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An Amateur AmongProfessionals

Robert M. Solow

Department of Economics, Massachusetts Institute of Technology,

Cambridge, Massachusetts 02139; email: jamu@mit.edu

Annu. Rev. Resour. Econ. 2009. 1:1–14

First published online as a Review in Advance on

June 22, 2009

The Annual Review of Resource Economics is

online at resource.annualreviews.org

This article’s doi:

10.1146/annurev.resource.050708.144305

Copyright © 2009 by Annual Reviews.

All rights reserved

1941-1340/09/1010-0001$20.00

Key Words

resource economics, Hotelling condition, sustainability, backstop

technology

Abstract

This brief retrospective note describes the author’s occasional con-

tributions to the economics of natural resources. It emphasizes the

role and interpretation of the Hotelling condition and discusses

the reasons why that result plays so small a role empirically. The

concept of sustainability is introduced in the simplest possible

content, that of directly consuming a finite stock over infinite time.

When the resources flow is an input into production along with

capital that can be accumulated, the nature of sustainability

changes and becomes more interesting. It is suggested, however,

that to consider instead the eventual availability of a resource-free

backstop technology may be just as interesting and more relevant.

That concept is illustrated in the direct-consumption context but

awaits further development in production economies.

1

Watch an interview with the author online.

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For good reason, this is a very short example of the genre “retrospective essay.” Although I

have had a long career as an economist, I have only a very brief and episodic record as a

resource (and environmental) economist. There is not a lot to retrospect about. But my

timing has been pretty good, and maybe not accidentally.

The theory of economic growth, and the role of capital accumulation in it, has been a

long-time preoccupation, however. I think I was always sort of subliminally aware (and

often superliminally aware) that natural-resource limitations (including those imposed or

mediated by the environment) were absent from theoretical and empirical model-building.

Most of the time that seemed to be more an intellectual gap than a practical error. I was

well acquainted with the book by Barnett & Morse (1963). (Harold Barnett was a friend

from my graduate-student days.) So resource scarcity did not seem to be a pressing

practical problem. And I remembered having been told by a distinguished chemist friend

that untold quantities of nitrogen could be fixed from the air (given only a large supply of

cheap energy), that the energy would eventually be available from the Sun in one form or

another, and that nitrogen could provide the basis of a whole materials economy. For a

macroeconomist like me, there were other things to think about.

Then came the splash over the Club of Rome’s Limits to Growth (Meadows et al.

1971). I tend to react badly when opprobrium, especially ignorant opprobrium, is heaped

upon “economists.” When I read the book, it seemed to me to draw sweeping conclusions

from unverified assumptions and thin-air-invented dynamics, meanwhile ignoring some

normal market mechanisms. I commented on the book twice (Solow 1972, 1973), but in

rather inaccessible places. Probably not coincidentally, in 1974, came two opportunities:

to contribute an article to a special issue of the Review of Economic Studies (Solow

1974a) devoted to the economics of natural resources and to give the Ely Lecture (Solow

1974b) at the annual convention of the American Economic Association. So I could do

some academic research that fit into my normal scheme of things and also help to open

up the analytical issue of resource limitations to a wider group of economists who would

actually understand the substance. And so began my mini career as a resource economist.

A second active current of thought also helped to lead me—as if by an Invisible

Hand?—to the topic of the technical paper “Intergenerational Equity and Exhaustible

Resources” (Solow 1974a), introducing the theory of optimal economic growth stemming

from Frank Ramsey’s (1928) famous article. The connection is easy to see in terms of the

simplest “cake-eating” problem. Consider a cake of finite size to be consumed over

the infinite future: At what rate should it be consumed? Diminishing marginal utility of

cake suggests equal consumption in every interval, but no constant consumption level

other than zero is feasible forever. So perhaps future utility should be discounted according

to subjective time preference. (Ramsey opposed this practice on ethical grounds.) That

would suggest equalizing discounted marginal utility over time. With a constant discount

rate—the only time-consistent possibility—the marginal utility of cake would have to

grow exponentially and indefinitely with time, so the rate of consumption would have to

converge to zero. That is feasible, but it does not seem fair to the future. (I hardly need

to mention that these same puzzles about discounting—it matters so much and rests on

so little—are again at the center of controversies about the proper response to global

warming.)

The finite-cake story seems relevant to the problem of exhaustible or nonrenewable

resources, but it misses too much. (It is understood that the notion of “running out” can

be replaced by the notion of prohibitively rising extraction costs.) The natural resources

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we are concerned about are not consumed directly; they are used in varying amounts,

along with other inputs, to produce the goods we consume. The finite-resource problem

needs to be embedded in a model of production and consumption. Then the urgency of the

resource-scarcity problem will, in a commonsense way, depend on the importance of

resource inputs, on the ease or difficulty with which other inputs can be substituted for

nonrenewable resources, and on technological progress that allows more consumable

output to be extracted from any combination of natural-resource and other inputs.

