Efficient Allocation of a Non-renewable Mineral Resource Over Time Monday, March 13

Number 1 P = 8 – 0.4 q P 0 = 8 – 0.4(8.004) = 4.80 P 1 = 8 – 0.4(7.305) = 5.08 Etc. P = MEC + MUC MUC 0 = 4.80 – 2.00 = 2.80 MUC 1 = 5.08 – 2.00 = 3.08 Etc. 2.80(1.1) = (1.1) = 3.39 Etc. MUC increases at the rate of discount (10%)

#1 - Graph P, MEC and MUC over time

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  Number 4 Option for efficiency and sustainability

Number 2  What is the maximum price you would expect for the resource in period 5? Why? P = 8 – 0.4 q P 0 = 8 – 0.4(8.798) = 4.48 P 1 = 8 – 0.4(8.177) = 4.73 Etc. $6.00 = 8 – 0.4q 0.4q = 2 q = 5 If q=5, of depletable is units q of renewable is units

P = MEC + MUC MUC 0 = 4.48 – 2.00 = 2.48 MUC 1 = 4.73 – 2.00 = 2.73 … MUC 5 = 6 – 2.00 = (1.1) = (1.1) = 3.00 … 3.63(1.1) = 4.00 MUC increases at the rate of discount (10%) Number 2 (continued)

#2 - Graph P, MEC and MUC over time

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

P = 8 – 0.4 q P 0 = 8 – 0.4(7.132) = 5.15 P 1 = 8 – 0.4(6.523) = 5.39 Etc. MEC = q MEC 0 = (7.132) = 2.71 MEC 1 = (13.66) = 3.37 MEC 2 = (19.68) = 3.97 Etc. (In this case, q is the cumulative amount extracted.) Number 3

Number 3 (continued) P = MEC + MUC MUC 0 = 5.15 – 2.71 = 2.44 MUC 1 = 5.39 – 3.37 = 2.03 MUC 2 = 5.59 – 3.97 = 1.63 MUC is not increasing at the rate of discount. Why?

#3 - Graph P, MEC and MUC over time

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

Impacts on optimal extraction rates when market conditions change  When marginal extraction costs are an increasing function of quantity extracted: The resource is used more slowly since cost is increasing However, increasing extraction cost means net value declines over time. Opportunity cost of use declines over time.  Value of foregone resource is less as extraction cost rises

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?

Sustainability efforts – building a capital stock (Number 4)  PV of net benefits is $  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 =  2.144x =  X=16.43 – to be paid into fund at time 0  16.43(1.1) 8 = – will be in fund at time 8

 PV of net benefits is $  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 =  1.949x =  X=15.47 – to be paid into fund at time 0  15.47(1.1) 7 = – will be in fund at time 8

Alaska Permanent Fund   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

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?

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

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

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

P t = MEC t + MUC t  Can predict changes in price by predicting changes in MEC or MUC  E.G. incident in Middle East Oil prices rise Price gouging? Or increase in MUC? Once more certainty in availability is established, MUC goes back down