2. There are many examples of externalities in urban economics. Externality occurs when- ever your behavior affects other people's welfare [either in a positive way or a negative way}, yet that effect on other people's welfare is not reected in the price (or cost) you pay for your behavior. A classic example of negative externality is smoking. When you smoke, you pay the (monetary) cost of buymg a pack of cigarettes and the (implicit) cost due to the harm it does to your health, but you do not pay the cost derived from its harm to other people around you, whose health is also negatively affected. Whenever there is externality, price does not reect the true cost [or benet) of a behavior and the outcome of market equilibrium does not maximize the society's total welfare. This is what we call a mricet failure. This question guides you through another example of economic behavior in urban life which exhibits extemality. The COVID-I'J pandemic has stirred a heated debate about 1 mask wearing. Consider a city with a total of 10,000 residents. Each resident can choose to wear a mask or not to. If the resident chooses to wear a mask, the cost of mask-wearing [from buying masks and the inconvenience and discomfort from mask-wearing} is 21 dol- lars. If the resident chooses not to wear a mask, there is no direct cost. although the risk of getting COVID will be higher. The probability of getting COVID is out i'am itone wears a mask, p _ {[103 U-m, itone doesnotwearamask where N is the number of residents who choose to wear a mask. The equations make it clear that wearing a mask lowers [though does not eliminate) the probability of getting COV'ED. The probability of getting COVID also depends on how many other people de- cide to don a mask. For both those who wear a mask and those who do not, the probability of getting COVID declines when more people in the city choose to wear a mask. Because those who wear a mask are already better protected, the decline in the probability as more people in the city wear a mask is smaller than the decline in probability for those who do not already put on a mask themselves. If one unfortunately gets COVE), the cost, due to medical expenses and lost productivity, is 1,001] dollars. (a) Suppose you just travel to the city and observe that no one in the city is wearing a mask. should you wear a mask? Let us forget about social responsibility just for now and suppose you make the decision considering only your own cost and benet To make the decision, you should weigh the cost of wearing a mask and the cost of not wearing a mask. (b) How does you answer in part (a) change it you nd that everyone in the city is already wearing a mask? {c} What is the total social cost if everyone wears a mask (the sum of the cost of the 10,000 residents in the city) ? (d) What is the total social cost if no one wears a mask? How does it compare with the total social cost you nd in part (c)? (e) What is the \"market equilibrium" number of mask-wearing residents? (Hint: the market equilibrium is achieved when the marginal person is indifferent between wearing a mask or not.) What is the total social cost associated with this market equilibrium? Does the market equilibrium achieve the "best-possible\" result, that is, when the total social cost is the lowest? (1-) [this part is optional} What is the soctal' ly-optim' al number of mask-wearing resi- dents? (g) [this part is optional) Now consider 20% of the residents believe that masks are com- pletely useless in reducing the probability of getting COVE). Let's assume that these people believe the probability of getting 00er is 0.08 no matter whether you put on a mask or not The remaining 80% of the residents have the (correct) beliefof the 2 probabilities as indicated earlier. What will be the market-equilibrium number of mask-wearing residents