Economics Homework Help

There are two consumers in a neighborhood: Consumer 1 and Consumer 2. They consume a private good X and a public good T (trash collection). Overall level of provision of a public good (T) is the sum of consumption by both consumers: T = T1 +T2 . The price of a unit of a private good is $1. The price of a unit of T is $2. Both consumers have an income of $100.

The utility function of each consumer is given by: U = log X + log(T1 +T2 )

1. Find socially optimal (efficient) level of production of a public good.
2. Find market (private) level of provision of a public good.
3. Compare answers to question 1 and 2. Do they differ? If the do, explain the intuition why.
4. Suppose the government recognizes, that there is a problem with a private provision of public goods. The government attempts to solve the problem by mandating that each consumer contributes at least $16 to the public good. The government collects $16 from each consumer and provides 8 units of the public good per consumer with this money. The total level of provision of public good in this case is T = T1 +T2 +16.
5. What will be the quantity of a public good provided in this case?
6. Compare level of provision of a public good in question 2 and 4. Does the government intervention in question 4 solve the problem of under provision of trash collection? Why?How is this related to crowding out.