You are risk neutral, and care only about your income. With prob...
Question
You are risk neutral, and care only about your income.
With probability p, you will catch a disease that reduces your income from y, its level when you are healthy, to y-k, where k > 0. A vaccine is available, at cost c, that reduces the probability of your catching the disease from p to q<p.
a) Suppose that you know the values of p, q, y, k, and c, so that the only thing about which you are uncertain is whether you will catch the disease. Write the condition that determines whether or not you should buy the vaccine.
b) Now suppose that you know y, k, and c, but neither p nor q . Which is more relevant to your decision, the percentage amount by which the vaccine reduces the probability of catching the disease (what is usually reported in the press), or the absolute amount? Explain.
c) How do your answers to (a) and (b) change if you are a risk-averse expected-utility maximizer?
With probability p, you will catch a disease that reduces your income from y, its level when you are healthy, to y-k, where k > 0. A vaccine is available, at cost c, that reduces the probability of your catching the disease from p to q<p.
a) Suppose that you know the values of p, q, y, k, and c, so that the only thing about which you are uncertain is whether you will catch the disease. Write the condition that determines whether or not you should buy the vaccine.
b) Now suppose that you know y, k, and c, but neither p nor q . Which is more relevant to your decision, the percentage amount by which the vaccine reduces the probability of catching the disease (what is usually reported in the press), or the absolute amount? Explain.
c) How do your answers to (a) and (b) change if you are a risk-averse expected-utility maximizer?
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Expected (Net) Income:
(1 - p)y + p(y – k) No Vaccine
(1 – q)(y – c) + q(y – c – k) Vaccine
Vaccinate if:
(1 - p)y + p(y – k) < (1 – q)(y – c) + q(y – c – k)
(1 – p + p)y – pk < (1 – q + q)(y – c) – qk
(1 - p)y + p(y – k) No Vaccine
(1 – q)(y – c) + q(y – c – k) Vaccine
Vaccinate if:
(1 - p)y + p(y – k) < (1 – q)(y – c) + q(y – c – k)
(1 – p + p)y – pk < (1 – q + q)(y – c) – qk
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