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The forces of the demand for British Columbia's mining labour : an analysis of the trends of wage rates… Meekison, James David 1962

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THE FORCES OF THE DEMAND FOR BRITISH COLUMBIA'S MINING LABOUR: AN, ANALYSIS OF THE TRENDS OF WAGE RATES AND - EMPLOYMENT OF BRITISH COLUMBIA'S MINING INDUSTRY JAMES DAVID MEEKISON A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of Economics and P o l i t i c a l Science We accept t h i s t h e s i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1962 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission for extensive copying of t h i s thesis f o r scholarly purposes may be granted by the Head of my Department or by his representatives. It i s understood that copying or publication of th i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Economics and P o l i t i c a l Science The University of B r i t i s h Columbia, Vancouver 8, Canada. Date September 7. 1962 ABSTRACT This t h e s i s attempts to analyse the i n f l u e n c e s of changes i n demand f o r B r i t i s h Columbia's mining labour upon the wage r a t e s and employment of B r i t i s h Columbia's mining i n d u s t r y . The competitive elements of B r i t i s h Columbia's mining indus t r y sug-gests that changes of wage r a t e s and employment w i l l be sh a r p l y a f f e c t e d by changes of metal p r i c e s . The t h e o r e t i c a l e f f e c t s of a change of metal p r i c e s i n -d i c a t e that the ind u s t r y ' s output v a r i e s i n the same d i r e c t i o n as metal p r i c e changes. Furthermore, i t i s expected that em-ployment w i l l vary d i r e c t l y w i t h output changes. Therefore, the number of labourers employed should vary d i r e c t l y with metal p r i c e changes. The trends of employment of B r i t i s h Columbia's mining labour and metal p r i c e s are studied to evaluate these t h e o r e t i c a l expectancies. As an element of demand f o r B r i t i s h Columbia mining l a b o u r , the l e v e l of metal p r i c e s i s expected to i n f l u e n c e wage r a t e s of B r i t i s h Columbia's mining l a b o u r . Wage r a t e s have increased i n every year of the twelve year p e r i o d but one, while metal p r i c e s have f l u c t u a t e d over the p e r i o d . These phenomena pro-vide questions f o r f u r t h e r a n a l y s i s . The second major topic of the t h e s i s i s concerned with i n f l u e n c e s of changes of p r o d u c t i v i t y of B r i t i s h Columbia's mining labour upon wage r a t e s and employment. The f i r s t task i s to describe concepts of p r o d u c t i v i t y of mining labour and then to determine the meaning of a p r o d u c t i v i t y index. F o l l o w i n g t h i s , the meaning of a change i n the p r o d u c t i v i t y i n -dex must be described as the p r o d u c t i v i t y of mining labour has v a r i e d considerably over the twelve year p e r i o d . The trends of the d i f f e r e n t i a l s of employment and the d i f f e r e n t i a l s of labour's p r o d u c t i v i t y suggest that an inverse r e l a t i o n s h i p e x i s t s between these v a r i a b l e s . This r e l a t i o n s h i p i s evaluated and i t s s i m i l a r i t y to a t h e o r e t i c a l average pro-duct curve i s described. However, the r e l a t i o n s h i p between the trends of wage rates and mining labour's p r o d u c t i v i t y provides l i t t l e evidence of any a s s o c i a t i o n of these v a r i a b l e s . I t i s suggested that i f the changes of mining labour's p r o d u c t i v i t y have i n f l u e n c e d wage r a t e s , then t h i s i n f l u e n c e has been hidden by other f a c t o r s of wage determination. i i i T A B L E OF C O N T E N T S P A G E A B S T R A C T ACKNOWLEDGMENT i v I N T R O D U C T I O N C H A P T E R I I N F L U E N C E S ON T H E P O S I T I O N O F THE U P P E R WAGE BOUND O F B R I T I S H C O L U M B I A ' S M I N I N G I N D U S T R Y C H A P T E R I I THE I N F L U E N C E O F C H A N G E S I N M E T A L P R I C E S UPON T H E T R E N D S O F WAGE R A T E S AND E M -P L O Y M E N T I N B R I T I S H C O L U M B I A ' S M I N I N G I N D U S T R Y 19 C H A P T E R I I I C O N C E P T S OF P R O D U C T I V I T Y I N T H E M I N I N G I N D U S T R Y 44 C H A P T E R I V THE I N F L U E N C E O F C H A N G E S I N T H E P R O D U C -T I V I T Y OF B R I T I S H C O L U M B I A ' S M I N I N G L A B O U R UPON T H E I N D U S T R Y ' S . W A G E R A T E S AND E M P L O Y M E N T 54 C O N C L U S I O N 85 B I B L I O G R A P H Y 91 i v ACKNOWLEDGMENT I would l i k e to thank the I n s t i t u t e of Indus-t r i a l R e l a t i o n s of the U n i v e r s i t y of B r i t i s h Columbia f o r the generous grant they provided f o r t h i s study. I would also l i k e to express my a p p r e c i a t i o n to Professor S c o t t , P r o f e s s o r Jamieson and Dr. Montague f o r t h e i r c o n s t r u c t i v e c r i t i c i s m s and advice concern-ing my t h e s i s . F i n a l l y , I wish to thank Mr. M. M i l l e r f o r h i s a r c h i t e c t u r a l t a l e n t s * THE FORCES OF THE DEMAND FOR BRITISH COLUMBIA'S MINING LABOUR: AN ANALYSIS OF THE TRENDS OF WAGE RATES AND EMPLOYMENT OF BRITISH COLUMBIA'S MINING INDUSTRY INTRODUCTION The o b j e c t i v e s of t h i s t h e s i s are to describe and to ana-l y s e the i n f l u e n c e s of determinants of demand f o r labour upon trends of wage earnings and employment of labour i n B r i t i s h Columbia's non-ferrous metal mining i n d u s t r y 1 f o r the p e r i o d 1949 to I960. A study of an i n d u s t r y ' s wage r a t e s and employment i s usu-a l l y i n t e r e s t i n g and u s e f u l f o r i t s own sake. I t i s i n t e r e s t i n g because i t attempts to e x p l a i n or to descr i b e causes and e f f e c t s of a c t u a l happenings. I t i s u s e f u l because i t may c o n t r i b u t e knowledge of d e s c r i p t i o n or p r e d i c t i o n to economic theory. How-ever, an a n a l y s i s of wage r a t e s and employment of B r i t i s h Colum-bia ' s mining i n d u s t r y i s i n t e r e s t i n g not only f o r the sake of a n a l y s i s but al s o f o r reasons p e c u l i a r to t h i s i n d u s t r y . A cursory i n s p e c t i o n of a v a i l a b l e wage r a t e and employment data f o r mining suggests the general trends of r i s i n g wage r a t e s and f a l l i n g employment. These trends are cu r i o u s as l i t t l e evidence can be found of i n s t i t u t i o n a l or other r e s t r i c t i o n s upon the sup-p l y of mining labour. This s i t u a t i o n c o n t r a d i c t s conventional economic theory and t h i s c o n t r a d i c t i o n poses a question to be answered. The clo s e approximation of the labour market of B r i t i s h Columbia's mining i n d u s t r y to co n d i t i o n s of open competition i s another i n t e r e s t i n g f a c e t of the proposed t o p i c . The p o s s i b i l i t y ^To avoid needless r e p e t i t i o n , "non-ferrous metal mining i n d u s t r y " i s abbreviated to "mining i n d u s t r y " unless otherwise i n d i c a t e d . 2 of r e l e g a t i n g the determination of wages and employment to a competitive model i s appealing but probably not r e a l i s t i c . Even i f a s u i t a b l e model cannot be found, the competitive c o n d i t i o n s of the ind u s t r y remain i n t e r e s t i n g and worthy of i n v e s t i g a t i o n . Two of the more important reasons f o r a study of the trends i n wage r a t e s and employment of B r i t i s h Columbia's mining industry have been given above. Other reasons w i l l become apparent with the p r e s e n t a t i o n of theory and f a c t s . Throughout the t h e s i s there i s a broad framework which w i l l be described i n d e t a i l , so that each piece of a n a l y s i s can be recognized as a part of a whole. This framework i s con-s t r u c t e d from a s i n g l e concept which has been described by most labour economists. They have suggested, d i r e c t l y or i n d i r e c t l y , that the wage s t r u c t u r e of an i n d u s t r y i s found between boun-2 d a r i e s which are set by market f o r c e s . These economic bounds, while not p r e c i s e , are very r e a l . The upper bound i s deter-mined by the f o r c e s of the demand f o r labour and the lower bound i s determined by the forces of the supply of labour. The forces o f the demand f o r B r i t i s h Columbia's mining labour w i l l be ana-l y s e d i n turn . Some references w i l l be made to the supply of B r i t i s h Columbia mining labour. However, the f o r c e s of the sup-p l y of mining labour w i l l not be s t u d i e d . In each of the studies 2 See Arthur M. Ross, "The E x t e r n a l Wage S t r u c t u r e " , New  Concepts i n Wage Determination, New York, McGraw-Hill Book Company Inc., 1957, pp. 173-205-E. Robert Livernash, "The I n t e r n a l Wage S t r u c t u r e " , New  Concepts i n Wage Determination, pp. 140-172. John T. Dunlop, "The Task of Contemporary Wage Theory", The Theory of Wage Determination, New York, MacMillan and Co. L t d . , 1957, pp. 3-27-3 of the demand f o r mining labour the impact of changes of the independent v a r i a b l e or force upon wage rates and employment w i l l be assessed and described. Between the economic l i m i t s or boundaries l i e s a range of a l t e r n a t i v e p o s s i b l e wage l e v e l s . The r e s u l t a n t wage l e v e l depends upon i n s t i t u t i o n a l f a c t o r s such as unionism or p o l i t i c a l p r essure. However, except f o r a l i m i t e d a n a l y s i s of the i n -f l u e n c e of the union upon wage r a t e s , the t h e s i s i s almost ex-c l u s i v e l y concerned with a study of the upper boundary com-ponents. The determinants of the upper bound can be considered as the elements of a derived demand f o r mining labour. This de-3 r i v e d demand w i l l be defined as the product of the marginal 4 revenue of metals and the marginal p h y s i c a l product of labour. The i n f l u e n c e of changes i n each of these f a c t o r s upon the wage r a t e s and employment of labour w i l l be studied i n a sepa-r a t e chapter. Before the s t u d i e s of the component forces of the upper bound are attempted, two aspects of the market s t r u c t u r e of This d e f i n i t i o n may meet w i t h conceptual d i f f i c u l t i e s w i t h respect to aggregation and measurement, but f o r i t s par-t i c u l a r use i n t h i s t h e s i s i t i s s u f f i c i e n t . ^Increments of c a p i t a l and labour w i l l probably be s i m u l -taneously added or deleted from the mining i n d u s t r y . There-f o r e the marginal product provided by an a d d i t i o n a l u n i t of mining labour should be considered as a marginal net product. Unless the amount of c a p i t a l i s assumed constant, the marginal product curve f o r mining labour i s a marginal net product curve. Throughout the t h e s i s , labour's marginal net product i s simply c a l l e d "marginal product". . 4 B r i t i s h Columbia's mining indus t r y w i l l be described i n Chap-te r I. The competitive determination of p r i c e s and the basing p o i n t system of p r i c e s , while not e n t e r i n g the wage bounds as determinants, i n f l u e n c e the p o s i t i o n of the upper wage bound. The probable impacts of these two elements upon the wages and employment of B r i t i s h Columbia w i l l be assessed and described. The proposed method of a n a l y s i s has one obvious weakness — a s each element of the economic wage bound i s being s t u d i e d , the i n f l u e n c e s of the remaining v a r i a b l e s are more or l e s s i g -nored. Over a p e r i o d of time the impact of one or a l l of the neglected v a r i a b l e s may change, but any change which i s induced upon wage rates or employment w i l l be a t t r i b u t e d to the par-t i c u l a r v a r i a b l e being s t u d i e d . However, the a l t e r n a t i v e to the proposed method of study does not appear to be a p p l i c a b l e i n t h i s t h e s i s . The complexity and i n t e r a c t i o n of the wage determining v a r i a b l e s p r o h i b i t an a n a l y s i s which permits simu l -taneous v a r i a b i l i t y i n some or a l l of the v a r i a b l e s . Whenever p o s s i b l e , an important change of a neglected v a r i a b l e w i l l be noted and the p o s s i b l e r e s u l t s of the change w i l l be discussed. In summary, the separate stud i e s of each of the wage determining forces are l i n k e d together through t h e i r a s s o c i a -t i o n w i t h the economic wage boundary. In Chapter I i t w i l l be suggested that the competitive de-te r m i n a t i o n of metal p r i c e s has i n f l u e n c e d the p o s i t i o n of the upper wage bound. The p o s i t i o n of the bound r e s t r i c t s the p o s s i b l e number of wage incr e a s e s . I f the upper wage bound i s low, then few wage r a t e increases are p o s s i b l e unless the 5 upper wage bound s h i f t s upwards. Chapter I I i s concerned with the r e l a t i o n s h i p s between changes i n metal p r i c e s and employment, and with the r e l a t i o n -s h i p s between changes i n metal p r i c e s and wage r a t e s . Metal p r i c e s are determinants of both the upper wage bound and the demand f o r mining l a b o u r . Emphasis w i l l be placed upon the for c e s of metal p r i c e s as a determinant of the demand f o r min-in g labour i n B r i t i s h Columbia. Employment i n B r i t i s h Columbia's mining i n d u s t r y w i l l be found to vary d i r e c t l y with metal p r i c e s . Furthermore, the absolute y e a r l y d i f f e r e n t i a l s of employment w i l l be found to vary d i r e c t l y w ith the absolute y e a r l y d i f f e r e n t i a l s of metal p r i c e s . The wage r a t e s of B r i t i s h Columbia's mining labour have increased i n almost every year, but metal p r i c e s have f l u c t u a t e d over the p e r i o d . Therefore, no r e l a t i o n s h i p can be expected to be found between the trends of wage ra t e s and metal p r i c e s . However, a strong r e l a t i o n s h i p between the absolute y e a r l y d i f f e r e n t i a l s of metal p r i c e s and the wage r a t e s of B r i t i s h Columbia's mining labour w i l l be described. I t w i l l be con-cluded that the degree of the y e a r l y change of wage rates v a r i e s d i r e c t l y w ith the d i r e c t i o n and degree of metal p r i c e changes. In Chapter I I I concepts of the marginal p r o d u c t i v i t y of mining labour w i l l be introduced and the d i f f i c u l t i e s of s e l e c t i n g an index of labour's p r o d u c t i v i t y w i l l be described. 6 The marginal p h y s i c a l product schedule of mining labour i s the other determinant of both the upper wage bound and the demand f o r mining labour. I t w i l l be suggested that changes i n the marginal p h y s i c a l product curve of B r i t i s h Columbia's min-ing labour have had l i t t l e i n f l u e n c e upon employment and wage rate s of the i n d u s t r y . The absolute y e a r l y d i f f e r e n t i a l s of employment i n B r i t i s h Columbia's mining i n d u s t r y w i l l be found to be i n v e r s e l y r e -l a t e d to the absolute y e a r l y d i f f e r e n t i a l s of output-per-man-per-year. Therefore, i t w i l l be suggested that t h i s r e l a t i o n -ship i s s i m i l a r to the expected r e l a t i o n s h i p g iven by a number of p o i n t s on a t h e o r e t i c a l average product curve. The trends of wage r a t e s and p r o d u c t i v i t y of B r i t i s h Columbia's mining labour w i l l be found to be r e l a t e d i n a "general" f a s h i o n . However, t h i s r e l a t i o n s h i p doesn't have very much meaning. The trends of the y e a r l y absolute d i f f e r -e n t i a l s of wage rates and y e a r l y absolute d i f f e r e n t i a l s of metal p r i c e s w i l l not be found to be r e l a t e d . I t w i l l be shown that the i n f l u e n c e s of other wage determining v a r i a b l e s have probably d i s t o r t e d any p o s s i b l e r e l a t i o n s h i p s between the trends of these d i f f e r e n t i a l s . In summary, i t w i l l be concluded that the changes of metal p r i c e s have had a strong i n f l u e n c e upon the trends of both wage rates and employment i n B r i t i s h Columbia's mining i n d u s t r y . Furthermore, i t w i l l be suggested that the changes of employ-ment i n B r i t i s h Columbia's mining indus t r y have a f f e c t e d the 7 trends of mining labour's p r o d u c t i v i t y , but the i n f l u e n c e of changes of mining labour's p r o d u c t i v i t y upon employment has been s m a l l . No important conclusions w i l l be o f f e r e d con-c e r n i n g the r e l a t i o n s h i p s between mining labour's p r o d u c t i v i t y and the wage r a t e s of B r i t i s h Columbia's mining labour. The f i n a l i ssue of the i n t r o d u c t i o n concerns the period of a n a l y s i s . The twelve year p e r i o d from 1949 to I960 was s e l e c t e d as the most s u i t a b l e i n t e r v a l of time f o r the study. As there i s i n s u f f i c i e n t data to extend the p e r i o d beyond I960, t h i s t e r m i n a t i n g year was g i v e n , not s e l e c t e d , assuming that the immediate years are the most relevant f o r a n a l y s i s . A d u r a t i o n of more than ten years was assumed to be necessary to r e v e a l the i n d u s t r y ' s trends i n wage ra t e s and employment. The trends of a p e r i o d of s h o r t e r l e n g t h may suggest conclusions which are the r e s u l t s of events or happenings of one or two years. On the other hand, a p e r i o d of more than f i f t e e n years would include the impact of the economic a b n o r m a l i t i e s generated by World War II. To give these abnormalities a proper per-s p e c t i v e , a p e r i o d of twenty-five to t h i r t y years long would be necessary, but then the e f f e c t s of a vast depression must be accounted f o r . Furthermore, the f o r c e s a c t i n g upon wage rates and employment at the beginning of a t h i r t y year p e r i o d may be much d i f f e r e n t from the analogous f o r c e s a c t i v e at the end of the p e r i o d . 