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Efficient Allocation of a Non-renewable Mineral Resource Over Time

Efficient Allocation of a Non-renewable Mineral Resource Over Time. Wednesday, March 2. Number 1. P = MEC + MUC MUC 0 = 4.80 – 2.00 = 2.80 MUC 1 = 5.08 – 2.00 = 3.08 Etc. P = 8 – 0.4 q P 0 = 8 – 0.4(8.004) = 4.80 P 1 = 8 – 0.4(7.305) = 5.08 Etc. 2.80(1.1) = 3.08 3.08(1.1) = 3.39

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Efficient Allocation of a Non-renewable Mineral Resource Over Time

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  1. Efficient Allocation of a Non-renewable Mineral Resource Over Time Wednesday, March 2

  2. Number 1 P = MEC + MUC MUC0 = 4.80 – 2.00 = 2.80 MUC1 = 5.08 – 2.00 = 3.08 Etc. P = 8 – 0.4 q P0 = 8 – 0.4(8.004) = 4.80 P1 = 8 – 0.4(7.305) = 5.08 Etc. 2.80(1.1) = 3.08 3.08(1.1) = 3.39 Etc. MUC increases at the rate of discount (10%)

  3. #1 - Graph P, MEC and MUC over time

  4. Impacts 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 sustainability

  5. Number 2 P = MEC + MUC MUC0 = 4.48 – 2.00 = 2.48 MUC1 = 4.73 – 2.00 = 2.73 Etc. P = 8 – 0.4 q P0 = 8 – 0.4(8.798) = 4.48 P1 = 8 – 0.4(8.177) = 4.73 Etc. 2.48(1.1) = 2.73 2.73(1.1) = 3.00 Etc. MUC increases at the rate of discount (10%)

  6. 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 – 0.4q 0.4q = 2 q = 5 If q = 5, q of depletable is 2.863 units q of renewable is 2.137 units

  7. #2 - Graph P, MEC and MUC over time

  8. Impacts 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 quickly

  9. Number 3 P = 8 – 0.4 q P0 = 8 – 0.4(7.132) = 5.15 P1 = 8 – 0.4(6.523) = 5.39 Etc. MEC = 2 + 0.1q MEC0 = 2 + 0.1(7.132) = 2.71 MEC1 = 2 + 0.1(13.66) = 3.37 MEC2 = 2 + 0.1(19.68) = 3.97 Etc. (In this case, q is the cumulative amount extracted.)

  10. Number 3 (continued) P = MEC + MUC MUC0 = 5.15 – 2.71 = 2.44 MUC1 = 5.39 – 3.37 = 2.03 MUC2 = 5.59 – 3.97 = 1.63 MUC is not increasing at the rate of discount. Why?

  11. #3 - Graph P, MEC and MUC over time

  12. What happens to MUC over time if MEC is increasing? $ = MUC MEC + MUC = P MEC TIME

  13. Impacts 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 increasing

  14. Increases 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?

  15. 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. Sustainability efforts – building a capital stock (Number 4)

  16. 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

  17. 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 8

  18. Alaska 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 law

  19. Policy 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?

  20. Your Savings Account $ $ $ $ Use money now Save and use more money later OR

  21. Why would taxing away rents result in faster rate of resource extraction? Q mineral Q mineral Q mineral Q mineral $ mineral $ mineral $ mineral $ mineral Mine and use income now Save, mine later, and use income later OR

  22. Why 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 growth

  23. Pt = 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 down

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