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Savings Account
From SystemsWiki
In this module we will cover the final two modeling elements, Auxiliaries and Links and begin to investigate the basics of structure using a Savings Account model.
Contents |
[edit] Savings Account
Open a new model in MapSys and save it as savact. Note that models are saved with the msys extension.
Add a Stock and name it principal, then add a Flow into principal and name it interest. You should now have a model that looks like Fig. 1.
Notice that you should now have two error messages in the lower Task List window. If this window is not visible please select it from the Window menu. The error messages in this window are simply indicating that equations have not been defined for an item. If you Double-Click on an Error it will highlight the model element that needs to be defined, which is also defined under the Source column in the Task List.
Since you're probably quite familiar with a Savings Account you can tell right away that this sketch doesn't quite describe a Savings Account. What's missing is the interest rate that is applied to the principal periodically to create interest.
Go ahead and add an Auxiliary variable and name it interest rate. Then add the Link connections to create Fig. 2.
You should now have three error messages in the Task List. Not to worry. We'll take care of them shortly.
- MapSys Note:
- Once you create a model item you can click on the text for that item and move it around as needed to make the diagram more readable. MapSys continues to remember which model item it's the text for so if you move the item the text will move along with it.
- The default for loop polarity is +/-, which you can change in File>Global Settings>Causal Loop Diagram>CLD Loop Polarity. I also set the color for the CLD Arrow and CLD Arrow Polarity to Blue so I only have to change the ones I want to be Red, though that's just a personal preference.
Use the Equation Editor and assign the following values to the model elements.
- interest rate = .025
- principal = 100
- interest = principal * interest_rate
Add a Graph Element to the workspace using the Graph Tool. Then open the Graph Editor, select the Variables tab and move interest_rate, interest and principal to the Selected Variables area. Click OK to close the Graph Editor.
[edit] Setup & Simulate the Model
We're almost there. Select Simulation Specs from the Simulation menu and assign the following values:
- starttime = 0
- stoptime = 10
- dt = 1
We're assuming the model will run for 10 years and interest is computed once a year.
When you run the model you should see a graph as in Fig. 3.
MapSys Notes
- There are multiple Y-Axis scales on the graph, each one in the color of the variable they represent.
- Any time you want to make a change to a graph first open the Graph Editor either by double-clicking on the graph or by right-clicking and selecting Edit Graph from the popup menu.
- If you right-click on one of the Y-Axis scales and select Properties... you can edit the various properties of the scale.
At this point you can change values in the model and run the simulation to see how values change.
[edit] Observations and Insights
There are several aspects of the Savings Account structure that are noteworthy:
- Growth: Did you notice as you ran the simulations that principal grows over time? And the larger the interest rate the faster it grows.
- Emergent Properties: If you look at the individual elements of the Savings Account model there are no elements that individually exhibit growth, yet the model taken as a whole exhibits growth. This growth is referred to as an emergent property. Somewhere along the way you've probably heard the saying that, "the whole is greater than the sum of its part", well this is an explicit example.
- Positive Feedback: The reason for the growth is the connection between principal and interest rate producing interest which adds to principal. This link represents what's referred to as positive or reinforcing feedback. Any time an action produces a result which encourages more of the same action you have reinforcing feedback. There is also negative, or balancing, feedback, though not in this model. We'll get to balancing feedback in due course.
- Reinforcing Loop: The Savings Account structure is referred to as a Reinforcing Loop, specifically because it exhibits the emergent property of growth. There is one other basic structure called a Balancing Loop and we'll get to it before too long.
- System Archetype: The Reinforcing Loop is also referred to as a System Archetype. The reason for this is that the Reinforcing Loop is a structure that occurs very frequently across all disciplines of science.
Can you think of instances of Reinforcing Loops you encounter on an ongoing basis, or in the news?
The next module, Savings Account Continued, will cover some additional aspects of the Savings Account you may find most interesting.
[edit] References
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