Myopia, Emmetropia or Hypometropia? Competitive Markets and Intertemporal Efficiency in the Utilization of Exhaustible Resources

NOT FOR QUOTATION WITHOUT PERMISSION OF THE AUTHOR

W P M , EXliETROPIA

OR

HYPEXMEI'ROPIA?

COMPCI?TIYE liMXEI'S

AND

-ORAL EFFICIENCY

IN

THE

UTllSZATION

OF

EXHAUSI?BLE RESOURCES

Stephen P. Dresch

June 1984 WP-84-48

Working Arpers a r e interim reports on work of t h e International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of t h e Institute or of its National Member Organizations.

INTERNATIONAL INSTITUTE FOR APPLIED SYSTEMS

ANALYSIS

2361 Laxenburg, Austria

Stephen

P.

Dresch is chairman of the Institute for Demographic and Economic Studies in New Haven, Connecticut, and currently a IlASA

*search scholar in the program on Economic Structural Change. While best known for his research in the economics of human resources, in this particular paper h e focuses on an important concern for the theory of resource exhaustion and the discipline of mineral economics. Specifi- cally, he assesses the widespread concern that the markets for minerals and other exhaustible resources may be myopic in the sense t h a t they do not save enough of these limited resources for future use.

In association with the Economic Structural Change Program, led by Wilhelrn Krelle, the Mineral Trade and Markets Project is circulating this study as a working paper in the hope of stimulating interest in t h e topic in general and specific comments and suggestions on t h e paper in partic- ular.

John

E.

Tilton Research Leader

Mineral Trade and Markets Project

Over a period of y e a r s m y a t t e n t i o n h a s been repeatedly drawn t o t h e concept of m y o p i a as i t is employed in t h e l i t e r a t u r e s of economics a n d o t h e r social a n d . olicy sciences. While ostensibly a "scientific" concept.

?

myopia a s conventionally utilized almost invariably is associated with a n u n d e r t o n e of religiosity, p a t e r n a l i s m a n d e - a o r t a t i o n . Whatever t h e putatively scientific observer finds objectioriable in t h e behavior a n d performance or individuals a n d institutions is c h a r a c t e r i z e d a s "myo- pic',': attributable only t o t h e failure of t h e involved parties t o adequately recognize a n d t a k e i n t 4 a c c o u n t t h e f u t u r e consequences of c u r r e n t actions. This paper r e p r e s e n t s a first a t t e m p t t o provide a m o r e scien- tific basis for t h e concept of myopia, and in p a r t i c u l a r t o e m p h a s i z e t h e possibility of t h e converse form of "misperception" of t h e f u t u r e , hyper- m e t r o p i a . conjoining t h e conceptual elaboration with empirical t e s t s in t h e c a s e of m a r k e t s for "exhaustible resources."

Preparation of this p a p e r was stimulated by conversations with Christian Lager. Ryoicbi Nishimiya, k i t s u o Saito, Ern6 Zalai a n d Wolfgang Schbpp of IWA. Eduard Loser of t h e IIASA library disabused m e of m y .nabre belief in t h e originality of t h e terminological c o n s t r u c t s , h y p e r - , m e t r o p i a .and e m m e t r o p i n . The c u r r e n t version h a s benefited signifi- c a n t l y from t h e constructive criticisms of a n earlier draft of R u t h a n n Moomy, Anatoli Smyshlyaev, John Tilton and, especially, Wilhelm Krelle, also of

IMk

I alone r e m a i n responsible for e r r o r s a n d for duplication of . w h a t m a y well be a prior l i t e r a t u r e with which

I

am inadequately fami-

liar.'

Stephen

P.

Dresch Laxenburg, Austria

MYOPIA. EKMETROPLA

OR

HYPICRMETROPXA?

C O M F ' E m MARKEX3 AND 1NTHZTEKPORA.L EFFICIENCY

IN

THE

UTZLIZATlON OF KXHA- RESOURCES

Stephen P. Dresch

1. Pseudoscientimn and the Concept of Myopia

~ y o p i a , ' i.e., systematic " u n d e r v a l u a t i ~ n " ~ of future consumption possi- bilities by comparison to consumption in the present, is frequently alleged to vitiate t h e efficiency of market-determined intertemporal allo- cations of resources. While emmetropin, t h e "correct" relative

em or rowing

from the terminology of optics and opthalrnology, economics and related social rciences have made extensive use of the concept of myopia (shortsightedness), a distortion of vision in which the image falls behind the retina of the eye (producing clear perception only of objects relatively close to the observer). Unfortunately, economics and other wcial rciences have not made comparable use of the converse form of ametropicr (distortion of vi- sion, in contrast to emmefropiu, normal vision in which the image falls upon the retina, pro- viding clear perception of both near and distant objects), hypermetropiu (farsightedness), a

&stortion in which -he image i d s in front of the retina (producing relatively clear percep tion of objects very far from the observer). The only reference in the economics literature t o hypermetropia (of which the present author is aware) is that of John F. O'Connell, "Wages and Job Change: Myopia or Hypermetropia," humal of B o n o m i c s and Business Fall 1980).

