Environmental Systems

Modelling Assignment: Luckiness of the Commons

A modelling assignment on sensitivity analysis and the tragedy and luckiness of the commons.

Software and data you need for this modelling assignment:

Tasks

For this modelling assignment you have to analyse the importance of initial system conditions for the development of commons over time.

Time has shown that not all commons face the tragedy (see e.g. the publication of Ostrom et al. (1999) to which we will come back in the next session). While certain conditions favor a tragedy or not, sometimes, the commons must just be lucky. The luckiness of the commons is what we want to highlight in this model assignment.

Sensitivity analysis

To define the luckiness of the commons a little more formal we state that the commons are "lucky", if they will not be eroded by ongoing economic exploitation. This means that the natural-economic system stabilizes at some point in time. While more than one factor might determine the luckiness, we focus un the initial values of the stocks. Hence, our hypothesis is the following:

Given a standard model on the tragedy of the commons, some combinations of the initial conditions of the stocks renewable resources and production capital prevent a tragedy.

To verify or falsify the hypothesis, please perform a sensitivity analysis of the initial stock variable conditions of model EZ417.

Please prepare the following for the assignment:
  • Extend your EZ417 model by the respective functionality required to compute a sensitivity analysis of the initial stock values (see tip below).
  • Compute a sufficiently large sensitivity simulation to test the above hypothesis (see settings in the tip below).
  • Visualize the simulation results using a custom graph showing information on the production capital on the X and the renewable resource on the Y axis.
  • Provide an answer for the hypothesis based on the custom graph. If you verify the hypothesis, define a range of "lucky" initial conditions.

Tip for the sensitivity analysis

To analyze the influence of initial conditions of two stocks, one has to define a lower and upper boundary of the initial values for each stock and an increment which defines the amount of change of the initial condition from one run to another.

Changing initial conditions systematically by hand is time consuming. Therefore, we will use model EZ115 from Bossel (2004a) as a template.

Start with copying the EZ115 model into your EZ417 model. Afterwards, adapt the model as described in the info text in model EZ115. In the end, the only change to your original model is, that the stock equations which have the general form

inflow - outflow

are extended to

(inflow - outflow) * limit n + new state n

where n is either 1 or 2 and inflow and outflow are the respective flows of the two stock variables, e.g.
(regeneration-consumption)*limit 1+new state 1)

To do so, you must link the limit and new state variables to your model. Use so called shadow variables to keep the drawing "tidy". You must also connect the EZ115 model part with your stock variables. Use shadow variables for this task, too.

The lower and upper limits of the initial condition values are defined in the respective MAX STATE and MIN STATE variables and the COMPUTE LENGTH sets the time span used for each of the individual simulation runs. You must also adjust the FINAL TIME in the model settings to 100 times the COMPUTE LENGTH value.

Since this is the first time we are using such a sensitivity analysis, here are some settings sufficient for this modelling assignment:
  • Iterate the stock renewable resource between 0 and 1.25
  • Iterate the stock production capital between 0 and 0.25
  • Set COMPUTE LENGTH to 50 (remember to adjust the overall computation length in the model settings!)

Submission

Include the graphical representation of your model used for the sensitivity analysis (i.e. stock and flow model), the custom graph and your notes on the hypothesis verification, "lucky" conditions and simulation settings in a single PDF file and upload the file in time via the exercises module of this course system.

The submission deadline and the upload function can be found in the section Modelling Assignment: Luckiness of the Commons of the exercise module.

Review and grading

The assignment will be reviewed by the course supervisors.



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