The notion that technological progress could make the resource-scarcity problem

go away seemed too simple and obvious, even if possibly true, so I started from a fairly

traditional growth model without technological change. The problem was then to find and

characterize the largest constant level of consumption that could be permanently sus-

tained, starting with a finite stock of a nonrenewable resource that was essential to

production (in the sense that zero resource input implied zero output). The other produc-

tive inputs were capital and labor. With the supply of labor constant for the very long run,

the game was all about the accumulation of capital played against the depletion of the

resource. In this setting, constant positive consumption forever cannot simply be ruled out,

as it can in the cake-eating case. Indeed, intuition was confirmed and made precise:

Enough substitutability would do the trick, and in the borderline case, the outcome

depended on the relative importance of capital and resources as inputs (as measured by

the elasticity of output with respect to each of those inputs).

That sort of logic was clearly a way of getting at the general issue of sustainability.

A large, ingenious, and useful literature has evolved on these important questions, some of

which is summarized in a recent note by John Hartwick (2009). One especially interesting

result was what I called Hartwick’s Rule: The investment of all (competitive) resource

rents along an efficient path leads to just enough capital accumulation to maintain a

constant level of consumption. This thought, too, has been further elaborated in the

literature.

My only further contribution was expository. In one invited lecture (Solow 1992b), I

tried to explain to a scientifically literate audience that “sustainability” did not and should

not mean the preservation of every individual resource and environmental amenity, but

rather the preservation of a general capacity to produce well-being. The common injunc-

tion to leave Nature as we found it is neither feasible nor sensible. In another lecture

(Solow 1992a), I used Hartwick’s Rule to argue for comprehensive “green” national

accounts that would, among other benefits, allow some approximation to the volume of

net investment in reproducible capital required for sustainability of national consumption.

The Ely Lecture “The Economics of Resources and the Resources of Economics”

(Solow 1974) was intended not only to introduce a broad audience of economists to the

economic theory of nonrenewable resources, but also to defend our fair discipline against

ignorant statements about its incapacity to deal with the role of nature in economic life.

The particular device that came naturally was to treat Hotelling’s original analysis as

an application of capital theory to a nonreproducible resource. There is no need to

rehearse those ideas here, but see Hartwick (2009) and other articles in the symposium in

the first issue of the Journal of Natural Resources Policy Research.

I would like to comment, however, on one aspect of the Hotelling-based theory. It

leads, as is well known, to the proposition that the scarcity rent on a nonrenewable

resource, the excess of price over marginal extraction cost, should be rising through time

at a proportional rate equal to the (real) rate of interest. But empirical work aimed at

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testing this proposition against facts has yielded, at best, mixed results, and probably less.

It is safe to say that it is very difficult to detect this sort of price behavior in actual time

series, for several reasons.

For one thing, it is possible that, in many cases, the scarcity rent has been relatively

small during the period of observation, if the ultimate exhaustibility of the resource is seen

as a very distant or even unlikely event. Then its movement through time could be lost in

the noise. More important, for many natural-resource products, short-run supply and

demand curves may be rather inelastic with respect to price. Then the inevitable shifts in

supply and demand curves—related to weather, politics, the business cycle, downstream

shifts in demand, occasional innovations, and so forth—will generate large and erratic

changes in price, perhaps further exaggerated by speculation. Modest scarcity rents will be

even harder to detect and isolate.

A recent and as yet unpublished paper by James D. Hamilton (2008) makes this point

well and concludes, “The $140/barrel price in the summer of 2008 and the $60/barrel in

November of 2008 could not both be consistent with the same calculation of a scarcity

rent warranted by long-term fundamentals. Notwithstanding, the algebra of compound

growth suggests that if demand growth resumes in China and other countries at its

previous rate, the date at which the scarcity rent will start to make an important contri-

bution to the price, if not here already, can not be far away.” That sounds reasonable.

Considerations like this may help to account for the apparent empirical irrelevance

of the Hotelling (1931) model. But they also remind us of the proper function of an

abstract theory of that kind. It is both a guide to the intuition and a very general frame-

work, not a precise template, for empirical investigation. Hotelling reminds us that the

existing stock of a natural resource, renewable or nonrenewable, is a capital asset, even if

it has some special characteristics not shared with other types of capital assets such as

printing presses or inventories of canned goods. So we have a notion of how to start

thinking about them and observing what happens in their markets. Even apart from the

particular difficulties mentioned above, you would not expect to see the price of oil or

copper behaving exactly like a well-defined marginal extraction cost plus an exponentially

rising scarcity rent, any more than you would expect to see the price of spinach looking

exactly like the ratio of the marginal utility of spinach to the marginal utility of income for

the well-defined marginal buyer of spinach.