The foregoing optical/opthalmological concepts and terminology are summarized under the topic of ''Vision," B u y c l o p a e d i a ZMwanua, vol. 29, p. 70 (Chicago: Encyclopaedia Britanni- ca Press, 1873).

2~ this introduction the terms "undervaluation," "correct valuation" and "overvaluation."

all ieferring t o the relative valuation of future by comparison t o present consumption, are used without formal d e f ~ t i o n . Such definitions will be provided in the following aection.

valuation of consumption possibilities a t different points in time, is taken a s the norm or standard, myopia is considered to be pervasive, possibly even endemic. Thus, for example, conservationists, environ- mentalists and advocates of zerc-population-growth conjoin the concepts of myopia and externalities to explain t h e failure of contemporary societies to control the growth of population, to reduce t h e excessively rapid r a t e of exploitation of nonrenewable resources, and to anticipate the adverse future environmental consequences of c u r r e n t economic activities.'

Despite the prevalence with which recourse is made t o alleged myo- pia a s an explanation for (similarly alleged) m a r k e t failure, it is notable that empirical tests are rarely performed to confirm t h e existence and influence of The observed phenomena, e.g., "excessively rapid"

population growth, resource "exhaustion," environmental "degrada- tion," etc., ad infindurn, a r e apparently conceived a s selfevident, both normatively and with - reference to their underlying sources. Also, surprisingly, despite t h e frequency with which myopia is alleged, the literature is virtually devoid of t h e suggestion t h a t markets might fail due t o t h e converse distortion of perception, hypemetropia, t h e "exces- sive" valuation of future relative t o c u r r e n t consumption possibilities.

Certainly, if one can be scientifically defined, t h e other should also be subject to scientific definition, and on theoretical grounds one should be

3 ~ o r a review ( m d pointed critique) of these claims, see Julian Simon, ?he V l t i m d e IZlssource (New York: Oxford University Press, ^1881).

4~resupposing an analysis such as that developed here, Simon, ibid., emphasizes the obser- vation of declining relative resource prices ^as refuting claims of excessjvely rapid resource exhaustion.

as subject to operational observation as the other. In short, i f myopia is to be convincingly offered a s an explanation for a m a r k e t failure of any specific type, a meaningful empirical t e s t m u s t be offered, and t h a t t e s t m u s t permit the finding e i l h e r of myopia, of emmetropia or. of hyper- metropia. This paper develops and applies such a t e s t with reference t o the market-determined, intertemporal utilization of exhaustible resources.

2. Emmetropic Resource Price Trajectories with Certainty and Perfect Capital Markets

The focus of i n t e r e s t h e r e is t h e r a t e of utilization over time of an

"exhaustible resource." However, it is useful t o define t h e problem as generally, a n d realistically, as possible. Thus, an exhaustible resource, for present purposes, c a n be conceived as follows: A t a point i n time t h e r e exists a "kmown resource s t o c k " denoted h e r e , for short-hand pur- poses, as a "known reserve. ^"5 Subject t o (modifiable) "extraction" capa- cities,' this known reserve can be extracted and "used" (embodied in final goods and services) a t any point in times7 While c u r r e n t u s e cannot '

i

n tbe resource-economics literature the concept of a resource reserve is commonly r e s tricted t o those known sources t h e exploitation of which is economical, i.e., for which price exceeds extraction costs, given current factor prices and extraction technology. The

"resource base" then consists of reserves plus resource endowments which i t is not (currently) economical to exploit. Here the term is used essentially a s a synonym for resource base in this broad sense.

or

present p ' q o s z s i= is cozvenient to assarne that known reserve is horr.cgenec.us and can be extracted at constant costs (constant both a t a point in time and over time).

However, this restrictive assumption i s in fact unnecessary, as Kill be discussed further.

Thus, extraction costs can either rise with cumulative extraction (due t o a deterioration in the quality of remaining reserves, i.e., to "resource exhaustion") or can rise/fall with time per se (due t o secular changes in factor prices or to changes in extraction technology).

None of these possible extraction-cost developments requires a significant modification of the ementiel conclusions of this analysis.

7& just suggested, the terms '.use," and also .,end use" and 'mfinal use" are employed here interchangeably to refer to embodiment of the resource in final goods and services (con- sumption, investment, etc.) o t h r t binventories o j t h s resource itselj.

e'xceed t h e known reserve, cumulative uses over t h e infinite f u t u r e c a n exceed t h e reserve a s a result of ( a ) the d s c o v e r y of previously unknown reserves, (b) c h a n g e s in extraction and r e l a t e d technologies (increasing t h e efficiency of physical e x t r ~ r t i o n , deiined as t h e r a t i o of usable r e s o u r c e e x t r a c t e d relative t o t h e total q u a n t i t y e x t r a c t e d ) a n d ( c ) recy- cling of previously used reserves.

