Homework #8 Econ 611, Prof. Hanson

1.      Assume that your initial beliefs about the height and wealth of the next man you meet are captured by the table below.

a.       (2pt) What is the chance you assign that he is rich?

b.      (2pt) If you learn he is not short, what is the chance he is rich?

c.       (3pt) If you learn he is neither short nor rich, what is the chance he is tall?

 Short Medium Tall Rich 10% 12% 15% Moderate 10% 8% 10% Poor 15% 10% 10%

2.       Assume Mary’s utility is given by square root of her wealth, as in u(w) = √w.

a.       (2pt) What is the certainty equivalent of a 10% chance of 100, and a 90% chance of nothing?

b.      (2pt) What chance of getting 25 (or getting nothing) is worth the same?

3.      Assume that it costs \$6 to carry an umbrella around for the day, and that it costs \$20 to be stuck in the rain without an umbrella.

a.       (2pt) If the chance of rain is 20%, should you carry an umbrella?

b.      (5pt) If you buy a weather report, you learn either (80% of the time) that the chance of rain is 1/8, or you learn (20% of the time) that it is 1/2.   What is the most you are willing to pay for a report?

4.      Assume that the cost of getting a parking ticket is \$100, and that putting \$2 into a parking meter will prevent a ticket.

a.       (2pt) If the chance that police will check your meter is 3%, should you pay the meter?

b.      (5pt) Someone offers to sell you a map distinguishing the 50% of places that are checked often (with a 4% chance of checking you) from the 50% of places that are checked less often (with a 1% chance of checking you).  Assuming that you cannot change where you park, but just whether you pay the meter, what is the most you are willing to pay for this map?