Question 1 The Pandora Virus (known as Pavid) is out of its box!' Epimetheus has an initial wealth of $10,000 and a von-Neumann Morgenstern utility function (over wealth) given by u(w) = In w. 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) (Level A) Calculate Epimetheus's expected utility. (b) (Level B) 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 r dollars. Write down the equation that defines the maximum amount of z that Epimetheus is willing to suffer for the lockdown. (Note: There is no need to solve for x numerically.) (c) (Level A) 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 vac- cine is free and causes no reduction in utility. (d) (Level A) 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