The Pandora Virus (known as Pavid) is out of its box!1 Epimetheus has an initial wealth of $10,000 and a von-Neumann Mor

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The Pandora Virus (known as Pavid) is out of its box!1
Epimetheus has an initial wealth of $10,000 and a von-Neumann
Morgenstern utility function (over wealth) given by u(w) = lnw.
Living a relatively vibrant social life, Epimetheus has a
probability of 30% of contracting the virus. Conditional on
contracting the virus, there is a 30% chance that it becomes
severe, which has the effect of reducing his wealth by $6000; and a
70% chance that he suffers minor illnesses, which has the effect of
reducing his wealth by $100
A)Suppose the government can enforce a lockdown, which will
reduce Epimetheus’s probability of contracting the virus to 10%.
However, a lockdown will also reduce Epimetheus’s wealth (whether
or not he contracts the virus) by x dollars. Write down the
equation that defines the maximum amount of x that Epimetheus is
willing to suffer for the lockdown. (Note: There is no need to
solve for x numerically.)
B)Hippocrates Pharmaceuticals has developed a vaccine against
Pavid. For simplicity, suppose vaccination brings no externality.
The vaccine reduces the vaccinated person’s probability of
contracting the virus to 5%. Moreover, upon contracting the virus,
a vaccinated person develops a severe illness with a probability of
10%, and suffers minor illnesses with probability 90%. Calculate
Epimetheus’s expected utility after receiving the vaccine, assuming
that the vaccine is free and causes no reduction in utility
C)Unfortunately, Epimetheus reads misinformation on social media
and suffers a disutility of 0.1 utils (utility unit) if he gets a
vaccine. Will Epimetheus take the vaccine voluntarily?