Nowadays the main practical focus of attention in the economics of natural resources

is the future supply of energy. The rapid growth of the large Chinese and Indian econo-

mies; the possibility that the peak of world oil production is just ahead or already behind

us; and the special difficulties, political and environmental, associated with coal and

nuclear energy have all conspired to create a lively interest in alternative, nonfossil-fuel-

based sources of usable energy. With this in mind, I mention a line of thought and research

that brings together the insights of the Hotelling model and the issue of sustainability, the

two topics I have been discussing so parochially in terms of my own writing.

In 1973, needing it to establish reasonable terminal conditions for an intertemporal

model of oil production, William Nordhaus (1973) introduced the concept of a “backstop

technology.” In context he meant a technology for producing useful energy that was not

dependent on a nonrenewable resource base and, thus, could provide an indefinitely

sustainable tail to an episode of oil-based economic life. The idea was that the backstop

technology might not be available at all until some time in the future or that it might be

available now but at an uneconomically high cost, although this cost could be expected to

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fall over time. Eventually the Oil Age links up with the Backstop Age, with or without an

interval of overlap, until the Oil Age ends and the (in principle, infinite) Backstop Age

begins.

This struck me at the time—I was teaching a course on the economics of natural

resources—as a more sensible, more realistic, way to think about the very long run than

the kind of maximum-feasible-constant-consumption-path exercise I described above.

This backstop-technology concept is probably what will eventually play out in history. So

far as I know, there has not been much literature, either purely theoretical or empirically

calibrated, following up Nordhaus’s idea. There should be more, and the widespread

interest in energy from direct solar, wind, biofuels, and the like should stimulate this

research.

At a summer school in 2003 (see Appendix below), I gave a lecture whose broad topic

was the relation between ecology and economics. There I tried to offer an expository but

fairly complete treatment of the backstop-technology idea applied to the simplest cake-

eating problem. It does manage to synthesize the Hotelling model with intuitions about

sustainability, without any need for time discounting. I never published that lecture, but

I include it here as an Appendix (see section below), in the hope of stirring up some more

sophisticated work on what seems to me to be the right way in practice—in theoretical

practice, that is—to deal with the sustainability issue. Once again, the backstop idea needs

to be embedded in a model with production. There will be some difficult modeling

decisions: For example, is the capital employed in the resource-using technology shiftable

to the backstop technology when the transition occurs? It is hard to guess in advance

whether anything very different will happen, but the presence of more margins to play

with should lead to some interesting economics.

An explicitly retrospective essay like this may tend to encourage an unhealthy concern

with oneself. I want to mention—for a reason, I hasten to say—that I can remember writing

only two papers on renewable resources, although I always included them in my teaching.

The first (Solow 1976) was on an optimal fishing strategy when a natural predator on the

valued species is present; I did the best I could, but I was unhappy that I could provide

only a dual characterization of the optimal strategy, not a straightforward primal descrip-

tion. The second (Solow 2002) was a modification of the standard when-to-cut-a-tree

formula if the standing stock of trees also conveyed a benefit.

I mention this to point out that both papers were composed for Festschriften: the first

in honor of William Vickrey, who was interested in everything, the second in honor of

Karl-Goran Maler, a mainstay of the field. It has struck me that essentially everything

I have written on resource economics, with maybe a fractional exception for the first paper

on constant-consumption paths, has been a response to an invitation: a lecture, a Fest-

schrift, a conference. That is what happens to a (curious) amateur among professionals.

APPENDIX: BACK TO BACKSTOP TECHNOLOGY

The following is extracted, with minor revision, from a previously unpublished talk given

at the Summer School on Economics and Ecology held in Trieste, Italy, in June 2003.

This is not a talk on sustainability. The notion of sustainability has become a buzzword in

current discourse about economic policy. The path traced by the concept is a rather

familiar one in economics. It starts as a fairly vague, but not meaningless, characteristic

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of possible paths for an economy or part of an economy, and generally a desirable

characteristic at that. The next step was to give the notion some precision. In the intellec-

tual style of modern economics, this meant embedding it in a well-conceived model, so

that we could discuss things like measurement, implications, trade-offs, equilibrium con-

ditions, optimality properties, and the rest of the routine apparatus.

Then, in the spirit of the man who said “I know how to spell ‘banana’ but I don’t know

when to stop,” we continued to refine the concept well past our capacity to actually use it.

This is not necessarily bad; the marginal value of refinement may be pretty low, but very

likely the marginal cost is even lower. [By the way, Y. Hossein Farzin (2002a,b) provides a

very useful recent attempt to put some order and simplicity into the literature on sustain-

ability.]

Nevertheless, the point I want to make in this talk is that, for practical purposes, there

is a more useful set of theoretical and empirical investigations we could be pursuing with

roughly the same applied-analytical goal in mind, namely understanding the constraints

imposed on economic evolution by the natural environment (more realistically, by some

aspects of the natural environment).

Some 30 years ago, set in motion by the first OPEC oil shock, Professor William

Nordhaus of Yale University sketched a programming model of the world oil economy.

