Efficient Allocation of a Non-renewable Mineral Resource Over TimeNumber 1#1 - Graph P, MEC and MUC over timeImpacts on optimal extraction rates when market conditions changeNumber 2Number 2 (continued)#2 - Graph P, MEC and MUC over timeSlide 8Number 3 (continued)#3 - Graph P, MEC and MUC over timeWhat happens to MUC over time if MEC is increasing?Slide 13Increases in demandSustainability efforts – building a capital stock (Number 4)Sustainability efforts – building a capital stock (Number 5)Slide 17Alaska Permanent FundPolicy QuestionSlide 20Why would taxing away rents result in faster rate of resource extraction?Slide 22Pt = MECt + MUCtEfficient Allocation of a Non-renewable Mineral Resource Over TimeWednesday, March 2Number 1P = 8 – 0.4 qP0 = 8 – 0.4(8.004) = 4.80P1 = 8 – 0.4(7.305) = 5.08Etc.P = MEC + MUCMUC0 = 4.80 – 2.00 = 2.80MUC1 = 5.08 – 2.00 = 3.08Etc.2.80(1.1) = 3.083.08(1.1) = 3.39Etc.MUC increases at the rate of discount (10%)#1 - Graph P, MEC and MUC over timeImpacts on optimal extraction rates when market conditions changeNumber 2When a renewable substitute is addedNumber 3When marginal extraction costs are an increasing function of quantity extractedNumbers 4 and 5Options for efficiency and sustainabilityNumber 2P = 8 – 0.4 qP0 = 8 – 0.4(8.798) = 4.48P1 = 8 – 0.4(8.177) = 4.73Etc.P = MEC + MUCMUC0 = 4.48 – 2.00 = 2.48MUC1 = 4.73 – 2.00 = 2.73Etc.2.48(1.1) = 2.732.73(1.1) = 3.00Etc.MUC increases at the rate of discount (10%)Number 2 (continued)MUC does not increase at the rate of discount between periods 4 and 5. Why?What is the maximum price you would expect for the resource in period 5? Why?$6.00 = 8 – 0.4q0.4q = 2q = 5If q = 5, q of depletable is 2.863 unitsq of renewable is 2.137 units#2 - Graph P, MEC and MUC over timeImpacts on optimal extraction rates when market conditions changeWhen a renewable substitute is added:Opportunity cost of use is lower The resource is used more quicklyP = 8 – 0.4 qP0 = 8 – 0.4(7.132) = 5.15P1 = 8 – 0.4(6.523) = 5.39Etc.MEC = 2 + 0.1qMEC0 = 2 + 0.1(7.132) = 2.71MEC1 = 2 + 0.1(13.66) = 3.37MEC2 = 2 + 0.1(19.68) = 3.97Etc.(In this case, q is the cumulative amount extracted.)Number 3Number 3 (continued)P = MEC + MUCMUC0 = 5.15 – 2.71 = 2.44MUC1 = 5.39 – 3.37 = 2.03MUC2 = 5.59 – 3.97 = 1.63MUC is not increasing at the rate of discount. Why?#3 - Graph P, MEC and MUC over timeWhat happens to MUC over time if MEC is increasing?TIME$MECMEC + MUC = P== MUC MUCImpacts on optimal extraction rates when market conditions changeWhen marginal extraction costs are an increasing function of quantity extracted:Opportunity cost is lowerThe resource is used more slowly since cost is increasingIncreases in demand Increases in population, income, etc.Expect higher prices for any level of extractionThis means opportunity cost of current extraction is higherSo MUC is higher for every time period than if demand were constant.What does this mean for the rate of extraction?Sustainability efforts – building a capital stock (Number 4)PV of total net benefits from mineral resource is $152.17.For a perpetuity: So Payment = $15.22At t=0, NB=$35.22Keep $15.22, put 20.00 into fundAt t=1, PV NB=$33.17Keep $15.22, put 17.95 into fundIn PV termsKeep $13.84, put $16.32 into fundEtc.ipaymenttyPVperpetui 1.22.152$xSustainability efforts – building a capital stock (Number 5)PV of net benefits is $152.17In period 0, $35.22 is usedSo, period 0 needs to deposit into capital fund enough to insure there is $35.22 at the start of year 8 (first year after mineral is depleted)x(1.1)8 = 35.222.144x = 35.22X=16.43 – to be paid into fund at time 016.43(1.1)8 = 35.22 – will be in fund at time 8PV of net benefits is $152.17In period 1, $30.15 is used (in PV terms)So, period 1 needs to deposit into capital fund enough to insure there is $30.15 at the start of year 8 (first year after mineral is depleted)x(1.1)7 = 30.151.949x = 30.15X=15.47 – to be paid into fund at time 015.47(1.1)7 = 30.15 – will be in fund at time 8Alaska Permanent Fundwww.apfc.orgWhat is the purpose of the Permanent Fund?According to language in the state law which established the Permanent Fund (AS 37.13), the Permanent Fund was created with three purposes:(1) to provide a means of conserving a portion of the state's revenue from mineral resources to benefit all generations of Alaskans(2) to maintain safety of principal while maximizing total return(3) to be a savings device managed to allow maximum use of disposable income for purposes designated by lawPolicy QuestionWhen Price exceeds MEC, does that mean that the mine owner is earning excess profits and they should be taxed away?What happens to extraction rate if rents are taxed away?$$$$Use money nowSave and use more money laterORYour Savings AccountWhy would taxing away rents result in faster rate of resource extraction?$ mineral $ mineral $ mineral$ mineralMine and use income nowSave, mine later, and use income laterORQ mineralQ mineralQ mineralQ mineralWhy would taxing away rents result in faster rate of resource extraction?If mine owner does not get to keep rent, the incentive is to extract the resource quickly and invest the returns in some alternative income-earning venturee.g. Extract the mineral, sell it, and invest the money at some positive rate of growthPt = MECt + MUCtCan predict changes in price by predicting changes in MEC or MUCE.G. start of war in Middle EastOil prices risePrice gouging? Or increase in MUC?Once more certainty in availability is established, MUC goes back