In order to reduce carbon emissions, the Green Party has proposed a carbon tax which would increase the price of gasoline. To analyze the impact of the policy on consumer welfare, they calculate the effective wealth lost by consumers as a result of the price change. The Red Party objects, arguing that the impact of the policy should instead be measured by how much consumers would need to be subsidized to accept the price change. An external think tank proposes that the two parties compromise by measuring the lost area under the demand curve. Demonstrate the discrepancy between these measurements, and why each side has chosen the measurement it has, via a three-good example.

Instructions:

Write down a three-good utility maximization problem with fully specified preferences, prices, and wealth. Designate one of the goods to be "gasoline". Calculate the consumer's optimal consumption bundle and indirect utility.

Choose a new, higher price for gasoline. Calculate the three proposed measures of the welfare lost by this price increase.

Identify the most likely reason why each political party prefers its respective metric. In what sense is the think tank's proposal a compromise?