His immediate goal was to estimate the shadow price, i.e., the true scarcity value, of a

barrel of crude oil in the ground. You can easily understand how interesting and significant

it would have been to compare this shadow price with the world market price of crude oil

in 1974. (One of my favorite professorial reminiscences is connected with that paper. I was

explaining Nordhaus’s work in a graduate course I was then teaching on the economic

theory of natural resources. As a strong believer in economics as a handicraft industry, I

mentioned, teasingly, to the class that this remarkable piece of work had been done by an

extraordinarily powerful research apparatus, not to be undervalued by advocates of Big

Economics: one professor and one undergraduate research assistant. When the class was

over, one of the students came shyly up to me and said, “I was the undergraduate research

assistant.” It turned out to be Paul Krugman. Teaching can be an unexpected pleasure.)

Today’s shadow value of an oil deposit is a forward-looking concept, like any other

asset price. To take an obvious example, it must depend on expected future discoveries of

oil, on future availability of alternative sources of energy, as well as on future demand.

There is an obvious connection with sustainability: Along an unsustainable path, one

would expect the shadow price to be rising, and this must have an effect on the current

price.

Nordhaus chose a way of dealing with this problem that still strikes me as sensible.

Instead of worrying about the infinite-time possibilities for an economy with a finite stock

of oil, he took it for granted that the world would sooner or later revert to a technology

for mobilizing energy that was not based on an exhaustible resource. He called this the

“backstop technology.” Such technologies already exist, and they existed then; they have

not yet taken over from fossil-fuel technologies because they are more costly. But they will

eventually become cheaper than fossil-fuel-based technologies both because the backstop

technology will improve over time and because the shadow price of oil will increase

(for reasons already discerned by Harold Hotelling in 1931).

So Nordhaus made what seemed like plausible assumptions about the evolution of

energy costs associated with the most likely backstop technologies; he used these assump-

tions to anchor the future shadow price of oil, from which he could work backward

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toward the current shadow price. This was an application of Herbert Stein’s deep philo-

sophical remark to the effect that, “Anything that can not possibly go on will stop.” Since

I was teaching a graduate course in the economic theory of natural resources, I went on to

work out for my class the timing and details of the transition from an exhaustible-

resource-based technology to a resource-free (or renewable-resource-based) technology.

I really like those refinements, and I think that learning about them is an important part

of the education of an economist. I also think that it is probably more useful to investigate

the emergence of backstop technologies and their implications than to focus on the version

of sustainability that motivates the literature today. I want to say clearly that this is not an

aesthetic or theoretical judgment, but an empirical one. The backstop scenario is a more

likely one to play out in the future, so the value of a marginal refinement in that arena is

likely to exceed the value of further refinements in modeling sustainability.

I propose to illustrate the nature of the backstop story by dealing informally with the

oldest and simplest problem of allocating a finite resource over infinite time, indeed a case

in which there is obviously no indefinitely sustainable path in the usual sense. You will

guess that I have in mind the so-called cake-eating problem. It has the advantage that I can

make the important general points without technical detail.

Let me remind you of the story. An economy—possibly a single shipwrecked sailor,

possibly something more complex—has at its disposal a given stock S of an essential

resource. A flow use of the resource can serve as a productive input, and that can lead to

some interesting economics, now well explored, but it is simpler if we imagine the

resource to be directly consumed. The instantaneous social utility function is u(c),

with all the usual properties and, to make things easy but still interesting, u(0) ¼ 0 and

u0(0) ¼ 1, so that zero consumption is truly painful. [The alternative assumption that

u(0) ¼ �1 may be more interesting, but it requires more detail than is useful here.] The

question is, What is the best time pattern of use of the stock S? A strong assumption,

almost always adopted in this part of economics, is that utility is time additive: The

criterion of goodness isR10 u (c(t))dt. Notice that I have not allowed for a utility discount

rate. I will have to say more about that soon; I would be very happy to be able to do

without it, because it was never struck me as a convincing assumption, neither for a

shipwrecked sailor nor for a society.

If the stock S had to last only for a finite time T, then the obvious solution is steady use:

c(t) ¼ S/T for 0 5 t 5 T. Mere diminishing marginal utility tells us that any nonconstant

flow can be improved by transferring some consumption from an instant with higher flow

(and therefore lower marginal utility) to an instant with lower flow (and therefore higher

marginal utility). The value for that path is Tu(S/T). Once S is used up, however, the

society or the sailor is condemned to utter misery for the rest of time; so that is not really

a good solution. If we ignore this crucial fact for a moment, it is easy to calculate that

d/dT[Tu(S/T)] ¼ u(S/T) � (S/T)u0(S/T) > 0. (This is where the assumption that u(0) ¼0 helps.) In that sense, a longer period of lower use is always better than a shorter period

of higher use. In contrast, T¼1 is not a solution because then c¼ 0; that is a way of saying

that there is no sustainable pay for this economy. We have reached a well-known impasse.

The standard way out of this box, as I assume everyone knows, is to introduce a

positive utility-discount rate, so that the society or the sailor maximizesRe–rt u(c(t))dt.

