Topics Today (4/2/13)  Review of the basic model of dynamic nonrenewable resource extraction  Clicker game  Building on the basic model: the marginal user cost of resource extraction  Factors mitigating resource scarcity  Substitutes, exploration, technology.  “The Bet” 1Dynamic Extraction of a Nonrenewable Resource  Graphically with two periods, the socially efficient allocation of extraction is the following: 70$Marginal Net Benefit in 0PV of Marginal Net Benefit in 1 70/1.1 = 63.6$70$Quantity in 0 q0= 50.95; q1= 49.05Marginal Net PV of Marginal 70/1.1 = 63.6Quantity in 1$10019.052 Major points using two-period graph on the board  Discount the MNB curve for period 1 (the second period)  Because the MNB for period 1 is discounted, more of the resource is used in period 0, less in period 1  Equating MNB in period 0 to PV_MNB in period 1 maximizes the social net benefit of the resource (i.e., generates the efficient amount of the resource)  For example, why not extract the resource in the current period to the point where MNB in the current period =0?  Private good Dynamic Extraction of a Nonrenewable Resource 3 Major points using two-period graph on the board con’t  This outcome is also the market equilibrium allocation of the resource  Equilibrium in the sense that no firm would want to alter its allocation of the resource over time  Private good, competitive market and so MEmaximize social net benefit  This outcome satisfies Hotelling’s Rule concerning the allocation of a resource over time  In other words, Hotelling’s Rule is both an observation of how resource markets with rational agents will behave over time and a statement of how resources should be allocated over time. Dynamic Extraction of a Nonrenewable Resource 4 You are a mine owner  You have 7 units of stock  Marginal cost of extracting your stock:MC=0 for all 7 units  Discount rate is 40% (r=.4)  You must decide how to allocate your 7 units over 2 periods to maximize your net benefits (your profit)  Must decide how many units to extract in the current period (integer values only)  Remainder is allocated to next period  The price that emerges is an equilibrium price that depends on the amount of stock bid into the market by current mine owners, and the demand for the mineral  Similar to the process faced by farmers in making cropping decisions Resource Extraction Game 5 Demand curve for the mineral is the same in both periods Resource Extraction Game 1100 $ Q Q0 P0 7 6 You want to maximize the present value of your profit  The present value of your profit is given by the equation,  Q0xP0 + Q1 xP1/(1+r)  Because all stock left over in the second period is put on the market, and every mine owner starts with 7 units, this formula can be restated as,  Q0xP0 + (8-Q0) xP1/(1+r)  I will provide a “profit schedule” indicating profits as a function of the amount of stock bid into the market in the current period, based on the formula above.  Up to10 rounds  A random winner in each of the last 4 rounds with payment equal to 10% of profits for the round. Resource Extraction Game 7 For each round, clickers are used in 2 phases: Resource Extraction Game Set 1: A=0 B=1 C=2 D=3 E= Set 2 Set 2: A=4 B=5 C=6 D=7 E= Set1 8 Record your choices in each round here: Resource Extraction Game Set 1: A=0 B=1 C=2 D=3 E= Set 2 Set 2: A=4 B=5 C=6 D=7 E= Set1 Round Q0 Q1 (7-Q0) PV of profits 1 2 3 4 5 6 7 8 9 10 9 ? Hotelling’s Rule is supported  ? Invisible Hand: rational, profit-maximizing mine owners who don’t actually “know” the demand for a mineral nonetheless arrive at the market equilibrium allocation  The equilibrium does not necessarily involve all mine owners extracting the same amount of the stock, even though the mine owners are identical from an economic perspective (all have the same extraction cost=0) because P0 is the same as PV_P1  ? The market equilibrium allocation maximizes the net benefit of the mineral (maximizes the present value of the net benefit of the mineral)  This is expected according to economic theory  ? More of the mineral is extracted today than in the future (though again, not all mine owners need to extract more today than in the future for this outcome). Resource Extraction Game: Lessons 10 Rate of extraction according to Hotelling’s rule  Hotelling’s Rule is a market equilibrium rule:  If it applies, no firm would prefer to change its allocation of the resource over time;  If it is violated, firms would prefer to change their allocation of the resource over time (i.e., the market is not in equilibrium).  Hotelling’s Rule is associated with maximizing the social net benefit of the mine under certain conditions  Private good, competitive industry Dynamic Extraction of a Nonrenewable Resource 11Hotelling’s Rule of Resource Extraction  Summary:  When conditions are right, the market rate of extraction is the economically efficient rate  Rate of extraction according to Hotelling’s rule: prices increase over time, extraction starts high, falls over time  Why does extraction fall over time even when the marginal cost of extraction is constant?  With higher discount rates, extraction starts higher, falls faster; stock is depleted sooner. Time Extraction Discount rate is high Discount rate is low 12The concept of Marginal User Cost  Two costs to extracting a non-renewable resource, such as oil, today:  Extraction cost (MEC)  The cost at the margin of actually extracting the resource  In the previous lecture this was simply MC  Extraction takes place only if P >= MEC  User cost -- the opportunity cost of not having the resource in the future.  As a result, the price of the resource is usually greater than the MEC. 13Quantity in 0 MNB in 0 Quantity in 1 $ 70 $ PV of MNB in 1 70/1.1 = 63.6 MNB= P-MEC = (80-Q)-10 = 70-Q 70 70 150 The Concept of Marginal User Cost This illustrates the case where MNB0(Q*)=0, i.e. P=MEC 14Quantity $ MEC 70 MC=MEC+MUC Q* P* Demand The Concept of Marginal User Cost: General Case (many-period world) 15Summary  P(t) = MUC(t) + MEC(t)  But we also know from Hotelling’s Rule that P(t)-MEC(t)=[P(t+1)-MEC(t+1)]/(1+r), and so…MUC(t)= ? See slide 2  This market equilibrium result –the result that everyone in the market