1) You just got a new car. You have $150 to spend each month on gasoline (x1) and all other goods (x2). Assume that p2 = 1 so x2 represents the

amount you have to spend on other goods after paying for gas. Initially gasoline costs $2.50 per gallon. However, if you purchase more than 20 gallons of gasoline per month, you pay a tax of $0.50 per gallon (in addition to the market price of $2.50) on the amount purchased above 20 gallons. a) Sketch the budget constraint in two-dimensional space with x1 on the horizontal axis. Label the vertical intercept, the horizontal intercept, and the slopes of the budget line.2 b) Suppose the tax on gasoline quintuples to $2.50 per gallon (i.e., gas is taxed at 100% after 20 gallons). Make a plot showing the old and new budget lines. Give the new value(s) of vertical intercept, horizontal intercept, and/or slope (whichever changed as a result). c) Now suppose gas is tax free up to 20 gallons per month, is taxed at $0.50 per gallon up to 30 gallons, and then $2.50 per gallon after 30 gallons. Draw the new budget constraint. d) Finally suppose that the taxes apply retroactively. That is, you can still buy up to 20 gallons of gas tax free, but if you buy any quantity beyond 20, you pay $0.50 per gallon on the total amount purchased (not just the amount above 20). Likewise, if you buy more than 30 gallons in a month you must pay an additional $2.50 per gallon on every gallon purchased. Draw the new budget constraint (Hint: The budget line is discontinuous.