Determine value of a life saved by the experimental protocol
Microeconomics
Suppose the government has an experimental treatment that cures ebola in some patients and makes other patients who have contracted ebola more likely to die. Suppose that at time period 0, half of patients who contract ebola die from ebola in the absence of treatment. And suppose at time period 0 it is believed that the experimental treatment will cure people with probability 0.5. But with probability 0.3 (or 3/10), it will kill patients who take the treatment, and otherwise it will increase the fatality rate of ebola by 50%. Assume throughout that the government cannot identify ex ante how individual patients will react to the treatment, so it either administers the treatment to everyone or to no one.
(a) How might the government determine the value of a life saved by the experimental protocol (or, equivalently, the value of a life lost due to the experimental protocol or the infection)?
(b) For the rest of the problem, assume the government values a statistical life at $1 million. And suppose that 100 people contract ebola in period 0 and there are no infections in future periods. What is the value of the treatment (in dollars)?
(c) Suppose that once the government administers the treatment to the infected patients, it cannot reverse course. But further suppose the government can postpone administering the treatment until period 1, at which time the eects of the treatment are better known. In particular, it is known in period 1 that the treatment is fully curative. However, ten of the patients will die from ebola in period 0 waiting for the treatment. If the government waits to administer the treatment, how many lives are saved? And what is the value (in dollars) of the treatment? Assume the government values a life saved in period 1 just as much as it values a life saved in period 0. (Hint: if ten lives are lost in period 0, then the probability of fatality among the remaining 90 infected patients is not still 50%).
(d) What is the option value (in dollars) of postponing the treatment?
(e) Now suppose it is period 1 (i.e., period 1 has become period 0) and the government has learned about the ecacy of the treatment. Further suppose the planner faces another 100 infected patients and expects to have 100 infected patients every year forever. If the government now discounts future benets at a rate r = 0:10, what is the present value of the treatment administered into perpetuity if the laboratory cannot deliver the treatment to hospitals until one period hence?
