It has been suggested that one way to reduce worldwide carbon dioxide (CO₂) emissions is to impose a single tax that would apply to all nations. The accompanying graph shows the relationship between different levels of the carbon tax and the percentage of reduction in CO₂ emissions.

a. What tax rate would have to be imposed to achieve a worldwide reduction of 50% in CO₂ emissions?

b. Use the graph to estimate the rate of change of the percentage reduction in CO₂ emissions when the tax rate is $200 per ton.

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Percentage reduction of CO2 (relative to baseline) 100 90 80 70 60 50 40 30 20 10 0 0 Estimates of the Reductions of CO₂ Emissions Produced at Different Tax Rates 100 200 300 Tax rate ($ per ton carbon) 400 500