14.1 The Intertemporal Nature of Natural Resource Allocations 14.2 Present Values and Dynamic Efficiency 14.3 Nonrenewable Resource Extraction - Chapter14 Natural Resource Economics


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Chapter 14 Natural Resource Economics

14.1 The Intertemporal Nature of Natural Resource Allocations 14.2 Present Values and Dynamic Efficiency 14.3 Nonrenewable Resource ExtractionA Simple Two-Period Hotelling Model 14.4 Hotelling and Ricardian Scarcity Rents 14.5 Market Power in Nonrenewable Resource Industries 14.6 Renewable Resources: The Fishery 14.7 Open-Access Common Property Fisheries

14.1 The Intertemporal Nature of Natural Resource Allocations

  For many nonrenewable resources, such as mineral ores, the marginal costs of extraction increaseover time as it becomes increasingly difficult to physically raise the resource from the ever-deepening level of the mine to the surface of the earth. In the end, it may not be economically viable to exhaust the resource; it may cost more to extract the last few unitsof the resource than anyone is willing to pay.

14.2 Present Values and Dynamic Efficiency

  Another way of describing the efficiency property of the competitive equilibrium is to note that thebetween consumers’ total willingness-to-pay (as measured by the area under difference the demand curve) and producers’ total cost (as measured by the area under the supply curve) is maximized at the point where quantity demanded equals quantity supplied. Recall from Chapter 10, that whether due to an explicit positive rate of time preference or simply a desire to smooth consumption overtime in a growing production economy, capital markets establish a positive price for the earlier availability of the right to use goods.

14.3 Nonrenewable Resource Extraction

  Demand in each period is given by , where is P =11− Q P t t t the per-unit price and is the quantity of extraction and consumption in period t , with Q tt =1, 2. Assuming that the initial stock of the nonrenewable resource is 10 units, and that each unit of the resource may be extracted at a constant marginal cost of $1, what pattern of resource extraction would be dynamically efficient?

1 A similar two-period model of resource extraction with constant marginal extraction

  If the nonrenewable resource were abundant (if the initial stock size was nearly infinite rather than 10), economic efficiency would dictate that we extract 10 units eachperiod, for a sum total of 20 units over the course of two periods. An additional unit of extraction in period 1 is necessarily at the expense of net benefits that could be generated by extracting the unit in period 2.

2 Although L.C. Gray discussed some of the incentives facing the owner of a single mine

in his article, “Rent Under the Assumption of Exhaustibility,” Quarterly Journal of, 28: 466-489, 1914, Harold Hotelling is generally credited with our Economics understanding of a competitive exhaustible resource industry for his article, “TheEconomics of Exhaustible Resources,” Journal of Political Economy, 39: 1314-175, 1931. Table 14-2 Present Value Sum of Total Net Benefits Over Time (1) (2) (3) (4) (5)Quantity Quantity Present Value Present Value Present ValueExtracted in Extracted in Sum of Total of the Marginal of the MarginalPeriod 1: Period 2: Net Benefits Net Benefit in Net Benefit in Q Q 1

2 Period 1 Period

  In other words, in a world with constant marginal extraction costs and a scarcenonrenewable resource, dynamic efficiency requires that the present value of marginal net benefits of extraction be the same across time periods. In our numerical example, only with a discount rate of zero (r = 0) and an initial resource stock of 10 units would dynamicefficiency require 5 units be extracted in each period, because the net benefits generated in each period would be equally valued.

14.4 Hotelling and Ricardian Scarcity Rents

  If, for example, 4 units of the resource were extracted in period 1, then MEC = Q + Q 2 1 2 the first unit produced in period 2 (the fifth unit overall) would cost $5, and the second unit produced in period 2 (the sixth unit overall) would cost $6. This cost increase in period 2 has a present discounted value of $2.2 (= $3.3/(1+r) = $3.3/1.5),which is, of course, precisely the value of the marginal net benefit of extraction in period 1.

1 P

=11− Q 2 2 P =11− Q

1 Q

1 Quantity Quantity Q

1 Every additional unit of the resource extracted in period shifts the marginal extraction

  The increasing marginal costs of extraction in our numerical example are sufficient to preclude exhaustion of the resource stock. By the end of the final time period, a total of Q 1 2 units of the resource are extracted, and 2.3 units of the nonrenewable resource are left= 3.3 units in period 2, the final time period, is 2 efficient because the willingness-to-pay for marginal extraction (price) by some consumer is just sufficient to just cover the cost of marginal extraction.

5 The distinction between Hotelling and Ricardian scarcity rents is discussed at length by

  Unlike the Hotelling scarcity rents that emerged in our previous model with constant marginal extraction costs and complete exhaustion of the resource stock, Ricardianscarcity rents do not rise at the rate of interest over time. The popular P − MEC = $2.2 P − MEC = $0.0 1 1 2 2 characterization that nonrenewable resource economics establishes the proposition that scarcity rents rise at the rate of interest is incorrect when it comes to the case of resourcesthat will not be completely exhausted.

14.5 Market Power in Nonrenewable Resource Industries

  In deciding whether to cheat, a cartel member must weigh the short run gain in profits to expanding output in the short runagainst the long run loss of its share of the cartel’s future profits. The larger the competitive fringe, in terms of numbers of firms and the sizeof the resource stocks they own, the smaller the profitability of the cartel.

