ECO 451 NOTE PART 3
Economics of Natural Resources
Natural resources essential for human survival on planet earth include oxygen to breathe and water to drink. Our use of the natural environment is not, of course, limited to these most fundamental of resources. Within the atmospheric, terrestrial, and aquatic natural realms, we can identify scores of other natural resources whose exploitation or conservation enhance the quality of human life. These resources include plant and animal species, the natural habitats that support those species, minerals, and energy hydrocarbons. As a factor of production, natural resources are often combined with labor and capital to produce a wide variety of final goods that consumers enjoy. Even a simple activity such as eating a tuna fish sandwich at a wood table in one’s natural gas-heated dining room, makes it easy to appreciate the contribution of natural resources to everyday life.
The Intertemporal Nature of Natural Resource Allocations
Natural resources come in two varieties: renewable and nonrenewable. Renewable resources, as the name implies, are those that potentiallycan be supplied to an economic system indefinitely.
Nonrenewable resources are those with a finite stock, incapable of renewal in a length of time that is meaningful to us. Petroleum is nonrenewable, for our purposes, because millions of years are required for its natural formation. If it is all extracted and used up in the next few decades (which is quite unlikely), we say that it is exhausted. Not all nonrenewable resources are likely to be extracted until exhaustion. For many nonrenewable resources, such as mineral ores, the marginal costs of extraction increase over 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. The quality of the ore may also deteriorate with the level of cumulative extraction. In the end, it may not be economically viable to exhaust the resource; it may cost more to extract the last few units of the resource than anyone is willing to pay.
Regardless of whether a nonrenewable resource is extracted until exhaustion, current period extraction and use of the resource involves an intertemporal tradeoff. A unit of a nonrenewable resource used today is gone forever. It cannot be used to generate economic net benefits at some later date. The appropriate pattern of nonrenewable resource use over multiple time periods is thus the main focus of natural resource economics. Intertemporal tradeoffs are also inherent in the use of renewable resources.
A forest that is harvested for timber today will take decades to regenerate. On the other hand, delaying harvest today means a delay in replanting for the next growth cycle because trees cannot be replanted until the land occupied by the current stand is cleared.
When, if at all, should a stand of trees be harvested? A fish taken from the sea today will not have the chance to grow or reproduce in future years. On the other hand, a fish
harvested today can generate an immediate benefit to the consumer and thus immediate profit for the fisherman. What is the appropriate level of current period harvesting versus conservation for the future? To begin to answer these fundamental questions, we develop the dynamic analogue to the notion of economic efficiency .
Present Values and Dynamic Efficiency
One way of describing the efficiency property of the competitive equilibrium is to note that thedifferencebetween consumers’ total willingness-to-pay (as measured by the area under 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. The difference between consumers’ total willingness-to-pay and producers’
total cost of production of a particular quantity is customarily referred to as the level of total net benefit generated by the equilibrium. Static efficiency requires the maximization of total net benefits in a given time period.
In the case of natural resource utilization, with its inherent intertemporal tradeoffs, we must often compare the net benefits generated in one time period with those generated in another. Since income produced or received in different time periods have different present values, we cannot simply compare these amounts without correctly evaluating one amount in terms of the other. Capital markets establish a positive price for the earlier availability of the right to use goods. In monetary terms, interest is the premium for earlier availability of funds. In an economy with a positive rate of interest, a net benefit of
$100 enjoyed a year from now is not worth as much as a $100 net benefit received today.
The present value criterion allows us to extend the notion of economic efficiency to a multi-period analysis. In a world of intertemporal tradeoffs, we say that an allocation of resources is dynamically efficientif it maximizes the sum of the present value of net benefits that can feasibly be generated over time. In considering an allocation of natural resource usage over time, we wish to compute the net benefits generated in each time period by the allocation, convert them to present values, and then add them up. A dynamically efficient allocation will maximize the present value sum of net benefits. We begin by considering a simple two-period model of nonrenewable resource extraction.
Nonrenewable Resource Extraction
The simplest sort of model that allows for the passage of time is a two-period model.
