Expected Utility

Problem set 1

 

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Answer the following questions, and upload your answers to Canvas.  You can write your answers in word, or write them by hand and upload a picture or scanned copy as long as it is clearly readable.  You may collaborate with any of your classmates, but make sure that you fully understand how to answer each problem so that you can do a similar problem on the exams.

 

Expected utility

In the following problems, you will be required to calculate the expected utility of various actions.  Make sure to show your work, so that partial credit can be awarded if you make minor mistakes

  1. Claire is thinking about whether to run for a seat in the Scottish Parliament. She believes that she has a 60% chance of winning the election. She believes that gaining a seat would gain her 100 utility relative to not holding the seat.  However, the effort and costs of campaigning would cost her 20 utility, which she must pay regardless if she wins or loses.  What is Claire’s expected utility for running in the election?  Should Claire run for election?
  2. The country of Brittany is considering going to war against Aquitaine. They believe they have a 25% chance of winning, a 45% chance of a draw and 30% chance of losing. Winning would gain them 50 utility relative to the status quo, a draw would retain the status quo (0 utility), and losing would lead to a loss of 60 utility.  Regardless of the outcome, they would also have to pay 20 utility for the costs of the war.  What is Brittany’s expected utility of going to war?  Should Brittany go to war?
  3. Assume that there is some deadly virus that has been going around, which kills 0.5% of those it infects. A vaccine against this virus has recently been developed. The vaccine will not change the chances of getting infected, but has 80% efficacy at preventing serious illness and death.  Efficacy is defined as , so the risk of dying of a vaccinated individual is the (1-efficacy) multiplied by the risk of dying of an unvaccinated.  However, the vaccine kills 1 out of 1,000,000 people that take it.  Further, assume that your chances of encountering the virus sufficient to contract it are 50%.  What is the expected utility of taking the vaccine?  What is the expected utility of not taking the vaccine?  (Assume that living gives you 1 utility and dying 0).  Should you take the vaccine?
  4. Assume all the facts from the previous problem. Except, it is unclear how dangerous the vaccine is. Assume the vaccine kills with probability p.  What would the value of p have to be for a rational person to be indifferent between taking the vaccine and not taking the vaccine?  (Another way to think of this is: what would the minimum value of p be such that it would no longer make sense to take the vaccine?)

 

 

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