Bauxite and Aluminum

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    Bauxite andluminum lntroduction tothe Economics ofNonfuel Minerals

    Ferdinand BanksU.niversity of New outh WalesUniversity of Uppsala

    Lexington BooksD.C. Hea th and o p a n yLexington Ma achu e tt sToronto

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    Some Political Economy of the Trade in Resources 74 List o iguresAppendix Exhaustible Resources 79

    Cbapter 5 Demand, Supply, and P c e 83 1-1 Inputs and Outputs in the Bauxite-Alumina-Aluminum 7Consumption 83 Production CycleElasticities 88 1-2 The Classification of Mineral Supplies 10"Dynamic" Demand Curves 90 2-1 Two Profit Streams Discounted at Different Discount Rates 36Supply 94Prices and Pricing 99 2 1 Intertemporal Consumption Preferences and Investment 40The Price of Aluminum JOJ Possi bili iesAppendix SA : The Substitutability of Aluminum 3-1 Payment Scheme for a 2-Period Model 54for Copper; and an Econometric Commenton Elasticities JOS S-1 Typical Demand Curves and Their Aggregation 88

    Cbapter 6 Prices, Markets, and Inventories 1 S-2 Dynamic Demand Curves Showing an Increase in 9MetaJ Exchanges and Exchange Pricing 111 Demand Following a Decrease in PriceExchange Con tracts for Copper 114 5-3 The Producer Price for Aluminum and Domestic ShipmentsHedging 115 of Primary Unalloyed Aluminum lngot in the United 97Some Simple Analytics of Hedging and Speculating 119 States 1970-1978)Commodity Prices and Inventories 12 1 5 4 Producer and Free Market Prices for Aluminum Metal inAppendix 6 : Stock-flow Model 125 the United States and the United i n g o m 1971-1974) 103

    Cbapter 7 Ore Grades, Energy, and Investrnent 133 SA-1 The Price Ratio ofCopper to Aluminum 1945-1973) 106Ore Grades and the Price of Nonfuel Minerals 136 SA-2 The Cyclical Fluctuation in Aluminum Consumption inEnergy Problems and Ocean Resources 139 Relation to the Percentage Change in ManufacturingInvestment and Pollution 142 Output for the Noncentrally Planned l n d s t r i l Countries 107Appendix 7 Depletion Allowances and Taxes 147 Producer and Market Prices for Copper , Aluminum , Nickel ,-1Cbapter 8 Survey of the World Nonfuel Mineral Economy 149 and Zinc (in Dollars per Ton) 118The General Background 5 6-2 The Demand D) and Supply (S ) of Futures Contracts byThe Mining-Processing Cycle 153 Hedgers and Specu ators as a Function of Their Price Pr) 120Secondary Materials , Substitution, and Scarcity 158 6-3 The Spread between the Expected Future and the SpotThe ReaJ Price and Scarcity 159The Price of Nonfuel Minerals 162 Price as a Function of the Ratio of Inventories to 123The London MetaJ Exchange 165

    ConsumptionMinerals and Australia 167 6 1 Stock and Flow Demand and Supply Curves 126Bibliography and Note on the Literature 7-1 The Real Cost of Some Industrial .Raw Materials 137175

    8-1 Mining-Refining-Final-Use Cycle for a Typical Industriallndex 185 Raw Material 153About the Author 8-2 Prices and Inventories on the London Metal Exchange 167189

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    List of Figures ixst of Tables xi

    Preface xiiiChapter 1 Background and lntroductory Survey

    Aluminum and lts Ores 3Production Theory : An lntroduction 5Reserves Resources and Bauxite 9Elementary DiscountingAppendix 1 Discounting and the i m e

    to ExhaustionChapter 2 Exploration an d Mining: Some Economic Aspects 19

    Some Economics of Exploration 20An lntroduction to the Economics of Mining 23Economic Development and Minerals Exports 28An lntroduction to the Theory of Capital Values 33Appendix Interest and Discount Rates andDerivation of the Present Value Rule. 39

    Chapter 3 Processing Secondary Metal Market Forms andCapital Costs 43Alumina and Aluminum MetalPrimary Aluminum and S e m i f a b c a t e s 45Secondary Materials 47The Simple Ana1ytics of Recycling 49Aluminum and Market Forms: An Introduction 5The Price of Capital Services 53Appendix Note on Economic Profit 6

    Chapter 4 Intemational Trade 63The Trade in Bauxite Alumina and Aluminum 63Commodity Politics and the Trade in Bauxite 67Multinational Companies and the Structure of the

    Aluminum lndustry 70

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    Library of Congress Cataloging in Publication DataBanks FerdinandBauxite and aluminum.1 Aluminum industry and trade. 2. Bauxite. 3. Mineral industries-Australia. Title .HD9539 .A6B35 338.2 7 492 78-24632ISBN 0-669-02771-5

