Nash Equilibrium - Resource Exploitation
3.Common pool(or open access natural resource exploitation:Consider an open access village forest of size y>0, where y is the maximum number of trees which can be harvested. In period 1 each of two villagers can withdraw a non-negative quantity (respectively c and c,for consumption,provided c+c, y. If they try to consume more than the remaining resource y their conflict is arbitrated and each ends up with y/2. When total
consumption in the first period is less than y the remaining amount y-c+c,) forms the
base for 2n(and last) period consumption. As there is no reason to save the resource beyonc the last period (the world ends) the total harvestable amount is simply divided in that last
This means that the only real choice is how much
2
each player consumes in the first period.All this can be summarized by saying that player 1 chooses c1 to solve
2
where c, is the amount he conjectures player 2 will harvest/consume.Player 2's objective is defined symmetrically. e Suppose player I could act as a Stackelberg leader and harvest trees in period 1 before player 2 has access. Show how you would setup player 1's maximization problem to solve for c. How do outcomes change (if you can't get the math easily just explain in
words)? Use a reaction function diagram to illustrate what is happening
f) Finally, suppose the forest were privatized. Villager 1 gets share of the forest trees (or y and villager 2 the remainder. How would the villagers manage their private forests (setup and solve their simple intertemporal consumption problem.Is the exploitation efficient? g) Should the forest be privatized? How would this have to be done to make sure that everyone gained compared to the earlier Nash equilibrium outcome without private
d In y-c+c dIn(c,) 1 2 t's useful to note that and dc, dey
1
y=cl+c2
4
property rights? Write a few sentences on the pros and cons of privatizing the resource including distributional concerns and any alternatives you might think of to outright privatization.
