Okay, now I’m confused. When I did this question, I remember I ignored C as being strictly dominated by B and pulled out a calculator. When I saw this question in the analysis, I did the same thing before scrolling down. Here’s what I got:
Drug A saves you from 70 headaches at $350/yr, for a cost of $5 per averted headache. Drug B saves you from 50 headaches at a cost of $100/yr, for a cost of $2 per averted headache.
This seems to contradict your statement “Cost-benefit reasoning seems to favor Drug A”. Drug A has a higher cost per prevented headache according to my calculations, which would make Drug B the better one. Am I failing at basic arithmetic, or misunderstanding the question, or what? Please help.
EDIT: I was solving the wrong problem, and a bunch of people showed me why. Thanks for the explanations! I’m glad I got to learn where I was wrong.
Since each drug only reduces the number of headaches to a certain number, cost per headache isn’t the right way to look at it. Compare a drug that reduces the headaches to 99/year and costs $0, to a drug that eliminates the headaches completely for $1.
Instead of comparing the cost per headache, it’s better to assign a value to time, and calculate the net benefit or harm of each drug. If we assume one hour of time is valued at $7.25, or the US minimum wage, and using the stated information that each headache lasts three hours, the free drug nets you 1*3-0=21.75, drug A nets 70*3*7.25-350=1172.50, and drug B nets 50*3*7.25-100=987.5
Instead of comparing the cost per headache, it’s better to assign a value to time, and calculate the net benefit or harm of each drug.
That’s not a good way of looking at severe pain. People often will do long hours of mind-numbing tasks in order to prevent real or imaginary future short-term discomfort, like working out to get in shape for a one-time event.
Assuming I did the math right, it seems that folks valuing their time at more than $4.16 an hour should prefer drug A, and those valuing it at less should prefer drug B. To really make this unambiguous, “low income” needs to be defined; assuming it’s at least minimum wage, drug A wins pretty clearly...
I think I did the wrong math ($ per headache saved) when taking the actual survey, sadly...
You’re right about the cost per averted headache, but we aren’t trying to minimize the cost per averted headache; otherwise we wouldn’t use any drug. We’re trying to maximize utility. Unless avoiding several hours of a migraine is worth less to you than $5 (which a basic calculation using minimum wage would indicate that it is not, even excluding the unpleasantness of migraines—and as someone who gets migraines occasionally, I’d gladly pay a great deal more than $5 to avoid them), you should get Drug A.
Okay, now I’m confused. When I did this question, I remember I ignored C as being strictly dominated by B and pulled out a calculator. When I saw this question in the analysis, I did the same thing before scrolling down. Here’s what I got:
Drug A saves you from 70 headaches at $350/yr, for a cost of $5 per averted headache. Drug B saves you from 50 headaches at a cost of $100/yr, for a cost of $2 per averted headache.
This seems to contradict your statement “Cost-benefit reasoning seems to favor Drug A”. Drug A has a higher cost per prevented headache according to my calculations, which would make Drug B the better one. Am I failing at basic arithmetic, or misunderstanding the question, or what? Please help.
EDIT: I was solving the wrong problem, and a bunch of people showed me why. Thanks for the explanations! I’m glad I got to learn where I was wrong.
Since each drug only reduces the number of headaches to a certain number, cost per headache isn’t the right way to look at it. Compare a drug that reduces the headaches to 99/year and costs $0, to a drug that eliminates the headaches completely for $1.
Instead of comparing the cost per headache, it’s better to assign a value to time, and calculate the net benefit or harm of each drug. If we assume one hour of time is valued at $7.25, or the US minimum wage, and using the stated information that each headache lasts three hours, the free drug nets you 1*3-0=21.75, drug A nets 70*3*7.25-350=1172.50, and drug B nets 50*3*7.25-100=987.5
That’s not a good way of looking at severe pain. People often will do long hours of mind-numbing tasks in order to prevent real or imaginary future short-term discomfort, like working out to get in shape for a one-time event.
You’re right; I was generalizing from my experiences with migraines, where the pain goes away if I’m lying in a quiet, dark room
Assuming I did the math right, it seems that folks valuing their time at more than $4.16 an hour should prefer drug A, and those valuing it at less should prefer drug B. To really make this unambiguous, “low income” needs to be defined; assuming it’s at least minimum wage, drug A wins pretty clearly...
I think I did the wrong math ($ per headache saved) when taking the actual survey, sadly...
You’re right about the cost per averted headache, but we aren’t trying to minimize the cost per averted headache; otherwise we wouldn’t use any drug. We’re trying to maximize utility. Unless avoiding several hours of a migraine is worth less to you than $5 (which a basic calculation using minimum wage would indicate that it is not, even excluding the unpleasantness of migraines—and as someone who gets migraines occasionally, I’d gladly pay a great deal more than $5 to avoid them), you should get Drug A.