Modeling peak oil and the geological constraints on oil production

(Design of this presentation totally based on "Bash Introduction", by André Santos, https://speakerdeck.com/62gerente/bash-introduction)

Hotelling type extraction-exploration models for non-renewable resources that is common used does not include geological constraints, that is one of the most factors that is taken in consideration in an oil exploration. In this paper is proposed a model that introduces such constraints in a Hotelling model. This model explains the fact that at some point, the increasing in production leads to a lower marginal costs, using the combination of geological constraints and the Hotelling resource models.
This also can explain the fact that some explorers are not rising their production, and how the recent high oil price (before the last big drop of price) of around 100 USD can affect the production in the small producer countries.

Transcript

3. ↑ ↓
9. = – = −
11. 0 < < 1
12. 0 < < 1
13. 0 < < 1 =
14. 0 < < 1 = ≤
15. max {,} = 0 ∞ { − − ( )−} ( ) =
16. ℒ = ℛ , − − + − − + ( − )
17. ℒ = ℛ , − − + − − + ( − ) ℛ , − − − ≤ 0 ⊥ ≥ 0 − + − ≤ 0 ⊥ ≥ 0 − + = 0 − = 0 ( − ) = 0
18. ℛ , − − = +
19. ℛ , − − = +
21. = − () = ( − )
24. γ γ