Final answer:
A household consuming an average of 1000 gallons of gasoline per year will be equally well off after the introduction of a 50-cent gasoline tax with a matching $500 annual tax rebate, since the additional cost is exactly offset by the rebate.
Step-by-step explanation:
The question is about determining whether a household will be financially better or worse off after the introduction of a 50-cent gasoline tax coupled with a $500 annual tax rebate per household. To evaluate this, we must consider the average household's annual gasoline consumption.
If the average household consumes 1000 gallons of gasoline per year, the new tax will result in an additional annual cost of $500 (1000 gallons × $0.50 per gallon). This is the exact amount of the annual tax rebate provided. Therefore, the household will be equally well off financially, as the additional cost due to the gasoline tax is offset by the tax rebate. The impact on the household budget from the tax and the rebate cancels each other out.