We will assume that a finite stock of a nonrenewable resource will be extracted over the course of two periods: period 1, representing the current period, and period 2 representing the future. Net benefits in both time periods are in inflation-adjusted dollars, and for ease of calculation, we will convert any net benefits generated in period 2 into a present value by assuming a real interest or discount rate of r = 0.50 = 50%. For simplicity, we will assume that an extracted unit of resource can be immediately consumed without any further need of processing. Demand in each period is given by Pt11 Qt, where Pt is the per-unit price andQtis the quantity of extraction and consumption in periodt,with
t1, 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?
Table 14-1 provides for the calculation of total net benefits in each period as a function of the quantity extracted and consumed. Total willingness-to-pay is described by the area under the demand curve up to the quantity in question. With a linear demand curve, this area is easily computed as the sum of the area of a triangle and rectangle, and it is provided in column 3. Total cost is the product of the quantity extracted and the constant marginal extraction cost of $1. Total net benefit is provided in column 6, and it is simply the difference between total willingness-to-pay and total extraction cost.
Marginal net benefit is given in column 7, and it is defined as the difference between marginal willingness-to-pay (price) and marginal extraction cost.
Table 14-1 Net Benefits from Extraction in a Particular Time Period
(1)Quantity ofExtraction
(2)Marginal Willingness- to-Pay
(3)Total
Willingness- to-Pay
(4)Marginal Extraction Cost
(5) =(1x4) Total Extraction Cost
(6)=(3-5)
Total NetBenefit
(7)=(2-4)
Marginal NetBenefit
1 10 10.5 1 1 9.5 9
2 9 20 1 2 18 8
3 8 28.5 1 3 25.5 7
4 7 36 1 4 32 6
5 6 42.5 1 5 37.5 5
6 5 48 1 6 42 4
7 4 52.5 1 7 45.5 3
8 3 56 1 8 48 2
9 2 58.5 1 9 49.5 1
10 1 60 1 10 50 0
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 each period, for a sum total of 20 units over the course of two periods. At a quantity of 10 units extraction per period, price would equal marginal cost, and total net benefits in each period would be maximized. Maximizing the total net benefits in each period would, trivially, also maximize the present value sum of total net benefits over the two periods, and dynamic efficiency would be achieved. Without binding resource scarcity, the resource allocation problem would no longer involve intertemporal tradeoffs. However, in this example, with an initial endowment of only 10 units of the nonrenewable resource, we face the fundamental intertemporal tradeoff at the heart of exhaustible resource economics. 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. With an initial stock size less than 20, we are confronted with precisely the exhaustible resource scarcity described and analyzed by the very influential economist Harold Hotelling in 1931.
With an initial stock size of 10, Table 14-2 describes the feasible patterns of extraction over the two time periods. For instance, if we only extract 1 unit in period 1, then 9 units may be extracted in period 2. If 2 units are extracted in period 1, then 8 may be extracted in period 2, and so forth. For each of the rows in Table 14-2,Q1andQ2sum to 10, the size of our assumed nonrenewable resource endowment. Column 3 of the table describes the present value sum of the total net benefits generated by the various patterns of extraction. Extracting 6 units of the resource in period 1 and 4 units of the resource in period 2 achieves dynamic efficiency. Extracting 6 units generates total net benefits of
$42 in period 1. Extracting 4 units generates total net benefits of $32 in period 2. In present value terms, these second period benefits equal $21.33 (=$32/(1+r) = $32/1.5).
In the dynamically efficient solution to the resource allocation problem presented here, a present value sum of $63.33 of total net benefits is generated. The key to understanding the dynamic efficiency of this allocation is to focus on the present value of the marginal unit extracted in each period.