    Copyright 1979 y DC Heath and CompanyAll rights reserved. part of this publication may be reproduced or trans-mitted in any form or by any means electronic or mechanical includingphotocopy, recording or any information storage or r e t e v l system with-out permission in writing from the publisher.Published simultaneous1y in Ca nadaPrinted in the United States of m e c aInternational Standard Book Number: 0-669-02771-5Library of Congress Cata log Card Number: 78-24632

    or Thomas Pocke Banks

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    auxite andAluminum lntroduction to theEconomics of NonfuelMinerals

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    Background andlntroductory SurveyThis is a book in applied economics. lts purpose is to introduce the readerwhether he or she is an economist, engineer, worker, student, or interestedlayperson- to the economics of nonfuel minerals in general and the baux.itealumina-aluminum industry in particular. Thus t l s book is suitable text m t e lor collateral reading for all types of courses in the economics of natural resourcesor the economics of i n d u s t a l raw m a t e a J s ln addition, the book provides acomplete and up-to-date analysis of the outJook for and problems of l s industry in Australia, which presently is the largest supplier of bauxite in the world . e elementary reader , that is, t e reader with no background at all in economics, will find a brief but fairly complete survey of the worJd mineral economy inchapter 8, which can be read independently of the rest of the book.Note that nearly all the technical material in this book has been placed inchapter appendixes. These and other technical presentations can be bypassedwith a clear conscience by all except those readers interested in q u a n t i t a t v eeconomics or speculation of an abstract or quasi-abstract nature. However, themain body of the book introduces some important but simple aspects of c eand production theory , which, while requiring a comprehension of secondaryschool algebra, would not overstress the concentration of most people and cer

    i l y one who has had a course or two in elementary economic theory.begin, we will take a brief look at the history and uses of bauxite andaluminum . Although aluminum was not separated out as a metal until 1825,various bauxite-type silicates were being treated as early as 5300 BC in NorthernIraq for making pottery. Exposing various clays to the hot sun or placing themnext to a fire would eventually make them as hard as stone. ln time some peoplesuspected that these cJays contained a metal. Early in the nineteenth century SirHumphrey Davy named the substance al uminum ; however, actual extractionof the metal from the clay eluded his genius.1821 large quantities of an ore subsequently named baux.ite were dis

    covered at Les Baux, France; and in 1825 the Dane Oersted produced the metaJaluminum in l s laboratory. F r e d e c h Wohler of Germany duplicated Oersted'sresults in 1845 , obtaining in the course of his work some aluminum particles aslarge as pin heads. Nine years later the French scientist Sainte-Claire Deville wasable to obtain aluminum lumps about the size of marbles.s far as it can be estimated, the money price of aJuminum around the year1852 was $1200 per kiJogram. With Sainte-Claire Deville's discovery, the pricecame down to $598 per kilogram, and production on a commercial scaJe, begin-

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    ning in 1858, drove the price down to about 2 5 per kilogram. The price was1 7 in J886 when almost at the same tim e Charles Hall of the United States and

    Paul Heroult of France discovered a low-cost method of producing aluminumfr om aluminum oxide. Their di sc overy prompted a f u r t l e r decline in the price ofal uminum. lndeed , two years later Karl Bayer of r a n y developed a comparatively efficient meth od for extra cting aluminum oxide- or alumina - frombauxite , and the price of the metal reached $11 .55 . At this point it should benoted that the Bayer pro cess treats bauxite chemically to form alumina. On theaverage, the production of 2 kg of alumina requires 4 to 6 kg of bauxite. Other

    n p u t s are 0.5 kg of coal , 0.25 kg of fuel oil, 0.5 kg of soda, 0.13 kg of lime , andcertain other n g r e d i e n t s t l a t will be identified Jater. Similarly , a typical HallHe roult process requires 2 kg of alumina (and a number of other inputs) to produce 1 kg of aluminum.

    Toward the end of the nineteenth century , aluminum entered its modernera . By 1895 when the Hall-Heroult and Bayer processes were being employedon a commercial scale , t l e price of aluminum was $3.2 per kilogram.ln 1950 itcould be purchased for $1.8 per kilogram, and at the present time its money

    p r c e is $1.2 per kilogram. The p l e n o m e n o n that the reader should be aware ofhere is the continuous fall in the real price of aluminum over the years , wherethe real price is usually defined as the money price divided by some consumer orindustrial price index. Thus if the money price of a com.mod .ity were to doublewhile the consumer price index increased by a factor of 4 , the real price of thecommodity would be halved . As a result, t would take twice as much of the

    o m m o d t y to purchase the same amount of consumer goods as were being purchased before the change in prices or, inversely, one half as many consumergoods could purchase the original amount of the commodity . 1t also appears thatthe real price of bauxite has fallen even more rapidly than that of aluminum .

    Concerning the uses of these substances, bauxite is the basic raw m a t e a lfo r alumina, but some bauxite is used in the manufacture of abrasives, as acatalyst in the processing of crude oil , and in the production of insulatingmaterials, refractories , water- and sewage-treatment equipment, and so on.Analogously, alumina is the i p a l raw-material input of aluminum , but about6% of the global output of alumina goes into the production of abrasives , chemical filters , and artificial sapphires.

