Example 2 demonstrates.

Example 2

These systems’ functions and purposes are obviously not what we often think of as a function or purpose of a system. They are in one instance somewhat familiar and in another instance esoteric.

In this article, we have used mathematics along with a couple of examples from economics and chemistry to distinguish the difference between a set and a system. Moving forward, we will be able to continue building off of these axioms, notions, and examples as we begin to apply these ideas to more familiar systems such as economic systems, political systems, and social systems.

Let us now, as we have done before, attempt to disprove our notions and work in the tradition of natural philosophy until the next blog.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News.

Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. He is also a professional member of the Society of Industrial and Applied Mathematics and the International Society for the Systems Sciences and a scholarly member of Omicron Delta Epsilon, which is an International Honors Society for Economics. 

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

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: Pixabay

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

The Bright Side of the Blight Side of Minneapolis

As we know, the 55411 zip code, which is in Minneapolis’ 5th Ward on the north side of the city, has the most depressed economic system in Minneapolis. It has the highest concentration of condemned and vacant buildings; it has the second highest concentration of foreclosures (the 4th Ward has the most); it has the highest unemployment rate in the city; and it has the second highest crime density in the city (the 3rd Ward has the highest).

But we also know from our previous articles that the 55411 zip code is a subsystem of the Minneapolis system. This means that the 55411 satisfies the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.

It has a system’s boundary and behavior (how a system’s performance changes over time) for which condemned and vacant buildings, foreclosures, the unemployment rate, and crime are all examples of in this economic system. But how does the systems’ behaviors of educational attainment of the 55411 zip code compare to the educational attainment of Minneapolis?

Do the residents of the 55411 experience greater earnings with greater attainment of education? Is it the case that a person from the north side zip code would earn more with a college degree than a person from the north side without a college degree? Is there a correlation between education and earnings in the 55411 zip code?

Graph 1

As Graph 1 of the Minneapolis system illustrates, there is an obvious increase in wages as a person’s education increases. That is, the odds are good that a person with a high school diploma will make more than a person with less than a high school education; a person with some college will more than likely make more than a person with a high school education; a person with a college degree will more than likely make more than a person without a college degree; and a person with a graduate level education will more than likely make more than a person with only a college degree.

And so the question is, will the 55411 zip code follow this system’s behavior? Indeed it will.

Graph 2

Considering the sensitivity of the marketplace on the north side, this is really remarkable. And despite the number of adverse economic conditions in the 55411 zip code, education is still a game changer. The question is now, would this behavior remain stable during a great recession just like a few years ago? And would Minneapolis policy makers utilize this data?

Indeed there are obvious differences in earnings from educational attainment between the 55411 and Minneapolis. But the fact remains, this is a bright side to blight side of Minneapolis.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News. Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. 

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

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: army.mil

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

Minneapolis: How do we partition a city into sub-systems?

By Matt Johnson

So far we’ve established the (3) systems’ axioms; we’ve touched on the notion of systems’ boundaries by using examples of cities; and we’ve established what a system’s behavior is by analyzing the labor force, average weekly wages, and unemployment rate of Minneapolis. Today, we are going to begin to partition the Minneapolis system into its respective subsystems and we are going to do it by ward.

In the next blog, we will decompose Minneapolis by zip-code. And in a future article, we will decompose Minneapolis’ wards into their respective subsystems – neighborhoods – which will introduce us to the notion of systems’ levels.

Minneapolis is a city with 413,651 residents as of July 1, 2016 according to the U.S. Census Bureau. Furthermore, those 413,651 residents obviously live in different parts of the city. Those parts of the city are called wards and Minneapolis has 13 Wards. According to Minneapolis City Government data, each ward contains about 32,000 residents, which of course varies every few years.

This means that each ward in Minneapolis contains about 32,000 residents; those residents interact with each other; and each ward has a function, which in this case is to provide political opportunity in voting and representation, and allocation of resources.

Thus, we have just shown that all 13 wards in Minneapolis satisfy the (3) systems’ axioms:

  1. A system consists of a set of elements.
  2. Elements in a system interact.
  3. A system has a function, or purpose.

Besides illustrating that these 13 wards are systems, we have also established that these wards are themselves subsystems of the general system of Minneapolis. This is because we have shown they satisfy the systems’ axioms, they are contained within Minneapolis, and they have established boundaries, i.e., political boundaries.