1949 was picked as the p e r i o d o r i g i n because the economic e f f e c t s and a f t e r - e f f e c t s of war had more or l e s s disappeared and the r e s u l t a n t period was more than the minimal 8 ten y e a r s . Although the pe r i o d i n c l u d e s the economic e f f e c t s of the Korean War, these e f f e c t s are incomparable to the i n -fluences of World War I I . CHAPTER I INFLUENCES ON THE POSITION OF THE UPPER WAGE BOUND OF BRITISH COLUMBIA'S MINING INDUSTRY The s t r u c t u r e of B r i t i s h Columbia's mining i n d u s t r y may have an important i n f l u e n c e upon the wage r a t e s and employment of mining labour. T h i s i n f l u e n c e i s manifested i n the p o s i t i o n , and shape of the upper wage bound. The elements of the bound-a r i e s are the same, no matter what the s t r u c t u r e of the ind u s t r y may be, but the p o s i t i o n s and shapes that the economic l i m i t s assume are d e f i n i t e l y i n f l u e n c e d by the ind u s t r y ' s s t r u c t u r e . Rather than suggesting how the upper bound i s i n f l u e n c e d by va r i o u s i n d u s t r y s t r u c t u r e s , i t i s simpler to describe B r i t i s h Columbia's mining i n d u s t r y and then i n t i m a t e how some aspects of t h i s i n d u s t r y ' s s t r u c t u r e have a f f e c t e d i t s economic wage bound. B r i t i s h Columbia's mining i n d u s t r y i s only a part of a world mining i n d u s t r y which i n f l u e n c e s the s t r u c t u r e s of i t s component i n d u s t r i e s . Therefore, the d e s c r i p t i o n begins by d i s -c ussing b r i e f l y some of the relevant f a c t s of the general mining i n d u s t r y . Most of the d e s c r i p t i o n s of the general mining i n -d u s t r y and B r i t i s h Columbia's mining i n d u s t r y have been derived from the Report by P r o f e s s o r J . J . Deutsch: Economics of P r i -mary Production i n B r i t i s h Columbia, "The Mine r a l I n d u s t r i e s " , "The Marketing of M i n e r a l Products" and " I n d u s t r i a l R e l a t i o n s i n the Basic I n d u s t r i e s of B r i t i s h Columbia". This Report was the only general reference which provided considerable i n f o r m a t i o n concerning B r i t i s h Columbia's mining i n d u s t r y . Many quotations have been taken from t h i s source to develop some of the t o p i c s 10 of the thesis and to support some of the arguments. To return to the subject of t h i s chapter, metal prices are, more or less, competitively determined i n world markets. That mining i s a competitive business was seen for instance . . . when, uncontrolled, some copper mines i n the United States closed consequent upon , the onset of production i n other countries; . . . The supply side of the lead and zinc market i s dominated by numerous small producers and poten-t i a l producers who on the whole are sensitive to ,-price fluctuations. Some of the larger mining companies, such as Consolidated Min-ing and Smelting Company, could exert some influence upon metal prices by manipulating the supply of ores and metals. During periods of low prices, some of these companies might act as a group to r e s t r i c t the supply of metals and force prices up. Nevertheless, competition i s s t i l l the dominating force deter-mining metal prices. I f metal prices are competitively determined, then for any buyer or s e l l e r the prices of metals are given. S i m i l a r l y , f o r the whole of B r i t i s h Columbia's mining and smelting industry, "there i s one price for each metal. Each l o c a l industry—such as B r i t i s h Columbia's mining and smelting i n d u s t r y — i s composed of smaller units which s e l l refined metals and which cannot, or or w i l l not, influence the prices of metals. Aside from the "^S. J. Truscott, Mine Economics, Salisbury House, London, E.C.2, Mining Publications Ltd., 1947» p. 2. 5 Report by Professor J . J . Deutsch, Economics of Primary  Production i n B r i t i s h Columbia, "The Marketing of Mineral Products" (unpublished), p. 22. 11 o c c a s i o n s when the metal market i s s u f f e r i n g from r e l a t i v e l y -low p r i c e s , l a r g e companies w i l l p r obably not i n f l u e n c e metal p r i c e s d e l i b e r a t e l y . So great i s the importance a t t a c h e d to the maintenance of an o r d e r l y metal market that a l l producers tend to respect quoted market p r i c e s , which i n any case tend r to be a f a i r l y good r e f l e c t i o n of the market. The s e l l e r s of metals are u s u a l l y the s m e l t i n g companies which, i n t u r n , buy ore from mine-owners. The r e t u r n s a c c r u i n g to the mine-owner from the s a l e s of r e f i n e d ore and metals are d e s c r i b e d as f o l l o w s : R e f i n e d metal q u o t a t i o n s are used to determine the value o f custom ore and concentrate. The amount a c t u -a l l y r e c e i v e d by a mining company f o r the metal content of ore and concentrate i s l e s s than the metal's market value by two amounts: (1) smelting and treatment charges and (2) marketing charges. Smelting charges appear as a deduction from the metal's quoted market p r i c e , while treatment charges are a p p l i e d against each ton of ore or c o n c e n t r a t e t r e a t e d . Marketing charges are deducted from the gross value of the ore or c o n c e n t r a t e ' s c o n t a i n e d metal and c o n s i s t of the f r e i g h t from the mine to smelter, other h a n d l i n g c o s t s i f any, and i n the case of imported ore, customs duties'. Before s h i p p i n g ore to T r a i l , f o r example, the i n -dependent mine operator knows what s p e c i f i c charges and deductions the smelter w i l l make from the quoted market p r i c e s of the metals contained i n h i s ore. He a l s o knows that the p r i c e s used f o r determining the value of the metal content of h i s ore are the quota-t i o n s p r e v a i l i n g at the date the ore a r r i v e s at t h e 7 smelter. This q u o t a t i o n i n t i m a t e s that c o m p e t i t i v e p r i c e s f o r metals are the b a s i s f o r the d e t e r m i n a t i o n of ore p r i c e s . The mine-owner i s unable to a f f e c t the s e l l i n g p r i c e of h i s output. Managers of mines which are v e r t i c a l l y i n t e g r a t e d w i t h b I b i d . , p. 16. 7 I b i d . , p. 18. 12 smelting companies, govern t h e i r operations i n a s l i g h t l y d i f -ferent manner than independent mine-owners. The managers of Q i n t e g r a t e d mines are "given" an "accounting p r i c e " which must be lower than, or equal t o , the ordinary p r i c e of ore. For example, "The Consolidated Mining and Smelting Company operates Q i t s own mines at the most economical l e v e l . . . ." Thus, the accounting p r i c e s of each of these mines are equal to the m i n i -mum average c o s t s - p e r - u n i t of output f o r each mine. I f the smelter were required to pay an accounting p r i c e higher than a normal p r i c e f o r ore, then the i n t e g r a t e d mine might not be p r o f i t a b l e to operate and i t -may be e l i m i n a t e d from the i n -dustry. To summarize, the p r i c e s of metals are given t o , and usu-a l l y not i n f l u e n c e d by, the s e l l e r s of metals. From these p r i c e s , the p r i c e s of ores " f a c i n g " the mine-owners are determined. The managers of v e r t i c a l l y i n t e g r a t e d mines are given accounting p r i c e s which d i f f e r from o r d i n a r y p r i c e s . However, a l l mine operators have a given p r i c e f o r t h e i r o u t p u t — a given p r i c e which cannot be i n f l u e n c e d by the mine operators. The preceding d e s c r i p t i o n , while r e l e v a n t to the wage and employment theory of t h i s chapter, i s important f o r an understanding of the e n t i r e t h e s i s . o The p r i c e c a l c u l a t e d by the "owners" of an i n t e g r a t e d mining and smelting company i s c a l l e d an "accounting p r i c e " to d i f f e r -e n t i a t e i t from the p r i c e of ore described i n the l a s t quotation, and because the accounting p r i c e i s not a p r i c e i n the usual sense of the word. 9 I b i d . , p. 10. 13 I t i s necessary to diverge from the present t o p i c of mar-ket s t r u c t u r e and. introduce other concepts which are needed to suggest the in f l u e n c e of the market s t r u c t u r e of B r i t i s h Columbia's mining in d u s t r y upon wages and employment. The concept of upper and lower wage bounds may be app l i e d to a f i r m as w e l l as an in d u s t r y , The upper wage bound of a f i r m l i m i t s the number of a l t e r n a t i v e wage l e v e l s which are greater than the e x i s t i n g one. I f there i s a p o s s i b i l i t y of an i n -crease i n wage r a t e s , then there e x i s t s at l e a s t one a l t e r -n a t i v e wage l e v e l above the e x i s t i n g l e v e l . I f p r o f i t s are considered as a p o t e n t i a l source of l a -bour income, then the upper wage bound of any mine, which re c e i v e s economic p r o f i t s , has at l e a s t one a l t e r n a t i v e wage l e v e l above the e x i s t i n g one. Moreover, i t i s l i k e l y that the number of a l t e r n a t i v e wage l e v e l s above the e x i s t i n g l e v e l v a r i e s with the amount of p r o f i t received by a f i r m . 1 ^ The a n a l y s i s r e t u r n s to the study of the impact of c o m p e t i t i v e l y determined p r i c e s of ore upon the p o s i t i o n of the upper wage bound. The p r o f i t s r e c e i v e d by a mine-owner are "^Suppose the employed labour of two mines receive i d e n -t i c a l wage increases which are derived from p r o f i t s . I f one f i r m i s reduced to a marginal f i r m a f t e r the wage incr e a s e , then any a l t e r n a t i v e wage l e v e l above the e x i s t i n g wage l e v e l of t h i s f i r m cannot be created by p r o f i t s . I f the other f i r m s t i l l r e c e i v e s p r o f i t s a f t e r the wage i n c r e a s e , then there i s an a l t e r n a t i v e wage l e v e l created f o r t h i s f i r m by p r o f i t s . The l a r g e r p r o f i t s of the second f i r m created at l e a s t two a l t e r n a t i v e wage l e v e l s higher than i t s o r i g i n a l wage l e v e l . Thus the number of a l t e r n a t i v e wage l e v e l s does seem to vary with the amount of p r o f i t s r e c e i v e d by a f i r m . 14 p a r t i a l l y determined by the competitive p r i c e of ores. I f the costs of mining increase, the mine-owner cannot i n f l u e n c e the p r i c e of ore to keep p r o f i t s at a constant l e v e l . I t does seem probable that the competitive nature of p r i c e determina-t i o n i n B r i t i s h Columbia's mining i n d u s t r y has tended to r e -s t r i c t the p r o f i t s of many of the mine-owners. In the mining i n d u s t r y there are always marginal or p o t e n t i a l l y marginal f i r m s . The given p r i c e of ore and the i n e v i t a b i l i t y of r i s i n g c o s t s as the mine approaches exhaustion ensures the p o t e n t i a l m a r g i n a l i t y of every mine."'"''" I f there i s a preponderance of marginal mines, then the p o s i t i o n of the upper wage bound of the industry i s r e l a t i v e l y low. In c o n c l u s i o n , as the wage l e v e l of the i n d u s t r y cannot be greater than the upper wage bound, the p o s i t i o n of t h i s bound has a decided e f f e c t upon the degree of p o s s i b l e wage changes f o r the i n d u s t r y . The p o s i t i o n of the upper wage bound f o r t h e ' i n d u s t r y as a whole w i l l depend l a r g e l y upon the pro-f i t s received by each f i r m . I f the competitive nature of the determination of the p r i c e s of ores has l i m i t e d the p r o f i t s of many mine-owners, then the p o s i t i o n of the upper wage bound i s lower than i t would have been i f ore p r i c e s had been determined i n some other manner. No proof can be given to support the pre-ceding a n a l y s i s but i t i s probable that competition i n the general mining i n d u s t r y has r e s t r i c t e d p r o f i t s i n B r i t i s h 11 V a r i a b l e c o s t s of prod u c t i o n over a p e r i o d of time are studie d i n Chapter I I I . 15 Columbia's i n d u s t r y . The mining industry s e l l s ores and concentrates through a 12 basing point. system of p r i c e s determined at a few world centers. The use of base p r i c e s i n the metal market, par-t i c u l a r l y f o r lead, z i n c and copper, developed q u i t e n a t u r a l l y . Basing p o i n t p r i c i n g o f f e r s a number of advantages over any other system of p r i c i n g , the most important of these being a high degree of p r i c e u n i f o r m i t y and the r e d u c t i o n of a c t i v e p r i c e com-p e t i t i o n . . . . The base p r i c e or market quota-t i o n s f o r metals serves to keep a l l buyers and s e l -l e r s informed of the s t a t e of the market, f a c i l i t a t - - , , i n g custom ore purchases. The base p r i c e s introduce order i n t o what otherwise might be an extremely u n c e r t a i n market. At any moment of time, each metal has only one p r i c e f o r a p a r t i c u l a r geographical l o c a t i o n . P r i c e competition between the s e l l e r s of metals i s r e s t r i c t e d but p r i c e f l u c t u a t i o n s from changes i n market c o n d i t i o n s are common. The i n f l u e n c e of base p r i c e s upon B r i t i s h Columbia's mining i n d u s t r y i s not e a s i l y determined. Under the e x i s t i n g system of p r i c i n g metal pro-ducers are able to s e l l i n almost any market, a lower net r e t u r n on metal bearing high t r a n s p o r t a t i o n costs being the only major discouragement to d i s t a n t s a l e s . B r i t i s h Columbia on the whole b e n e f i t s from the bas-i n g point p r i c i n g of lead and z i n c . The market f o r B r i t i s h Columbia metal products i s l a r g e r and more d i v e r s i f i e d as to end use as a r e s u l t of basing p o i n t p r i c i n g , and l o c a t i o n or remoteness from market tends 1 P See J . M. C l a r k , "Basing Point Methods of P r i c e Quot-i n g " , The Canadian J o u r n a l of Economics and P o l i t i c a l Science, 1938, V o l . 4, p. 477. 13 Deutsch, op_. c i t . , p. 21. 