This leads to the equalization of discounted marginal utility at every instant, or u0(c(t)) ¼kert, with the constant k chosen so as exactly to use up the initial stock S. But then

consumption decreases steadily toward zero, and instantaneous social utility decreases

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with increasing painfulness to zero. Exponential discounting cleans up the mathematical

mess and leaves everything finite. The trouble with this “solution” is that discounting is so

arbitrary and therefore ultimately unconvincing. There is an intelligent but inconclusive

literature that tries to evade this arbitrariness. (The most up-to-date source is probably

Portney & Weyant 1999.) This is not what I want to discuss. One of my goals is precisely

to be able to do without an arbitrary discount rate.

Instead I introduce a backstop technology. Suppose there is now, or will be in the

future, a way of producing a perfect (meaning very close) substitute for the nonrenewable

resource. That is to say, it is possible even now, or will be possible in the future, to

get along without the resource, but perhaps—though not necessarily—at a very low level

of utility. It should be understood that this is not intended as some kind of analytical

device; it is an assumption about the physical world (and not about preferences). I think it

is worth exploring because I think it is usually empirically true. If it is not empirically

valid, it is pointless.

The historically interesting situation is that a primitive backstop technology is known,

but it is expected to become more productive in the future. Obviously the future produc-

tivity of any backstop technology is uncertain; I will argue deterministically, but a proba-

bilistic theory is needed if the basic idea is useful. My basic belief is that the theoretical and

empirical investigation of backstop technologies is a better use of intellectual effort than

the refinement of arguments about discounting and sustainability.

The simplest case for elementary exposition is that the backstop technology already

exists and is not expected to improve. We can cut out some intermediate steps (like

calculating the maximum level of utility achievable using only the backstop technology)

by simply assuming that the best such utility level is ub. In addition I will assume that the

resource-based and backstop technologies cannot be used simultaneously; it is a case of

one or the other at any time. This simplification is inessential, but it economizes on routine

calculation.

The problem can now be formulated in this way: Over how long an interval T should

the nonrenewable resource be used? While it is being used, it should be used at a constant

rate, for the diminishing-marginal-utility reasons already mentioned, so the utility level

achieved will be u(S/T). In the absence of discounting, it does not matter when that

interval occurs, or even whether it consists of one interval or several with lengths adding

up to T. I put resource use at the very beginning, for definiteness. This is obviously the

right thing to do if the backstop technology is expected to improve over time; this is the

realistic presumption, and I take it up in a moment.

Suppose the Oil Age extends from 0 to T and the Solar Age extends from T to Z, where

Z is some arbitrary date that will turn out to play no role at all. I stay with the conventional

assumption of time additivity. Then total undiscounted utility is Tu(S/T) + (Z � T)ub. The

best value of T satisfies u(S/T) � (S/T)u0 (S/T) � ub ¼ 0. Obviously, then, T* is independent

of Z. So this solution (steady flow of resource use for the first T* units of time, best use of

backstop technology thereafter) is valid for all time, with zero discounting. There is a

simple graphical solution for T*. Figure 1 plots the utility function u(c). Rotate a ray

starting at (0,ub) until it is tangent to the utility function at c*. Then T* ¼ S/c*.

The utility path for the economy is shown in Figure 2. It may be worth mentioning

explicitly that if ub > u(c)*, then the economy never consumes its nonrenewable resource;

the backstop technology is superior. But that is uninteresting: The “deposit” would not

even be seen as a “resource.”

8 Solow

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ub

u(c)

cc*

Figure 1

Optimal current consumption c* is determined by the tangecy of the line from ub with u(c). Then T* =

S/c*. Variables: c*, the optimal level of consumption; S, the original stock; T*, the optimal time over

which to exhaust the original stock; ub, the level of utility achievable with the backstop technology;

u(c), the level of utility associated with consumption level c.

t

u

ub

u(c*)

T *

Figure 2

The corresponding path for u(c), from which the path for c follows. Variables: c*, the optimal level of

consumption; t, time; T*, the optimal time over which to exhaust the original stock; ub, the level of

utility achievable with the backstop technology.

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A more interesting and more “realistic” scenario occurs when the net social value

associated with the backstop technology is an increasing function of calendar time ub(t).

The backstop technology may not even be available now or in the near future, but it is

expected to appear at a fixed date in the future, say t1, and to improve in productivity

from then on. [There is room for elaboration here: ub(t) should be probabilistic rather than

known with certainty, and a more inclusive model could allow for learning by doing or

some other endogenous influences on ub(t).] So the situation is as described in Figure 3,

and the problem is once again to choose the best pattern of use of the stock S of the natural

resource in these circumstances.

As always, when the resource-based technology is in use, the flow should be constant;

peaks and valleys are wasteful. Now, however, the interval of use of the resource should

definitely come at the beginning, even without discounting. It is better to use the backstop

technology when it is more productive rather than less (unless possibly if there is a learn-

by-doing component). A time interval (0,T*) is to be chosen, with the resource being used

up at the rate c* ¼ S/T*; thereafter the backstop technology is employed, yielding social

utility ub(t).

