Recall the travails of Agatha, from the previous chapter. She had to travel 1,500 miles from Istanbul to Paris. She had only $200 with which to buy first-class and second-class tickets on the Orient Express when the price of first-class tickets was $.20 a mile and the price of second-class tickets was $.10 a mile. She bought tickets that enabled her to travel all the way to Paris, with as many miles of first class as she could afford. After she boarded the train, she discovered to her amazement that the price of second-class tickets had fallen to $.05 a mile while the price of first-class tickets remained at $.20 a mile. She also discovered that on the train it was possible to buy or sell first-class tickets for $.20 a mile and to buy or sell second-class tickets for $.05 a mile. Agatha had no money left to buy either kind of ticket, but she did have the tickets that she had already bought.
(a) On the graph below, use pencil to show the combinations of tickets that she could afford at the old prices. Use blue ink to show the combinations of tickets that would take her exactly 1,500 miles. Mark the point that she chooses with the letter A.
(b) Use red ink to draw a line showing all of the combinations of first-class and second-class travel that she can afford when she is on the train, by trading her endowment of tickets at the new prices that apply on board the train.
(c) On your graph, show the point that she chooses after finding out about the price change. Does she choose more, less, or the same amount of second-class tickets?