1 6 to be of l e s s importance as a competitive f a c t o r . Lower cost s of prod u c t i o n i n B r i t i s h Columbia than i n the United States and many other producing coun-t r i e s permit Canadian metal to compete with f o r e i g n metal despite high t r a n s p o r t a t i o n c o s t s and t a r i f f , . b a r r i e r s . I t may only be assumed that l a r g e r metal markets are f o s -t e r e d by a basing p o i n t system of p r i c e s than some other system of p r i c i n g . As the base p r i c e s have been i n e f f e c t f o r some time there i s no b a s i s f o r comparing t h i s system to some other h y p o t h e t i c a l system of p r i c e s . However, the qu o t a t i o n suggests that i t i s not unreasonable to assume that B r i t i s h Columbia's metal markets are l a r g e r under the e x i s t i n g system of p r i c e s than under any other system. I f the markets are l a r g e r then output f o r the i n d u s t r y w i l l be g r e a t e r . The e l i m i n a t i o n of some of the u n c e r t a i n t y of the market encourages low p r o f i t and marginal mines to produce. Furthermore, i t i s probable that base p r i c e s encourage a l a r g e r output from i n f r a m a r g i n a l mines. However, p r o f i t s per mine may not be greater simply because out-put i s greater under a basing point system of p r i c e s than under any other system of p r i c e s . The number of low p r o f i t and mar-g i n a l mines may be l a r g e and the p r o f i t s of these mines may be s m a l l . I f t h i s i s the case, then the upper wage bound f o r most mines may be low but f o r the few large p r o f i t mines the upper wage bound may be high. Thus the in f l u e n c e of base p r i c e s upon the i n d u s t r y ' s upper wage bound i s indeterminate'. The only d e f i n i t e c o n c l u s i o n forthcoming i s that employment 1 4 I b i d . , p. 21. ) 17 w i l l be g r e a t e r i f output i s greater under base p r i c e s than under any other p r i c e system. The i n f l u e n c e of two elements—the determination of metal and ore p r i c e s and the basing point system of p r i c e s — u p o n the upper wage bound of B r i t i s h Columbia's mining industry has been described f o r two reasons. F i r s t l y , a d e s c r i p t i o n of these two elements of market s t r u c t u r e provides necessary and i n t e r e s t i n g information which w i l l be used throughout the the-s i s . Secondly, the study g i v e s some i n s i g h t to the determina-t i o n of the p o s i t i o n of the upper wage bound. I f the com-p e t i t i v e determination of ore p r i c e s r e s t r i c t s p r o f i t s , t h e n the upper wage bound of B r i t i s h Columbia's mining i n d u s t r y i s lower than i t would be i f p r i c e s were determined i n some other manner. I f base p r i c e s encourage a greater output than any other p r i c e system, then employment i s l a r g e r but the i n f l u e n c e of base p r i c e s upon the p o s i t i o n of the upper wage bound i s indeterminate. Other elements—such as power costs or t r a n s p o r t a t i o n c o s t s — o f market s t r u c t u r e could have been studied to de t e r -mine t h e i r i n f l u e n c e upon the p o s i t i o n of the upper wage bound of B r i t i s h Columbia's mining i n d u s t r y . While there i s l i t t l e doubt that other elements do in f l u e n c e the p o s i t i o n of the upper wage bound, t h e i r i n f l u e n c e was not considered as im-portant as the influ e n c e of the two elements studied i n t h i s chapter. I t i s not important to determine a l l of the i n f l u -ences on the upper wage bound of B r i t i s h Columbia's mining 18 i n d u s t r y . Rather, the object of t h i s chapter was to suggest that the p o s i t i o n of the i n d u s t r y ' s upper wage bound can be in f l u e n c e d by elements of the market s t r u c t u r e of the indus-t r y . The e x i s t i n g wage l e v e l cannot be g r e a t e r than the upper wage bound. I f t h i s bound i s low, then the number of p o s s i b l e wage increas e s i s low. Furthermore, i f the upper wage bound s h i f t s upwards, then the number of p o s s i b l e l e v e l s above the e x i s t i n g wage l e v e l i n c r e a s e s . F i n a l l y , i f the upper wage bound of B r i t i s h Columbia's mining i n d u s t r y has tended to be low, wage r a t e increases w i l l depend l a r g e l y upon changes of the i n d u s t r y ' s upper wage bound. CHAPTER I I THE INFLUENCES OF CHANGES IN METAL PRICES UPON THE TRENDS OF WAGE RATES AND EMPLOYMENT IN BRITISH COLUMBIA'S MINING INDUSTRY The main forces of the upper wage bound f o r B r i t i s h Colum-bia's mining industry were defined as the marginal net p h y s i c a l product of mining labour and the marginal revenues of ores. While these f o r c e s are a l s o the two determinants of the defined derived demand f o r mining labour i n B r i t i s h Columbia, the de-r i v e d demand i s not i d e n t i c a l to the upper wage bound. The upper wage bound l i m i t s the number of a l t e r n a t i v e wage l e v e l s above the e x i s t i n g wage l e v e l , but the derived demand f o r l a -bour i s a determinant of wage rates and employment. Both of these c o n c e p t s — t h e upper wage bound and the derived demand — a r e important to the t h e s i s as a whole, but t h i s chapter i s p r i m a r i l y concerned with the derived demand f o r mining labour i n B r i t i s h Columbia. The o b j e c t i v e s of t h i s chapter are to study the e f f e c t s of changes i n the marginal revenues of ores upon the trends of wage r a t e s and employment of B r i t i s h Columbia's mining i n d u s t r y . These trends w i l l be d e s c r i b e d by studying the changes i n the supply of, and the demand f o r , labour i n B r i t i s h Columbia's mining i n d u s t r y . As ore p r i c e s are c o m p e t i t i v e l y determined, the marginal revenues of ores are equal to the p r i c e s of ores. Furthermore, as ore p r i c e s are determined by metal p r i c e s , i t i s assumed that ore p r i c e s p l u s a constant amount are equal to metal p r i c e s . 20 This assumption i s necessary because the s t a t i s t i c s , which are used i n t h i s t h e s i s , provide metal p r i c e s but not ore p r i c e s . The a n a l y s i s i s now reduced to a study of the i n f l u e n c e s of metal p r i c e changes upon the trends i n wage r a t e s and employ-ment . As the marginal revenues of ores are d e f i n e d as forces of both the upper wage bound and the derived demand f o r labour, then by d e f i n i t i o n a change i n metal p r i c e s changes both the upper wage bound and the d e r i v e d demand f o r mining labour. The change i n the derived demand f o r mining labour means that a change i n metal p r i c e s could r e s u l t i n a change i n employment.^ I f B r i t i s h Columbia's mining i n d u s t r y i s responsive to metal p r i c e changes then rate of output w i l l vary with metal p r i c e changes. Therefore, v a r i a t i o n s i n metal p r i c e s l ead to changes i n the r a t e of output and employment. However, i f the r a t e of output f o r the mining i n d u s t r y i s not responsive to metal p r i c e changes, then there i s no reason f o r employment to vary w i t h metal p r i c e changes. Thus, before the s t a t i s t i c a l r e l a t i o n s h i p s of wages, employment, and metal p r i c e s are explored i t would be h e l p f u l to understand the general r e a c t i o n s of B r i t i s h Columbia's mining i n d u s t r y to a change i n metal p r i c e s . I t w i l l be found that the immediate impact of a change i n "^If wage ra t e s remain constant, then a change i n the derived demand f o r mining labour w i l l change employment, assuming that f a c t o r proportions remain approximately the same. An increase or decrease i n metal p r i c e s may induce some employers to change the p r o p o r t i o n s of f a c t o r s employed. However, the i n f l u e n c e s of changes i n the amount or form of c a p i t a l upon employment are ignored i n t h i s chapter. 21 metal p r i c e s i s upon the production plans of the mine owner. The amounts and p r i c e s of f a c t o r s of production employed i n a mine adjust to the new production p l a n s . For example, an i n -crease i n the p r i c e of metals w i l l r e s u l t i n an increase i n the rate of output of ore. More of a l l f a c t o r s w i l l be demanded to f a c i l i t a t e the increase i n industry output. Therefore i t would be expected that an increase i n metal p r i c e s would be followed by an increase i n employment. The ensuing a n a l y s i s begins by d e s c r i b i n g the determination of the r a t e of output of ore f o r one mine. F o l l o w i n g t h i s , the impact of a change i n metal p r i c e s upon the rate of output f o r a mine i s described. The a n a l y s i s concludes w i t h a d e s c r i p t i o n of the probable a d j u s t -ments of B r i t i s h Columbia's mining i n d u s t r y to an increase i n metal p r i c e s . Given the p r i c e of ore and assuming t h i s p r i c e to remain constant f o r the l i f e - t i m e of the mine, the mine-2 owner must choose between a l t e r n a t i v e r a t e s of e x t r a c t i o n . Assuming the s i z e of the deposit i s known or estimated, then the t o t a l revenue to be d e r i v e d from the mine can be determined. Given the relevant f a c t o r p r i c e s and assuming d i m i n i s h i n g mar-g i n a l r e t u r n s f o r c a p i t a l and labour are phenomena that e x i s t i n mining, then t o t a l , average t o t a l , and marginal cost curves can 3 be constructed. I f f o r every rate of output or e x t r a c t i o n the 2 The f o l l o w i n g a n a l y s i s i s adapted from Donald C a r l i s l e ' s "The Economics of a Fund Resource With P a r t i c u l a r Reference to Mining", The American Economic Review, 1 9 5 4 , p. 5 9 5 * •^For a f u r t h e r d i s c u s s i o n of d i m i n i s h i n g marginal returns i n mining, see Chapter I I I . 22 t o t a l costs are summed for a l l periods, then these t o t a l s sub-tracted from the constant t o t a l revenue f o r every rate output give a t o t a l p r o f i t s curve for every rate of output. This t o t a l p r o f i t s curve has a maximum for the rate of extraction which has minimum average t o t a l costs. For any one period, the most p r o f i t a b l e rate of output i s determined where marginal cost equals marginal revenue. However, by computing the sums of the present values of every period's p r o f i t s for each rate of p r o f i t a new t o t a l p r o f i t s curve i s produced. The new t o t a l p r o f i t s curve i s lower and has a maximum point for a greater rate of output than rate determined by the maximum point of the previous t o t a l p r o f i t s curve. The mine owner w i l l extract ore at a rate greater than the rate determined by the minimum of the average t o t a l cost curve as he w i l l wish to substitute pre-sent income for future income. The most profitable rate w i l l probably be smaller than the rate f o r which marginal costs equal marginal revenue because of the higher average costs at t h i s 4 rate, however this i s not certain. An explanation of the effects of a change in metal prices requires a sligh t extension of the given model. An increase i n metal prices increases the l i f e time t o t a l revenue derived from the mine. The increase in t o t a l revenue w i l l not be divided into equal parts and spread over the l i f e time of the mine. ^The model described above i s one of three models that C a r l i s l e presents to i l l u s t r a t e the determination of the rate of output in the mining industry. 23 Instead, a new discounted t o t a l p r o f i t s curve i s constructed. This curve has a maximum f o r a gre a t e r rate of output than the f i r s t discounted t o t a l p r o f i t s c u r v e — t h e mine owner sub-s t i t u t e s present income f o r f u t u r e income and the rate of out-5 put increases. The preceding d e s c r i p t i o n of the determination of the rate of output depends l a r g e l y upon the assumptions that the s i z e of the deposit can be estimated, and that the mine-owner maximizes h i s long run p r o f i t s , regardless of "how long" the long run may be. I f the s i z e of the deposit were not known, the mine-owner might maximize short run p r o f i t s or he might i n t u i t i v e l y choose a r a t e of output s l i g h t l y lower than the r a t e which maximizes short run p r o f i t s . I t i s p o s s i b l e that the mine-owner's "time h o r i z o n " ^ i s nearer than the end of the l i f e time of the mine. In t h i s case, the owner w i l l s e l e c t a rate of output which maximizes pro-f i t s f o r the p e r i o d of time encompassed by h i s time horizon. On the whole, the model provides informative d e s c r i p t i o n s of the determination of the r a t e of output and of the e f -f e c t s of a p r i c e change upon the r a t e of output. The r e a c t i o n of a mine which i s v e r t i c a l l y i n t e g r a t e d 5 The e f f e c t s of a decrease i n metal p r i c e s are analogous to the e f f e c t s of an increase i n metal p r i c e s w i t h the d i r e c t i o n of change reversed. The "time h o r i z o n " i s d e f i n e d here as the p e r i o d of time beyond which no future plans are made by the mine owner. 24 w i t h a smelting company may be q u i t e d i f f e r e n t from the r e a c t i o n of an independently owned mine to a change i n metal p r i c e s . I f managers of i n t e g r a t e d mines produce 7 output at a r a t e which minimizes c o s t s - p e r - u n i t of output , then metal p r i c e changes have no e f f e c t upon the r a t e of output f o r an i n t e g r a t e d mine. However, the i n t e g r a t e d mining and smelting company w i l l attempt to maximize the p r o f i t s of i t s e n t i r e operation. There i s no reason why the rate of output of an i n t e g r a t e d mine w i l l not be v a r i e d w i t h metal p r i c e changes to achieve t h i s maximizing g o a l . Nevertheless, i t has been suggested that changes i n the ra t e of output of an i n t e g r a t e d mine are much sma l l e r than the changes i n the rate of output of an independently owned mine f o r the same change i n p r i c e . D e c l i n i n g metal p r i c e s , f o r example, have a p a r t i c u l a r l y severe impact on mining companies s e l l i n g ore to custom smelters, i n contrast to f u l l y i n t e g r a t e d companies. The reason t h i s i s so i s that smelting and marketing charges on custom ore are s p e c i f i c amounts and do not vary i n p r o p o r t i o n to quoted metal p r i c e s . These charges, over short periods of time, r e -present f i x e d deductions from the contained metal's quoted market p r i c e s , w i t h the r e s u l t that a f a l l i n metal p r i c e s brings about a more than proportionate r e d u c t i o n i n the amount received by mining companies f o r custom ore and concentrate. The f o l l o w i n g example i l l u s t r a t e s t h i s p o i n t . Assuming smelting charges alone of 3.5 and 7 cents per pound f o r lead and z i n c r e s p e c t i v e l y , a 10 per cent f a l l i n the quoted p r i c e of lead and zinc (from 15 and 13 cents See Chapter I , p. 3« 25 per pound to 13*5 and 11.7 cents r e s p e c t i v e l y ) , would r e s u l t i n a d e c l i n e of 16 per cent i n the value of a ton of custom ore c o n t a i n i n g equalo q u a n t i t i e s of these metals. The response of B r i t i s h Columbia's mining industry as a whole to changes i n the demand f o r metals i s w e l l described i n the f o l l o w i n g excerpt from the Report by P r o f e s s o r J . J . Deutsch The expected response to p r i c e i n c r e a s e s would be something l i k e the f o l l o w i n g : e x i s t i n g mines would increase t h e i r r a t e s of production, t h e i r higher c o s t s being covered by the higher p r i c e s . They would al s o t u r n to mineral faces i n lower q u a l i t y ore, w i t h higher recovery and m i l l i n g costs per ton . . . . Employment . . . would probably r i s e more r a p i d l y , r e f l e c t i n g the higher labour requirements per ton of concentrate . . . . The r e a c t i o n time f o r t h i s t r a i n of events might be q u i t e short: four to eight months would be s u f f i c i e n t f o r most mines to make quite l a r g e changes i n e x i s t i n g production and e x p l o r a t i o n methods * • • • The time required to get new mines i n t o production may be q u i t e long . . . . On the whole one would ex-pect new mines to respond slowly ( r e q u i r i n g a year or so) to l a r g e p r i c e i n c r e a s e s . However, since new mines are l i k e l y to produce at a high r a t e once they Q get s t a r t e d , employment may r i s e r a p i d l y . V e r t i c a l l y i n t e g r a t e d mines tend to dampen the impact of p r i c e changes. But as most of the mines i n B r i t i s h Columbia's indust are independently owned, the dampening e f f e c t on the i n d u s t r y r a t e of output caused by i n t e g r a t e d mines i s probably i n s i g n i -f i c a n t . The preceding quotation summarizes and concludes the study of v a r i a t i o n s i n the rate of output caused by changes i n Report by P r o f e s s o r J . J . Deutsch. op. c i t . , p. 22. q Report by P r o f e s s o r J . J . Deutsch, Economics of Primary P r o d u c t i o n i n B r i t i s h Columbia, "The M i n e r a l I n d u s t r i e s " , (Unpublished), p. 38-39-26 the demand f o r metals. A change i n metal p r i c e s r e s u l t s i n a change i n the r a t e of output i n an appreciably short p e r i o d of time. The concluding quotation a