    This summary can be concluded by no ting that aluminum is light, has ahigh strength-to-weight ratio , high thermal conductivity, and 62% of the elect c a l conductivity of copper . lt is also nontoxic, very malleable, and nonmagnetic. Because of its strength, it can be used in many ways in the home and theindustrial-construction sector where about 25% of aluminum output is directed .Worldwide , approximately 15% of the aluminum produced every year is consumed in the electrical and communications industry , 11 % in consumer durables ,14% in the manufacture of industrial and ag ricultural machinery, and another11 % in containers and packaging. Similarly, fairly large amounts go to the manu-

    fac tur e of motor-vehicles, aircraft , irrigation equipment , military supplies, andeta llurgical and chemical materials .

    u m i n u m and Its OresAlong with iron and copper , aluminum ranks at the top of the list of metals insofa r as its importance in industrial processes is concerned and in its value on worldmarket . The main reason for its importance is not just its usability but also the

    l e e r amount of it available in ore form . As pointed out earlier , aluminum begins as an ore, for the most part as bauxite ; but there are many other ores out_ofw h i c aluminum can be manufactured. Some of the most common are alumte,kaolinite , iJ]ite , dawsonite , and anorthosite . Unlike the ores of copper, thesematerial s are fairly dense in the crust of the e a r t l and thus for obvious statistical reasons they are more often found in concentrations suitable for exploitation copper ore. Table 1-1 compares the average concentrations of somemeta ls in the earth's crust.Th.e enrichment factor is the factor by which the substance must be concentrated, by nature , so that with a given state of technology , it can be consideredminable. Thus if we again consider aluminum and copper, we see that there issomething on the order of 25 times the probability t l a t we will find highlymi nable concentrations of aluminum bearing ores than copper in a randomsearch (assuming that the statistical distribution of ore concentration is the same

    Table 1 1Crustal Abundance, in Metric Tons, and Average Percentage Concentration ofSome Metals in the Earth s Crust Parts p er Million

    verageCrustal v rage in M i a b lA bundance Concentracion Deposits a ctor

    Meta / Ores) 1) 2) 3) 3) / 2Alum inum 2.0 10 18 83,000 185,000 2.2lron 1.4 1018 58 ,000 200 ,000 3.4Mangane e 31 .2 10 12 1300 250 ,000 190Chro mium 2.6 I 0

    15 110 230 ,000 2100Zinc 2.2 10 15 94 35 ,000 370Copper 1.5 1015 63 3,500 56Lead 2.9 1014 12 40,000 3300Silver 0.075 100 1330Go ld 8.4 10 10 0.0035 3.5 1000Source: United State Burea u of Mines.Noce: Th e Crustal Abundance is the total qu antity of the reso urce fo und in the ear th scrust . might be ca lled the ultimate amount of tl1e reso urce.

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    for aluminum and copper). The importance of the enrichment concept can beseen from the fact that if a metal such as tin were distributed evenly throughoutthe crust of the earth, it would be necessary to remove 60 tons of rock and dirtin order to get a single k i l o g r a n of metal. With the passing of time the enrichment factor necessary for economical extractio n has decreased, partially becausethe richest concentrations are used up, and partially because of technologicaladvances. For instance, with the huge capacities of today's mining and processing installations, large and relatively lean deposits are more economica1 to exploit than small orebodies that are comparatively rich.

    Goeller and Weinberg (1976) maintain that in the future it will be possibleto obtain so much aluminum and iron ore from low grade ores that, togetherwith such plentiful items as plastics and biological resources, the raw materia1basis for a rea1 Eldorado might come into existence. This may indeed be so, butas will be pointed out later in this book, the energy requirements for such aparadise will be enormous. J e opinion here , in fact , is that instead of beginningto contemplate a Garden of Eden which all natural resource constraints onunlimited prosperity are removed, it would be better for decision makers tobegin devoting a portion of their precious time to thinking about how civilizedstandards and conduct can be maintained o e r periods of extended shortages.

    Table 1 2 partially catalogues the various aluminum bearing ores. lt should

    Table 1 2The Most lmportant Aluminum-bearing MateriaJs

    Tons reA l u m n a Needed1 for 1ton o ton o

    re luminum Largest DepositsMaterial hemica/ Description Found in :Bauxite 50 4.75 South of France,Boehmite ALz03 Australia, Jamaica,Diaspore AL 20 3 Guyana, etc .Gibbsite AL203 Clay 30 6.0 Almost everywhereKaolinite A L z 0 3 2 S 0Shale lmpure clay 30 6.0 Almost everywhere

    northosite 14 7 U.S. (especiaUyAlbite ALz0 3 6Sj02 Georgia)A n o r t l i t C3 0 ALz03 2Sj02