Two distinct classes of demand for t h e c u r r e n t l y - h o ~ n r e s e r v e c a n be identified. First, t h e r e is a "flow demand" for c u r r e n t use. C u r r e n t a n d f u t u r e flow, or "end-use," demands for t h e r e s o u r c e a r e functions of (a) aggregate levels of economic activity (changing over t i m e a s a r e s u l t of i n c r e a s e s in population-cum-laborforce a n d in t h e capital stock, a s well a s g e n e r a l technological progress), ( b ) t h e composition of final d e m a n d (also s u b j e c t t o change over t i m e , a s a r e s u l t , e.g., of c h a n g e s in relative prices, in savings r a t e s a n d in c o n s u m e r p r e f e r e n c e s ) and (c) technological developments in resource-using s e c t o r s a n d activities.

Ceteris paribus, t h e quantity of t h e r e s o u r c e d e m a n d e d for c u r r e n t use a t any point in t i m e is a s s u m e d t o a d j u s t so a s t o m a i n t a i n equality between t h e t h e n - c u r r e n t price and t h e m a r g i n a l productivity of r e s o u r c e use.

The second category of d e m a n d is a "stock ( o r inventory) demand"

for h o w n reserves t o be c a r r i e d into t h e f u t u r e . I t c a n b e assilmed: pro- visionally, t h a t quantities of t h e resource fulfilling t h e s t o c k d e m a n d a r e held in raw, u n e x t r a c t e d form +rr situ, a t n o c o s t o t h e r t h a n deferral of final u s e (reflected in i n t e r e s t costs. e i t h e r i n t e r e s t paid or i n t e r e s t i n c o m e foregone), i.e., t h a t t h e r e a r e n o costs of storage o r losses to- deterioration.' This stock o r inventory d e m a n d s e t s a n u p p e r bound on 'ln fact, this assumption is unnecessarily restrictive. Even in those instances in which the

cumulative f u t u r e end uses. Thus, the stock demand must be greater than or equal to t h e sum of all future end uses less ( a ) future reserve discoveries, (b) augmentations of the extracted resource due to advances in extraction technology and ( c ) future supplies to final use accounted for by recycling.

In a regime of perfectly competitive markets, t h e stock demand is determined subject to the requirement of profit maximization of all par- ticipants in aL1 m a r k e t s (and market segments). A single price confronts all purchasers, whether the motive is end-use or stock demand. With perfect capital markets investors in reserve stocks can borrow in order t o acquire reserves a t the market interest rate. Under these cir- cumstances, investors will acquire stocks (for future sale) as long as t h e anticipated r a t e of change of price is a t l e a s t equal to the interest rate. ⁰ Were price t o increase a t a r a t e greater than t h e r a t e of interest, i t would be profitable for investors to acquire additional stock reserves, t h e (economic) profits on which would equal t h e difference between the r a t e of change of price and t h e interest rate.'' Under these circumstances, increases in demand for reserve stocks would drive up the c u r r e n t price, reducing c u r r e n t flows of t h e resource t o end use, while g r e a t e r future resource availabilities would reduce the future resource price, a process which would continue until the r a t e of resource price change was driven t o equality with the interest rate. Conversely, a r a t e of change in t h e stock demand is satisfied by resources in an extracted form or is subject to storage costs and deterioration, the essential conclusions of this analysis are unaltered, as will be ex- plained.

'This is simply the well-known "Hotelling rule." See H. Hotelling, "The Economics of Ex- haustible Resources," k u d of Political &ommy (1Q31).

''Profit here is used in its economjc sense, referring to a surplus over costs, where costs in- clude areturn t o capital at the market rate of interest.

r e s o u r c e price less than t h e interest r a l e would imply losses for inves- tors in reserve stocks, l e a d n g Lo reductions in reserve stocks which would r e d u c e t h e current price, while lesser f u t u r e resource availability would raise t h e future price, resulting, again, in a process which would continue until the rate of resource price change was brought i n t o equal- ity w i t h t h e i n t e r e s t rate.'' Thus, in equilibrium, t h e price of t h e r e s o u r c e m u s t rise over time a t t h e r a t e of interest.I2

This perfectly competitive m a r k e t equilibrium, determining t h e allocation of known reserves between end-use a n d reserve stocks, or, equivalently, between c u r r e n t and f u t u r e end-use, c a n also b e demon- s t r a t e d t o be socially optimal. Specifically, the change of t h e r e s o u r c e price over t i m e is a measure of the higher marginal productivity of the r e s o u r c e in t h e f u t u r e than in t h e p r e s e n t , while t h e i n t e r e s t r a t e is equal t o (a) t h e r a t e of r e t u r n t o physical capital and (b) t h e marginal r a t e of t i m e preference ( t h e r a t e a t which individuals a r e willing t o exchange p r e s e n t for future consumption). If t h e r a t e of c h a n g e of t h e r e s o u r c e price (marginal productivity of t h e resource) is g r e a t e r t h a n t h e r a t e of r e t u r n t o capital, t h e n total output, income and consumption ( p r e s e n t and/or future) can be increased i f reserve stocks of t h e

113trictly speaking, these market-equilibrating developments should be conceived as achieved uia a process of Balrasian tantonnemenf or Edgeworthian "recontracting," such that no tx.nsac'ri~ns ir facr occ-.I ^et disea-ilit5i;llr.l prices, since ?iseq-uili':rium rransac- t i m s may (through their effects on income distribution) alter the final equilibrium. The al- ternative solution to this problem is Marshall's assumption of the constant marginal utility of money (as reflected in his development of the pure theory of exchange, rsith reference to the "corn market"). See: Leon Walras, Elemenis d'dcommie polifique pure (Thdorie de la richesse s o c i d e ) [1874-71, 5th edition (Paris and Lausanne, 1926); Francis Ysidro Edgeworth, Ydhenzuficd k c h i c s (1881); and Alfred Marshall, Principles o j &onomics [1890], 4th edi- tion (London, 1898).

