Suppose my brother and I both go on a week-long vacation in Cayman and, when we arrive at the airport on the island, we have to choose between either renting a car or taking a taxi to our hotel. Renting a car involves a fixed fee of $300 for the week, with each mile driven afterwards just costing 20 cents — the price of gasoline per mile. Taking a taxi involves no fixed fees, but each mile driven on the island during the week now costs $1 per mile.
A: Suppose both my brother and I have brought $2,000 on our trip to spend on “miles driven on the island” and “other goods”. On a graph with miles driven on the horizontal and other consumption on the vertical axis, illustrate my budget constraint assuming I chose to rent a car and my brother’s budget constraint assuming he chose to take taxis.
(a) What is the opportunity cost for each mile driven that I faced?
(b) What is the opportunity cost for each mile driven that my brother faced?
B: Derive the mathematical equations for my budget constraint and my brother’s budget constraint, and relate elements of these equations to your graphs in part A. Use x1 to denote miles driven and x2 to denote other consumption.
(b) Where in your budget equation for my brother can you locate the opportunity cost of a mile driven?