l s o introduces the next subject f o r a n a l y s i s . As the rate of i n d u s t r y output v a r i e s w i t h metal p r i c e changes and the amount of employment v a r i e s w i t h the r a t e of i n d u s t r y output, i t i s expected that the amount of employment w i l l vary with metal p r i c e changes. In other words, a change i n the demand f o r metals changes the d e r i v e d demand f o r mining l a -bour and the amount of employment* A p r e l i m i n a r y a n a l y s i s of the p r i c e , wage rat e and employ-ment data of Table I presents a problem which i s of fundamental importance to the remainder of the t h e s i s . For t h i s reason, the present study of the r e l a t i o n s h i p between the trends of p r i c e s and employment i s i n t e r r u p t e d and w i l l be continued s h o r t l y * I f the changes i n employment f o l l o w i n g a change i n metal p r i c e s are considered as the r e s u l t of a s h i f t i n the derived demand f o r labour, then p r i c e changes must also i n f l u e n c e wages, as wages and employment are f u n c t i o n a l l y r e l a t e d . For example, i f the d e r i v e d demand f o r mining labour changes, then both em-ployment and wages w i l l change unless the supply of labour i s p e r f e c t l y i n e l a s t i c or p e r f e c t l y e l a s t i c . Assuming that a con-v e n t i o n a l l y shaped supply curve of mining labour f o r B r i t i s h Columbia e x i s t s and remains constant f o r the period'1949-1960, then a l l of the changes i n employment and wage rates f o r the p e r i o d are caused by changes i n the d e r i v e d demand f o r mining labour. The data of Table I show that p r i c e s and employment 27 have f l u c t u a t e d widely but wage rates have increased c o n t i n u a l l y with one e x c e p t i o n . A n increase i n wage r a t e s and a decrease i n employment f o r the same sub-period (one year) are d i f f i c u l t to e x p l a i n when changes i n the demand f o r labour are the only v a r i -ables being considered. The c o n t r a d i c t i o n — r i s i n g wage r a t e s and f a l l i n g employment—of the given model f o l l o w s n a t u r a l l y from the assumptions concerning the supply curve of mining l a -bour. The assumptions that the supply curve e x i s t s and that i t i s c o n v e n t i o n a l l y shaped are not u n r e a l i s t i c because very l i t t l e i n f o r m a t i o n can be found to r e f u t e them.'''"'" However, the The metal p r i c e s g iven i n Table I are the weighted averages of l e a d , zinc and copper p r i c e s , g i v e n i n the Annual Report, M i n i s t e r of Mines and Petroleum Resources, I960, pages A16 and A23- The p r i c e s were weighted by summing the revenues derived from the sale of each metal i n every year and then d i v i d i n g t h i s t o t a l by the t o t a l y e a r l y output of the three metals. The employment data was also taken from t h i s r e p o r t , page A49- These employment f i g u r e s r e f e r to the employment of lode-mines only. The Review of Man-Hours and Hourly Earnings, Dominion Bureau of S t a t i s t i c s , provides data of the average hourly earn-ings of B r i t i s h Columbia's metal mining l a b o u r . Average ho u r l y earnings depend upon the. number of hours worked per week and the average h o u r l y wage r a t e s . As the number of hours worked per week has remained approximately constant throughout the period 1949-1960, trends of average hourly earnings w i l l be almost i d e n t i c a l to trends of average h o u r l y wage r a t e s . Throughout the t h e s i s , average hourly earnings w i l l be r e f e r r e d to as "wage r a t e s " . F i n a l l y , the d i f f e r e n t i a l s given i n t h i s t a b l e , and a l l other t a b l e s , are derived by s u b t r a c t i n g the s t a t i s t i c of one year from the s t a t i s t i c of the succeeding year. The d i f f e r e n -t i a l s are y e a r l y , absolute d i f f e r e n t i a l s . I t i s p o s s i b l e but h i g h l y improbable that the supply curve of mining labour slopes downward or has a p e c u l i a r shape. .This remote p o s s i b i l i t y i s ignored. 28 assumption that the supply curve remains constant f o r the d u r a t i o n of the p e r i o d i s h i g h l y u n r e a l i s t i c . The c o n t r a d i c -t i o n created by the u n r e a l i s t i c assumption i m p l i e s that changes i n wage rates and employment over a p e r i o d of time are caused by f o r c e s of both supply and demand. While t h i s l a s t con-c l u s i o n i s not s t a r t l i n g i t i n f e r s that a study of the i n -fluences of metal p r i c e s upon wage rat e s and/or employment must account f o r the v a r i a t i o n s i n the supply of labour. The data given i n Table I i n d i c a t e that the supply curve of B r i t i s h Columbia's mining labour has tended to s h i f t up-wards f o r the p e r i o d 1 9 4 9 - 1 9 6 0 . The Mine, M i l l and Smelter Workers' Union has probably exerted an upwards pressure upon the wage r a t e s of mining l a b o u r . A l s o , the r a p i d increases of a l t e r n a t i v e occupations f o r mining labour have s h i f t e d the supply curve of mining labour upwards. These two forces are given as l i k e l y i n f l u e n c e s upon the supply curve of mining l a -bour. However, an a n a l y s i s of the i n f l u e n c e s upon the supply of mining labour i n B r i t i s h Columbia w i l l not be given. I f the d e r i v e d demand f o r B r i t i s h Columbia mining labour i s described as a derived demand curve, then t h i s curve s h i f t s when-ever e i t h e r of the determinants of the deri v e d demand change. I f the demand curve f o r labour remains constant, then i n every year (sub-period) wage r a t e s w i l l increase and employment w i l l de-crease. A "downward" s h i f t i n the demand curve w i l l accentuate the decrease i n employment and dampen or n u l l i f y the wage r a t e movement caused by the s h i f t i n g supply curve. A change i n 29 metal p r i c e s causes the derived demand curve f o r mining labour to s h i f t i n the same d i r e c t i o n as the changes i n metal p r i c e s . I t i s d i f f i c u l t to d i s t i n g u i s h between changes i n the derived demand curve f o r mining labour caused by v a r i a t i o n s i n the mar-g i n a l p h y s i c a l product of mining labour and changes i n the curve 12 caused by v a r i a t i o n s i n metal p r i c e s . However, the index of labour's p r o d u c t i v i t y i n B r i t i s h Columbia's mining industry — g i v e n i n Table IV of Chapter IV—shows a decrease i n output-per-man-per-year i n 1951, 1954, 1956 and 1957. The marginal p h y s i c a l product of labour i s assumed to decrease i n these four years and to increase i n the other seven years. Table I reveals that the number of mining labourers em-ployed each year i n B r i t i s h Columbia's lode-mining i n d u s t r y has v a r i e d considerably f o r the period 1949-1960. Chart I shows a f a i r l y c l o s e c o r r e l a t i o n between the trends of lagged p r i c e s 13 and employment f o r the p e r i o d . In 1954 and i n 1956 p r i c e s i n -creased but i n 1955 and i n 1957 employment decreased. The p r i c e increase of 1954 and the employment decrease of 1955 are such small changes that a small change i n some other f o r c e could have produced the discrepancy i n the two trends of p r i c e s and employ-ment. In 1957, output-per-man-per-year decreased s u b s t a n t i a l l y . 12 The reasons f o r the s e l e c t i o n of t h i s p a r t i c u l a r index as a measure of p r o d u c t i v i t y are given i n Chapter IV. 13 ^The p r i c e s of Chart I and the absolute p r i c e d i f f e r e n -t i a l s of Chart I I are lagged by one year. The reasons f o r l a g g i n g p r i c e s and absolute p r i c e d i f f e r e n t i a l s are given l a t e r i n t h i s chapter. The other variabiles, wage r a t e s , employment, and p r o d u c t i v i t y are unlagged. 30 Assuming that the p r o d u c t i v i t y index i s an i n d i c a t o r of the change i n the marginal p h y s i c a l product of mining labour i n B r i t i s h Columbia, then the derived demand curve f o r mining l a -bour i n 1957 has a tendency to s h i f t downwards. The decrease i n p r o d u c t i v i t y may have been s u f f i c i e n t l y dominant to cause a de-crease i n employment even though metal p r i c e s increased i n 1956. The trends of lagged y e a r l y absolute p r i c e d i f f e r e n t i a l s and y e a r l y absolute employment d i f f e r e n t i a l s are given i n Chart I I . The obvious r e l a t i o n s h i p between the trends of the two v a r i a b l e s i n d i c a t e s that metal p r i c e changes a c t u a l l y have i n -fluenced the changes i n employment i n B r i t i s h Columbia's mining i n d u s t r y . In every year except two—1952 and 1954—the d i f f e r e n -t i a l s of lagged metal p r i c e s and employment moved i n the same d i r e c t i o n . An examination of these two exceptions to the general trends suggests an important m o d i f i c a t i o n to.the assumption that the supply curve of mining labour i n B r i t i s h Columbia s h i f t s by an equal amount i n every p e r i o d . In 1951, metal p r i c e s increased by 4.4 c e n t s — t h e l a r g e s t metal p r i c e increase of the p e r i o d — a n d i n 1952 the p r o d u c t i v i t y index f o r B r i t i s h Columbia's mining labour increased by more than the same index i n 1951* Wage rate s i n 1952 increased by 22 cents, the l a r g e s t wage d i f f e r e n -t i a l of the e n t i r e p e r i o d . Thus, both components of the derived demand f o r mining labour i n 1952 increased by more than t h e i r counterparts of 1951. Nevertheless, employment i n 1952 increased by 6 1 4 — l e s s than the 1,566 increase i n employment of 1951* I f the supply curve of mining labour s h i f t e d by more than the assumed TABLE I Weighted D i f f e r e n - Weighted D i f f e r e n - Numbers D i f f e r e n -Average t i a l s of Average t i a l s of Employed t i a l s of P r i c e s of the Weighted Wage Rates the Weighted i n the the Lead, Z i n c , Average of Mining Average Wage Lode Min- Numbers Copper P r i c e s of Labour i n Rates ing Indus- Employed ( D o l l a r s ) Metal B r i t i s h Columbia ( D o l l a r s ) t r y of B r i t i s h Columbia ( U n i t s ) 1949 .150 .003 1.28 .04 5,758 :"56 1950 .153 .044 1.32 .14 5,814 1,566 1951 .197 -.029 1.46 .22 7,480 614 1952 .168 -.038 1.68 .08 8,094 -2,260 1953 .130 .002 1.76 .04 5,734 -570 1954 .132 .015 1.80 .03 5,164 -47 1955 .147 .009 1.83 .18 5,117 347 1956 .156 -.028 2.01 .06 5,464 -624 1957 .128 -.017 2.07 -.01 4,840 -1,112 1958 .109 .007 2.06 .13 3,728 -30 1959 .116 .012 2.19 .16 3,698 43 1960 .128 2.35 3,741 Sources: M i n i s t e r of Mines and Petroleum Resources, Annual Report, I960, B r i t i s h Columbia, p. A16, A 2 3 . Review of Man-Hours and Hourly Earnings, Dominion Bureau of S t a t i s t i c s , 1955, 1956, 1957, 1958, 1959, I960. 32 0-200 04oo o.i^o 6200 0OCX3 46oo 4<Joo 42oo 0120 — 4(300 Iboo o-uo TeeN05 OF ewpiovMewT AND OME ve^e LAGGED WEIGHTCD bueeA&e UETLL peices of BRITISH COUMBIA^ UIWUG IWDUSTEY 33 ^5 „, tt rs. O i a ^ < 5 i v i O a j v S W r J «s O- O c& H <^  ^ O o o 9 <0 < a . 53 f a o v3 to O O d o a ^ « o o o d 6 o § 8 o O Q 8 8 o 6 <x> o o o V 0 0 f N • O O P 6 6 o 0 c. 1 i o 34 amount i n 1952, then the wage rate and employment r e s u l t s of that year would be expected. In 1953 metal p r i c e s decreased by 3.8 cents, the l a r g e s t p r i c e decrease of the e n t i r e p e r i o d . In 1954 p r o d u c t i v i t y decreased by a much gr e a t e r d i f f e r e n t i a l change than i n 1953 and wage r a t e s i n 1954 increased by a mere 4 cents. In 1954 both determinants of the derived demand f o r mining labour caused the curve to s h i f t downwards by more than the change i n the curve i n 1953* However, the decrease i n em-ployment i n 1954 was 570—very much smaller than the decrease of 2,260 i n 1953. In t h i s case, i f the supply curve of mining •labour s h i f t e d by l e s s than the assumed amount, the employment r e s u l t s of 1954 could be explained. I f the supply curve of mining labour v a r i e d i n the same d i r e c t i o n as lagged metal p r i c e s , then the employment r e s u l t s would be expected. A p o s s i b l e cause of such v a r i a t i o n s i n the supply curve i s not d i f f i c u l t to d e s c r i b e . I f the demand f o r metals changes and metal p r i c e s change, then both the d e r i v e d demand f o r mining labour and the upper wage bound of B r i t i s h Columbia's mining i n d u s t r y change. With changes i n the upper wage bound, the number of a l t e r n a t i v e wage l e v e l s above the e x i s t i n g l e v e l v a r i e s . The leaders of the Mine, M i l l and Smelter Workers' Union are probably aware of large changes i n the a l t e r n a t i v e number of wage l e v e l s above the e x i s t i n g one. Moreover, the union leaders have some in f l u e n c e upon the wage rat e l e v e l and thus upon the changes of the supply 35 curve of mining labour. Suppose the wage demands of union l e a d e r s are v a r i e d d i r e c t l y with the number of a l t e r n a t i v e 14 wage l e v e l s above the e x i s t i n g wage l e v e l . I f metal p r i c e s change r a d i c a l l y , as i n 1951 and 1953, then the unions' i n f l u -ence upon the change i n the supply curve of mining labour could be s u f f i c i e n t l y dominant to produce opposing d i f f e r e n t i a l move-ments i n employment and lagged metal p r i c e s . There may be any number of forces a f f e c t i n g the supply curve of mining labour and only i n c e r t a i n c o n d i t i o n s would union i n f l u e n c e produce the employment r e s u l t s of 1952 and 1954* However, i t i s reason-able to assume that metal p r i c e changes w i l l have an i n d i r e c t impact upon the supply curve of mining labour, as the wage demands of union l e a d e r s depend, i n p a r t , upon lagged metal p r i c e s . In c o n c l u s i o n , the i n d u s t r y ' s supply curve o f labour tends to s h i f t upwards by an amount which depends upon the d i r e c t i o n and degree of metal p r i c e changes. The study of the trends of metal p r i c e s and employment r e -vealed that these v a r i a b l e s are c l o s e l y r e l a t e d . I n every year except two, p r i c e s and employment moved i n the same d i r e c t i o n . S i m i l a r l y , the p r i c e and employment d i f f e r e n t i a l s moved i n the same d i r e c t i o n every year, with two exceptions. An examination of these l a s t two exceptions produced the r e s u l t that the changes of supply curve of mining labour i n B r i t i s h Columbia 14 The union l e a d e r s may not a c t u a l l y be aware of a change i n the upper wage bound, but i t i s assumed that the leaders act as i f they were aware of a change i n the bound. 36 depend p a r t i a l l y upon lagged metal p r i c e changes. This sup-p l y curve s h i f t s upwards, but the degree of each s h i f t depends, i n p a r t , upon lagged metal p r i c e s . As output and employment of B r i t i s h Columbia's mining i n d u s t r y vary i n the same d i r e c t i o n as metal p r i c e changes, the wage rates o f B r i t i s h Columbia's mining labour would also be expected to vary i n the same d i r e c t i o n as metal p r i c e changes. However, mining labour's wage rates i n B r i t i s h Columbia have increased i n every p e r i o d except one, whereas metal p r i c e s have f l u c t u a t e d w i d e l y . Thus the r e l a t i o n s h i p between these two v a r i a b l e s must be d i f f e r e n t from the r e l a -t i o n s h i p between metal p r i c e s and employment. The study of the trends of metal p r i c e s and employment showed that the supply curve of mining labour tended to s h i f t upwards. For-t u n a t e l y , the i n f l u e n c e of metal.price changes upon the v a r i a t i o n s of wage r a t e s can be described without any i n f o r -mation concerning the supply of mining labour of B r i t i s h Columbia's mining i n d u s t r y . Table I I l i s t s the wage r a t e s , metal p r i c e s , and the year-l y absolute d i f f e r e n t i a l s of these two v a r i a b l e s . A l l of the data i s relevant f o r B r i t i s h Columbia's mining i n d u s t r y . Chart 15 I I I i l l u s t r a t e s the trends of lagged metal p r i c e s and wage The reasons f o r lagged metal p r i c e s are given l a t e r i n t h i s chapter. 