6 Pindyck, “Gains to Producers from the Cartelization of Exhaustible Resources,” Review of Economics and Statistics , 0: 238-251, 1978

  Given its dominant position in the nickel market and the importance of nickel in a variety of applications, Inco has been the subject ofseveral investigations by economists regarding scarcity rents, and most recently, the issue of its exercise of near-monopoly market power. In an earlier study of Inco, economist Robert Cairns argued that Inco’s nickel reserves are so abundant that there isno Hotelling scarcity rent because the reserves are unlikely to be exhausted, and therefore, the only relevant source of a scarcity rent for nickel is the effect that current 8 period extraction has on future costs.

14.6 Renewable Resources: The Fishery

  The quantity of fish harvested in a particular period of time is directly proportional to the level of human effort devoted to the activity (as measured by somesort of composite index of the number of fishing boats, the size of fishing crews, types of fishing gear, amount of time spent at sea, etc.) and the size of the fish stock. MSY Figure 14-3 Yield-Effort Curve Sustainable Harvest (Yield) H Effort E ′ E ′ ′ EMSY Although a full-fledged derivation of the steady-state stock and harvest levels consistent with dynamic efficiency is beyond the scope of this text, we can at leastdiscuss the intertemporal tradeoffs involved in considering the benefits of marginal 9 harvest versus marginal conservation of the fish stock.

9 Derivations of the conditions for dynamic efficiency for many standard fishery models

  Just as in the case of nonrenewable resources, the higher the discount rate, the higher the opportunity cost (in terms of forgone current period net benefits) of maintaining anygiven resource stock size for the purpose of generating future net benefits. While it istheoretically impossible to say whether the dynamically efficient stock size is larger or smaller than the stock size associated with maximum sustainable yield, we canunambiguously say that dynamic efficiency requires a larger maintained stock size than the one that emerges in equilibrium in the common property open-access fisheriesdiscussed in the next section.

14.7 Open-Access Common Property Fisheries

  When nobody has privateproperty rights with respect to a resource, so we say that the resource is common property. Without established private property rights to fish in the sea, anyone whocatches fish can keep them without paying fees to an owner.

10 H. Scott Gordon, “The Economic Theory of a Common-Property Resource: The Fishery,” Journal of Political Economy, 62: 124-142, 1954

  As long as price exceedsp = C(H OA OA OA the marginal cost of harvest, no fisherman has the incentive to conserve any fish (rather than harvest it immediately) because an individual fisherman has no property rights to thefuture benefits that current period conservation can bring, namely growth of the fish stock and lower fishing costs in the future. In an open-access common property fishery, ifprice is greater than the marginal cost of harvest, each fisherman realizes, “a fish not caught by me, will surely be caught by somebody else.” In the race to catch fish againsttheir rivals, all suffer the fate of the tragedy of the commons: rents are completely dissipated.

11 H. Scott Gordon, op. cit

  By the early 1970’s, the anchovy stock was severely depleted, and when El Niño arrived in 1973, the warming of the ocean, in combination with open-access fishing, led to the near collapse of the fishery and a dramatic increase in world food prices. Fine-tuning the management and enforcement of these systems is still an ongoing public policy process, but the fact that the use of ITQ, as an incentive basedmanagement tool, is spreading so quickly suggests that management authorities have recognized the importance of property rights and the stewardship of natural resourcesthey engender.

2 Ricardian rent in period 1) is . The present value

  MNB = P − MEC = 6.6 − 4.4 = $2.2 1 1 1 3.3 2 increase in costs in period 2 from marginal extraction in period 1 is= = $2.2 1.5 1.5 because the last unit extracted in period 1 increases the cost of extraction of every unitproduced in period 2 by $1. Of the 10 units in the initial resource stock, 2.3 units (=10 − Q − Q =10 − 7.7) remain in the ground and are not extracted by the end of 1 2 period 2.


  ƒWhen a nonrenewable resource stock is exhausted over time in a context of constant marginal extraction costs, the gap between price and marginal extractioncost in a particular time period is called the marginal net benefit of extraction or the Hotelling scarcity rent. The mere existence of cartels does not guarantee their success because members of cartels have a short run incentive to produce in excess of their productionquotas.ƒ When the quantity of fish harvested equals the amount of net natural growth, the fish stock is in steady-state and the fish harvest is described as a sustainable yield.


  Assuming that the marginal extraction cost ist t a constant $2 per unit, the rate of discount is r = 0.10 = 10%, and the initial resource stock is Q =10 , what are the dynamically efficient levels of extraction Q and Q ? How would the availability of a competitively-supplied perfect substitute (backstop technology) for a nonrenewable resource affect the competitive extraction of a scarcenonrenewable resource if the substitute could only be produced at a marginal cost that was twice as high as that of the nonrenewable resource?


  The environmental group Greenpeace has periodically demonstrated against the use of ITQ on the grounds that the government is giving away public property for free because quota are distributed to fishermen based on past historical catch records. In the name of reducing America’s dependence on foreign oil, a great deal of taxpayer money is currently spent on subsidies in support of the production of ethanol fromagricultural crops like corn.

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