    Alunite K2S0 4 AL2(S 04 ) 3 2AL20 3 17 7 U.S.S.R.U.S. (Wyoming, Utah)Dawso nite NA 3AL(C0 3)5 2AL(CH) 3 30 6.0 U.S. Colorado)China Manchuria)

    be noted that bauxite is not only the richest of the aluminum bearing ores, but italso contains the smallest percentage of impurities . The presence of impurities isrucial in determining the efficiency of the alumina-production process through

    contaminants are drained off to get the red mud t.hat is alumina. How-er students of the aluminum industry have not failed to notice the decline in,ore grades now characteristic of bauxite reserves. The tendency is to move from

    the best ores , which at present contain about 50 recoverable alumina, down toores that contain 35-40. ln addition , future supplies of bauxite may be locatedin areas where the cost of transporting them to where they will receive their finalprocessing is as great or greater than mining and preliminary processing expenditures. As a result , there is an ever-present incentive to advance the day when t l ecopious supplies of clay, anorthosite, laterites, shales, and similar materials in thecrust can be utilized .

    Production Theory: lntroductionOne of the most interesting topics in microeconomics is production theory ,

    for the most part deals with the relation between n p u t s and outputs. Inbroad outline , this branch of economics concerns the output of a particular commodi ty as it varies with the input of such things as capital and labor. At thispo int it is necessary to distinguish between two categories of inputs. The first arethe so-called primary inputs comprising capital , labor , and land . Of these, laborcould be said to occupy a special place since it is not produced; but it must beremembered that there is an important relationship between the amount of capital available and the productivity of labor , and in addition , much technical progress is introduced in the form of new equipment or improvements to existing

    t e r i a l The odd member of this trio is land , which, while obviously having avital role to play in the production of all kinds of minerals, is usually ignored inthe textbooks.On the other hand , the various categories of natural-resource and energyinputs , half-fabricates , and so on , are called intermediate inputs. Though extremely important , most students of economic theory have probably never encountered in their textbooks a production relationship that formally considersin termediate inputs. The reason for this omission is that in economics it is netoutput or value added that is usually found relevant . J i s concept involves o l ythe primary inputs since in value terms net output or value added is defined asgross output minus the payment for intermediate inputs. .get a better idea of this matter , the reader should consider the f o l l o w n gsim ple example that has been condensed from an algebraic presentation in B ~ n k s(1977b). (It should also be emphasized that the purpose of this e x a m p l e s _oillustrate some aspects of production theory rather than provide a r e a l i s t c n -sight into the functioning of the bauxite-aluminum industries.) superman, em-

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    ploying his bare hands , digs out 100 bauxite rocks a day on a plot of land thathe inheritedoHe sells these rocks to a processor on an adjacent plot of land for1 per rocko This processor, using only m a c l i n e s and labor, turns these rocks

    into 25 units of a valuable material called aluminu mo Let us now assume thatthese 25 units of l u m n u sell for $11000On the basis of these data, we can examine the exact relationship between

    outputs and inputso For the superman, t l e input is muscular exertion and thephysicaJ output 100 bauxite rockso The output vaJue terms 100 , andsince there were no i n t e r m e d a t e inputs , this also the value addedo ln this casethe 100 can be regarded as the return to the primary fa ctor or , e q u v a l e n t l ythe w ge or rent of laboro(ln some s t u a t o n s we m g l t want to stretch this illustration a little further and call the aforementioned 100 the return to the primaryfactor plus economic profito c o n o m c profit would arise here if the supern1an isgaining a larger monetary reward d g g i n g bauxite than l e would realize in analternative occupationo)

    On the other hand , bauxite is an intermediate good in the aluminum industry We have taken the output of this industry in value terms to be 1100 ; butsince 100 was paid for the intermediate good bauxite , the net output , or valueadded , amounts to 1000 0This sum is also equal to the payments to the primaryfactors used to produce aluminum , which in t h s case would be the total of thewages (or rents) paid to labor and the rents capital ownersoThe concept ofprofit will be bypassed for the time being, but it can be mentioned that as in thecase c t e d in t l e previous example , economic profit would accrue to the ownersof capital if the percentage return or y e l d on their investments in this n d u s t r yexceeded the yield on a perfectly safe financiaJ asset such as a government bondo

    Leaving simple examples in favor of simple diagrams, figure 1-1 presents asketch of inputs and pro cesses in the production of 1 lb of aluminumoNote thatthree distinct activities are being d i s p l a y e d b a u x i t e - a l u m i n a a l u m n u m a n dcan happen that t l e s e are found in three widely separate geographicallocationsoConversely , it is conceptually possible that we might have a fully integrated system where bauxite is mined at one end , and nearly pure metal in a variety ofshapes comes out the othero

    e intricacies of these activities will be discussed later , but for the purposeof t h s introduction , a few general comments are in orderoThe production ofbauxite is a fairly simple matter , assuming that a bauxite deposit of decent sizeand richness is avaiJableo t may be so, however, that the overaH economic advantage for a country (as opposed to a firm or a group of private individuals) isincreased through p r o c e s s n g rather than just extracting oreo h i s has been theclaim of a number of primary commodity-producing countries in the ThirdWorld for many years o