And this is a great place for us to dig a little deeper into the notion of boundary. Boundaries can be fuzzy or concrete; and boundaries can be regular or irregular. In the case of political boundaries, which are the wards we are observing, they are concrete and irregular. If we look at any of the 13 wards in Minneapolis, we can observe that the boundaries of the wards are well-defined, i.e., concrete. And we know this is because of the Minneapolis City Charter. But we can also observe that these boundaries are irregular. That is, they are not squares, rectangles, triangles, or circles.

In this short blog, we established that these 13 wards are subsystems of Minneapolis. We also established, with the help of the map, that the boundaries of these wards are concrete and irregular. As we keep moving forward, we will see that our new-found knowledge of systems will pay dividends when we begin to compare and contrast the different wards, neighborhoods, zip-codes, and other Minneapolis subsystems. And we will do this by adding a new tool to our systems’ took-kit – systems dynamics.

Let us now, as we have done before, attempt to disprove our systems’ notions and work in the tradition of natural philosophy until the next blog.

 

Matt Johnson is a blogger/writer for The Systems Scientist and the Urban Dynamics blog. He has also contributed to the Iowa State Daily and Our Black News. Matt has a Bachelor of Science in Systems Science, with focuses in applied mathematics and economic systems, from Iowa State University. 

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

You can also follow The Systems Scientist on Twitter or Facebook.

 

Photo Credit: The Systems Scientist

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

 

A quick view of an economic system

By Matt Johnson

In this short blog, I will illustrate one way an urban dynamicist, i.e., systems scientist, looks at an economic system and its data.

Diagram 1

Diagram 1 is hierarchical, derives from the U.S. Census Bureau, and represents a few of the many levels of an economic system. Moreover, each level of the economic system in Diagram 1 is further a sub-system, or sub-economy, of the general United States economy.

This means that a zip code, for example, can be examined as an economic system, and then it can be compared and contrasted with a city’s economic system. And this examination will illustrate similarities and differences between a sub-system, a zip code, and a general system, a city, for instance.

Thus, an urban dynamicist can partition out each level of the economic system and analyze each level as a distinct entity, although one system is still a sub-system of the one superior to it in the hierarchy. Within each level, differences, relationships, perspectives, dynamics, and models can be examined through data.

As stated before, each level of the system can be analyzed against the other levels of the system through data, because data provides a picture at each level of the system. For example, the State can be illustrated and compared to the Division, Zip Code, or Census Tract via crime densities, demographic comparisons and migration patterns, and economic variables such as median household incomes, unemployment rates, the labor force and labor participation rates.

Here is the stochastic (probabilistic) behavior of the labor force in Minneapolis over the past 10 years as seen here in Graph 1.

Graph 1

And here is the stochastic (probabilistic) behavior of the Minnesota labor force over the past 10 years as illustrated in Graph 2.

Future articles will delve deeper into the specifics of the behavior and dynamics of these two systems and their respective data sets. For now, the main point is that data can provide a picture of the economic systems at their respective levels of the system.

One last thought, Diagram 1 does not illustrate the interactions or dynamics that take place within each level of the system by itself, nor does it account for a lot of things. This is why the data is needed. So assumptions and conclusions should be limited.

As this focus on data continues, I will be utilizing the hierarchical model and other systems models to help illustrate and explain how economic systems can be better understood. In addition, I will be using systems theory along with applied mathematics to explore the complexity of systems. But I will also be working diligently and meticulously to convey this information to you the best I can.

As I get better at explaining this stuff to you, I hope your knowledge of systems, mathematics, and economics increases as well.

 

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 Facebook

Photo credit: Pixabay

 

 

 

 

 

Copyright ©2017 – The Systems Scientist

 

 

Minimum wage increases in 12 states as of January 1, 2017

By Matt Johnson

According to the National Conference of State Legislatures, 12 states raised their minimum wage as of January 1st. New York increased its minimum wage by $2, which was the most of the 12 states. And Arizona increased its minimum wage by $1.95, which was the second most of the 12 states.

Who will benefit from these minimum wage increases? This question may not be so obvious.

State Minimum Wage as of 12/31/16  Minimum Wage as of 1/1/17
Arizona $8.05 $10.00
Arkansas $8.00 $8.50
California $10.00 $10.50
Colorado $8.31 $9.30
Connecticut $9.60 $10.10
Hawaii $8.50 $9.25
Maine $7.50 $9.00
Massachusetts $10.00 $11.00
Michigan $8.50 $8.90
New York $9.00 $11.00 (Increased on 12/31/16)
Vermont $9.60 $10.00
Washington $9.47 $11.00

 
Nationally, odds are a minimum wage employee is white, female, between the ages of 16 to 24, and works part-time. As the Bureau of Labor Statistics and Pew Research report, minimum wage workers are

Disproportionately young: 50.4% are ages 16 to 24; 24% are teenagers (ages 16 to 19)…Mostly (77%) white; nearly half are white women…Largely part-time workers (64% of the total).

