The demand curve for flu shots is P = 100

Question

The demand curve for flu shots is P = 100 - 2Q,and the supply curve for flu shots is P = 19 + Q where Q is a million shots per year and P is the dollars per shot.Assume that the flu shots generate an additional benefit in that it reduces the likelihood of others getting sick.This benefit is valued at $6 per shot per year.The private market equilibrium quantity of shots produced is ____________________________,but the socially optimal amount of shots is ________________________________.

Quizplus · Accepted Answer

First,let's solve for the private equilibrium by setting the price equal to the demand and supply curve.100 - 2Q = 19+Q100 - 19 = 3Q81 = 3Q or Q = 27Next,we want to solve for the socially optimal amount of shots.Since each shot provides an additional $6 of benefit,we can take the private benefit + the marginal external benefit = 100 - 2Q + 6 = 106 - 2Q.Again,we set the price equal and find: 106 - 2Q = 19+Q106 - 19 = 3Q87 = 3Q or Q = 29.