Peter J Wilcoxen > PAI 300 Economics for Policy Analysis

D20: Carbon Tax Analysis

Use the spreadsheet in Teams to design and analyze a carbon tax for the Washington, DC, gasoline market. The market willingness to pay and willingness to accept curves are given below, where Q is measured in millions of gallons (i.e., Q=1 means 1 million gallons):

`WTP = 5 - (1/1200)*Q`

`WTA = (1/1800)*Q`

The marginal cost of the externality, `MC_e`, is $0.25 per gallon (about $100 per metric ton of carbon). Here's what to do to complete the analysis:

  1. Some of the cells are already filled in and don't need to be changed, including the WTP, WTA and externality data at the top, and the change and percentage change columns at the right. Also note that the form of the WTP, WTA and MCe equations are shown on the spreadsheet.
  2. We'll use goal seek twice: once by adjusting the Q in the "Market" column to make WTP=WTA and once to adjust the Q in the "Policy" column to make WTP=MSC. Those are the blue cells and the numbers in them are placeholder starting guesses.
  3. Fill in the cells with borders in the "Market" column with appropriate formulas. The `Rev` row is for tax revenue and the `Ext` row is for the total cost of the externality.
  4. Use goal seek to set the WTP-WTA cell in the Market colum to 0 by changing the Q cell in the Market column.
  5. Now fill in the formulas for the bordered cells in the Policy column. For the cells that appear in both columns it will be really easy if you think about it a bit.
  6. Fill in the tax burden cells at the bottom with appropriate formulas.
  7. Use the percentage changes in Q, Pd and Ps to fill in the demand and supply elasticity cells.
  8. Answer the question near the bottom about what tax is needed (no additional calculations: just reporting your results).
  9. For 1 point of extra credit, use goal seek to determine how large the externality would need to be in order for Q to be cut in half from the Market column value.

Save and submit the results.

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    Peter J Wilcoxen, The Maxwell School, Syracuse University
    Revised 02/22/2024