2. Trees and market failure: Theodora lives in a neighbourhood that has an empty tract of land which nobody owns, right next to the ocean. She is considering planting trees there. Each tree costs Theodora $20 to plant (you can think of this as including the time and effort Theodora has to put in, as well as the cost of saplings). Theodora must decide how many trees to plant.

Theodora gets a (marginal) benefit of $60 from the very first tree that she plants, but her marginal benefit decreases by $5 for every additionaltree she plants. Thus, Theodora gets a marginal benefit of $55 from the second tree she plants, a marginal benefit of $50 from the third tree she plants, and so on.

Theodora has 11 neighbours. 10 of them like trees: they get a benefit of $1 each from every tree that Theodora plants. 1 of them (Zenobia) dislikes trees since they block her view of the ocean. Zenobia incurs a cost of $5 for every tree that Theodora plants.

(a) Suppose Theodora chooses how many trees to plant, without regard for her neighbours. In a graph, plot Theodoras marginal cost and marginal benefit. How many trees will she plant?

(b) In a new graph, plot Theodoras marginal cost and marginal benefit, as well as the marginal social benefit (or MWTP), which includes the benefits and costs incurred by all of Theodoras neighbours. What is the socially efficient number of trees?

(c) Suppose we initially started with no trees. Would planting the so- cially efficient number of trees from (b) lead to a Pareto improve- ment? Explain carefully why or why not.

(d) Zenobia decides to leave the neighbourhood. What is the socially efficient number of trees now?

(e) Suppose we initially started with no trees. Would planting the so- cially efficient number of trees from (d) (with Zenobia now out of the picture) lead to a Pareto improvement? Explain carefully why or why not.