1 2 ~ o t e that the focus of interest here is the sehtionship between prices a t different points of time, not t h e Level of prices a t ^{m y} point in time. Thus, this analysis says nothing about the level of prices per se.

r e s o u r c e a r e increased while i n v e s t m e n t in physica! capital is correspondingly reduced, simply because the gain in f u t u r e o u t p u t asso- c i a t e d with g r e a t e r availability of t h e r e s o u r c e i s g r e a t e r t h a n t h e loss of f u t u r e o u t p u t associated will-i ltle reduction in t h e capital stock. This will c o n t i n u e t o be t r u e until t h e r a t e of change of t h e r e s c u r c e price (or r e s o u r c e productivity) is equal t o t h e i n t e r e s t r a t e a n d r a t e of r e t u r n t o capital. Conversely, a r a t e of change of t h e r e s o u r c e price l e s s t h a n t h e i n t e r e s t r a t e indicates t h a t a gain in p r e s e n t / f u t u r e welfare c a n be achieved if lesser reserve stocks of t h e r e s o u r c e a r e c a r r i e d i n t o t h e f u t u r e . compensating for t h e r e d u c e d f u t u r e availability of t h e r e s o u r c e by i n c r e a s e s in i n v e s t m e n t in physical capital; t h e loss in f u t u r e o u t p u t d u e t o t h e l e s s e r availability of t h e r e s o u r c e will be m o r e t h a n offset by t h e gain in f u t u r e o u t p u t achieved t h r o u g h t h e larger capital s t o c k , while t h e h i g h e r c u r r e n t r a t e of investment will be c o m p e n s a t e d by also h i g h e r c u r r e n t resource use.

3.

Myopic/Hypermetropic Resource Price Trajectories w i t h U n c e r t a i n t y and Imperfect Capital Markets

With complete information a n d perfect c e r t a i n t y concerning all p r e s e n t a n d f u t u r e prices, t h e foregoing perfectly-competitive, socially-optimal solution would be definitional. l n t h e absence of c e r t a i n knowledge of t h e f u t u r e , however, r e s e r v e s t o c k demands depend n o t on prior knowledge of f u t u r e prices b u t on investors' speculative e z p e c t a t i o n s concerning these. Moreover, if capital m a r k e t s a r e imperfect, t h e n i t m a y n o t be possible t o finance speculative i n v e s t m e n t s in reserve s t o c k s of a r e s o u r c e even if t h e s e i n v e s t m e n t s a r e expected t o be profitable a t

prevailing r a t e s of i n t e r e s t (and returns t o capital).13 Only if capital markets permit the financing of speculative investments up to t h e point t h a t t h e r a t e of resource price change e z p e c t e d by speculators is equal t o the m a r k e t i n t e r e s t r a t e and if speculative expectations of resource price change do not diverge systematically from t h e r a t e of resource price change which actually materializes will efficiency in intertemporal utilization of resources be achieved. The former requires perfect capital markets, while t h e l a t t e r requires speculative expectations which correctly anticipate f u t u r e resource discoveries and changes i n technol- ogy, composition of demand, etc.

At this point, u n c e r t a i n t y and imperfect capital markets permit t h e introduction of t h e possibility of myopia or hypermetropia, n e i t h e r of which could otherwise be defined consistently. With uncertainty myopia and hypermetropia will be manifested in systematic discrepancies between expected and actual r a t e s of resource price change. Thus, myo- pia m u s t imply and be reflected in systematic underestimation of future prices, i.e., prices which actually materialize m u s t be systematically higher than those anticipated in t h e past; equivalently, t h e r a t e of increase of resource prices m u s t be greater t h a n t h e r a t e of interest.

And, conversely, hypermetropia m u s t imply and be reflected i n sys- t e m a t i c overestimation of f u t u r e prices, i.e., prices which materialize m u s t systematically fall short of those expected; equivalently, the r a t e of resource price increase m u s t fall consistently below t h e interest r a t e .

effect, capital market imperfections may preclude equalizetion of the interest rate and (a) the individual's rate of time preference and (b) the rate of return t o capital.