37 TABLE II Weighted D i f f e r e n t i a l s Weighted D i f f e r e n t i a l s Average of the Average of the Prices of Weighted Wage Rates Weighted Lead, Zinc Average of Mining Average and Copper Prices Labour in Wage Rates B r i t i s h Columbia 1949 .150 1.28 .003 1232 .04 1950 .153 .044 - .14 1951 .197 1.46 -.029 .22 1952 .168 1.68 -.038 .08 1953 .130 1.76 .002 .04 1954 .132 1.80 .015 .03 1955 .147 1.83 .009 .18 1956 .156 2.01 -.028 .06 1957 .128 2.07 -.017 -.01 1958 .109 2.06 .007 .13 1959 .116 2.19 .012 .16 1960 .128 2.35 Sources: Minister of Mines-and Petroleum Resources, Annual Report, I960, B r i t i s h Columbia pp. A16, A23. Review of Man-Hours and Hourly Earnings, Dominion Bureau of S t a t i s t i c s , 1955, .1956, 1957, 1958, 1959, I960. 38 lAo 2-30 l l o 1-10 2.oo I SO l-8o 1.10 I bO \.So l-4o 1*0 0.140 o-i8o o.no 0-140 0-120 (•20 0- UO n Avee^e METAL prices / \ i \ i \ i \ i \ i \ ' \ 0160 _ l I I 0-150 \ J \ i 1^50 S\ SI S3 54 55 bb 57 58 54, 60 6l Teewos OF Tue WEIGHTCD LUEZLSE wA$e e & r e s AND OUE ve^e LA66EO wgi6HT£P Auee^g M6TAC PeiceS Of 62ITI5W COLOMBIA'S UIWIU6 lUQUSTeV. 39 o # a-f» O O o o o O 6 6 6 6 6 O 3 co O o o o OD o q o O O o o O o 6 6 o 6 d 6 6 o vO ro o o o O o 6 6 b Q O o o 6 < 2 3 £ 3 c> O o o 3D -a o d o o o 6 o 6 o 6 •3- <*> q o o o o O q 6 b o 6 6 6 40 r a t e s f o r the p e r i o d 1949-1960. As metal p r i c e s have f l u c t u -ated and wage r a t e s have increased i n every year but one, the l a c k of r e l a t i o n s h i p between the trends of the two v a r i a b l e s i s not s u r p r i s i n g . A comparison of the trends of y e a r l y ab-so l u t e wage d i f f e r e n t i a l s and lagged y e a r l y absolute p r i c e d i f f e r e n t i a l s i s given i n Chart IV. Except f o r one year, 1954, wage d i f f e r e n t i a l s moved i n the same d i r e c t i o n as p r i c e d i f f e r e n t i a l s . I t seems that wage r a t e s increase r e g u l a r l y , but the degree of increase depends l a r g e l y upon the d i r e c t i o n of metal p r i c e changes. The s i n g l e exception to the c l o s e c o r r e l a t i o n between the trends of wage r a t e and lagged metal p r i c e d i f f e r e n t i a l s cannot be explained i n a very s a t i s f a c t o r y manner. In 1954 metal p r i c e s increased by .2 cents and i n 1953 metal p r i c e s decreased by 3«8 cents. In 1955 output-per-man increased, but i n 1954 the index decreased. Therefore the derived demand curve f o r mining labour i n 1955 increased more than the same curve i n 1954. However, i n 1955 wage r a t e s increased by only 3 cents and employment decreased by 47» whereas i n 1954 wage ra t e s increased by 4 cents and employment f e l l by 570. The supply curve of mining labour must have s h i f t e d upwards i n both years but the upward s h i f t of 1954 must have been much greater than i n 1955* The l a r g e drop of employment i n 1954 may have caused union leaders to use t h e i r i n f l u e n c e and dampen the upward s h i f t of the supply curve of mining labour i n 1955« Unfortunate-l y the changes of the releva n t v a r i a b l e s are so small that i t 41 i s almost impossible to a t t r i b u t e the opposing d i f f e r e n t i a l movements of lagged metal p r i c e s and wage r a t e s to any one force of supply or demand. The study of the trends of y e a r l y lagged absolute p r i c e d i f f e r e n t i a l s and y e a r l y absolute wage rate d i f f e r e n t i a l s de-s c r i b e s the i n f l u e n c e of metal p r i c e changes upon wage ra t e s very c l e a r l y . Metal price., v a r i a t i o n s are not the cause of the re g u l a r increase i n wage r a t e s . But the degree or amount of change of wage r a t e s i n every p e r i o d i s p a r t i a l l y dependent upon the changes of lagged metal p r i c e s . The concluding t o p i c of t h i s chapter concerns the d i r e c t i o n of causation between changes i n metal p r i c e s and changes i n wage r a t e s . Throughout t h i s chapter, wages have been i m p l i c i t l y as-sumed to be a dependent v a r i a b l e with p r i c e s as an independent v a r i a b l e . However, there may be some doubt as to the d i r e c t i o n of causation or dependency. The chart of the trends of absolute metal p r i c e d i f f e r e n t i a l s lagged by one year and absolute wage rate d i f f e r e n t i a l s was the only g r a p h i c a l r e p r e s e n t a t i o n which suggested a c l e a r r e l a t i o n -s h i p between these two v a r i a b l e s . Charts i n which n e i t h e r v a r i -able was lagged or i n which absolute wage d i f f e r e n t i a l s were lagged by one year, were i r r e g u l a r and confused. I t was taken as a f a c t that mining wage r a t e s of B r i t i s h Columbia were i n -fluenced l a r g e l y by changes of metal p r i c e s of the previous year. The i n f l u e n c e of metal p r i c e changes lagged f o r two or more years, or not lagged at a l l , have been ignored. While ;such influences may e x i s t , no s t a t i s t i c a l evidence of t h e i r e x i s t e n c e could be 42 found. Thus, as wage r a t e s are compared to lagged metal p r i c e s , the independent v a r i a b l e i n the r e s u l t i n g r e l a t i o n s h i p must be metal p r i c e s . I t would be u n r e a l i s t i c to assume that expected future wage rat e changes could i n f l u e n c e metal p r i c e s . More-over, as wage rat e s and employment were assumed to be f u n c t i o n -a l l y r e l a t e d i n the same p e r i o d , metal p r i c e s were lagged by one year f o r the study of the trends of metal p r i c e s and employment. In summary, the o b j e c t i v e s of t h i s chapter were to describe the i n f l u e n c e s of changes i n metal p r i c e s upon the trends of wage rates and employment of B r i t i s h Columbia's mining i n d u s t r y . However, to reach these o b j e c t i v e s i t was necessary to describe the general r e a c t i o n s of B r i t i s h Columbia's mining i n d u s t r y to a change of metal p r i c e s . As the demand f o r metals changes, the r a t e of output i n B r i t i s h Columbia's mining i n d u s t r y v a r i e s i n the same d i r e c t i o n as the metal p r i c e change. As the rate of output v a r i e s w i t h metal p r i c e changes, the number of mining labourers employed i n the i n d u s t r y i s expected to vary i n the same d i r e c t i o n as p r i c e changes. The close c o r r e l a t i o n s between the trends of lagged metal p r i c e s and employment, and between the trends of lagged y e a r l y absolute p r i c e d i f f e r e n t i a l s and y e a r l y absolute employment d i f f e r e n t i a l s l e a d to the co n c l u s i o n that the amount of employment v a r i e s i n the same d i r e c t i o n as metal p r i c e changes. The study of metal p r i c e s and employment suggested that the union i n f l u e n c e on the supply curve of mining may vary i n the same d i r e c t i o n as metal p r i c e changes. However, t h i s r e s u l t depends upon the union leaders a d j u s t i n g t h e i r wage demands to changing market c o n d i t i o n s . 43 F i n a l l y , the study of the i n f l u e n c e of lagged metal p r i c e s and lagged metal p r i c e changes upon wage r a t e s provided the most i n t e r e s t i n g r e s u l t s . The trends of wage rat e s and lagged p r i c e s e x h i b i t almost no r e l a t i o n s h i p . However, the trends of the y e a r l y absolute d i f f e r e n t i a l s of these two v a r i a b l e s were c l o s e l y r e l a t e d . Metal p r i c e changes are a determinant of the degree of wage r a t e changes, but wage rates increase r e g u l a r l y whether p r i c e s increase or decrease. CHAPTER I I I CONCEPTS OP PRODUCTIVITY IN THE MINING INDUSTRY The derived demand f o r mining labour was defined i n the Introduction, as the product of the marginal p h y s i c a l product of mining labour times the marginal revenue received from the sale of ores. The marginal p h y s i c a l product of labour a r i s e s from the p h y s i c a l law of d i m i n i s h i n g marginal returns defined as This law a s s e r t s that i f the q u a n t i t i e s of a l l other inputs used by a f i r m remain constant, and one input i s subjected to successive increases i n q u a n t i t y , e v e n t u a l l y t h i s input w i l l begin (and continue) t o ^ y i e l d d i m i n i s h i n g (marginal) output r e t u r n s . Diminishing marginal returns may be a confusing concept at the best of times but i n the mining industry the concept i s even more complex. The f i r s t task i s to e s t a b l i s h whether or not dim i n i s h i n g marginal r e t u r n s are common to mining. Although common sense suggests that t h i s phenomenon i s present i n the mining i n d u s t r y , t h i s i s not s u f f i c i e n t as a proof. F o l l o w i n g the d i s c u s s i o n of d i m i n i s h i n g marginal r e t u r n s f o r a s i n g l e mine, some of the conceptual and p r a c t i c a l d i f f i c u l t i e s a r i s i n g from an aggregate study of labour's p r o d u c t i v i t y i n B r i t i s h Columbia's mining i n d u s t r y w i l l be described. As the t h e s i s i s concerned w i t h the trends of aggregates, i t i s important to understand the shortcomings of an aggregate study of the pro-d u c t i v i t y of labour. As the concept of d i m i n i s h i n g marginal returns i s of ^"William J . Baumol, Economic Theory and Operations A n a l y s i s , Englewood C l i f f s , N. J . , P r e n t i c e - H a l l Inc., 1961, p. 285. 45 fundamental importance to t h i s t h e s i s the f o l l o w i n g theory a r -gues the existence of t h i s p h y s i c a l law i n the mining i n d u s t r i e s * Suppose two concepts of time are d i s t i n g u i s h e d , one i s any i n -stant of time during which a l l f a c t o r s are f i x e d ; the other time p e r i o d i s anything longer than the f i r s t but a l l f a c t o r s are v a r i a b l e . In the f i r s t time p e r i o d , a l t e r n a t i v e amounts of c a p i t a l and/or labour may be ap p l i e d to a f i x e d amount of mine. This hypothesises the use of a l t e r n a t i v e combinations of f a c -t o r s other than the combination a c t u a l l y used except f o r mine which i s f i x e d . A l f r e d M arshall i m p l i e d that the rate of recovery from a mine increases at a constant rate as more u n i t s of labour and c a p i t a l are added. The produce of mines again, . . . i s s a i d to conform to the Law of Di m i n i s h i n g Return, but t h i s statement i s misleading. . . . mines are as i t were Nature's r e s e r v o i r . The more nearly a r e s e r v o i r i s exhausted, the greater i s the labour of pumping from i t ; but i f one man with one pump could pump i t out i n ten days, ten men wit h ten pumps could pump i t out i n one day:., and when once empty, i t would y i e l d no more. He acknowledges that returns decrease as the mine i s depleted. However, t h i s i s of no concern as both the one man and the ten men encounter t h i s phenomenon of d i m i n i s h i n g r e t u r n s . This phenomenon does not a r i s e from v a r y i n g f a c t o r proportions* 1 I f M arshall's a n a l y s i s were true and i f the f o l l o w i n g as-sumptions are made; the p r i c e of ore i s not appreciably a f -f e c t e d as the supply of ore produced by one mine i s increased, p The f i x e d f a c t o r , mine, w i l l simply be c a l l e d mine. ^ A l f r e d M a r s h a l l , Economics of Industry, London, MacMillan and Co., L i m i t e d , 1901, (3rd ed.) p. 102. 46 a small increase i n the demand f o r mining c a p i t a l goods would not a f f e c t the p r i c e s of these goods, c a p i t a l goods used are ca-pable of being used again a f t e r the exhaustion of a mine except i n such cases as "timbering" which can be considered as depreciat-ing i n p r o p o r t i o n to the r a t e e x t r a c t i o n , a p l e n t i f u l source of labour and other inputs i s a v a i l a b l e at p r e v a i l i n g p r i c e s , then the mine owner would p r e f e r to have a r a p i d exhaustion of ore be-cause he would s u b s t i t u t e present income f o r future income. Mar-s h a l l thought that some combination of the above assumptions would not be true and that market c o n d i t i o n s f o r both inputs and out-puts would l i m i t the rate of d e p l e t i o n . But as f a r as any' one mine owner i s concerned, the assumptions are not too s t r i n g e n t . At l e a s t some mine owners would attempt an e x t r a o r d i n a r y r a t e of e x t r a c t i o n . But mining h i s t o r y reveals that t h i s has not hap-pened. Each mine owner i s confronted with a l t e r n a t i v e amounts of labour and c a p i t a l that he may apply to a f i x e d amount of mine. Most mine-owners are unconcerned with depressing the p r i c e of ore because they are unable to do so. The most s u i t a b l e combination of f a c t o r s i s chosen through an a n a l y s i s of costs with respect to a l t e r n a t i v e r a t e s of exhaustion and the given p r i c e s of ores. The rate of output selec t e d i s not the most r a p i d rate because of the high c o s t s caused by d i m i n i s h i n g marginal r e t u r n s ^ - - not be-cause of r i s i n g f a c t o r supply p r i c e s and f a l l i n g output p r i c e s , a l l of which are given at any moment to any one mine-owner. A d e s c r i p t i o n of the determination of the rate of output of ore i s given i n Chapter I . 47 P r o f e s s o r John E. Orchard stated that The workings of r i c h and poor mines would i n d i c a t e that i t i s more p r o f i t a b l e to apply c a p i t a l i n the poor than to add i t to the c a p i t a l already a p p l i e d i n the r i c h e r mines. I t i s evident that the laWj-of d i m i n i s h i n g r e t u r n s does apply to mines. He suggests that a marginal mine e x i s t s i n v/hich the costs of e x t r a c t i n g ore j u s t equals the r e t u r n to the mine-owner. How-ever, a c l o s e examination of t h i s d e f i n i t i o n exposes i t to severe c r i t i c i s m . Suppose that d i m i n i s h i n g marginal returns do not e x i s t and that f a c t o r p r i c e s remain constant, then the marginal cost curve would be h o r i z o n t a l . As any one mine owner i s a " p r i c e t a k e r " , the i n d i v i d u a l marginal revenue curves are h o r i -z o n t a l . I f any mine can have a marginal cost curve below the h o r i z o n t a l marginal revenue curve, the mine w i l l enter production. The extensive margin of a p p l i c a t i o n of c a p i t a l and labour l i m i t s the number of mines i n the i n d u s t r y . But at any one point of time, the i n t e n s i v e margin f o r c a p i t a l and labour i s i n f i n i t e . This i n f i n i t e margin suggests, once again, that r a p i d mining would be prevalent i n the i n d u s t r y . The existence of poor mines beside r i c h ones does not prove that d i m i n i s h i n g marginal r e -turns e x i s t , i t only i n d i c a t e s that some mines have higher grades of ore than others, or that some mines are more adaptable to v a r i a b l e i n p u t s than o t h e r s . Donald C a r l i s l e presents one of the best d e f i n i t i o n s of d i m i n i s h i n g marginal r e t u r n s i n mining". . . . i t i s i l l u s t r a t e d by the decreasing e f f e c t i v e n e s s 5 -\John E. Orchard, "The Rent of M i n e r a l Lands", Q u a r t e r l y  J o u r n a l of Economics, 1922;'..Vol. 36, p. 290. 48 of more i n t e n s i v e a p p l i c a t i o n s of c a p i t a l and labour^ i n i n c r e a s i n g the " r a t e " of working a deposit. Instead of saying "more i n t e n s i v e a p p l i c a t i o n s of c a p i t a l and l a -bour . . .", he might have s a i d " a l t e r n a t i v e i n t e n s i v e a p p l i c a -t i o n s of c a p i t a l and labour at any one p o i n t of time". However, i f the f a c t o r mine i s assumed to be constant f o r a per i o d of time, then C a r l i s l e ' s d e f i n i t i o n i s exact. The returns to l a -bour and c a p i t a l increase at a decreasing r a t e as more of these f a c t o r s are added to the f i x e d mine f a c t o r . The c o n c l u s i o n that can be resolved from the preceding theory i s that d i m i n i s h i n g marginal returns e x i s t i n the mining i n d u s t r y because other phenomena do not e x i s t . Although the f a c t o r mine i s never constant, i t would be p o s s i b l e to consider one of the other i n p u t s — l a b o u r or c a p i t a l — a s being constant. However, t h i s a n a l y s i s i s n e i t h e r p r a c t i c a l nor relevant f o r t h i s t h e s i s and i t w i l l not be presented. The production of any mine i s l i m i t e d i n the second time period ( d e f i n e d e a r l i e r i n t h i s chapter) by i n c r e a s i n g c o s t s as the mine f a c t o r changes. To describe t h i s l i m i t i n g e f f e c t upon production i t i s simpler to r e f e r to the long run period r a t h e r than the defined "second time p e r i o d " . In the long run, or i n the "second time period" a l l inputs are v a r i a b l e . The amount of mine employed per u n i t of time can only increase to a poin t and then i t must decrease u n t i l the mine i s exhausted or u n t i l the mine has become too c o s t l y to operate. As f u r t h e r d e p l e t i o n g Donald C a r l i s l e , "The Economics of a Fund Resource With P a r t i c u l a r Reference to Mining", American Economic Review, 1954, p. 598. 