Hotelling’s Rule or where P is the net price (or rent, or royalty) of the resource.

9. Hotelling’s Rule or where P is the net price (or rent, or royalty) of the resource.

10. Intuition behind Hotelling’s Rule Owner of financial resources: two uses of the capital Invest capital in a mine An interest generating financial asset Return on mine must also be r in equilibrium r = return per period As mine is not intrinsically productive, price of mineral must rise at rate r.

11. Hotelling’s Rule By integration implies that and so …

12. Hotelling’s rule: the time path of the resource net price Pt Pt = P0et P0 t

13. Hotelling’s rule: non-uniqueness of efficient time paths of the resource net price Pt Pt = Pbet Pt = Paet Pb Pa t The optimal path will be that one which satisfies S  0 as t

14. The time paths of the resource net price and stock Pt St Remaining resource stock Pt Net price P0 t t

15. Hotelling’s rule: with a backstop technology available Pt Choke Price Pt = P0et P0 t=T t

16. The time paths of the resource net price and stock with a backstop technology. St Remaining resource stock Pt Net price P0 t=T t=T

20. A market economy will probably not deliver an efficient and optimal allocation of non-renewable resources because: • Monopoly: depletion too slow. • Social costs of resource depletion not considered. (e.g. pollution externalities). • Private (market) interest rate above the social discount rate.