Suppose that health care is provided privately in a free market and families are responsible for paying for polio vaccinations for their children. The following supply and demand diagram shows the private marginal costs and private marginal benefits in this market.

a. Show on the diagram the quantity of polio vaccinations that would be undertaken in the absence of government intervention.
b. Describe the externality associated with having a polio vaccination.
c. Draw a new demand curve that reflects the externalities associated with the vaccinations and show the socially optimal quantity of vaccinations. Explain.
d. Explain why the government might choose to subsidize vaccinations (or perhaps even provide them for free). Are there both efficiency and equity motivations for government involvement in this market?