    Alumina production yields considerably larger locaJ outlays for supplies ,labor , and various services th an bauxite mining; and some estimates indicate thatalumina provides as much as four times as much employment per ton of output



    EnergyI nternal transportationOther

    of bauxite



    TransportLimestone 1 /5 lb)Soda 1 /5 lb)Fuel oil 1/4 lb)Coal 1/2 lb)

    of alumina. . . . . = : ; ; ; ; ; ; . . . _ . . . . Raw cryoliteC r y o l t e (3 /50 lb)

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    His figures n d i c a t e d that in these countries, although an aluminum planthaving an average capacity of 150,000 t ons may r e q u r e an investment excessof 800,000 ,000 deutschmarks, while unfortunately c o n t b u t i n g only a smalldirect n c r e a s e employment , value added may come to as much as 44% of thegross or total value of output. 1 1 i s value added is f a r l y large in c o m p s o n tothe gain value added that would result from investments designed to increasecapacity in the smelting and/or r e f i n n g of copper, lead, and z n c many of theLDCs producing the ores of these metals. similar argument will be formulatedfor Australia Jater this book, where it will be contended that due to suchthings as the increase the p c e of energy after 1973-1974, it is probably inthe interest of both Australia and the i n d u s t a l world if a maximum amount offurther processing of energy-intensive items takes place Australia . Furthermore, due to such things as nationalizations and the threat of worldwide commodity cartels, it could be argued that i n d u s t a l c o u n t e s consuming largeamounts of bauxite would be palpably better off if Australia produced sufficientbauxite to counterbalance the designs of a more aggressive bauxite cartel. Thequid pro quo for this favor might conceivably be a very large increase theamount of processing capacity located Australia , to include a guarantee thatthe output of this capacity would not be interfered with on world markets bythe traditional processors of bauxite nor made the object of excessive tariffsand quotas.Habenicht ends his analysis of this issue with the rniners' maxim thatmoney is earned in the pits, by which he apparently means to imply that the

    further processing of ores should not be undertaken by even some of the mostadvantaged of the primary commodity-producing c o u n t e s As far as am concerned, this is probably an erroneous interpretation. What the maxim means isthat in many c o u n t e s miners are among the best-paid members of the laborforce. Chilean miners, for instance, both under the Allende government and before , were among the best paid workers South America ; and had it not beenfor the so-called energy crisis , the annual pay of Swedish mine workers mighteasily have exceeded that of Swedish professors of economics before the middleof the 1980s, which considering the utility of the work being c r e d out bysome of these economists, might have been a good thing. However, the issue hereis not the remuneration of miners and inept scholars nor, for that matter , theyield on money invested in the mining industry as compared to the processingindustry . Rather, assuming a satisfactory return on capital , it has to do withraising the 1evel of productive employment in c o u n t e s with high unemployment ; increasing the payments to local as compared to foreign factors of production ; and providing incentives for domestic firms to increase the quantity andquality of goods and services supplied the processing sector, thereby helping toraise the general technical and educationallevel.The reader should also be aware that in 1973 the value of the world production of all metallic ores at the mining stage was $30 b l l i o n , which was less than

    % f world gross national product ; while the value of the production of rela-1 1 pure metals (smelted and/or refined) came to approximately $90 billion.t e d d these figures do not tell the entire story. The value of r o n ore produceAn73 was only a few billion dollars ; but the total value of international trade19 . ore coking coal semifinished and finished steel products, and so on ,, reached almost $65 billion. . .Un der the circumstances, the c o n c l u s o n can hardly be a v o d e d that al-though mining is , for the world, an indispensable o c c u p ~ t i o n a n ~ o ~ t e n s i b l y thebackbone of the country for one lucky realm, there no p n t exaggerat. its significance in either financial terms or as a creator of employment . At n g th . . h t . tthe same time it may be possible to accept e p r o p o s t ~ n t a ~ r c u m s a n ~ e s

    t that m l i t a t e against an expansion in further p r o c e s s n g o u t s d e the maJore x s . . .industrial o u n t e s The ad valorem tariff on aluminum m p o r t s n t o the U n t e dStates, Canada , the European Economic Community , Britain, and Japan runfrom an average of 8.5% on aluminum ingot and billets to more than 20% oncable , pipe, and tubes. Given these t a f f levels, as well as the o ther discriminatory measures and restrictions placed on light manufacturers- to n c l u d e smeltedand re fined products- destined for North America, Japan, and Western Europe ,even processing facilities with an intrinsic high yield or profitability are doomedto be noncompetitive.