Something to keep in mind. Raising the minimum wage doesn’t address unemployment amongst black Americans or other non-whites (with the exception of Asians; very few participate in minimum wage jobs); it doesn’t address their participation rate in the market place; and it certainly doesn’t address black business, which doesn’t even have the economic horsepower to compete with white business. So what do these new minimum wage laws address?

If these 12 states follow national trends, then these new laws will address lower wages amongst new white workers entering the labor force.

Attention all white teenage girls and women between the ages of 16 and 24 who are working a minimum wage job! Rejoice! Your wages have just gone up.

 

Matt Johnson is a writer for The Systems Scientist and 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 Twitter or on Facebook

You can also follow The Systems Scientist on Twitter or Facebook as well. 

Photo credit: Fibonacci Blue

 

 

 

 

Copyright ©2016 – The Systems Scientist

Minneapolis Trends Update: The Good, the Bad, and the Ugly

“Foreclosures also increased in the 4th and 5th Wards by about 24 and 25 percent, respectively.”

By Matt Johnson, The Systems Scientist

The Minneapolis Trends: A Quarterly Overview of Socioeconomic & Housing Trends in Minneapolis (MT) released its 2015 4th Quarter findings today. For those not familiar, the Minneapolis Trends is released quarterly by the CPED (Community Planning & Economic Development) which is a city department that comprises four divisions:

  1. Long Range Planning,
  2. Housing Development and Policy,
  3. Economic Development and Policy,
  4. and Development Services.

Every quarter, MT releases its approximately 45 page report. In this report, the MT provides data on employment, labor force, number and percent of foreclosures, wages, construction and demolitions, and other economic and housing information.

Figure 1
Figure 1

Here are some highlights of the 4th quarter report and some differences from the 3rd quarter report:

Good News:

  1. Unemployment dropped from 3.5 percent in the 3rd quarter of 2015 to 2.8 percent in the 4th quarter of 2015. Minneapolis should retain its top position for unemployment for the 50 largest cities in the United States.
  2. The average number of jobs increased from 309,091 in the 1st quarter of 2015 to 317,086 in the 2nd quarter of 2015. Obviously that’s a nice little increase in job availability. Note, this economic category is behind by two quarters. In other words, there are no 3rd or 4th quarter numbers yet.
  3. Average weekly wages in Minneapolis are still higher than the Metro average weekly wages or the Minnesota average weekly wages, see Figure 1. The following numbers are for the 2nd quarter 2015:
    1. Minneapolis Average Weekly Wages: $1,255
    2. Metro Average Weekly Wages: $1,098
    3. Minnesota Average Weekly Wages: $977

Bad News:

  1. Foreclosures increased across the city by about 24 percent. There were 101 foreclosures in the 3rd quarter of 2015. However, that number increased to 125 in the 4th quarter of 2015.
  2. The number of condemned and vacant buildings (CVBs) also increased from the 3rd quarter to the 4th quarter of 2015. However, this was a very slight increase from 531 to 535. That’s about 0.8 percent. But there were still 535 CVBs in the 4th quarter of 2015.
  3. Average weekly wages dropped on average across all industries from $1,445 to $1,255. However, it should be noted that average weekly wages have been steadily increasing in Minneapolis since 2006. So although average weekly wages dropped from 1st quarter of 2015 to the 2nd quarter of 2015 (this category is two quarters behind in data), the trend is still positive. See Figure 1.

Ugly News:

  1. Foreclosures also increased in the 4th and 5th Wards by about 24 and 25 percent, respectively. In addition, foreclosures are mostly clustered and centered in the southern part of the 4th ward and the northern part of the 5th Ward.
  2. A vast majority of the CVBs were clustered in the 4th and 5th Wards in North Minneapolis. Again, CVBs, the same as foreclosures, tend to be clustered and centered in the southern part of the 4th Ward and the northern part of the 5th Ward.
  3. Unfortunately, the Minneapolis Trends Report does not distinguish the average weekly wages between the city of Minneapolis and its respective wards. However, utilizing a little bit of deductive logic and knowledge from past articles (education and unemployment levels), then it ought to make sense to assume that the average weekly wages in some parts of North Minneapolis would be lower than the rest of Minneapolis. However, data would confirm or deny this assumption.

