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 allocation that is efficient from the point of view of the whole world (i.e.: the quantities Qit for i = A,B and t = 0,1 that maximize the present value of the world's surplus value.
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 allocation that is efficient from the point of view of the whole world (i.e.: the quantities Qit for i = A,B and t = 0,1 that maximize the present value of the world's surplus value.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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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 allocation that is efficient from the point of view of the whole world (i.e.: the quantities Qit for i = A,B and t = 0,1 that maximize the present value of the world's surplus value.
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