    Reserves, Resources, and B a u x t eA c c o r d n g to the U.S. Geological Survey and Bureau of Mines, world reserves ofbauxite in 1977 came to almost 25 ,000 million L-T , corresponding to 5600 S-Tof aluminum. With a production rate of 84 million tons of bauxHe per year ,which was the figure for 1977 , these reserves would last 297 years ; but if bauxite

    p t i o n continues to grow at the trend rate of 9% a year, these reserveswill only suffice 37 years. i s Jast figure is someti.mes called the dynamicrese rve/production ratio.Quite apart from this, it should be appreciated that the amount of bauxitereserves is constantly b e n g adjusted upward. World bauxite reserves were estimated at 1 billion L-T 1945, 3 billion in 1955 , 6 billion in 1965, and 25billion in 1977. The jump between 1965 and 1977 can be accounted for by thegrowing attention paid Australia, Brazil, and the West Coast of f c a by v a o u spurchasers of bauxite in the major n d u s t r i a l c o u n t e s However, everything considered, some question must be asked as to whether there is any point in ferreting out additional reserves at the present t m e Remember that a dollar investedin a bond or a bank deposit at an interest rate of 8% (which probably typicalfor a long-term d e p o s t would y e l d (1 0.08) 37 = $17.25 after 37 years. Consequently, this amount would have to be the profit in money terms in 37 yearsin order to justify i n v e s t n g 1 creating a unit of reserves that would be ex-

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    tracted at that time. Given the h i s t o movement of bauxite prices , this maybe too much to ask. According to some economists , the ideaJ figure for thedynamic production/reserve ratio seems to be between 12 and 15 because if itwere less, a large part of the capacity or useful life of both the extraction andprocessing equipment might be wasted.

    Before taking a detailed look at bauxite reserves, it should be stressed thatreserves are only a portion of the total supplies of a mineral . We must also introduce the concept of resources which includes supplies that cannot be profitablyextracted given the structure of existing technology and t l e price of the mineral(or, .by extension, the price of the metal into which t l e mineral is processed).

    p o r t o n of these resources though are designated p a r a m a r g n a / which means thatthey lie on the brink of exploitability. 1t has been sa id tl1at a SS% ncrease inprice of aluminum would lead to a 40-45% increase in the stock of bauxite reserves. Equally important is the claim that a J5-25% rise in tl1e price of aJuminum would warrant the large-scale mining of a l u m i n u m b e a n g mat erials otherthan bauxite.

    One of the most useful devices for discussing this subject is the classificationsystem developed by the U.S. Geological Survey , which is shown in figure 1-2and which functions as follows. Along the horizontal axis are \isted total supplies,or reserves, plus resources. The two basic cate gories here are discovered and undiscovered supplies, which are described with respect to the information that isavailable about them . On the vertical axis the characteristic of interest is eco-nomic v a l u ~ and here the natural partition is between profitable and unprofitable . Thus the upper left-hand corner of the system, we can identify reservesas supplies that definitely or probably exist and are profitable (to extract).

    As implied earlier, resources are constantly being reclassified . On the extreme g h t of figure 1-2 are mineral deposits whose quantitative and qualitative

    CalculableKnown I robable Estimated Hypothetical Specu a t i e

    Profitable eserves

    ParamarginalUnprofitable I


    Figure 1-2 . The Cla ssification of MjneraJ Supplies


    K - ~

    at tributes have been assessed on the basis of a few boreholes and a study of adacent rock forn1ations . Still , it is a fairly widespread belief that almost any

    ~ t e g o of resource allotted a place in this system will eventually be designateda reserve. The reason for this belief is simply that given t l e modus operandi ofthe exploration s e r v c e s and geologi..:al surveys of the world , only prospects thatare potentially profitable are examined .

    1t is also interesting to observe that there are concepts of mineral availabilityeven more abstract than resources. One of these could be called crusta l abundance or crustal profusion and has to do with the total resources of a mineraldown to some specific depth, for instance , 1 km. Readers interested in considering t l i s topic can refer to Banks (1976b ), but in l n e with our present discussion ,it can be pointed out that the reserves of bauxite mentioned previously (25b i l l o n tons) are only a hundred thousandth of tl1e known amount of bauxite in

    ear th 's crust down to a depth of 200 m. r l u s it seems likely t l t there aree n o u g bauxite resources available to ensure a steady addition to bauxite reservesfor a great many years, with or without substantial increases in the price ofaluminum . Table 1-3 presents some information on bauxite production andreserves.La ter on this book will discuss b r i e y the pricing of bauxite ; but as an in-troduction, a few remarks can be made now . Between 1968 and 1973 the priceof ba uxite increased by about 50%, largely because of an acceleration in theincrease in demand for aluminum. In addition, during this period the price of aton of bauxite varied between $6 and $9 per ton because of the quality differences betwe en various bauxite deposits. In 1970 the Jamaican governn1ent insisted on doubling the bauxite price, and t l e foreign operating companies inJamaica not only acceded to this demand but allowed the price increase to takeplace re troactively . The main reason for this unprecedented generosity was notsimple altruism but rather the fact that these increased costs could be used toobtain tax deducations in their home countriesln 1974, however , further levies by the Jamaican government these companies we re not re ceived with such good humor . On occasion the Jamaicanstied the price of bauxite to the price of aluminum , setting the price at whichtl1ey wou]d sell bauxite as a fraction of the U.S. price of ingot. The immediateresu \t of this measure was a doubling of the cost of Jamaican bauxite , and moreover, the en tire price s e could not be covered by tax deductions in the buyers'

    l o m e countries. Just how this drama will turn out is uncertain at the presenttime, but there are signs that the Jamaican s l r e of t l e world bauxite marketl1as begun to weaken.