This uncertainty-based definition of myopia,/hypermetropia.

emphasizing systematic dsct-epancies between expected a n d a c t u a l f u t u r e prices is equivalent t o an imperfect-capital-market-based defini- tion c a s t in t e r m s sf systematic discrepancies beiwef.11 irl i e r r ~ a l r a t e s of r e t u r n t o speculative inventory i n v e s t m e n t s , on t h e one hand, a n d t h e m a r k e t r a t e of i n t e r e s t , on t h e o t h e r . That is, o p e r a t i o d l y t h e conse- q u e n c e s of systematic misperception of t h e f u t u r e a n d the consequences of capital m a r k e t imperfections are identical. Thus, myopia, t h e m o r e likely manifestation of capital m a r k e t imperfection, can b e defined as a s i t u a t i o n in which t h e realized i n t e r n a l r a t e of r e t u r n t o speculative s t o c k reserve investments (equal t o t h e r a t e of resource price change) systematically exceeds t h e m a r k e t i n t e r e s t r a t e (implying a discrepancy between between r a t e s of r e t u r n t o i n v e s t m e n t a n d savers' r a t e s of t i m e preference); conversely, hypermetropia is observed when t h e realized i n t e r n a l r a t e of r e t u r n falls systematically s h o r t of t h e m a r k e t i n t e r e s t r a t e .

To r e i t e r a t e , ignoring reserve holding costs o t h e r than i n t e r e s t ( e i t h e r i n t e r e s t expense i n c u r r e d or i n t e r e s t income foregone), t h e o p t i m a l i n t e r t e m p o r a l allocation t o e n d u s e of a n exhaustible r e s o u r c e will imply discounted f u t u r e prices equal t o t h e c u r r e n t price. Denoting p r i c e a t t i m e

t

by P t , t h e i n t e r e s t r a t e by r , and t h e r a t e of growth of p r i c e (equal t o the internal r a t e of r e t u r n t o i n v e s t m e n t in r e s e r v e s t o c k s ) by g [where Pt

=

( l + g

)'pol,

P t ( l + r ) - ' = P o or g = r : emmetropia P l ( l + t ) - '

>

Po or g > r : myopia

p t ( 1 + r ) - ' < P o or g < r : hypermetropin

Thus, a simple test for t h e existence of myopia/hyperrnetropia is readily available.

4. Incorporating Noninterest Inventory Costs and Costs of Extraction

and

Processing

As noted a t t h e outset, to simplify this analysis it was assumed t h a t t h e reserve stocks of the resource were held over time only in a raw, unpro- cessed form in situ, and t h a t t h e r e were no costs associated with holding t h e resource over time o t h e r than interest, i.e., t h a t t h e r e were no "car- rying costs," depreciation losses, e t ~ . Because the empirical t e s t s of t h e existence of myopia/hypermetropia presented in t h e next section, due to limitations of data, necessarily refer to resources in a t least semipro- cessed form, for which noninterest carrying costs cannot be assumed t o be zero, i t is important t o demonstrate t h a t the foregoing interest- rate/price-change relationships a r e essentially applicable i n these cases as well.

When the resource i s held in an extracted, processed form it is necessary t o take into account the costs of these activities. Assuming zero noninterest carrying costs, t h e "ernmetropic (Hotelling) rule" ( r a t e of price change equal t o r a t e of interest) sets an upper b o u n d on t h e ernmetropic rate of price change of the extracted, processed resource.

Three specific cases can be distinguished, differing in t e r m s of prospec- tive changes over time i n extraction/processing costs per unit of resource. F'irst, if (implausibly) extraction and processing costs a r e expected t o rise, purely a s a function of time (i.e., not as a r e s u l t of a deterioration in resource quality), a t a rate greater than t h e r a t e of

interest, an efficiently-functioning competitive market w i l l extract and process the resource now, transferring only stocks or the extracted and processed resource t o t h e future, with the consequence t h a t t h e price of t h e processed resource will also rise over time (in the absence of myopia or hyperrnetropia) a t the r a t e of interest.14 Second, if extraction costs rise not with time per s e but r a t h e r with cumulative o u t p u t (as a result of resource exhaustion, i.e., deterioration in resource quality), then the economic rents received by resource owners (raw resource prices) a t low cumulative output levels will reflect superior resource quality (lower extraction costs), with the price of the extracted resource rising over time a t the r a t e of interest ( a s increases in extraction costs a r e offset by reductions in rents); equivalently stated, for "deposits" of any given quality, prices will rise over time a t the rate of interest, price differen- tials between deposits of different quality will equal differences in extraction costs, and prices of t h e extracted resource will rise a t the r a t e of interest, independently of the level of extraction costs. Third, only if processing costs a r e expected to rise over time a t a r a t e less than t h e rate of i n t e r e s t will t h e price of t h e extracted, processed resource rise a t a r a t e o t h e r (lower) than t h e r a t e of interest, in which case effec- tively no speculative inventories of the processed resource will be held;

even in this case, however, t h e price of t h e raw resource will rise a t the r a t e of interest, and t h e r a t e of change of the processed resource price I4l'his, obviously, requires current investment equd to extraction and processing costs. It might be argued that this could lead t o a desired rate of investment greater than the current rate of savings. However, if this were the case, then the rate of interest would necessarily be driven upward, a process which would continue either until increases in sav- ings and d q l a c e m e n t of other investment were sufficient to permit complete, exhaustive extraction of the resource or until the rate of interest equalled the rate of change of resource extraction and processing costs, at whjch point there would be no incentive to ex- tract and process the resource in t h e present rather than in the future.