49 takes p l a c e , l e s s time per work day w i l l be spent upon removing ore from the untouched area of the mine. The same area of o p e r a t i o n may be employed but the u n i t of operating time w i l l d i m i n i s h . The f a c t o r mine must be considered as being two-d i m e n s i o n a l — a r e a of operating mine per u n i t of time. E i t h e r or both dimensions must change over a long enough time p e r i o d to cause f a l l i n g output-per-unit of time'. Suppose the mine-owner wishes to produce a c e r t a i n amount of ore per u n i t of time. With a given amount of labour and c a p i t a l , output-per-unit of time w i l l decrease over a pe r i o d of time as the mine f a c t o r becomes l e s s e f f i c i e n t . To o f f s e t the pressures of the decreasing e f f i c i e n c y of the mine, the mine-owner w i l l add u n i t s of labour and c a p i t a l to maintain the given l e v e l of output. Therefore, d i m i n i s h i n g marginal r e t u r n s f o r labour and c a p i t a l w i l l become more acute as time passes. The net e f f e c t w i l l be an a c c e l e r a t i o n of decreasing r e t u r n s from c a p i t a l and labour as more of each f a c t o r are added to a mine of decreasing e f f i c i e n c y . Thei t h e o r e t i c a l d e s c r i p t i o n of di m i n i s h i n g marginal returns was resolved i n the conclusion that t h i s phenomenon does e x i s t i n the mining i n d u s t r y . However, the p r o d u c t i v i t y schedule of any f a c t o r cannot be estimated i n the f i r s t time p e r i o d as only one combination of f a c t o r s i s employed. In the second time p e r i o d , the e f f i c i e n c y of the mine i s always changing and there-f o r e the p r o d u c t i v i t y schedules of v a r i a b l e amounts of labour and c a p i t a l combined wi t h a f i x e d amount of mine cannot be 50 determined i n t h i s time p e r i o d . The preceding a n a l y s i s has been concerned w i t h the concep-t u a l problems of d e s c r i b i n g and a s s e s s i n g d i m i n i s h i n g marginal r e t u r n s f o r any one mine. However, t h i s t h e s i s i s concerned p r i m a r i l y with the trends of aggregates of B r i t i s h Columbia's mining i n d u s t r y . The p r o d u c t i v i t y schedule of labour or c a p i t a l f o r the i n d u s t r y i s even more d i f f i c u l t to describe than a f a c -t o r ' s p r o d u c t i v i t y schedule f o r a s i n g l e mine. A problem becomes apparent when the d i f f e r e n c e s i n e f -f i c i e n c i e s between mine u n i t s are examined. I f a l l other things were equal, then at any in s t a n t of time, the marginal p h y s i c a l product of labour f o r any two mines i s never equal. That i s , i f the same number of labourers i s employed i n any two mines, then the marginal product of the labour employed i n the l e a s t e f f i c i e n t mine w i l l be l e s s than the marginal product of the labour employed i n the other mine. An aggregate marginal pro-duct curve f o r the labourers of both mines cannot be constructed because the f i x e d mine f a c t o r i s not homogeneous. The problem i s e a s i l y solved i n theory by c o n v e r t i n g each mine i n t o some s o r t of standard e f f i c i e n c y u n i t s and then aggregating the mine f a c t o r . But f o r a s t a t i s t i c a l study of marginal produc-t i v i t y such a conversion i s impossible. With one important exception, t h i s d i f f i c u l t y w i l l be ignored. A study of the trends of labour's p r o d u c t i v i t y u s u a l l y i n -v o l v e s the s e l e c t i o n of some so r t of p r o d u c t i v i t y index. This index provides some s o r t of measure of the change i n labour's p r o d u c t i v i t y over a p e r i o d of time. The s e l e c t e d index i s 51 u s u a l l y some measure of output-per-worker p e r - u n i t of time. However, changes i n t h i s index and changes i n labour's marginal product are not i d e n t i c a l . The two separate changes are r e -l a t e d but they have very d i f f e r e n t meanings. The changing number of mines i n B r i t i s h Columbia's mining in d u s t r y introduces a fundamental problem encountered i n the study of the trends of labour's p r o d u c t i v i t y f o r the i n d u s t r y as a whole. I f the changing e f f i c i e n c y of each mine i n the i n d u s t r y i s ignored, then the amount of "mine" i n the i n d u s t r y can be considered as a f i x e d f a c t o r . Suppose that an aggregate marginal p h y s i c a l product curve f o r labour i n B r i t i s h Columbia's minind i n d u s t r y e x i s t s at any moment of time. Both the number of mines and the amount of labour are v a r i a b l e i n any short p e r i o d of time. A change i n the amount of labour employed w i l l r e s u l t i n a movement along the curve. But a change i n the num-ber of mines i n the i n d u s t r y causes a s h i f t i n the curve and a movement along the curve. The s h i f t i n the curve i s caused by a change i n the amount of the f i x e d f a c t o r employed. The move-ment along the curve i s caused by the change i n the amount of labour employed i n the i n d u s t r y as the number of mines v a r i e s . The trends of labour's p r o d u c t i v i t y f o r B r i t i s h Columbia's min-ing i n d u s t r y w i l l i n c l u d e the r e s u l t s of both a change i n the h y p o t h e t i c a l marginal p h y s i c a l product curve and a movement along the curve. However, there i s no reason why the trends should r e v e a l the separate i n f l u e n c e s or r e s u l t s of a change i n the curve and a movement along the curve. This problem of i d e n t i f y i n g s h i f t s and changes of labour's 52 marginal p h y s i c a l product curve i s not r e s t r i c t e d to a study of the e f f e c t s of a change i n the number of mines. Other i n -fluences which a f f e c t labour's marginal product may a l s o not be i d e n t i f i e d by v a r i a t i o n s i n the p r o d u c t i v i t y trends. Any change i n the p r i c e s or the amounts used of other f a c t o r s com-bined w i t h labour w i l l cause t h i s curve to s h i f t . There i s no hope i n determining how much these changes i n parameters w i l l a f f e c t the c u r v e — e v e n the d i r e c t i o n of change i s d i f f i c u l t to a s c e r t a i n . A change i n employment w i l l produce a m u l t i p l e r e -a c t i o n on the curve. The f i r s t r e a c t i o n i s the change i n mar-g i n a l product caused by a movement on the curve. This change upsets the e q u i l i b r i u m of the other f a c t o r s of production which, i n t u r n , may vary and upset the s t a b i l i t y of labour's marginal product curve. Changes i n the amount of c a p i t a l employed may r a i s e or lower labour's marginal product curve, depending upon whether c a p i t a l i s s u b s t i t u t e d f o r , or complementary t o , labour. In c o n c l u s i o n , a change i n any f a c t o r whatsoever may produce movements along the curve and s h i f t s of the curve of unknown de-gree and d i r e c t i o n , but the index of labour's p r o d u c t i v i t y w i l l r e v e a l only the net change i n p r o d u c t i v i t y . In summary, d i m i n i s h i n g marginal r e t u r n s do e x i s t i n the mining i n d u s t r y , but t h e o r e t i c a l problems oppose the e s t i m a t i o n of labour's marginal product. As the amount of mine i s always v a r i a b l e , there i s no f i x e d f a c t o r which can be used to f a c i l i -t ate a s t a t i s t i c a l a n a l y s i s of labour's marginal or average product i n a s i n g l e mine. Turning to an aggregate study of 53 labour's p r o d u c t i v i t y i n B r i t i s h Columbia's mining i n d u s t r y , two problems become evident immediately. The d i f f e r i n g e f -f i c i e n c i e s of the in d u s t r y ' s mines create a conceptual d i f f i -c u l t y i f an aggregate marginal p h y s i c a l product curve f o r v a r i a b l e p r o p o r t i o n s of labour w i t h a f i x e d amount of mine i s hypothesized. However, these problems of aggregation w i l l be more or l e s s ignored i n l a t e r s t u d i e s . F i n a l l y , the trends of mining labour's p r o d u c t i v i t y must include every i n f l u e n c e upon labour's marginal p h y s i c a l product curve. An e x p l a n a t i o n of the trends or changes of the trends i s almost impossible. I t seems that the study of the p r o d u c t i v i t y of mining labour i s a r a t h e r discouraging task i n i t s e l f . However, many of the conceptual d i f f i c u l t i e s described i n t h i s chapter can be ignored f o r an a n a l y s i s of the i n f l u e n c e of p r o d u c t i -v i t y changes upon wage ra t e s and employment. CHAPTER IV THE INFLUENCE OF CHANGES IN THE PRODUCTIVITY OF BRITISH COLUM-BIA'S MINING LABOUR UPON THE INDUSTRY'S WAGE RATES AND EMPLOYMENT Changes of the p r o d u c t i v i t y of mining labour of B r i t i s h Columbia are expected to i n f l u e n c e the trends of wage r a t e s and employment of B r i t i s h Columbia's mining i n d u s t r y . However, the conclusions of the l a s t chapter i n d i c a t e that a study of the aggregate trends of mining labour's p r o d u c t i v i t y w i l l have d e f i -n i t e l i m i t a t i o n s . These l i m i t a t i o n s w i l l r e s t r i c t the a n a l y s i s and d e s c r i p t i o n s provided i n t h i s chapter. Nevertheless, i t i s bett e r to o b t a i n some inf o r m a t i o n of the i n f l u e n c e s of changes of mining labour's p r o d u c t i v i t y than nothing at a l l . Therefore, many of the conceptual and p r a c t i c a l d i f f i c u l t i e s of measuring mining labour's p r o d u c t i v i t y w i l l be ignored or assumed away, and the best p o s s i b l e index of mining labour's p r o d u c t i v i t y of B r i t i s h Columbia w i l l be s e l e c t e d . Once a p r o d u c t i v i t y index f o r mining labour has been se-l e c t e d , the p o s s i b l e e f f e c t s of a change i n labour's p r o d u c t i -v i t y w i l l be described. This d e s c r i p t i o n w i l l provide a con-t r a s t to the a c t u a l trends of p r o d u c t i v i t y and wage r a t e s , and of p r o d u c t i v i t y and employment of B r i t i s h Columbia's mining i n d u s t r y . The prime question of t h i s chapter i s , have the changes of the p r o d u c t i v i t y of B r i t i s h Columbia's mining labour i n -fluenced the wage r a t e s and employment trends of t h i s i n d u s t r y ? By answering (or attempting to answer) t h i s question, other m a t t e r s — s u c h as the degree and the manner i n which the changes 55 of the p r o d u c t i v i t y of mining labour have influenced the trends of wage r a t e s and employment of the i n d u s t r y — w i l l be described. F i n a l l y , the l i m i t e d c o n c l u s i o n s a f f o r d e d by the c o n s i d e r a t i o n s of t h i s chapter w i l l be g i v e n . Before any s t a t i s t i c a l r e l a t i o n s h i p s can be s t u d i e d , some index of mining labour's p r o d u c t i v i t y must be s e l e c t e d . There i s no point i n p r e s e n t i n g any f u r t h e r proof of the f u t i l i t y of attempting measures of t h e o r e t i c a l average or marginal product schedules. The a c t u a l s e l e c t i o n of an index i s simple, :the l a c k of any worthwhile a l t e r n a t i v e makes the measure of output-per-man-per-year the l o g i c a l choice."*" Perhaps some measure of "net product" should be derived from t h i s index, that i s , only a p o r t i o n of the t o t a l output be a t t r i b u t e d to the e f f o r t s of l a -bour. However, any s o r t of measure of "net product" i s ignored as there i s no p l a u s i b l e method of determining each f a c t o r ' s con-t r i b u t i o n to the t o t a l product. The a n a l y s i s of the p r o d u c t i v i t y of B r i t i s h Columbia's min-ing labour i s s i m p l i f i e d by i n t r o d u c i n g the concept of an aggre-gate marginal p h y s i c a l product curve f o r the labour of B r i t i s h Columbia's mining i n d u s t r y . Each mine f a c t o r i s assumed to be equal i n e f f i c i e n c y to every other un i t of mine f a c t o r . There-f o r e , at any moment of time, the sum of the u n i t s of mine f a c t o r "'"The Annual Report of The M i n i s t e r of Mines and Petroleum  Products, B r i t i s h Columbia, I960, pp. A49, A50, provides ac-curate data of the number of labourers employed each year i n B r i t i s h Columbia's lode mining i n d u s t r y and the t o t a l tonnage produced by the lode-metal mines each year. Output-per-man-per-year i s simply the r a t i o of the t o t a l tonnage produced each year to the number of labourers employed i n that year. 56 of B r i t i s h Columbia's mining i n d u s t r y comprises a homogeneous f i x e d f a c t o r . Every labourer i s assumed to be equal i n e f -f i c i e n c y to a l l other labourers, and the amount of c a p i t a l em-ployed i n the mining i n d u s t r y i s assumed to vary p r o p o r t i o n a t e -l y to the changes i n employment of mining labour. I f labour i s combined i n a l t e r n a t i v e amounts to the f i x e d mine f a c t o r at any moment of time, then an aggregate marginal net p h y s i c a l product curve (marginal p h y s i c a l product curve) f o r the mining labour of B r i t i s h Columbia can be hypothesized. The concept of an aggre-gate marginal p h y s i c a l product curve i s used to describe p o s s i b l e or expected r e s u l t s of changes i n v a r i a b l e s . However, t h i s con-cept i s not used to prove any hypothesis, and t h e r e f o r e no proof w i l l be o f f e r e d that such a curve can e x i s t . Rather, i t i s as-sumed that the curve does e x i s t . The supply curve of mining labour of B r i t i s h Columbia s h i f t s upwards i n every p e r i o d . The degree of the s h i f t i n each p e r i o d w i l l depend p a r t i a l l y upon the metal p r i c e s of the previous period. These three concepts, the p r o d u c t i v i t y index, the marginal p h y s i c a l product curve of mining labour, and the supply curve of mining labour, provide the necessary background i n f o r m a t i o n f o r the ensuing study of the p r o d u c t i v i t y of labour of B r i t i s h Columbia's mining i n d u s t r y . The marginal p h y s i c a l product of mining labour i s one of the two determinants of the defined d e r i v e d demand f o r B r i t i s h Columbia mining labour. I f there i s a change i n the marginal p h y s i c a l product curve f o r mining labour of B r i t i s h Columbia, then the amount of employment and the l e v e l of marginal product 57 change, assuming the i n d u s t r y ' s supply curve remains constant. An upward s h i f t of the marginal product curve r e s u l t s i n an i n -crease i n employment and an increase i n the l e v e l of marginal product. A downward s h i f t of the curve has the opposite e f f e c t s . I f the supply curve of B r i t i s h Columbia mining labour s h i f t s up-wards but the derived demand f o r labour remains constant, then the amount of employment increases and the l e v e l of marginal product decreases. Therefore, both a s h i f t i n the marginal p h y s i c a l product curve and a movement along the curve w i l l r e -s u l t i n a change of employment and a change i n the l e v e l of marginal product. I f the marginal p h y s i c a l product curve f o r mining labour of B r i t i s h Columbia s h i f t s , then the change i n the amount of employ-ment of the industry i s dependent upon the f o r c e which caused the curve to s h i f t . In t h i s case, the amount of employment of the i n d u s t r y becomes a dependent v a r i a b l e . However, i f the marginal p h y s i c a l product curve remains f i x e d and the supply curve of mining labour changes, then the l e v e l of marginal pro-duct i s dependent upon the changes of employment. Therefore, the l e v e l of employment i s sometimes dependent upon f o r c e s changing the marginal product of labour and at other times the l e v e l of the marginal product i s dependent upon the changes of employment. I t was suggested i n the l a s t chapter that the i d e n t i f i c a -t i o n of the major f o r c e s , which have i n f l u e n c e d the trends