    Elementary DiscountingS e e r a topi cs in thi s chapter \end themselves to an algebraic exposition, and inkeeping w i t l the aim of this book to eparate technical and descriptive materi ,

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    Table 1-3 hese expositions can be found the forthcoming chapter appendix . But theBauxite Capacity, Production, Reserves , and Resources (1977) t at ter of discounting is basic to a great deal of the ensuing discussion, and in

    Recoverable Aluminum ~ d t i o can be presented to readers with a minimal background in secondaryEquivalent million ST chool mathematics.CaP.acity Production Reserves O t l

    5 Our approach to discounting need involve no more than formalization ofJ0 3S-T) J0 3S-T) J06 S-T) Reserves Resources Total t l e well-known fact that a given amount of an asset is worth more today than

    North Americat l e same amount is worth in the future , all else remaining equal. If we have the

    United States 650 460 40 10 40 50 asset now , then we also have the option of e n j o y n g its s e r v c e s if we so desire;Jamaica 3800 2630 2000 450 50 500 o t l e r w i s e we face uncertainties concerning our desires and appetites up to andOther 500 310 180 40 30 70 including the date on which it is received. (Consider, for example , an auto-TotaJ 4950 3400 2200 500 100 600 n o b i l e . Usually if people have a choice, they demand some sort of c o n e n s a -South America tion for postponing present satisfaction. Thus a sum of money (which representsBrazil 300 250 2500 600 500 1100 genera lized purchasing power) today is related to a sum in the future through aGuyana 1100 700 1000 260 260Surinam 2000 1250 490 130 110 240 discount or interest rate that says something about the actual compensationOther 50 10 190 200 avai lable for someone prepared to defer a unit of consumption for a givenTotal 3400 2200 4000 1000 800 1800 period. This period is generally taken to be a year. For instance , if have $100Europe today and the interest rate is 10% then it is customary to say that this $100 isFrance 800 460 equiva lent to 100(1 r) =100(1 0.10) =$110 in a year's time since if [ give upGreece 900 670 750 170 50 220Hungary 700 680 200 45 20 65 $100 15 March 1979, [ can obtain a bond or bank deposit t l a t will provideItaly 10 10 n e with $110 on 15 March 1980.U.S.S.R . 1000 900 150 30 30 60 t is also enlightening to turn this formulation around. ln one year 11 isYugoslavia 800 480 400 80 85Other 200 200 90 20 50 70 worth 110/(l r) = 110/(1 0.10) =$100 today . The general expression thatTotal 4410 3400 1600 350 150 500 we are moving toward is :AfricaCameroons 1000 200 220 420hana 100 50 570 130 10 140 At +1 =A t (1 +r) or =Guinea 3300 2000 8200 1900 1900 t (1 r)Sierra Leone 130 30 30Other 200 150 100 20 300 320TotaJ 3600 3100 10000 2300 500 2800 expression, t signifies time period. Similarly , if we are interested in theAsia relationship between t andAt 2, we have :China (Mainland) 150 30 170 200lndia 400 330 1400 320 80 400 2 1 (1 r) (1 r) 1 r) (1 r)2Indonesia 700 150 60 210 t+ t+ t tOther 900 770 50 10 200 210Total 1300 1100 2300 500 500 1000 lf , for instance, the rate of interest is 10%, $100 today becomes 100(1Oceania 0.10)2 =$121 in 2 years, and 21 is the prernium fo r giving up control overAustralia 6700 5800 4500 1000 300 1300 00 of present purchasing power for a p e o d of 2 years.Other 50 10 40 50 We began this exposition with a brief reference to the agony of having to

    World Total 24360 19000 25000 5600 2400 8000 wait for our pleasure, and we are now talking about how money grows w l e nNote: Bauxite capacity and production is in thousand short tons (S-T) of aluminum of used to buy a bond or is put in a savings account. The connection is roughly as

    ~ l u n i n u m equivalent . This ca n be converted t l o u long tons of bauxHe by multiply- follows . The interest rate is an objective t e r i o n If you visit your local bankby 4.46 . Obse rve also that the column labeled reserves is in rnillion long tons of or brokerage office, you can be quoted the interest rate on such and such a typebau xite. of de posit or a security possessing a certain m a t u t y . Let us assume that this is

    I 0%. At t l e same time t e typical individual will possess a subjective preference


