A city has three types of consumers, with different preferences about the use of bike and the subway. Let's call B the number of rides in bike of each person per semester and S the number of rides in subway. Consumers of the first type have utility function U = B + 2.5S. Consumers of the second type use bike and subway in the fixed proportion 1:1, doing the same number of rides in bike and subway. And the third type of consumers have utility function U = B1/2s1/2. There are 1 million of consumers of each type, and each consumer has a semester transportation budget of $420. Price per ride in bike is PB =1, and the subway authority is considering a rise from Ps 2 to Ps = 3. The subway hires you to do some calculations. Use the X-axis for S and the Y-axis for B. a. (11 pts) How do we say that the goods rides in bike and subway are for consumers of the first type? Show in a diagram the equilibrium of one consumer of this type before and after the rise. How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place?
b. (11 pts ) How do we say that the goods rides in bike and subway are for consumers of the second type?. Calculate and show in a diagram the equilibrium of one consumer of this type before and after the rise. How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place?
c. (11 pts ) How do we say that the goods rides in bike and subway are for consumers of the third type? Calculate and show in a diagram the equilibrium of one consumer of this type before and after the rise. How many rides in bike and the subway make these consumers per semester? How many would make if the rise takes place? d. (7 pts) Is the raise going to be worthy for the subway revenue? Would it be if there were no consumers of the first type? Why?