Table 14-2 Present Value Sum of Total Net Benefits Over Time
(1)Quantity Extracted in Period 1:Q1
(2)Quantity Extracted in Period 2:Q2
(3)Present Value Sum of Total Net Benefits
(4)Present Value of the Marginal Net Benefit in Period 1
(5)Present Value of the Marginal Net Benefit in Period 2
1 9 42.5 9 0.67
2 8 50 8 1.33
3 7 55.83 7 2
4 6 60 6 2.67
5 5 62.5 5 3.33
6 4 63.33 4 4
7 3 62.5 3 4.67
8 2 60 2 5.33
9 1 55.83 1 6
Notice from Table 14-2, that the sixth unit extracted in period 1 results in a marginal net benefit of $4. In period 2, the fourth extracted unit results in a marginal net benefit of $6, and that has a present discounted value equal of $4 (=$6/1.5) as well. In other words, in a world with constant marginal extraction costs and a scarce nonrenewable resource, dynamic efficiency requires that the present value of marginal net benefits of extraction be the same across time periods. The last unit extracted in any time period must contribute the same to the present value bottom line. Otherwise, shifting extraction from periods with low present value marginal net benefits to those with high present value marginal net benefits would increase the present value sum of total net benefits. In the context of unchanging demand and constant marginal extraction cost, dynamic efficiency requires that the gap between price and marginal extraction cost rises at the rate of interest over time. In our example, it rises from $4 to $6. In a model with binding resource scarcity and a positive discount rate, extraction falls over time and price rises. The higher the discount rate, the more extraction will be shifted to the present because the future is relatively less valued. In our numerical example, only with a discount rate of zero (r = 0) and an initial resource stock of 10 units would dynamic efficiency require 5 units be extracted in each period, because the net benefits generated in each period would be equally valued. If the discount rate is positive and the initial resource stock is not large enough to equate price and marginal extraction cost in all time periods, price will exceed marginal extraction cost. The difference between price and marginal extraction cost has many names in the nonrenewable resource literature. We have already described it as the marginal net benefit of extraction, but it is also called marginal scarcity rent, royalty, marginal user cost, and, in a competitive industry, marginal profit.
Are competitive nonrenewable resource markets dynamically efficient? In a world with exhaustibility and constant marginal extraction costs, Hotelling reasoned that firms in a competitive market setting will duplicate the dynamically efficient pattern of
extraction over time.In every time period, price will exceed marginal extraction cost.
With price greater than marginal cost, one might well ask, “why would the owner of a mining firm ever conserve the resource for later time periods? Why not expand current period extraction, and invest the profits at the prevailing rate of interest?”
The answer must be that the mine owner expects price to rise over time, reflecting the increase in resource scarcity as exhaustible resource reserves decline. The individual mine owner correctly surmises that if everyone else in the industry exhausts their stock of the resource today, then they will be able to make windfall profits in the future as the sole remaining supplier. Of course, if every mine owner comes to this realization, then all will have the incentive to conserve some of their resource stock for the future. If the difference between price and marginal extraction cost is expected to rise at the rate of interest, then conservation of the resource for later time periods can be thought of as a rational capital investment. Hotelling argued that, in equilibrium, firm managers will be indifferent as to when they extract a marginal unit of the resource, because the present value of profit from marginal extraction will be the same in all periods.
Hotelling and Ricardian Scarcity Rents
In the model of extraction presented in the previous section, the resource was completely exhausted over time. The finite resource stock was characterized by constant marginal extraction costs, and the stock was not large enough to equate price and marginal cost in each time period. Consequently, dynamic efficiency required a gap between price and marginal extraction cost, a gap that rose at the rate of interest over time. In a world with eventual complete exhaustion of the resource, such a gap is referred to as a Hotelling scarcity rent. The nonrenewable resource stock, essential for production of certain final goods, is not replicable; rather, it is finite. For owners of finite resource stocks that will eventually be depleted, additional extraction of the resource in one time period is at the expense of profits that could have been generated in other time periods. The Hotelling scarcity rent (the difference between price and marginal extraction cost) represents the payment necessary to bring forth production of the marginal unit in the current rather than other time periods. This form of scarcity rent requires the economic viability of all units constituting the initial resource stock; it must be profitable to extract every last unit of the nonrenewable resource over time.