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    or subjective d s c o u n t rate concerning his or her willingness to surrender mon_ytoday in return for money tomorrow. Some people might regard 10 as a n c ereward for waiting and t l u s be i n c l n e d to put a sizable portion of their monthlypaycheck a savings account offering this rate of interest ; while the ~ u b j e c t i v ediscount rate of others might be so high that they would never c o n s d e r post-p o n n g any consumption un\ess they were rewarded with a 100% interest rate.Unfortunately, however, neither economists or psychologists have had muchluck measuring individual discount rates and no luck at al\ with aggregating l e m .Instead, t l e practice has been to use interest rates as a proxy for aggregate sub-jective discount rates, and so these two terms are often used n t e r c h a n g e a b l y ,both here and throughout most of the other literature of e c o n o m c s . Thus asociety with a low average rate of interest such as Switzerland might be regardedas a society where the average person has only a moderate preference for today'sgoods as compared to tomorrows.

    F n a l l y , note that if we receive various amounts of money at different timesin the future, these future income flows can be discounted and summed to ob-tain a present value. As an example, we can inquire into the present value of110 a year from now and 121 two years from now. Assuming an interest rateof 10 ,we obtain:

    110 121PV= + =200 r= 0.101+r) 1+r)2This concept can be generalized. Letting represent a money flow receivedat periods in the future and r the discount rate, we have as the present value ofa stream of n payments :

    PV = _ + 2 + .. . + + + n n(1 +r) l +r )2 l +r) 1 (1 +r)Later on we will compare payment streams, and the criterion we will adopt

    will reduce to ranking these streams on t l e basis of the size of their presentvalue. At this point the reader should experiment with discounting and compar-ing various n c o m e streams with the same and different lengths, employing dif-ferent rates of interest . One of the things he or she will notice is that as interestrates increase , present values decrease , assuming no change in the paymentstreams. This merely signifies a rise in impatience : The greater importance at-tached near as opposed to distant payments, and the downg.rading of moreremote satisfactions.

    ppendix Discounting nd theTime to Exhaustionln this and ensuing appendixes, material that b e l i e v ~ al\ r e a ~ e r s s h o u l ~ d e ~ nately ma ke an effort to read is marked with an a s t e r s k . For n s t a n c e , this

    en dix there are materials on discounting and present value, the effect of a~ ~ ~ t i rate of growth in the consumption of a mineral on the time to its ex-l a u s t i o and a few remarks on production theory . As far as am concerned,only the firs t of these is of immediate concern to readers of this book, althoughthe second is extremely important and definitely should be understood by thereader as a concept, even if he or she l a s no interest in its algebraic expression .lA 1 .* l i s section will extend the discussion at the end of the chapter thatdealt the present value of an i n c o n e stream. Let us take a situation wherewe a v e as present income, 1 income at t l e end of period 1, at the endof period 2, and so on . Assuming a constant rate of interest (or discount rate)r we defi ne present value as:

    2 nPV=A +RA +R + +R Anl + r) l + r)2 1 + r)n 2w l e r e we define R = 1/ l + r). If we also have 1 = = the pre-ced;ng ex pression can be simplified to :

    PV=A l +R +R 2 + +R Multiply ing both sides by 1 - , we get:


    PV l - R) =A I +R +R 2 + +R 11 ) 1-R)1 + R + + R R +R 2 + R 3 + + R +1

    =A I - Rn+l)l - Rn+lPV =A1-R

    Usually we l a v R 1, and thus if n - we get Rn +l In this situationlhe abo ve becomes:


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    PV= RlA 2. The next topic concerns the effect of the growth rate of mineral use onthe time to its exhaustion. lf we take g as the g r o w t l rate for the mineral andas the consumption of the mineral during year t we have:

    t ~ ttThe term 0 is the consumption of the resource in some arbitrary initial year.Cumulative resource use is then defined as :


    With of the resource available, we can rearrange this expression to get, as theyears to exhaustion, Te :

    = n - +1gX )e g

    t is also interesting to observe the effect of changes in on Te. Differentiating,we obtain:

    dT = ==dX gX+X0What we see here is that substantial changes in are not reflected in the time

    to exhaustion. For example , Banks (1977a) has constructed an example for theworld Jead supply that shows that with g =3, an increase in the amount ofreserves by a factor of 14 increases time to exhaustion by a factor of only 3.7.lA 3. The conventional algebraic designation for the production function isq = f K, L . We define the marginal productivity of capital MPk) as oq/oK, andin a neoclassical framework, we define Pk Similarly , is the marginalproductivity of labor and is equal to oq/oL. We also take for all positive values of the variables. s for the wage oflabor - or the rent oflabor,as it is sometimes called- and the rent of capital w if we take p as the price ofthe product , we get :

    oqp and qw

    ln tt1e production function, units must be carefully specified, particularly ifthey are not in va lue terms. Thus L is in labor hours, in machine hours, andq is units of physical output per t m period.