In Arbitrageville, 1 orange can be exchanged for 4 apples, and 4 apples for 1 orange. The mayor of Arbitrageville likes oranges a lot. He buys 100 oranges and 1 apple at the grocery store. As the mayor piles oranges onto the checkout counter, he tells the clerk, "I just love these oranges. In fact, I think you'd need to offer me three apples to pry one orange from my hands."
a. Explain why the clerk, a sharp entrepreneur, immediately reaches under the counter and offers the mayor 3 apples.
b. What should the mayor have said about how many apples the clerk would need to offer him for 1 orange, assuming that the mayor was maximizing his utility? What equation tells us how the mayor's preferences relate to prices?
c. If the mayor maintained his preferences, how could the clerk wind up with all of the mayor's oranges and the mayor (eventually) without a penny to his name?