The Taiwanese government recently announced that they would begin construction of a high-speed rail system linking the northernmost city of Taipei to the southernmost city, Tai-Nan. This high-speed train will alleviate the significant traffic problems that the country is experiencing. This is a highly lucrative construction project with many international companies involved in the bidding. However, it is clear that companies who have local negotiators possess a clear advantage in the bidding process.
A construction company from Thailand has asked you to work for them in the hope that your connections will successfully help to secure a portion of the high-speed rail contract. You have given serious thought to the proposal and are now sitting in a meeting with the CEO. As the meeting progresses, the CEO brings up the subject of compensation. You listen intently and are surprised when he discusses the terms.
The CEO proposes the following terms: you can take $20,000 per month for a period of two years regardless of whether or not you secure the high-speed rail contract, or you can gamble any portion of your salary you wish. He agrees that if you successfully acquire the contract for the company, he will double the portion of the salary that you decided to gamble. But if you do not secure the contract, you do not receive any bonus and will be paid only the amount you did not gamble. This deal applies to the entire amount that would have been gambled for the two-year contract no matter when the contract is obtained.
Additionally, if you happen to secure a second, unrelated contract while you are there, the CEO agrees to redouble your entire gambled amount for the two-year period (in effect giving you four times the gambled amount). This deal applies no matter when the second contract is obtained so long as it happens within the two-year period.
The high-speed rail system is going to be built and it will be divided between several companies. Based upon your previous work and investigation into the contract, you feel that there is a 60 percent chance that you can get the contract. However, since you have done little preparation for any other projects, the likelihood of a second contract is probably only 20 percent.
You are debating whether to quit your current job, which pays $122,500 a year, to take on this opportunity. Furthermore, if you decide to take this offer, you will have to face the question of how much to gamble if any.
a. If you were not able to gamble any money what should you do based upon an expected payoff analysis?
b. Suppose that you can gamble part of your salary, what amount would you gamble to be neutral to either decision?
c. Now suppose that you gamble $50,000 and have a risk aversion that can be captured in the exponential utility function U(x) = 1 - exp (-x / R). Your degree of risk aversion is $100,000. What is your decision based upon utility and what are the utilities of each decision to four significant digits?
d. Suppose the decision with the highest utility was to stay with your current job. How much would the Thai company have to offer as the base salary, to the nearest $100, to get you to change your mind? (Use a gamble amount of $50,000 and R = $100,000.)