Hotelling scarcity rents only emerge when the resource is to be completely exhausted. In our two-period numerical example, if the initial resource were larger than 20 units, Hotelling scarcity rents would not emerge. As previously discussed, dynamic efficiency would dictate extraction of 10 units each period for a sum total of 20 units over the two-period time horizon. Price would equal marginal cost in each period, and some of the initial resource stock would be left behind in its natural underground state. The resource stock would not be exhausted, and Hotelling scarcity rents would be zero.
Positive Hotelling scarcity rents only emerge in contexts of binding resource scarcity in
which there are intertemporal net benefit tradeoffs associated with the decision to extract more of the resource in a particular time period.
As previously discussed, for many nonrenewable resources, costs rise over time with cumulative extraction, so that not all units of the resource stock are worth extracting.
However, even without complete exhaustion, scarcity rents may nonetheless arise, albeit, in a different form. In a world in which marginal extraction costs increase with the amount of cumulative extraction,a Ricardian scarcity rent will arisewhich reflects the additional costs imposed in future time periods from current period extraction. In this world, reserves of the resource are not of equal quality. Some units are more highly valued than others because they can be extracted at lower cost. When resource stock reserves are not of equal quality, the first units extracted will be those that are most profitable--those that can be extracted at relatively low cost. This phenomenon bares a striking similarity to the idea that the farmlands that will be cultivated first are those that are most fertile, and that the most productive farmlands will therefore earn a Ricardian rent.
To illustrate the concept of Ricardian scarcity rent in the case of nonrenewable resources, reconsider the model of the previous section. In that model, every single unit of the resource stock could be extracted at a marginal cost of $1. Given the level of demand in each period, economic efficiency dictated complete exhaustion because extraction of all 10 units of the resource stock was profitable. What if, instead, only the first unit of the resource stock could be extracted for $1? What if the second unit could only be extracted for $2, the third for $3, and so forth? More precisely, in period 1, assume marginal extraction costs are MEC1 Q1. Entering period 2, Q1units of the resource will have already been extracted, so marginal extraction costs in period 2 will be MEC2Q1Q2. If, for example, 4 units of the resource were extracted in period 1, then 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. If, on the other hand, 5 units of the resource were extracted in period 1, then the first unit produced in period 2 would cost $6, and the second would cost $7. In this formulation, the costs of extraction in period 2 now critically depend on the amount extracted in period 1. An additional unit extracted in period 1 increases the cost ofeveryunit eventually produced in period 2 by
$1 (relative to what second period costs would have been if an additional unit were not extracted in period 1).
When marginal costs increase with cumulative extraction, what is the dynamically efficient pattern of extraction over time? To answer the question, consider Table 14-3, which describes the level of marginal net benefits generated in period 1 for various integer quantities of extraction. Table 14-3 reflects marginal costs that increase with cumulative extraction.
Table 14-3 Marginal Net Benefits from Extraction in Period 1
(1)Quantity of Extraction
(2)Marginal
Willingness-to-Pay
(3)Marginal Cost (4)
Marginal Net Benefit
1 10 1 9
2 9 2 7
3 8 3 5
4 7 4 3
5 6 5 1
5.5 5.5 5.5 0
6 5 6 -1
7 4 7 -3
8 3 8 -5
9 2 9 -7
10 1 10 -9
Clearly, extraction of six or more units in period 1 is not economically efficient because the marginal net benefits are negative at those levels. We never want to extract a unit of the resource if it costs more than some consumer is willing to pay. If we did not care about the level of second period net benefits, then we would extract 5.5 units in period 1 because marginal net benefits are zero at that level (price and marginal extraction costs are both $5.50). First periodtotalnet benefits are maximized atQ15.5, meaning that the difference between total-willingness-to-pay and total extraction cost is at its greatest when Q1 5.5. However, because we do care about the net benefits generated in the second as well as first period, the dynamically efficient level of extraction in period 1 will be less than 5.5. We want to extract less than 5.5 units in order to reduce the costs of second period extraction, even recognizing that extracting less than 5.5 units of the resource in period 1 entails a reduction in first period total net benefits.
The achievement of dynamic efficiency requires that we sacrifice some first period net benefits in order to lower costs and increase net benefits in the second period.
