SISL > 2012 Sustainability in Math Workshop > Activities > Modeling: (1) Revenue Neutral Carbon Taxes; (2) Accelerated atmospheric C02 concentrations

Modeling: (1) Revenue Neutral Carbon Taxes; (2) Accelerated atmospheric C02 concentrations

Martin Walter, University of Colorado, Boulder (based on original material in ``Mathematics for the Environment'', a text book published by CRC/Taylor&Francis)
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(1) Create a model where all "entities'' pay a (possibly international) tax for burning fossil carbon into a pool, from which all taxpayers get an annual payment more or less equally distributed.
(2) Over the last 200 years, the oceans have absorbed about 50% of CO2 emissions, now the marginal rate is down to 30%–while the rate of emissions has grown from 1 tonne/year/person to greater than 1 tonne/person/year. What might be the expected increases in ppm by volume in CO2 concentrations in the near future.

Learning Goals

Modeling a carbon tax shows students how our society actually functions, cf., centralized versus distributed/democratic decisions making. It highlights both obstacles and opportunities. It also encourages student to analyze the economic structure of society, flows, and the implications of decisions. The second part shows the urgency of stopping the burning of fossil carbon.

Prepares students to build effective coalitions

Engages students in civil discourse/ communications that lead to more effective decisions

Catalyzes collective actions

Shows how a math model can clarify implications of decisions

Encourages self-reflection and promotes creative visioning around sustainable futures

Clearly ``higher order,'' i..e., synthesizing multiple topics together in a single model, is involved/skills developed

Context for Use

These activities can be done using no more than arithmetic, greatly facilitated by using a (computer) spreadsheet, for example.

The tax example can easily get interdisciplinary, involving economics and political science–as well as the physics of carbon consumption/emissions.

The second part can be approached in a similar fashion using arithmetic (and spreadsheets), but for more advanced students calculus and differential equations can be used.

Description and Teaching Materials

This is an offshoot (largely not discussed) in the book:
``Mathematics for the Environment,'' by Martin Walter,
CRC Press/Taylor&Francis Group, 2011.

Teaching Notes and Tips

Students have two general difficulties: (1) Creating a logical "uber-structure'' for a model where guiding assumptions are clearly stated; (2) Fleshing out the implications of the overall logical structure using technical mathematical tools


There are local assessments possible (in a class), all the way to global assessment–did a revenue carbon tax become a reality.

References and Resources

Government data bases can be found with search engines.

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