Homework : Analytic Methods for Public Policy Analysis 

Topics Covered

• Decision Analysis
• Expected Value
• Risk Aversion

Question 1

Imagine that your client, Hillside County Forest Preserve (HCFP), is considering how best to protect their natural lagoons.  They have asked for your help, and you have found the following/

• If they do nothing, the lagoons are sure to deteriorate and have a societal cost of $100,000
• If they enact an experimental new program, called Lagoon Preservation Project ("LPP"), then there is a 50% chance that it will be successful, yielding a societal benefit of $70,000. There is a 50% chance it will not be successful, causing further harm to the lagoons, yielding a societal cost of $150,000
• Enacting LPP will cost $10,000

Assume all costs and benefits above are expressed in present values.

a.       Which option has the higher expected benefit to society? Show the decision tree that supports your answer.

b.      What would the likelihood of success of LPP need to be for enacting it to have the same Expected Value as not enacting it?

Question 2 

After successfully having navigated the LPP issue, HCFP has once again for your help.  Now, they are considering implementing a new drainage system to improve water flow across the various ponds within their property.  They have found that poor drainage yields significant bacteria build-up that negatively affects both the ecosystems within and human visitors to their preserves.  You have found the following:

• The new drainage system has an 80% chance of working well and a 20% chance of not working well
• A new drainage system that works well will yield $150,000 in benefit to HCFP
• A new drainage system that does not work well will yield only $40,000 in benefit to HCFP
• Not installing the new system (that is, keeping the status quo) provides $100,000 in benefit to HCFP
• A test of the drainage system costs $15,000; this test will tell them with absolute certainty whether the system will work well.

Assume all costs and benefits above are expressed in present values. 

a.       If HCFP's goal is to maximize the expected net benefit, should they test the system?  Be sure to draw the decision tree that supports your answer.

b.      Assume for this part only that installing a drainage system that does not work well has a benefit of $0, instead of $40,000.Should HCFP test the drainage system?  What is the most that HCFP should be willing to pay for the test?

Question 3 -

Imagine you are faced with the opportunity to play two coin flips, in which you get to call heads or tails prior to the flip of a fair, two-sided coin.  (That is, heads and tails have equal likelihoods of occurring on any given flip.)

In Game A, a correct call wins you $1000; for an incorrect call, you neither win nor lose money.  Game A costs $0 to play.In Game B, a correct call wins you $10,000; an incorrect call loses you $3,000.  Game B costs $0 to play.

a.       What is the expected value of each game?

b.      If you had to play one of the two games, which would you choose and why?  Please answer this as realistically as you can, given your (and/or your group members') actual preferences, wealth, risk aversion, etc.  Do not answer this question for some hypothetical person.  Imagine that you, yourself, have been given this actual choice and must now make a decision.

c.       At what cost of your preferred game would you be indifferent between the two games?  How did you arrive at this number?

Question 4 

The unfortunately-named (and fictitious) town of Avalanche, Utah maintains a vibrant and growing ski industry.  As Director of Avalanche's search-and-rescue operations, you are always interested in the latest technologies that can help you find skiers and others who find misfortune.  Most recently, you have been exploring the use of a Snow Sonogram Machine (SSM), which allows you to scan very deep sections of snow for evidence of buried bodies.

The SSM is a good, but not perfect, machine.  If someone is buried in a pile of snow, the SSM will correctly identify the presence of person in that pile 90% of the time.  If someone is buried, the SSM will say that the buried person is not actually there 10% of the time.  If someone is not buried, the SSM will correctly say that there is no one buried 70% of the time, but incorrectly say that there is someone buried 30% of the time.

Sure enough, after a recent small avalanche, a girl has gone missing, and you suspect she might be buried in a small section of one nearby mountain.  Specifically, there is a 90% chance she is buried and 10% chance she is not.

Assume that if she is buried, the only way you can find her is to dig, and assume that you will definitely find her if you dig.  If she is not buried and you dig, you have no chance of finding her.  If she is not buried and you choose not to dig (that is, you put your resources towards other search processes), you have a 10% chance of finding her.

For simplicity's sake, assume that - if you find her - you find her alive. 

Now, estimating costs and benefits can be a tricky and emotional business when talking about human lives, but you do live in the real world of limited resources and accountability.  As such, you rely on the significant body of literature on the value of human lives, which estimates the value of finding the girl at $10 million.  If you do not find her, the benefit is $0.

The other relevant costs and benefits are as follows:

• If you choose to use the SSM on the relevant section of mountain, you can rent it for $100,000
• Digging in the section of mountain (regardless of whether the SSM is used) costs $150,000
• Not digging (again, regardless of whether the SSM is used) costs $50,000, since you will engage in other, but less costly, search processes

If you are an expected value maximizer, should you rent the SSM?  (This question is undoubtedly challenging and your instructor recognizes it as such.  Note that all necessary information is provided above, and that all information provided above is relevant to the problem.)