will rise over time, asymptotically approaching the r a t e of interest as processing costs relative to r e n t s asymptotically approach zero. Thus, regardless of t h e relationship of processing costs to time and cumulative resource output, ir! t h e absence of myopia/hyperrnetropia t h e r a t e of change oi price of t h ~ resource (in extracted, more-or-less processed form) will be less than or equal t o t h e i n t e r e s t rate, and, if less than t h e i n t e r e s t r a t e , will asymptotically approach t h e i n t e r e s t rate.

The existence of noninterest carrying costs associated with stock reserves (held in either raw or processed form, with t h e form determined by differentials in carrying costs and by t h e anticipated r a t e of change over time in extraction costs, as just discussed) will introduce a wedge between t h e r a t e of resource price increase and t h e interest r a t e , raising t h e emmetropic r a t e of price increase above t h e interest rate. However, unless, implausibly, real noninterest inventory carrying costs were t o increase over time a t a r a t e a t least equal t o t h e real interest r a t e , this wedge would contract over time as resource prices increased, i.e., nonin- t e r e s t costs would decline as a proportion of total costs, and t h e ernmetropically required r a t e of price increase would decline, asymptoti- cally approaching t h e i n t e r e s t r a t e .

Thus, extending t h e analysis t o include n o t only t h e raw, in situ form of t h e resource and relaxing the restrictive assumption of zero noninterest carrying costs, t h e essential relationships between r a t e s of resource price change and i n t e r e s t r a t e s as indicators of myopia, emmetropia or hypermetropia a r e only marginally altered. Processing costs rising a t a r a t e less t h a n t h e i n t e r e s t r a t e would give rise t o an ernmetropic r a t e of resource price increase less than t h e i n t e r e s t r a t e ,

while positive noninterest carrying costs would imply a positive differen- tial between the emmetropic r a t e of price increase and the interest r a t e . In both cases, however, over time t h e emmetropic r a t e of price increase would asymptotically approach t h e i n t e r e s t r a t e .

5. An Empirical Test of Myopia/Hypermetropia in Resource Markets Fortunately, substantial data a r e available t o permit suggestive, if indirect, tests of t h e presence of myopia or, conversely, of hypermetro- pia in primary resource markets. Here r a t e s of change of U.S. resource prices a r e examined, with identification of t h e following specific resources: ¹⁵

bituminous coal (average value per t o n , f.o.b. mine) crude petroleum (average value at well p e r bbl.) iron ore (average value per long t o n )

nickel (electolytic, c e n t s per pound)

copper (New York, electrolytic, f.o.b. refinery, c e n t s per lb.) lead (New York, pig lead, c e n t s per lb.)

zinc (New York, slab zinc, c e n t s per lb.)

silver (New York, average price per fine ounce)

Mean annual r a t e s of change of nominal prices and of real (relative) prices [i.e., resource prices relative t o t h e Consumer Price lndex (cP~)]"

a r e presented in Table 1 for t h e periods 1919 t o 1981 and 1890 to 1981.

These relatively long periods of t i m e a r e examined because, as indicated above, t h e fundamental issue with reference t o myopia/hypermetropia is t h e existence of systematic discrepancies between r a t e s of i n t e r e s t and

1 5 ~ o u r c e s of data are identified in t h e notes to Table 1.

16~irtuelly identical results are obtained when resource prices are deflated (a) by the whole- sale price index and (b) by the implicit price deflator for gross national product (restricted t o the period 1930 t o lW1).

of resource price change. For this purpose it is necessary t o a b s t r a c t f r o m from s h o r t - t e r m , cyclical or aberrational challges in e i t h e r i n t e r e s t r a t e s or r a t e s of resource price change.

For purposes of classifying r e s o u r c e m a r k e t s a s myopic (M), ernmetropic (E) or hypermetropic

