2.3† Everyday Application: Renting a Car versus Taking Taxis. Suppose you and a friend go on a week-long holiday to Cyprus and are choosing between renting a car or taking a taxi to tour the island for the week.

Renting a car involves a fixed fee of €300 for the week, with each kilometre driven thereafter costing €0.20, which is the price of fuel per kilometre. Taking a taxi involves no fixed fees, but each kilometre driven on the island during the week costs €1 per kilometre.

A. Suppose you have both brought €2000 to spend on ‘kilometres driven on the island’ and ‘other goods’.

On a graph with kilometres driven on the horizontal and other consumption on the vertical axis, illustrate your budget constraint assuming you choose to rent a car and your friend’s budget constraint assuming they choose to take taxis.

a. What is the opportunity cost for each kilometre driven that you face?

b. What is the opportunity cost for each kilometre driven that your friend faces?

B. Derive the mathematical equations for your budget constraint and your friend’s budget constraint, and relate elements of these equations to your graphs in part A. Use x1 to denote kilometres driven and x2 to denote other consumption.

a. Where in your budget equation can you locate the opportunity cost of a kilometre driven?

b. Where in your budget equation for your friend can you locate the opportunity cost of a kilometre driven?