More can be said, without much fuss. For instance, the path shown in Figure 4 is not

efficient. When the resource is exhausted at T*, there should not be a discrete upward

jump in social utility as the economy switches to the backstop technology. The reason is

that a slightly smaller value of T* (larger value of c*) would improve social welfare during

the (slightly shorter) resource-use period, and the first stages of use of the backstop

technology would still improve on the last stages of resource use under the initial trail

program. So u(c*) � ub(T*).

Can social welfare take a discrete drop at T*? Yes, it can. Start with the path in

Figure 5.

tt1

ub(t )

Figure 3

A backstop technology that is first available at t1 and then becomes more productive over time.

Variables: t, time; ub, the level of utility achievable with the backstop technology.

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t

u(c*)

ub(t)

T *

u

Figure 4

A nonoptimal value of T*: A slightly smaller value would increase utility as an interval with no

decrease elsewhere. Variables: t, time; T*, the optimal time over which to exhaust the original stock;u(c), the level of utility associated with consumption level c; ub, the level of utility achievable with the

backstop technology.

t

u(c*)

ub(t )

T *

u

Figure 5

A discrete decrease in c and u at T* is optimal. Variables: t, time; T*, the optimal time over which toexhaust the original stock; ub, the level of utility achievable with the backstop technology; u(c), thelevel of utility associated with consumption level c.

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Would it be better to choose a slightly smaller T*? That would increase the flow of

social utility during the new resource-use phase. But that phase would end sooner. The net

gain in undiscounted social welfare would be the area of the horizontal shaded sliver,

offset by a loss equal to the area of the shaded vertical sliver at the end shown in Figure 5.

The comparison could go either way, depending on the exact shape of ub(t) and the utility

function u(c). Actually, assuming only that ub(t) is smoothly increasing, it is easy to see

that there must be a discrete reduction in instantaneous social utility at the instant

at which the economy switches from the resource-based to the backstop technology.

[Social welfare for any choice to T is W ¼ Tu(S/T) þ R ZT ub(t)dt, where the irrelevant Z is

introduced. So dW/dT ¼ u(S/T) � (S/T)u0(S/T) � ub(T). If u(S/T) ≦ ub(T), it follows that

dW/dT 5 0 at T. It would be an improvement to reduce T a little, which would create a

positive gap between u(S/T) and ub(T). It is amusing that I can see this in Figure 5, but

I have a hard time putting it into words.]

It should be understood that this kind of model can be elaborated in several directions.

The resource-based and backstop technologies could be specified in more detail, with

labor and other costs made explicit. Then there would be a normal allocation problem

within the economy, to be studied in the usual way. A demand side could be added, with

consumption and investment endogenized. It would be possible to relax the assumption

that only one of the resource-based and backstop technologies can be used at any time, so

that there could be an interval when oil and solar share the energy market. In brief, a

whole general equilibrium apparatus can be built and wrapped around the basic techno-

logical choice.

I repeat, this technical maneuver is precisely not the prospect that interests me now. It

seems to me that the organization and development of backstop technologies is in fact the

way a growing economy typically evades the sustainability problem. Societies typically do

not conserve scarce nonrenewable resources; instead, societies typically work around

them, either by shifting to technologies based on more abundant resources or, in the limit,

by reducing use of scarce resources to a minimum. Two or three decades ago, when I first

got interested in this part of economics, I asked an eminent chemist friend (Professor Paul

Doty of Harvard University) how far he thought it would ultimately be possible to

economize on scarce nonrenewable resources. He answered that, with cheap enough

energy and more or less unlimited access to nitrogen (a very abundant element in the

atmosphere), it would be possible to create new materials and, with them, manufacture

just about everything.

I do not know if that forecast looks valid today. But that way of thinking certainly

suggests that the algebra of backstop technologies is more relevant to sustainability in our

society than the refined algebra of conservation of exhaustible resources and the fairly

unproductive discussion of the logic and morality of discounting that seems to accompany

it. At least there are some rough empirical calculations to be made.

In taking the first steps in this direction, it is convenient to assume that the backstop

technology produces a perfect substitute for the resource-based output. This is certainly

the case with electric energy, usually the first context one thinks of. Obviously “very good

substitute” is a very good substitute for “perfect substitute.” There are also contexts in

which the backstop perspective may be inappropriate. Think of scenic wonders—natural

or man-made—for instance. Could we provide a near-perfect substitute for the Giant

Sequoia or the Parthenon? What makes me suspicious is that people might have to be

“taught” that some other species of tree—or fish or landscape—is “just as good as” the

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giant redwoods. This puts one in mind of the sort of brainwashing described by Aldous

Huxley (1932) in his anti-utopia Brave New World. Once that analogy occurs to you, it

looks more attractive to leave the Giant Sequoia alone. (A rule of reason should apply:

The lack of perfect substitute for an enormous old redwood does not imply that none

exists for a not-very-distinguished species of fish.)