(Hj,

i t is necessary t o c o m p a r e t h e s e r a t e s of price change t o a n appropriate b e n c h m a r k m e a s u r e of t h e m a r k e t i n t e r e s t r a t e . For t h e 1919 t o 1981 period t h e m e a n a n n u a l yield of Corporate Aaa bonds ( a s reported by Moody's) i s utilized, while t h e m e a n annual prime commercial paper r a t e is employed for t h e period 1890 t o 1981. The advantage of t h e s e i n t e r e s t r a t e s is t h a t t h e y a r e e n t i r e l y " m a r k e t determined," unlike, e.g., t h e prime bank lending r a t e (which is "administratively determined" a n d also not reflective of r a t e s actually paid by borrowers, due t o compensating balance r e q u i r e m e n t s , discounts, etc.). However, t h e i r disadvantage for present purposes is t h a t they r e p r e s e n t relatively "riskless" yields, while t h e appropriate r a t e for purposes of t h e a s s e s s m e n t of t h e efficiency of primary r e s o u r c e m a r k e t s is one associated with a s s e t s t h e risks of which a r e comparable t o t h e risks associated with r e s o u r c e portfolios. As can be s e e n in Table 1, which p r e s e n t s s t a n d a r d deviations a s well a s m e a n s for both r a t e s of r e s o u r c e price change a n d i n t e r e s t r a t e s , resources r e p r e s e n t m u c h h i g h e r risk assets, over t i m e , t h a n do representative portfolios of high- g r a d e (Aaa) corporate bonds or prime commercial paper, with s t a n d a r d deviations of real r e s o u r c e p r i c e s one t o five t i m e s g r e a t e r t h a n s t a n d a r d deviations ol r e a l i n t e r e s t r a t e s . 01 c o u r s e , a s implicitly suggested, a comparison of t h e variance of a single r e s o u r c e price change t o t h e vari- a n c e of t h e yield oC a balanced portfolio of financial a s s e t s is, in f a c t ,

Table 1.

Retes of Interes? and of Resource Rice Change 'eriod ;

nterest Rate:

Interest rate 15.0% 2.4 14.51. 2.7

101418B1 18DG1881

Corporate Aaa

Mean Std. Dev. Mean Srd. Der.

Real

I

Bituminous coal Crude petroleum Lron ore (1) Nickel (2) Copper Lead Zinc Silver

h t e r e s t rate

12.1 4.6 6.6 9.9 4.0 9.3 4.5 4.1 6.7

Bituminous coal Crude petroleum Lron me (1) Nickel (2) Copper Lead Zinc Silver

Myopia (M Emmetropia (E Hypermetropia (H

k n e r a l notes: Y l p e m e t m p i u is defined as rate of price change more than one percen tage point less then rate of interest.

Emmotropia is defined a s rate of price change within plus or minus onc percentage point of rate of interest.

mpiuis defined 8s rate or price change more than one percentagc point greater than r a t e of interest.

Specific notes: (1) Time periods for iron ore are 1818-1 881 and 189518B1, respectively with respective nornind (real) interest rates of 5.0 (2.1) percen and 4.4 (1.7) percent.

(2) Time periods for nickel are l8lB-1981 and 1914-1881, respectively with respective nominal (real) interest rates of 5.0 (2.1) percen

4.1 (0.8) percent.

Sources: AU resource prices, price indices and interest rates through 1870 arc derived from U.S. Bureau of the Census, tfistorical SLatistics of the Vnit ad W e s , &Lonirrl: Tunes t o 1870 (Washington, D.C.: Government Print ing Office, 1875). For the period 1871 through 1981 the source is U.S Bureau of the Census, Statistical Abstract o j the h i f e d States, [ I 676 1882-84 (Washington, D.C.: Government Printing Office, [ 1976, 18821).

inappropriate, since a representative portfolio of resources would exhibit a lower variance t h a n would a single resource. However, it is probably still t h e case t h a t even optimal resource portfolios constitute relatively high risk (high yield variance) assets by comparison to highly rated a n d easily traded financial assets. A t the least, i t can be argued t h a t rates of r e t u r n to physical capital (as measured, e.g., by r e t u r n s t o corporate equity), were they available over sufficiently long periods of time (which they a r e not), would provide a more appropriate (neutral) basis on which to t e s t for t h e existence of myopia or hypermetropia. Utilization of lower risk Corporate Aaa bond and prime commercial paper rates, by understating t h e appropriate benchmark interest r a t e , will lend a bias in favor of a finding of myopia when markets a r e in fact emmetropic or, even, hypermetropic.

A further bias in t h e direction of a finding of myopia is introduced by t h e fact t h a t noninterest carrying costs a r e ignored, i.e., implicitly assumed to be zero. However, especially in light of t h e fact that the resource prices refer in all cases to extracted and a t least semiprocessed forms of t h e resource, this assumption is almost certainly violated. In addition to storage costs i t is probable t h a t a t least some extracted and processed resources a r e also subject to physical deterioration.17 While t h e s e costs a r e ignored here, i t need not be the case t h a t they a r e of only second-order significance.

"Thus, for example, extracted tin ores are subject to a contagious "tin dieease" caused by fungal atteck, while iron and steel are subject to oxidizetion. Also, while the probability of theft (and/or insurance against theft) does not represent a cost to society, it is does consti- tute a cost to speculative investors, a cost which is probably greater if reserve stocks are held in extracted q d processed or semiprocessed form.

While t h e utilization of a relatively lo^^ risk interest r a t e and t h e assumption of zero noninterest carrying costs introduce biases toward a finding of myopia, a bias in t h e opposite direction results from t h e f a c t t h a t in all c a s e s t h e resource prices r e t e r t o a t least semiprocesserl f o r m s of t h e resource, for which positive extraction and processing c o s t s a r e incurred. While, in principle, t h e s e costs need not imply a n emrnetropic r a t e of price increase less t h a n t h e i n t e r e s t r a t e , because of technological change i t would be expected t h a t extraction and process- ing c o s t s (controlling for t h e quality of t h e raw in situ deposit) would decline over time, while a r a t e of increase of t h e s e costs less t h a n t h e i n t e r e s t r a t e would result, a s discussed previously, in an emrnetropic r a t e of price change which would also be less t h a n t h e i n t e r e s t r a t e .

