Question

Suppose we want to analyze a consumer’s weekly consumption of gasoline. Let good one be “gallons of gasoline” and good 2 be “dollars spent on everything else”. The consumer has a weekly income of $100 and gas is $4 a gallon.
i. Graph the consumer’s budget constraint.
ii. Suppose that the government makes drivers pay $0.50 a gallon in tax. Graph the new budget constraint. Is the budget set smaller or larger?
iii. Suppose that the government only wants to punish those who drive excessively. Drivers that buy more than 20 gallons of gasoline will pay a $1 in tax for each additional gallon. Those that buy 20 gallons or less will pay the original price ($4 a gallon). Draw the budget line and set for a consumer in this situation. How does it compare to the budget set in ii.?
iv. Because gas prices fluctuate, the government decides instead to tax gasoline purchases at 5% (ex: $40 of gasoline purchases would ultimately cost the consumer $42). Graph the new budget constraint. What is the new price of a gallon of gasoline? Is it different from ii.? Which budget set is smaller (when the consumer must pay $0.50 a gallon or when the consumer must pay 5% gas tax)?