The Who-Needs-A-Doctor? Company makes a do-it-yourself rhinoplasty kit. The company is deciding whether to include a safety feature that would cost $40 for each kit

Question

The company estimates the probability of death without the safety feature is 1/10,000 and the death cost per kit is $50. Based on this information, answer the following questions: a. What is the value the company has placed on a life? b. What is the company's cost-benefit recommendation? c. If the company has overestimated the probability of death and the true probability of death is 1/15,000, what is the true death cost per rhinoplasty kit? d. If the company has overestimated the probability of death and the true probability of death is 1/15,000, what would the true cost-benefit recommendation be for the company? e. If the company has correctly estimated the probability of death but has underestimated by one-half the true value of a life, what is the true death cost per rhinoplasty kit? f. If the company has correctly estimated the probability of death but has underestimated by one-half the true value of a life, what would the true cost-benefit recommendation be for the company?

Answer 1

a. The value placed on life is: [50 / (1/10,000 )] = $500,000.
b. Since the safety feature costs $40 per kit, and the death cost per kit is $50, the company should include the safety feature.
c. The true death cost per kit is: $500,000 × (1/15,000 ) = $33.33.
d. Since the safety feature costs $40 per kit, and the true death cost per kit is $33.33, the company should not include the safety feature.
e. The true value of a life is now $500,000 × 2 = $1,000,000., so the true death cost per kit would be $1,000,000 × (1/10,000 ) = $100.
f. Since the safety feature costs $40 per kit, and the actual death cost per kit is $100, the company should include the safety feature.