Sensitivity analysis of the probabilities of the payoff

Congressman Ned Froemer has approached you with an offer. He would like for you to create a compelling script and produce a YouTube video featuring a doctor (or at least an actor that can play one convincingly), supporting his claim that having health insurance shortens one’s life expectancy by up to 10 years. The premise being, going to the doctor is a sure way to get misdiagnosed, sent to a hospital and contracting an antibiotic resistant strain of pneumonia. He is hoping this video will go viral (so to speak) and torpedo the opposition who thinks health insurance for everyone is a good idea. Your cost to hire the actor and rent a chair, desk and books to create a medical-office looking set is $1,000. Congressman Froemer tells you that if you get this done in one week, he’ll pay you $6,000. If you get it done in three days, even better; he’ll pay $11,000, but if it takes longer than a week it’s no good because, by then, the opposition will have mobilized a team of real doctors (or better actors) to refute his claim, and he won’t pay you one red cent. You’ve never undertaken a project like this before but your guess is that the chances of each outcome (profit of $5,000, $10,000 or -$1,000) are the same (1/3). Before you decide to take on this project you would like would like to conduct a sensitivity analysis looking at what happens if each probability could range from 0 to ½.

1. Use a Monte Carlo simulation to perform a sensitivity analysis of the probabilities of the payoff.

2. Suppose you would like to choose each of the three probabilities from a uniform distribution between 0 and 1. Can you incorporate this information into your simulation? If so, how? If not, explain why not, or what additional information you would need.

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