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Transcript Mar_11_Resourcesx

Resources contd.
March 11th 2013
• 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
Coal and Natural Gas
• Gas – 81 years (reserves/annual consumption)
• Coal – 861 bln tons worldwide reserves112
Other Resource Availability
• These figures are from 1974, but the amounts
would be similar still.
Reserves are not good indicators of
• 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 welldesigned 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.
• 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
– 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
– 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?
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.
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
1. There is no scarcity (MB=MCq=14 today)
2. 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
Detailed Solution
There is no scarcity
In this case, without scarcity, the efficient quantity occurs where
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
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
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)
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
– 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