How much of a first period sacrifice should we be willing to make?
We should be willing to sacrifice precisely that amount of net benefit in period 1 that covers the present value increase in costs in period 2 from marginal extraction in period 1. In present value terms, we should be indifferent between extracting and conserving a marginal unit of the resource in period 1. If we extract an additional unit in period 1, we generate some additional net benefits in that period. If we conserve an additional unit of the resource in period 1 (by not extracting it), we increase net benefits by reducing costs in period 2. Demand in period one is given by P1 11 Q1 and
extraction in period 1 creates a net benefit in that period equal to the subsequent present value increase in second period costs.
In our example, marginal costs increase with cumulative extraction, and dynamic efficiency requiresQ*14.4 andQ*23.3. This pattern of extraction over the two
periods maximizes the present value sum of total net benefits. The optimality of this solution is provided by the link between the marginal net benefit of first period extraction and its effect on costs in period 2. WithQ*14.4 ,P1114.4$6.6 , andMEC1$4.4.
The marginal net benefit of extraction in period 1 isP1MEC1$2.2 . WithQ*23.3,
P211 3.3 $7.7, andMEC2Q1Q2 $7.7 . The marginal net benefit of extraction in period 2 isP2MEC2$0.0 . The marginal net benefit is zero in period 2 because, by definition, in a two-period model, there is no period 3 that would provide benefits to consumers and producers. The gap between price and marginal extraction cost in period 1 is called a Ricardian scarcity rent at the margin, and it reflects the intertemporal tradeoff between current and future extraction. It represents the net benefits in period 1 necessary to justify the increase in extraction costs and subsequent reduction in net benefits in the second period.
In our numerical example, marginal extraction costs in period 2 are described by MEC2Q1Q2. Second period costs are a function of first period cumulative extraction.
The last unit extracted in period 1 increases the cost of producing all 3.3 units extracted in period 2 by $1 (relative to what second period costs would have been had the marginal unit not been extracted in period 1), for a total cost increase of $3.3. 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. The marginal scarcity rent in period 1 is this $2.2. Even though price exceeds marginal cost by $2.2, production of more than 4.4 units of the resource in period 1 would be dynamically inefficient because it would entail too large an increase in extraction costs in the next period. The dynamically efficient pattern of extraction is presented graphically in Figure 14-1.
2
2
Figure 14-1 Dynamic Efficiency in a Model with Increasing MEC
Period 1
$
MEC1Q1
P11Q
Period 2
$
Q*
MEC2 Q1Q2
P211Q2
1 1 1
Quantity
1*
Quantity
*2
Every additional unit of the resource extracted in period 1 shifts the marginal extraction cost curve in period 2 vertically by a unit. The positive gap between price and marginal cost (the Ricardian marginal scarcity rent) that is present in period 1 disappears in period 2. In the final period, price equals marginal cost, and there are no scarcity rents. This result generalizes to models with more than two time periods. 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 ofQ*1Q*24.43.37.7
units of the resource are extracted, and 2.3 units of the nonrenewable resource are left behind in the ground. ProducingQ* 3.3 units in period 2, the final time period, is efficient because the willingness-to-pay for marginal extraction (price) by some consumer is just sufficient to just cover the cost of marginal extraction. Production greater thanQ*3.3 units in period 2 would be inefficient because marginal extraction cost would exceed marginal-willingness-to-pay.
Q Q
When marginal costs rise sufficiently with cumulative extraction, so that the resource stock is not exhausted, Ricardian scarcity rents decline to zero in the last period.
Unlike the Hotelling scarcity rents that emerged in our previous model with constant marginal extraction costs and complete exhaustion of the resource stock, Ricardian scarcity rents do not rise at the rate of interest over time. In a model with increasing marginal extraction costs and incomplete exhaustion, Ricardian scarcity rents actually decline over time! In period 1, the Ricardian scarcity rent at the margin is
P1 MEC1 $2.2 , and in the final time period it is P2 MEC2 $0.0 . The popular 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 resources that will not be completely exhausted.
