Suppose that the world is comprised of two countries, A and B, that jointly exploit a common pool of a non-renewable natural resource, say oil, whose total stock is Q = 300. Country i's net well-being TS(Qit) in period t (i.e.: social benefit from using the resource net of extraction costs) depends on the quantity of oil Qit that country i extracted in period t from the common pool, where i = A,B. Suppose that oil in these countries is fated to be depleted within two periods: 0 (the present) and 1 (the future), so t = 0,1, and that future well-being is discounted at the rate r = 0.25 (so the discount factor δ=0.8). Also suppose that the marginal surplus value in period t is: ΔTS/ΔQit = 100 - Qit. Find the oil extraction schedule that would prevail at a non-cooperative equilibrium (i.e.: the quantities Qit , for i = A,B and t = 0,1, that would prevail at at a Nash equilibrium of the oil extraction game played by these two countries).
Suppose that the world is comprised of two countries, A and B, that jointly exploit a common pool of a non-renewable natural resource, say oil, whose total stock is Q = 300. Country i's net well-being TS(Qit) in period t (i.e.: social benefit from using the resource net of extraction costs) depends on the quantity of oil Qit that country i extracted in period t from the common pool, where i = A,B. Suppose that oil in these countries is fated to be depleted within two periods: 0 (the present) and 1 (the future), so t = 0,1, and that future well-being is discounted at the rate r = 0.25 (so the discount factor δ=0.8). Also suppose that the marginal surplus value in period t is: ΔTS/ΔQit = 100 - Qit.
Find the oil extraction schedule that would prevail at a non-cooperative equilibrium (i.e.: the quantities Qit , for i = A,B and t = 0,1, that would prevail at at a Nash equilibrium of the oil extraction game played by these two countries).
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 4 images
