Market Failure Practice Problems

Question $1$

a$.$ In class, we identified different types of externalities. Externalities may arise in production or consumption and can be positive $($external benefits or negative $($external costs$).$ Provide a real$-$world example of each type.

b$.$ Consider the market for vaccines for measles. In a diagram, identify the $($private$)$ marginal benefit, the $($private$)$ marginal cost of vaccines, and the external benefits from a highly vaccinated population. Will the market provide too few or too many doses of vaccines? Why? Identify the deadweight loss in your diagram.

c$.$ To reduce the welfare loss from the externality, what type of policy might the government implement? In a new diagram, identify the impact of such a policy on the equilibrium outcome.

Question $2$

Consider the case of a new development of $10$ houses surrounding an open space that could be used as a nice forest$/$recreation area for the homeowners. Assume all homeowners would benefit from a forested area, and each has willingness to pay given by MWTP $=50-$T$,$ where $T$ is the number of trees planted in the area.

a$.$ Derive the aggregate MWTP function for this group of $10$ homeowners.

b$.$ Suppose the cost of planting each tree is $$100.$ Based on the benefits to households $($see parta$)$ and the costs of planting a tree, what is the optimal number of trees that we would hope to see planted?

c$.$ Assuming no cooperation among the $10$ homeowners that surround the open space. how many trees will be planted privately by the homeowners? Support your answer.

d$.$ If your answers to part $($b$)$ and part $($c$)$ are different, what is the deadweight loss in the market? What is the difference in welfare between the two scenarios?

e$.$ Now, suppose the homeowners form a homeowners association. The association will plant the trees and then split the cost of planting tree equally across the ten homeowners, That is$,$ each household will be charged $$10$ for each tree planted. Will the homeowners association plant the optimal number of trees through this arrangement $($you may assume that the homeowner association can collect the money via the annual homeowners assessment$)?$