Recent public discussions of possible backstop technologies for energy have not been

exactly confidence inspiring. Many alternatives to oil and gas have been mentioned: direct

solar, wind, biomass, hydrogen, fuel cells, tar sands. But the accompanying analysis often

has the faint odor of hype. Too often we are told that backstop technology X will become

viable when the real price of oil rises $Y a barrel; if the real price of oil does just that, we

are told that the next increment of $Y will be the key. Obviously that kind of research

would be better taken out of the hands of interested parties, including governments.

I am only too conscious that the trail I have been following is resource economic rather

than ecologic economic in substance. When I began working in this field, the resource-

economic research area was the economics of fisheries. Ecological economics began

to take shape only when I was working on other things altogether, so I am not up to date.

I tend to doubt that it has taken shape yet; maybe this conference will mark an inflection.

In any case, as an old dog, I could not hope to contribute new tricks to ecological

economics.

There is a generic difference between resource economics and ecological economics. In

the first, the resource stock does not react to its exploitation (except, of course, by

becoming depleted). In the second, it does. In ecological economics, the resource stock

has an interesting and important dynamic of its own. The case of the fishery, in its early

development, was sort of intermediary. The fish population does have a dynamic, but

in the old days, it was modeled as pretty simple, usually logistic. Maybe modern fishery

economics pays more attention to the interrelated ecology of the ocean. (I did once, about

30 years ago, write a paper introducing a natural predator into an otherwise standard

fishery model but did not get very far, probably because computer simulation was not then

as available as it is now.)

The function of economic theory is to help train the intuition of economists and, as part

of that process, to help guide empirical work. I have kept emphasizing, perhaps to the

point of boredom, that models combining an exhaustible resource with a backstop tech-

nology are interesting only if access to backstop technologies is, in fact, an important part

of the history of societies casting about for sustainability. In that case, it is a good idea for

economists to polish their intuition on problems associated with the transition to backstop

technologies, and perhaps to the endogenous evolution of such technologies.

I am not sure that I can provide a lesson for ecological economics, nor am I sure that it

is my duty to provide one. If my earlier suggestion is correct, that the significant difference

between ecological economics and resource economics is that the reciprocal dynamics of

an ecological system subject to human exploitation is radically more complicated than

that of a simple resource, then one natural object of research is to classify and categorize

those dynamic responses. I am a great believer in simple models and “representative”

special cases. That may be the proper approach in this bilaterally complicated field. The

problem may be to locate the key simplifications, whether they are on the ecological or the

economic side. Probably, they will have to be on both sides.

If one were setting out to model the interaction of economists and ecologists in creating

and extending a subdiscipline of ecological economics, it would be interesting to observe

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conferences like this and to think whether a predator-prey model is appropriate—and who

is the predator and who is the prey—or else a situation where complementarities are

exploited and cooperation rules. I am hoping for the best.

DISCLOSURE STATEMENT

The author is not aware of any affiliations, memberships, funding, or financial holdings

that might be perceived as affecting the objectivity of this review.

LITERATURE CITED

Barnett HJ, Morse C. 1963. Scarcity of Growth: The Economics of Mineral Extraction. Baltimore,

MD: Johns Hopkins Univ. Press

Farzin YH. 2002a.Can an exhaustible resource economy be sustainable? Work Pap. 47.2002, FEEM.

doi: 10.2139/ssrn.317933

Farzin YH. 2002b. Sustainability and Hamiltonian value. Work. Pap. 48.2002, FEEM. doi: 10.2139/

ssrn.317959

Hamilton JD. 2008. Understanding crude oil prices. Work. Pap., Dep. Econ, Univ. Calif., San Diego

Hartwick J. 2009. What would Solow say? J. Nat. Resour. Policy Res. 1(1):1–6

Hotelling H. 1931. The economics of exhaustible resources. J. Polit. Econ. 39(2):137–75

Huxley A. 1932. Brave New World. New York: Harper & Brothers Publ.

Meadows DH, Meadows DL, Randers J, Behrens WW. 1971. The Limits to Growth. New York:

Universe Books

Nordhaus W. 1973. The allocation of energy resources. Brook. Pap. Econ. Act. 3:529–70

Portney P, Weyant JP, eds. 1999. Discounting and Intergenerational Equity. Washington, DC: Resour.

Future

Ramsey F. 1928. A mathematical theory of saving. Econ. J. 38(Dec.):543–59

Solow R. 1972. Notes on ‘Doomsday Models.’ Proc. Natl. Acad. Sci. USA 69(2):3832–33

Solow R. 1973. Is the end of the world at hand? Challenge 16(1):39–50

Solow R. 1974a. Intergenerational equity and exhaustible resources. Rev. Econ. Stud. 41:29–45

[1973. Work. Pap. 103, Dep. Econ., MIT]

Solow R. 1974b. The economics of resources or the resources of economics? Am. Econ. Rev. Pap.

