The U.S. government wants to determine whether immigrants should be tested for a contagious disease, and it is planning to base this decision on financial considerations. Assume that each immigrant who is allowed to enter the United States and has the disease costs the country $100,000. Also, assume that each immigrant who is allowed to enter the United States and does not have the disease will contribute $10,000 to the national economy. Finally, assume that x percent of all potential immigrants have the disease. The U.S. government can choose to admit all immigrants, admit no immigrants, or test immigrants for the disease before determining whether they should be admitted. It costs T dollars to test a person for the disease, and the test result is either positive or negative. A person who does not have the disease always tests negative. However, 10% of all people who do have the disease test negative. The government’s goal is to maximize the expected net financial benefits per potential immigrant. a. If x 5 5, what is the largest value of T at which the U.S. government will choose to test potential immigrants for the disease? b. How does your answer to the question in part a change if x increases to 10? c. If x 5 5 and T 5 $500, what is the government’s optimal strategy? 44. The senior executives
The U.S. government wants to determine whether immigrants should be tested for a contagious disease, and it is planning to base this decision on financial considerations. Assume that each immigrant who is allowed to enter the United States and has the disease costs the country $100,000. Also, assume that each immigrant who is allowed to enter the United States and does not have the disease will contribute $10,000 to the national economy. Finally, assume that x percent of all potential immigrants have the disease. The U.S. government can choose to admit all immigrants, admit no immigrants, or test immigrants for the disease before determining whether they should be admitted. It costs T dollars to test a person for the disease, and the test result is either positive or negative. A person who
does not have the disease always tests negative. However, 10% of all people who do have the disease test negative. The government’s goal is to maximize the expected net financial benefits per potential immigrant.
a. If x 5 5, what is the largest value of T at which the U.S. government will choose to test potential immigrants for the disease?
b. How does your answer to the question in part a change if x increases to 10?
c. If x 5 5 and T 5 $500, what is the government’s optimal strategy? 44. The senior executives
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