1 (25 pts) A student dedicates 6 hours a day to classes and study and 8 hours to rest. This leaves 10 hours a day for leisure that the student reduces taking a part-time job. The student considers leisure and consumption as imperfect substitutes and her preferences are given by a utility function U(Y,N) =Y N, where Y is consumption and N is the number of hours of leisure. Hourly wage is w = 10 and the price of consumption is normalized to 1. All monetary values are in dollars. a. (4) Write and draw the budget restriction of the student calling H the hours of work, taking into account the relationship between H and NV, and that she already has Y = 20 of stipend per day coming from her parents. b. (6) Compute the equilibrium choice of N, H and Y. Represent in a graph. c. (6) Suppose that her parents do not like that she works (because the effect on the grades) and withdraw the daily stipend of = 20. Compute the new equilibrium. Draw. Does the student work less or more? Why? d. (9) The parents realize that measure has not worked well: they wanted that she stopped working and now works more. Starting from the current sit- uation (her utility now), can you advice to the parents a solution that would obtain that she stops working? 1. (25 pts) 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 + 2.55. Consumers of the second type use bike and subway in the fixed proportion 1:1, doing the same number or rides in bike and subway. And the third type of consumers have utility function U = B/28'/2 There are 1 million of consumers of each type, and each consumer has a semester transportation budget of $300. Price per ride in bike is Pg =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. 1) (7 pts) What type of goods are subway and bike rides 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 bike/subway rides do these consumers make per semester? How many would make if the rise takes place? 2) (7 pts ) What type of goods are subway and bike rides 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 bike/subway rides do these consumers make per semester? How many would make if the rise takes place? 3) (7 pts ) What type of goods are subway and bike rides 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 bike/subway rides do these consumers make per semester? How many would make if the rise takes place? 4) (4 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