D21: Designing a Vaccination Policy

Use the spreadsheet in Teams to design and analyze an optimal vaccination policy for a small hypothetical community with the market WTP, market WTA, and marginal benefit of the externality, `MB_e`, curves shown below:

`WTP = 500 - 2*Q`

`WTA = 3*Q`

`MB_e = 280 - Q`

The marginal benefit starts out high when no one is vaccinated (Q=0) but then falls as more people are get the shot (Q rises) and there are fewer and fewer unprotected people to gain from the externality.

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, such as the WTP, WTA and externality data at the top. Also note that the form of the WTP, WTA and MBe equations are shown on the spreadsheet.
2. As in the carbon tax exercise, 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 MSB=WTA. Those are the blue cells and the numbers in them are placeholder starting guesses.
3. Fill in the other cells with borders in the "Market" column of the Policy Design section with appropriate formulas.
4. Use goal seek to set the WTP-WTA cell in the Market column 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 of the Policy Design section. As before, for the cells that appear in both columns it will be really easy if you think about it a bit.
6. Fill in formulas for the Change and % Change cells in the Policy Design section.
7. Now fill in the cells at in the Welfare Impacts section with formulas for `Delta Rev`, `Delta CS`, `Delta PS`, `Delta Ext`, and `Delta SS`.
8. Create a waterfall chart for `Delta Rev`, `Delta CS`, `Delta PS` and `Delta Ext`.
9. Answer the question near the bottom about what subsidy is needed (no additional calculations: just reporting your results).

Save and submit the results.