Proc. 64(2):1–14

Solow R. 1976. Optimal fishing with a natural predator. In Public and Urban Economics: Essays in

Honor of William S. Vickrey, ed. R Grieson. Lexington, MA: Lexington Books

Solow R. 1992a. An almost practical step toward sustainability. Invited lecture on the occasion of the

40th Anniversary of Resources for the Future, Washington, DC, October 8, 1992. Resour. Policy

19(3):162–72

Solow R. 1992b. Sustainability: an economist’s perspective. Res. Explor. 8(1):3–6 [Condensed from

the 18th J. Seward Johnson Lecture, 14 June 1991, Marine Policy Cent., Woods Hole Oceanogr.

Inst., Woods Hole, MA]

Solow R. 2002. What if Jevons had actually liked trees? In Economic Theory for the Environment,

Essays in Honour of Karl-Goran Maler, ed. B Kristrom, P Dasgupta, K-G Lofgren. Cheltenham,

UK/Northampton, MA: Edward Elgar

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Annual Review of

Resource Economics

Contents

Prefatory Article

An Amateur Among Professionals

Robert M. Solow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

Policy Analysis and Design

Agriculture for Development: Toward a New Paradigm

Derek Byerlee, Alain de Janvry, and Elisabeth Sadoulet . . . . . . . . . . . . . . . 15

Governance Structures and Resource Policy Reform:

Insights from Agricultural Transition

Johan F.M. Swinnen and Scott Rozelle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Distortions to Agricultural Versus Nonagricultural

Producer Incentives

Kym Anderson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

Public-Private Partnerships: Goods and the Structure of Contracts

Gordon Rausser and Reid Stevens. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

Environmental Regulations and Economic Activity:

Influence on Market Structure

Daniel L. Millimet, Santanu Roy, and Aditi Sengupta. . . . . . . . . . . . . . . . . 99

The Development of New Catastrophe Risk Markets

Howard C. Kunreuther and Erwann O. Michel–Kerjan . . . . . . . . . . . . . . 119

The Curse of Natural Resources

Katharina Wick and Erwin Bulte . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

Experiments in Environment and Development

Juan Camilo Cardenas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

Behavior, Environment, and Health in Developing Countries:

Evaluation and Valuation

Subhrendu K. Pattanayak and Alexander Pfaff. . . . . . . . . . . . . . . . . . . . . 183

Volume 1, 2009

vii

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Resource Dynamics

Irreversibility in Economics

Charles Perrings and William Brock. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219

Whither Hotelling: Tests of the Theory of Exhaustible ResourcesMargaret E. Slade and Henry Thille . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

Recent Developments in the Intertemporal Modeling of Uncertainty

Christian P. Traeger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261

Rent Taxation for Nonrenewable Resources

Diderik Lund . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287

Land Use and Climate Change Interactions

Robert Mendelsohn and Ariel Dinar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309

Urban Growth and Climate Change

Matthew E. Kahn . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333

Reduced-Form Versus Structural Modeling in Environmental and

Resource Economics

Christopher Timmins and Wolfram Schlenker . . . . . . . . . . . . . . . . . . . . . 351

Ecology and Space

Integrated Ecological-Economic Models

John Tschirhart . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381

Integrating Ecology and Economics in the Study of Ecosystem Services:

Some Lessons Learned

Stephen Polasky and Kathleen Segerson . . . . . . . . . . . . . . . . . . . . . . . . . . 409

The Economics of Urban-Rural Space

Elena G. Irwin, Kathleen P. Bell, Nancy E. Bockstael,

David A. Newburn, Mark D. Partridge, and JunJie Wu . . . . . . . . . . . . . . 435

Pricing Urban Congestion

Ian W.H. Parry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 461

The Economics of Endangered Species

Robert Innes and George Frisvold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485

On the Economics of Water Allocation and Pricing

Yacov Tsur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513

Technology and Innovation

The Economics of Agricultural R&D

Julian M. Alston, Philip G. Pardey, Jennifer S. James, and

Matthew A. Anderson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

viii Contents

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Supply and Demand of Electricity in the Developing World

Madhu Khanna and Narasimha D. Rao . . . . . . . . . . . . . . . . . . . . . . . . . . 567

Energy Efficiency Economics and Policy

Kenneth Gillingham, Richard G. Newell, and Karen Palmer . . . . . . . . . . 597

Recent Developments in Renewable Technologies: R&D Investment in

Advanced Biofuels

Deepak Rajagopal, Steve Sexton, Gal Hochman, and David Zilberman . . . 621

Fuel Versus Food

Ujjayant Chakravorty, Marie-Helene Hubert, and Linda Nøstbakken . . . 645

The Economics of Genetically Modified Crops

Matin Qaim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

Errata

An online log of corrections to Annual Review of Resource Economics articles

may be found at http://resource.AnnualReviews.org

Contents ix

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