There is obviously a lot more data and information in this most recent Minneapolis Trends report to explore and analyze. As the readers of this blog understand very well, the data and information will be optimized for systems analyses of Urban Dynamics in forthcoming articles along with lots and lots of questions.

**Remember, there is nothing more American than discourse. You are always welcome to post your comments, thoughts, and questions below. Feedback is always appreciated!

Economies, Policies, and Systems

Author’s Note: 

As a scientist, and someone who studies systems, it is not my job to take a political side. Sure, I have my own political and social views. However, as a systems scientist, it is imperative for me to consider the perspective of “the other” in all forms, i.e., economic, political, social, ecological, etc… And I must stress, the questions I pose in this article are but just the beginning of the exploration into the science. Even if my scientific findings suggest disagreement with proposed arguments and policies by policy makers, I still know that the intentions from those who originally proposed such ideas came from a place of empathy and solidarity with those who struggle economically, politically, and socially. 

By Matt Johnson, The Systems Scientist

Policies can affect a city and its inhabitants in different ways. Some of these effects can be positive; some of these effects can be negative; some of the these effects can have no affect at all; and some of these effects can affect a city in a variety of positive and negative ways and combinations. In other words, where a policy, or policies, can change one part of the city in a positive way, it can change another part of the city in a negative way.

Table 1
Table 1

This is important to keep in mind because as this author has demonstrated in previous articles, depressed areas of Minneapolis tend to be more sensitive to systems’ fluctuations than non-depressed areas of Minneapolis. And there are a variety of reasons for why this may be. However, it should be recognized that when it comes to systems, the why is very difficult to ascertain, but some information and knowledge can still be gained.

Since its peak in 2008, the number of foreclosures has been decreasing rather steadily with the exception of a hiccup here and there, according to Table 1. This clearly illustrates a positive behavior for the general system. Taken together with the decreasing unemployment rate, the increase of more than 22 thousand jobs in Minneapolis since 2012, the increase in the number of employed since 2012, the steady increase in weekly wages since 2006, and the decreasing numbers of foreclosures and condemned and vacant buildings over the past 8 years, Minneapolis is showing some economic power, vitality, and stability. However, where some of Minneapolis’ sub-systems (Wards) aren’t necessarily affected or dependent on market fluctuations, other sub-systems are, at least that’s the thinking.

As Table 2 suggests, the 4th and 5th Wards are highly sensitive to market forces; whereas, the 2nd Ward, as can be seen, is not, at least with respect to foreclosures. Why might this be? Well that’s the question.

But here’s an observation from the data. While those on the north side were wrestling with the great recession, it appears that the 2nd Ward was on economic cruise control, although one variable doesn’t tell the entire story. Not even close.

Figure 1
Table 2

Systems are complex entities. In the case of a city like Minneapolis, the general system is composed of an economic system, a political system, and a social system. These systems are further intertwined with the ecological system of Minneapolis, and with each policy implemented, it could have a positive or negative effect, or no effect at all. So the question becomes, should policy makers in Minneapolis be implementing general policies to the entire system? Or should they be focusing on sub-systems within Minneapolis?

As an example, would it make sense to legislate rent control for the entire city of Minneapolis when wages have been steadily increasing and the labor force has been increasing? Would it make sense for policy makers to legislate a $15 minimum wage when wages have been steadily increasing and the labor force has been increasing? And if these policies were implemented to the system, how would the system react? Would the respective sub-systems illustrate similar behavior to that of the foreclosure behavior?

Or would it make more sense to focus in on those depressed areas of Minneapolis and their respective sub-systems? Would it make sense to pass policy that addresses the economic turbulence that those in North Minneapolis, for example, have been experiencing for the past few decades? Wouldn’t development from within be a more viable policy rather than attempting to penetrate the entire system with policies that may or may not be necessary, or that would perpetuate adverse effects?

These questions of course beg more questions, which they ought to. That’s the beauty of science and scientific analysis. If curiosity, exploration, discovery, and patience are emphasized and accepted, then time, data, policies, research, and the scientific method will eventually answer these questions, tell the story, and provide guidance on urban policy.

For further exploration of this subject, please feel free to explore Analyzing a Crime Pattern of a General System and Patterns of the 5th Ward: Unemployment.

**Remember, there is nothing more American than discourse. You are always welcome to post your comments, thoughts, and questions below. Feedback is always appreciated!