Whether t h e biases toward a finding of myopia, stemming from a n inappropriately low measure of t h e i n t e r e s t r a t e and from t h e a s s u r n p tion of zero carrying costs, more o r less t h a n fully offset t h e probable bias toward a finding of hypermetropia, s t e m m i n g from t h e failure t o explicitly take into account (presumably declining) extraction a n d pro- cessing costs, cannot be determined a p7-iori, and, unfortunately, d a t a which would permit an empirical a s s e s s m e n t of t h e magnitudes of t h e s e biases a r e n o t readily available. However, t e s t s for myopia, e m m e t r o p i a o r hypermetropia ignoring t h e s e biases will a t l e a s t provide suggestive evidence of t h e efficiency of intertemporal resource utilization.

In t h e final column of Table 1 r e s o u r c e m a r k e t s a r e classified as myopic (M), emmetropic

(E)

or hypermetropic

(H)

on t h e basis of t h e relationship between t h e r a t e of price change (nominal o r real) a n d t h e i n t e r e s t r a t e (nominal or real), defining e m m e t r o p i a as a r a t e of price

change equal to the interest rate plus or minus one percentage point, myopia as a r a t e of price change more than one percentage point greater than the interest r a t e , and hypermetropia as a r a t e of price change more than one percentage point less than t h e rate of ir~teresl..

Despite the possible biases incorporated in t h e present tests for myopia, emmetropia or hypermetropia, t h e somewhat suprising conclu- sion from t h e evidence presented in Table 1 is t h a t myopia is clearly evi- dent for only one resource, crude petroleum, and is observed in t h e more r e c e n t period but not over t h e entire period in the case of silver. How- ever, hypermetropia is discovered over t h e 1919-1961 period (but not over t h e entire 1890-1981 period) for iron ore, nickel, copper and (margi- nally) zinc. If t h e stipulated interest r a t e s understate t h e appropriate r a t e s by only one percentage point (and continuing t o allow a plus or minus one percentage point dfferential to represent emmetropia), myo- pia would not be found any of these resources, while hypermetropia would be determined for bituminous coal, iron ore, nickel, copper, lead a n d zinc, i.e., for six of t h e eight resources examined.

6. Conclusion

In summary, on t h e basis of evidence covering relatively long spans of time (63 and 92 years) minerals markets do not s e e m to be character- ized by "pervasive myopia." Especially when t h e biases toward t h e

"discovery" of myopia a r e considered, if anything these markets seem t o t e n d toward hypermetropic misperception of t h e future. Thus, despite t h e apparently general view t h a t markets tend to "sacrifice" the future for t h e present, t h e preponderance of the evidence is t h a t market out-

comes result in relatively efficient balancing of t h e Interests of present and future, or, m o r e accurately, In relatively efficient lntertemporal utilization of exhaustible resources. Moreover, t h e suggestive evidence t h a t in some m a r k e t s t h e present may be inefilciently sac:rificr.d for t h e future, or, again more accurately, that consumption possibilities in both t h e present and t h e f u t u r e could be increased through higher rates or c u r r e n t utilization of resources, raises serious questions concerning t h e virtually total lack of attention to the possibility of this type of market failure in t h e relevant literatures.

The focus in this paper has been on t h e clussificatzon of individual markets as myopic, emmetropic or hypermetropic. Thus, t h e paper has not addressed t h e issue of t h e causes of either myopic or hypermetropic m a r k e t failure. In conclusion it may be useful t o note t h a t t h e t h r e e most likely candidates a s sources of myopic/hypermetropic market failures a r e (a) incorrect (presumably static) forecasts of technology, (b) incorrect forecasts of f u t u r e reserve discoveries and (c) imperfect capi- tal markets. The first two are more plausible as sources or hypermetro- pia, i-e., it i s more likely t h a t anticipations underlying t h e market deter- mination of prices will underestimate resource-saving (-substituting) technological developments and future resource discoveries. Interest- ingly. i n light of t h e apparently common assumption t h a t markets a r e myopic, t h e only inherently plausible explanation for myopic market performance which comes readily to mind is capital m a r k e t imperfection (implying r a t e s of t i m e preference systematically above m a r k e t r a t e s of interest, with nonprice rationing of access t o borrowed funds). Thus, t h e present finding of a m o r e general tendency toward hypermetropia is

perhaps not surprising. ^{1 l9}

" ~ o t e t h a t monopoly of resource ownership, to which reference is frequently made in t h e context of intertempord resource utilizetion, although somewhat complicating the analysis of intertempord price determination, would itself not give rise t o myopia, since even t h e monopolist must consider the present value of future monopoly profits; in fact, monopoly is a not implausible explanation for hypermetropia, in t h a t the monopolist would not offer sup plies, in any period, beyond the point s t which t h e elasticity of demand was unity.