of p r o d u c t i v i t y , w i l l be a d i f f i c u l t task. The p r o d u c t i v i t y trends of B r i t i s h Columbia mining labour do not d i s t i n g u i s h between 58 the r e s u l t s of a movement along the marginal p h y s i c a l product curve f o r mining labour and the r e s u l t s of a s h i f t of the curve. However, the o b j e c t i v e s of t h i s chapter are to describe and to analyse the i n f l u e n c e s of changes of mining labour's p r o d u c t i -v i t y upon the wage ra t e s and employment of mining labour of B r i t i s h Columbia. Thus the study should be focused p r i m a r i l y upon the f o r c e s which cause s h i f t s of mining labour's marginal p h y s i c a l product curve. Movements along the curve imply that the l e v e l of marginal product i s determined by changes of em-ployment—the l e v e l of employment i s not i n f l u e n c e d by changes i n l a b o u r f s p r o d u c t i v i t y . Only two f o r c e s which cause a s h i f t of the marginal p h y s i c a l product curve of mining labour of B r i t i s h Columbia w i l l be analysed i n t h i s chapter. The f i r s t of these forces i s a change i n the amount of c a p i t a l or techniques used i n B r i t i s h Columbia's mining i n d u s t r y , and the second f o r c e i s a change i n the number of mines i n the mining i n d u s t r y of B r i t i s h Columbia. These two f o r c e s are s t u d i e d because they have probably had the greatest i n f l u e n c e upon labour's marginal p h y s i c a l product curve. The c o n c l u s i o n w i l l be tendered at the end of the study that changes i n the marginal p h y s i c a l product curve of mining labour have probably had l i t t l e i n f l u e n c e upon the l e v e l of employment and wage r a t e s of B r i t i s h Columbia's mining industry. Therefore, i t seems p o i n t l e s s to analyse a l l of the forces which may have i n f l u e n c e d t h i s curve. According to Mr. C. M i t c h e l l , Secretary of the Mining 59 2 A s s o c i a t i o n of B r i t i s h Columbia , there have been considerable changes i n mining techniques, the forms of c a p i t a l , and the amount of c a p i t a l - p e r - l a b o u r used i n B r i t i s h Columbia's mining i n d u s t r y i n the period 1949-1960. The e f f e c t of these changes upon labour's marginal p h y s i c a l product curve are more or l e s s Indeterminate. Some of the changes of c a p i t a l and technique have been complementary to labour and others have been sub-s t i t u t e d f o r labour. Mr. M i t c h e l l suggested that the numbers of mining labour employed i n B r i t i s h Columbia have been reduced by the changes of c a p i t a l and techniques. However, he added that the r e d u c t i o n i n employment from t h i s cause has been s m a l l . For any change i n the amount of c a p i t a l or techniques used i n B r i t i s h Columbia's mining i n d u s t r y , output-per-man-per-year w i l l increase or remain approximately the same as i t was before the change. I f complementary c a p i t a l i s added to the i n d u s t r y , employment w i l l increase, assuming that the supply curve of labour remains constant. As the marginal p h y s i c a l product curve f o r mining labour s h i f t s upwards, the l e v e l of marginal and average product w i l l be at l e a s t as high a f t e r the s h i f t as before the s h i f t . Therefore, as output-per-man-per-year i s a crude measure of average product, t h i s index should be at l e a s t as high a f t e r the s h i f t of the curve as i t was before the s h i f t of the curve. I f c a p i t a l i s s u b s t i t u t e d f o r labour, then, 2 The w r i t e r r e f e r s to a personal i n t e r v i e w w i t h Mr. M i t c h e l l , November, 1961. 60 3 assuming the l e v e l of output to remain the same , fewer labour-ers w i l l be employed to produce the same output. Output-per-man-per-year f o r the remaining employed labourers w i l l increase. Therefore i f changes i n c a p i t a l or technique have been a domin-ant force determining changes of employment, output-per-man-per-year would be expected to increase regularly'.' Table IV shows that output-per-man-per-year has increased i n seven out of the eleven years of the p e r i o d 1949-1960. Sup-pose these seven changes of output-per-man-per-year were caused by v a r y i n g the proportions o f c a p i t a l and labour employed i n B r i t i s h Columbia's mining i n d u s t r y . In three years—1950, 1952, and I 9 6 0 — o u t of these seven years, employment increased. But i n 1951 and 1959 metal p r i c e s increased. The increases of employment and wage rat e s i n 1952 and I960 imply that the de-r i v e d demand f o r B r i t i s h Columbia mining labour s h i f t e d upwards i n these years. But the marginal p h y s i c a l product curve f o r mining labour could have s h i f t e d upwards or downwards i n 1952 and I960. I f metal p r i c e s v/ere the dominant f o r c e s of the derived demand curve f o r B r i t i s h Columbia mining labour, then 3 ^This assumption i s not necessary but the argument i s sim-p l e r with the assumption. Assuming that each mine-owner maxi-mizes p r o f i t s , then a change of the proportions of c a p i t a l and l a b o u r — c a p i t a l being s u b s t i t u t e d f o r l a b o u r — l e s s labour w i l l be required p e r - u n i t of output. Therefore, output-per-man-per-year w i l l i n c r e a s e . ^ I t i s not known whether metal p r i c e s increased or de-creased i n 1949» However, knowledge of the 1948 metal p r i c e i s not very important f o r t h i s a n a l y s i s . 61 TABLE III Output-per- D i f f e r e n t i a l s Numbers D i f f e r e n -man-per-year of out-put- employed t i a l s of in B r i t i s h per-man-per i n the the Columbia 1s year lode min- numbers mining ing indus- employed industry try of (Tons) B r i t i s h Columbia (Units) 1949 1,063.8 5,758 10622 56 1950 1,170.0 5,814 -237.9 1,566 1951 932.1 7,480 201.4 614 1952 1,133.5 8,094 551.2 -2,260 1953 1,684.7 5,734 -36.0 -570 1954 1,648.7 5,164 134.9 -47 1955 1,783.6 5,117 -128.1 347 1956 1,615.5 5,464 -110.9 -624 1957 1,504.6 4,840 212.7 -1,112 1958 1,717.3 3,728 173.2 -30 1959 1,890.5 3,695 312.8 43 1960 2,203.3 3,741 Source: Annual Report of the Minister of Mines and Petroleum  Products, B r i t i s h Columbia, I960, pp. A49, A50. 62 the changes of metal p r i c e s i n 1951 and 1959 could have more than n u l l i f i e d the employment e f f e c t s caused by a downward s h i f t of the marginal p h y s i c a l curve i n 1952 and I960. Therefore, i n 1952 and I960 complementary c a p i t a l could have been combined wit h labour or c a p i t a l could have been s u b s t i t u t e d f o r labour. Furthermore, i t i s p o s s i b l e that there was no change i n the amount of c a p i t a l employed i n the i n d u s t r y i n 1952 and I960. In four years—1953, 1955, 1958 and 1959— out of the seven years i n which output-per-man-per-year increased, employment de-creased. However, i n 1952, 1957 and 1958, metal p r i c e s de-creased. Both the marginal p h y s i c a l product curve and the marginal revenues of metals could have s h i f t e d downwards to pro-5 duce the employment and wage r e s u l t s of 1953, 1958 and 1959* However, i t i s also p o s s i b l e that the decreases of metal p r i c e s i n 1952, 1957 and 1958 reversed the employment e f f e c t s caused by an upward s h i f t of the marginal p h y s i c a l product curve f o r mining labour i n B r i t i s h Columbia i n 1953, 1958 and 1959. Therefore i n these three years the amount or form of c a p i t a l employed i n the i n d u s t r y might not have changed at a l l . In 1954 metal p r i c e s increased, but i n 1955 employment de-creased and output-per-man-per-year and wage rates increased. However, the assumed s h i f t of the supply curve of B r i t i s h Columbia's mining labour precludes a determination of the d i r e c t i o n of change of the marginal p h y s i c a l product curve f o r The supply curve of mining labour i s assumed to s h i f t upwards i n every sub-period. The degree of every upwards s h i f t depends, i n pa r t , upon one year lagged metal p r i c e s . 63 mining labour of B r i t i s h Columbia i n 1955• I t i s impossible to determine whether the amount or form of c a p i t a l employed i n B r i t i s h Columbia's mining indus t r y has changed i n any of the seven years. Moreover, i n the four years i n which output-per-man«per-year decreased, the amount or form of c a p i t a l employed i n the i n d u s t r y may have changed. These changes may have been completely hidden by v a r i a t i o n s i n other v a r i a b l e s . The f a i l u r e to f i n d a s t a t i s t i c a l r e l a t i o n s h i p between the changes of the amount and form of c a p i t a l and the changes of wage rate s and employment does not mean that such a r e l a t i o n s h i p does not e x i s t . The changes of other v a r i a b l e s may have d i s t o r t e d the trends of labour's p r o d u c t i v i t y , employment and wage r a t e s i n B r i t i s h Columbia's mining i n d u s t r y . Nevertheless, i t seems reasonable to conclude that changes i n the amount and form of c a p i t a l employed i n B r i t i s h Columbia's mining i n d u s t r y have not been a dominant for c e upon the trends of wage rates and employ-ment of the i n d u s t r y . A change i n the number of mines i n B r i t i s h Columbia's min-ing i n d u s t r y also causes a s h i f t i n mining labour's marginal p h y s i c a l product curve. A mine e n t e r i n g or l e a v i n g the i n d u s t r y i s u s u a l l y marginal. Suppose a marginal mine i s e l i m i n a t e d from the i n d u s t r y by a small decrease i n the p r i c e of metals. I f the p r i c e decrease i s small enough that the production plans of a l l other mine owners remain unchanged, then the in d u s t r y ' s employ-ment i s reduced by the number of labourers who were employed at the e l i m i n a t e d mine. I f the i n d u s t r y ' s marginal p h y s i c a l 64 product curve f o r labour d i d not change, then the reduction i n employment would cause a movement on the curve and a new l e v e l of marginal product would be determined. But by e l i m i n a t i n g a mine the f i x e d f a c t o r f o r the aggregate marginal product curve f o r labour changes and therefore the curve changes. To describe the change of the aggregate marginal p h y s i c a l product curve when the f i x e d f a c t o r changes, i t i s h e l p f u l to begin the a n a l y s i s by c o n s i d e r i n g i n d i v i d u a l mines. Suppose every mine i s converted to some s o r t of standard e f f i c i e n c y u n i t s , and then a marginal p h y s i c a l product curve i s hypothe-s i z e d f o r each mine at any moment of time. I f a l l mines are approximately the same s i z e , then the amount of the f i x e d f a c -t o r i n standard e f f i c i e n c y u n i t s f o r any mine w i l l be i n pro-g p o r t i o n to the mine's e f f i c i e n c y . I t i s assumed that the mar-g i n a l p h y s i c a l product curve of every mine has a unique height which v a r i e s d i r e c t l y with the amount of f i x e d f a c t o r of each mine. The lowest curve i s the marginal p h y s i c a l p r o d u c t i v i t y curve of the marginal minei 1 7 I f the i n d i v i d u a l marginal product curves are aggregated, then the l e v e l of marginal product and the amount of employment i n the i n d u s t r y can be determined. When the marginal p h y s i c a l product curves of the i n d i v i d u a l mines are aggregated, the ^The d i f f e r i n g e f f i c i e n c i e s of the mines at any one moment of time must be recognized f o r t h i s a n a l y s i s . 7 The aggregate marginal p h y s i c a l product curve f o r the mining labour of B r i t i s h Columbia i s assumed to be a regular and continuous curve. 65 marginal p h y s i c a l product curve of the marginal mine w i l l be i n -cluded i n the lower p o r t i o n of the aggregate curve. I f the marginal mine i s e l i m i n a t e d from the i n d u s t r y , only t h i s lower p o r t i o n of the aggregate marginal p h y s i c a l product curve changes. The aggregate curve w i l l p i v o t downwards f o r a l l l e v e l s of mar-g i n a l product which are common to both the aggregate marginal p h y s i c a l product curve and the marginal p h y s i c a l product curve of the marginal mine. Employment w i l l be reduced by the amount of employment of the marginal mine. The new l e v e l of marginal product w i l l be given by a poin t on the new p o r t i o n of the ag-Q gregate marginal p h y s i c a l product curve. The new amount of employment i s , by d e f i n i t i o n , equal to the o l d amount of employment l e s s the number of labourers em-ployed i n the marginal mine. I f the aggregate curve had not s h i f t e d downwards, the new l e v e l of marginal product would have been determined by a movement along the aggregate curve. How-ever, the downward s h i f t of the aggregate curve tends to lower the l e v e l of marginal product. The new l e v e l of marginal pro-duct cannot be higher than the l e v e l which would be determined by a movement along the curve caused by a red u c t i o n of employ-ment equal to the employment of the marginal mine. But i t i s po s s i b l e f o r the new l e v e l of marginal product to be lower than Q I f the l e v e l of marginal product of the marginal mine were a maximum of that mine's marginal p h y s i c a l product curve, then the new l e v e l of marginal product and employment f o r the indus-t r y would be determined by a point on the o r i g i n a l aggregate marginal p h y s i c a l product curve. This p o i n t would be the poin t at which the new s e c t i o n of the aggregate marginal p h y s i c a l product curve p i v o t s downwards. 66 the o r i g i n a l l e v e l of marginal product. I t i s suggested that the aggregate curve w i l l change very l i t t l e w i t h the e l i m i n a t i o n of an i n e f f i c i e n t mine. I f there is . , a l a r g e number (50-100) of mines i n the i n d u s t r y , then the e x i t of the l e a s t e f f i c i e n t mine from the indus t r y w i l l not s i g -n i f i c a n t l y change the aggregate marginal p h y s i c a l product curve. Therefore, the predominant e f f e c t of the e l i m i n a t i o n of a mar-g i n a l mine w i l l be s i m i l a r to a movement along the aggregate Q marginal p h y s i c a l product curve. I f more than one mine are e l i m i n a t e d or added to the indus-t r y , then the s h i f t of the aggregate marginal p h y s i c a l product curve may be s i g n i f i c a n t . However, the influence of the change of the number of mines would be g r e a t e s t on the lowest p o r t i o n of the aggregate curve and l e a s t on the highest p o r t i o n of the curve. I t i s d o u b t f u l whether the s h i f t of the curve would y i e l d a new l e v e l of marginal product very much d i f f e r e n t from the l e v e l which would r e s u l t from a movement on the aggregate c u r v e . I f t h i s i s the case, then a change of the number of mines i n B r i t i s h Columbia's mining i n d u s t r y has not had a s i g -n i f i c a n t i n f l u e n c e upon the aggregate marginal p h y s i c a l product 9 An a d d i t i o n of a marginal mine to the i n d u s t r y w i l l also i n f l u e n c e labour's aggregate marginal p h y s i c a l product curve. This i n f l u e n c e w i l l be s i m i l a r to a downwards movement along the aggregate curve. 10 I f the mines are of d i f f e r e n t s i z e s or i f the heights of the marginal p h y s i c a l product curves do not vary with the amount of f i x e d f a c t o r ( i n standard e f f i c i e n c y u n i t s ) of each mine, then the r e s u l t s of the model w i l l be s l i g h t l y d i f f e r e n t . The s h i f t s of the aggregate marginal p h y s i c a l product curve may be greater. The new l e v e l of marginal product may be lower than i t would be i f the assumptions were true. The p o s s i b l e r e s u l t s of t h i s e f -f e c t are described l a t e r i n t h i s chapter. 