2. There are two goods, X and leisure (L), two individuals, and an endowment that is equal to the wage and the number of hours available to work. The original allocation is Pareto Efficient.

a) Demonstrate the relevant budget constraint for this scenario

b) Suppose the government were to tax each of these goods with tX and tL. Under what conditions would this result in and efficient allocation?

c) What is the problem with the suggested policy in (a.)?

d) What alternative to the suggestion in part (a.) would result in an identical outcome? Demonstrate this mathematically.

3. You and your neighbor jointly share a pond of water. You like to fish in the pond, but your neighbor is always swimming in the water during the best fishing hours scaring away most of the fish.

a) Draw a graph indicating the marginal benefit your neighbor receives from swimming, the marginal private cost, the marginal social cost, and the marginal damage. Label all axes and curves.

b) What would be the optimal solution if the government were to impose a unit tax on your neighbor for each hour of swimming? Show this on the graph. Why might it be difficult to obtain the optimal point in real life?

c) Is it possible to obtain the same outcome if the government were to subsidize your neighbor for every hour he/she refrains from swimming? Show this solution on a similar graph.

d) Explain the Coase solution and how this might result in a preferable outcome. In what situations might the Coase solution not work very well?