#### Transcript Mar_11_Resourcesx

Resources contd. March 11th 2013 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 Coal and Natural Gas • Gas – 81 years (reserves/annual consumption) • Coal – 861 bln tons worldwide reserves112 years http://www.worldcoal.org/coal/where-is-coal-found/ Other Resource Availability • These figures are from 1974, but the amounts would be similar still. 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 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. 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? 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=MCq=14 today) 2. There is scarcity. Now, NMB1=NMB2/(1.1) to maximize surplus. 1. 2. Q1+ Q2=20, r=10% Q1=10.19 Q2=9.81 1. 2. 3. 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 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 Graphically 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 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