1. Resources contd.
March 11th 2013

2. Outline Recap why reserves/production figures are not helpful
What efficient extraction looks like
Two period models
Hotelling’s rule
Applicability to real prices
Ehrlich-Simon Bet

4. Coal and Natural Gas Gas – 81 years (reserves/annual consumption)
Coal – 861 bln tons worldwide reserves112 years

5. Other Resource Availability
These figures are from 1974, but the amounts would be similar still.

6. Reserves are not good indicators of scarcity
Known amount that can be profitably recovered.
Price, technology affect reserves
A reserve estimate can be compared to a grocery warehouse's holding capacity. If one divides the capacity to hold a certain product, say baked beans, by the daily consumption of a city, one sees how many days the warehouse can supply a city out of current stock, say 45 days. That does not mean that the city will face a catastrophe as it runs out of baked beans in 45 days, because the warehouse itself is constantly being replenished with baked beans from canned food manufacturers. A well-designed warehouse will hold enough baked beans to meet expected demand for a length of time that has been determined to be optimal in the grocery wholesale business.
Need something that takes into account future scarcity.

7. Problem
Congratulations! You just won a million-barrel oil well! You are now trying to manage your asset. The previous owner pumped all the oil out of the well and put it into storage tanks; it will cost you nothing to sell it. Oil now sells for $15/barrel. Interest rates are 1% per month. With your well comes membership in the Good Resource Extraction and Sale Enterprise, an organization for well owners to exchange information, socialize, and get cheap drinks.
At a party, Dr. Rig (head of the Enterprise) announces that oil prices will double next month. How much oil will you sell this month, before the price increase?
Dr. Rig then announces that the price will also double the following month. How much oil will you sell next month, before the following month's price increase?
Dr. Rig then says that in the fourth month (the current month is the first), oil prices will drop to $10/barrel and will stay that low for years. How much oil do you decide to sell in the third month, before the fourth month's price drop?

8. Scarce Natural Resources
Nonrenewable resources are limited in supply and not producible
Consequence?
Extraction today has a user cost – the lost ability to sell that unit of the resource next year – in addition to the cost of extraction itself.
I.E. owners impose a temporal externality by extracting today
Instead of the usual efficiency condition, (MB=MC), we have:
MB=MC+ marginal opportunity cost.
This implies that resource owners will wish to extract less today than they would if the resource were producible, where q* is the optimal level of extraction and q’ is the level at which price equals marginal cost.

9. Ex: ? Efficient Extraction Path
Consider an owner of an oil well and two periods, today and tomorrow. Demand in both periods MB=10-.5q. MC = 3
There is no scarcity (MB=MCq=14 today)
There is scarcity. Now, NMB1=NMB2/(1.1) to maximize surplus.
Q1+ Q2=20, r=10%
Q1=10.19 Q2=9.81
P1=$4.91 P2=$5.10
P-MC in Period 1 = $1.91. P-MC in Period 2=$2.10
$1.91=$2.10/1.1 Thus, the net benefit (royalty / scarcity rent) rises at the rate of interest

10. Detailed Solution There is no scarcity
In this case, without scarcity, the efficient quantity occurs where
MB=MC
10-.5q=3
q=14 today and tomorrow
There is scarcity – total stocks are limited to 20 barrels and the interest rate is 10%
The efficient quantity occurs where the MB of extracting today equals the MC, which includes the MC of extraction and the marginal opportunity cost.
At the margin, we know that this implies that the net marginal benefit today must equal the net marginal benefit (discounted) of extracting tomorrow to
NMB1=NMB2/(1.1)
10-.5Q1-3=(10-.5 Q2-3)/(1+.1)
1.1*(7-.5 Q1)=7-.5 Q2 (multiply by 1.1)
1.1*(7-.5 Q1)=7-.5 (20-Q1) (sub in for Q2)
Q1=10.19 Q2=9.81
P1=$4.91 P2=$5.10
P-MC in Period 1 = $1.91. P-MC in Period 2=$2.10
$1.91=$2.10/1.1 Thus, the net benefit (royalty / scarcity rent) rises at the rate of interest

11. Graphically

12. Problem 2 Consider the same setup as before
MB=10-.5q MC=3
What is the efficient extraction quantity in both periods if r=30%?
10.52 and 9.48
What is the efficient extraction quantity in both periods if the stock doubles to 40 units (assume r = 10%)?
14 in both periods (satiated demand)

13. Interesting Notes
The marginal opportunity cost is a special type of externality. Will it really be incorporated into market prices?
With pollution, we found that the externality often is ignored.
For natural resources, it depends on property rights – if we own the oil ourselves, the externality is inflicted upon ourselves (just in the future).
Thus we have a strong incentive to take it into account. If we do not, we are not maximizing profits