Right of sale, extraction of a non-renewable resource and future generations Book II of the French Civil Code, entitled On property and different modifications of property, contains article 544 which states the following with regard to property: Property is the right to enjoy and dispose of things in the most absolute manner, provided that they are not used in a way prohibited by laws or regulations. In what follows, we propose a model of exploitation of a non-renewable resource that will allow us to understand the fundamental role played by the right to dispose of things. Indeed, we will see how this right encourages the owner to exploit his resource in a sustainable way by taking into account the well-being of future generations in his present choices and that, even if he does not he is in no way altruistic. Ms. McBain is the proud owner of an underground oil field. Ms. McBain has only two remaining periods to live, namely periods t = 0 and t = 1. (Think of each period as being 30 years. Each person will live for 90 years. and will pass through youth (0 to 30 years old), middle age (30 to 60 years old) and old age (60 to 90 years old). Mrs. McBain is therefore 30 years old in her early years. period 0.) According to the customary law of her village which precedes the adoption of the Civil Code, Ms. McBain cannot sell her oil field because it is attached to the surface land and the latter cannot be resold. Mrs. Mcbain having no heir, she will have to return her deposit to the village after her death.

(a) Let S0 = 500 be the total amount of barrels of oil in the field. (There is no uncertainty in this problem.) A barrel of oil sells for a given unit price of $ 50 in the market, that is, p0 = p1 = 50. The total cost of extraction per p Period is C (Rt) = Rt2 / 20, where Rt represents the quantity extracted from barrels at t. The net profit per period is therefore t = ptRt - C (Rt). Assuming a constant discount rate r between periods, write down Mrs. McBain's present value maximization problem V0 and determine the optimal extraction levels R0 and R1 when r =10%

(b) We define marginal rent by Pt = pt - C (Rt). Calculate the value of the marginal annuity at each period. At what rate does this annuity increase between the two periods? How much would V0 increase if the initial size of the field increased by one additional barrel, from 500 to 501? (NB No new calculation is necessary to answer this last one.)