67 curve of mining labour of B r i t i s h Columbia. Therefore, a change i n the number of mines has not s i g -n i f i c a n t l y i n f l u e n c e d the trends of wage rates and employment through changes of labour*s marginal p h y s i c a l product curve of B r i t i s h Columbia's mining i n d u s t r y . However, changes i n the number of mines have i n f l u e n c e d wage r a t e s and employment which have i n f l u e n c e d the l e v e l of mining labour's marginal product. The changes i n the l e v e l of marginal product have i n f l u e n c e d the trends of the p r o d u c t i v i t y of B r i t i s h Columbia's mining l a -bour. In summary, the study of the i n f l u e n c e s of changes of the p r o d u c t i v i t y of mining labour upon employment and wage rates of B r i t i s h Columbia's mining indus t r y considered two forces—changes i n the amount and form of c a p i t a l or techniques used i n the min-ing i n d u s t r y , and changes i n the number of mines i n the i n d u s t r y . No s t a t i s t i c a l evidence was found of the i n f l u e n c e s of changes of the amount of c a p i t a l employed i n B r i t i s h Columbia's mining in d u s t r y upon the indus t r y ' s wage rates or employment. I t was concluded that i f such an i n f l u e n c e e x i s t e d , i t s force was l i k e l y to be small. The study of the i n f l u e n c e s of a change i n the number of mines i n the i n d u s t r y upon the i n d u s t r y ' s wage r a t e s and employ-ment led to the conclusion that the predominant e f f e c t of t h i s f orce was s i m i l a r to the e f f e c t of a movement along mining l a -bour's aggregate marginal p h y s i c a l product curve. The preceding a n a l y s i s suggests that the changes of mining 68 labour's p r o d u c t i v i t y , caused by s h i f t s i n the marginal p h y s i c a l product curve of mining labour, have not s i g n i f i c a n t l y i n f l u e n c e d the wage r a t e s and employment of B r i t i s h Columbia's mining i n -dustry. However, i f a change i n the number of mines does cause a s i g n i f i c a n t s h i f t i n the aggregate marginal p h y s i c a l product curve f o r mining labour, then the wage ra t e s of mining labour may be i n f l u e n c e d by the s h i f t of the aggregate curve. Wage ra t e s may be a f f e c t e d because the marginal p h y s i c a l product of mining labour i s one of the two determinants of the derived de-mand f o r mining labour. The simplest explanation of the impact upon wages as the number of mines changes, f o l l o w s when the e f f e c t s are treated as s t a t i s t i c a l phenomena. There are two mining-plant extremes i n the i n d u s t r y — t h e marginal mine, which i s j u s t able to cover c o s t s , and the high rent mine, which y i e l d s . t h e highest economic rent per u n i t of output. As each mine i s d i f f e r e n t from a l l others, the employed resources have d i f f e r e n t p r o d u c t i v i t i e s i n each mine. Various demands e x i s t f o r the d e s i r e d resources and, i n the case of labour, wages vary between mines. Because a mine i s marginal, the e f f i c i e n c y of labour i s probably lower i n t h i s mine than i n others. Incentive bonuses w i l l be r e l a t i v e l y low. Therefore i t i s reasonable to assume that marginal mines pay lower average wages than i n f r a m a r g i n a l mines. The aggregate average wage i s derived from the weighted sum of the average wages of the i n d i v i d u a l mines d i v i d e d by the number of mines i n the i n d u s t r y . I f low wage earning labourers employed i n a marginal mine are e l i m i n a t e d from the i n d u s t r y , 69 then the aggregate average wage w i l l increase. The increase i n aggregate average wages f o l l o w s from an a r i t h m e t i c manipulation. The wages of the remaining employed mining labour have not i n -creased. Table IV l i s t s the wages, p r i c e s , number of mines and wage, p r i c e and number of mines d i f f e r e n t i a l s f o r the p e r i o d 1949-1960. A comparison of the changes i n the number of shi p p i n g lode mines and changes of average wages suggests almost no r e l a t i o n s h i p be-tween these two v a r i a b l e s . I f t h i s s t a t i s t i c a l wage phenomena i s p r evalent, then a decrease i n the number of shipping lode mines should increase aggregate average wages. An increase i n the number of shi p p i n g lode mines would have the opposite e f f e c t . A probable reason f o r the l a c k of c o r r e l a t i o n between these v a r i a b l e s i s i n d i c a t e d by the strong r e l a t i o n s h i p between wages and p r i c e s . As metal p r i c e s change, the demand f o r labour and wage r a t e s change i n the same d i r e c t i o n . S i m i l a r l y the number of mines en t e r i n g or l e a v i n g the i n d u s t r y seems to be r e l a t e d d i r e c t l y to p r i c e changes. The p r i c e changes i n f l u e n c e wage r a t e s i n one d i r e c t i o n while the changing number of mines i n -fluences.' wage r a t e s i n the other d i r e c t i o n . The impact of p r i c e changes upon wage r a t e s more than n u l l i f i e s the a r i t h -metic change i n aggregate average wage rates caused by a change i n the number of mines. Nevertheless the i n f l u e n c e of the changing number of mines probably d i s t o r t s the r e a l e f f e c t upon wage rates as metal p r i c e s change, but t h i s d i s t o r t i o n cannot be recognized i n the given data» TABLE I V Number of D i f f e r e n - Weighted D i f f e r e n - Weighted D i f f e r e n Shipping t i a l s of Average t i a l s of Average t i a l s of Mines i n Number Wage Rates the P r i c e s of the B r i t i s h of of Mining Weighted Lead, Zinc, V/eighted Columbia Shipping Labour i n Average Copper Average Mines B r i t i s h Wage Rates ( D o l l a r s ) P r i c e s o: Columbia Metal ( D o l l a r s ) 1949 118 -6 1.28 .04 .150 .003 1950 112 7 1.32 .14 .153 .044 1951 119 -24 1.46 .22 .197 -.029 1952 95 -15 1.68 .08 .168 -.038 1953 80 -17 1.76 .04 .130 .002 1954 63 -10 1.80 . 0 3 .132 .015 ' 1955 5 3 17 1.83 .18 .147 .009 1956 70 -11 2.01 .06 .156 -.028 1957 5 9 -2 2.07 -.01 .128 -.017 1958 57 1 2.06 .13 .109 .007 1959 60 7 2.19 .16 .116 .012 I960 67 2 . 3 5 .128 Sources: M i n i s t e r of Mines and Petroleum Resources. Annual Report, I960, B r i t i s h Columbia, p. A16, A50. Review of Man-Hours and Hourly Earnings, Dominion Bureau of S t a t i s t i c s , 1955, 1956, 1957, 1958, 1959, I960. 71 Therefore, a decrease i n the number of mines i n the i n -dustry probably increases wage r a t e s . Although the aggregate marginal p h y s i c a l product curve may be lower a f t e r a decrease i n the number of mines, t h i s has no impact upon wage r a t e s . The l e v e l of marginal product of each of the remaining mines would have remained constant i f metal p r i c e s or costs had not changed. I f the labourers of the e l i m i n a t e d mine r e c e i v e d higher wages than la b o u r e r s of some other mine, then aggregate average wages could increase or decrease. However, i t seems l i k e l y that the labourers of the l e a s t e f f i c i e n t mine w i l l r e -c e i v e the lowest wages. Therefore, a r e d u c t i o n i n the number of mines w i l l increase wages. In summary, the study of the i n f l u e n c e s of changes of the p r o d u c t i v i t y of mining labour upon employment and wage r a t e s of B r i t i s h Columbia's mining industry considered two f o r c e s — c h a n g e s i n the amount and form of c a p i t a l or tech-niques used i n the mining i n d u s t r y , and changes i n the number of mines i n the i n d u s t r y . No s t a t i s t i c a l evidence was found of the i n f l u e n c e of changes of the amount of c a p i t a l employed i n B r i t i s h Columbia's mining i n d u s t r y upon the i n d u s t r y ' s wage ra t e s or employment. I t was concluded that i f such an i n -fluence e x i s t e d , i t s force was l i k e l y to be s m a l l . The study of the i n f l u e n c e s of a change i n the number of mines i n the i n d u s t r y upon the i n d u s t r y ' s wage r a t e s and em-ployment l e d to the conclusion that the predominant e f f e c t of 72 t h i s f o r c e was s i m i l a r to the e f f e c t of a movement along mining labour's aggregate marginal p h y s i c a l product curve. The preceding a n a l y s i s suggests that the changes of mining labour's p r o d u c t i v i t y , caused by s h i f t s i n the marginal p h y s i c a l product curve of mining labour, have not s i g n i f i c a n t l y i n f l u e n c e d the wage ra t e s and employment of B r i t i s h Columbia's mining i n d u s t r y . However, there are other r e l a t i o n s h i p s which may e x i s t between the p r o d u c t i -v i t y , employment and wage rat e s of mining labour of B r i t i s h Columbia. The trends of the y e a r l y absolute d i f f e r e n t i a l s of output-per-man-per-year and the y e a r l y absolute d i f f e r e n -t i a l s of employment i n B r i t i s h Columbia's mining industry are given i n Chart V; the r e l e v a n t data i s g i v e n i n Table I I I . For every year except two—1954 and I 9 6 0 — t h e two v a r i a b l e s changed i n opposite d i r e c t i o n s . This r e s u l t sug-gests that the dominant r e l a t i o n s h i p between output-per-man-per-year and employment i s s i m i l a r to movements on an ag-gregate average p h y s i c a l product curve f o r labour of B r i t i s h Columbia's mining industry^ The average product curve w i l l s h i f t w i t h changes i n the amount of c a p i t a l employed or changes i n the number of mines i n the i n d u s t r y (or w i t h changes i n other parameters). 72a However, i t has been suggested that the s h i f t s of the aggregate marginal p h y s i c a l product curve f o r B r i t i s h Columbia mining labour are i n s i g n i f i c a n t . Therefore, the changes of the aggregate average product curve f o r the i n d u s t r y would not be s i g n i f i c a n t . Thus, the con-c l u s i o n i s tendered that the trends given i n Chart V are r e l a t e d i n a manner which i s s i m i l a r to the measures of average products and employment given by s e v e r a l p o i n t s on a t h e o r e t i c a l average product curve f o r mining labour of B r i t i s h Columbia. An a p p r e c i a t i o n of the methods of wage payments i s necessary f o r an understanding of the r e l a t i o n s h i p s be-tween the trends of changes of labour's p r o d u c t i v i t y and the changes of wage rates of mining labour i n B r i t i s h Columbia. The wages p a i d to mining labour are a combination of time rates and i n c e n t i v e bonuses. Most underground workers r e c e i v e a basic wage and then some form of i n -cen t i v e bonus. Incentive bonuses are a d d i t i o n a l payments f o r production exceeding some minimum quota per u n i t of time. I f the degree or amount of i n c e n t i v e bonuses are given, then the more e f f i c i e n t labour and c a p i t a l are the higher w i l l be labour's r e t u r n s . The methods of 73 o. <1 o ^ LL> 5 >u O ^ tt ^ 5 5 o o o a Q o p o S3 S^> <^> o 74 wage payments have some influence upon the average l e v e l of wages primarily because of incentive bonuses. The changing e f f i c i e n c i e s of factors of production have an immediate effect upon wage rates as each worker's output per unit of time i s changed. Above ground workers usually receive straight time earnings. In the following section, the analysis turns to the study of the relationship between changes i n productivity and wage rates of mining labour i n B r i t i s h Columbia. In an a r t i c l e e n t i t l e d "A Theory of Interindustry Wage Structure Variation","'""'' Professor Garberino develops an in t e r e s t -ing model explaining secular d i f f e r e n t i a l wage movements. He states that Permissive factors are those which make a change i n wages possible, which open up a range of alt e r n a t i v e s . P o s i t i v e factors are those which determine which of the alternatives actually materialize i n a s p e c i f i c case. 1 2 Productivity changes are considered as both permissive and positive factors. They are permissive factors because an increase 13 i n productivity lowers costs-per-unit of output. A decrease i n costs-per-unit of output increases the re s i d u a l revenues ac-cruing to the fi r m , other things remaining equal, and labour may -^Joseph W. Garberino, "A Theory of Interindustry Wage Struc-ture Variation", Quarterly Journal of Economics, Vol. 64,I960,p.282. 1 2 I b i d . , p. 294-13 v I f labour's productivity i s increased by adding factors to the production process or by substituting other factors f o r l a -bour i n the production process, i t i s assumed that costs-per-unit of output w i l l decrease. 75 procure some of the increase i n p r o f i t s . P r o d u c t i v i t y changes f o r labour are p o s i t i v e f a c t o r s i f a part of the increase i n labour's e f f i c i e n c y i s immediately returned to labour i n the form of i n c e n t i v e bonuses. I f labour uses e x i s t i n g c a p i t a l and techniques more e f f e c t i v e l y , t h e i r increased revenue from i n -centive bonuses i s probably permanent. However, i f labour's p r o d u c t i v i t y increases by combining new c a p i t a l with labour, the s t r u c t u r e of wage r a t e s and bonuses may be a l t e r e d to r e -14 duce the increase i n wages. Therefore, a change of mining labour's p r o d u c t i v i t y has a s i m i l a r e f f e c t as a change i n the upper wage bound. A change of e i t h e r of these v a r i a b l e s changes 15 the p o s s i b i l i t y of a wage in c r e a s e . I f the p o s s i b i l i t y o f a change of wage r a t e s v a r i e s when the p r o d u c t i v i t y of labour changes, then the trends of wage rates might be r e l a t e d to p r o d u c t i v i t y trends. As the change i n mining labour's p r o d u c t i v i t y i n B r i t i s h Columbia i s a p o s i t i v e f a c t o r as w e l l as a permissive f a c t o r , then the trends of pro-d u c t i v i t y and wage rat e s of B r i t i s h Columbia's mining labour would be expected to be r e l a t e d , i f a l l other things remained equal. A comparison of the trends of the y e a r l y absolute d i f f e r e n -t i a l s of wage r a t e s and the trends i n the y e a r l y absolute "^See S. J . Tr u s c o t t , Mine Economics, S a l i s b u r y House, Lon-don, E.C.2, Mining P u b l i c a t i o n s L t d . , 1947, pp. 247-259. 15 ^A decrease of mining labour's p r o d u c t i v i t y can a l s o be described as a permissive and a p o s i t i v e v a r i a b l e f o r a decrease i n wage r a t e s . 76 d i f f e r e n t i a l s of output-per-man-per-year—both v a r i a b l e s being considered f o r B r i t i s h Columbia's mining i n d u s t r y — i s given i n Chart VI. The r e s u l t i n g trends of the changes of wage rates and the changes of output-per-man-per-year seem unassociated. But t h i s l a c k of a s s o c i a t i o n between these two v a r i a b l e s i s not very s u r p r i s i n g as "other things" have not remained equal. Suppose changes i n mining wage r a t e s vary d i r e c t l y with changes i n the p o s s i b i l i t i e s of wage r a t e increases i n B r i t i s h Columbia's mining i n d u s t r y . I f metal p r i c e s had remained con-stant over the p e r i o d 1949-1960, then the p r o f i t s of B r i t i s h Columbia's mining i n d u s t r y would have v a r i e d d i r e c t l y with changes of c o s t s - p e r - u n i t of output f o r the i n d u s t r y . I f min-i n g labour's p r o d u c t i v i t y i n B r i t i s h Columbia changes, then the l e v e l of p r o f i t s i n the i n d u s t r y changes and the p o s s i b i l i t i e s of an increase i n mining wage r a t e s are a l t e r e d . However, i f the returns of other f a c t o r s of production can be a l t e r e d , then both the c o s t s - p e r - u n i t of output and the p o s s i b i l i t i e s of an increase i n wage rates are changed. Thus, i f labour's product-i v i t y and the r e t u r n to other f a c t o r s of production are changed at the same time, c o s t s - p e r - u n i t of output and the change i n labour's p r o d u c t i v i t y may not vary i n the same d i r e c t i o n . The l e v e l of p r o f i t s f o r the i n d u s t r y , and the p o s s i b i l i t i e s of a wage rate increase f o r B r i t i s h Columbia mining labour w i l l vary d i r e c t l y w i t h changes i n c o s t s - p e r - u n i t of output. Therefore, i f mining labour's p r o d u c t i v i t y and the r e t u r n s to other f a c t o r s of production i n B r i t i s h Columbia's mining i n d u s t r y are a l t e r e d 77 at the same time, then changes i n wage rat e may not be c l o s e l y r e l a t e d to changes i n mining labour's p r o d u c t i v i t y . The e f f e c t s of changes i n the returns of other f a c t o r s of production i n B r i t i s h Columbia's mining industry have probably i n f l u e n c e d the trends given i n Chart V, but the impact of t h i s i n f l u e n c e upon the gi v e n trends cannot be determined. The de-s c r i p t i o n of the e f f e c t s of changes i n the returns of other mining f a c t o r s of production assumed that metal p r i c e s remained constant. However, the trends given i n Chart V would be very d i f f e r e n t i f metal p r i c e s had remained constant. I f the p o s s i b i l i t i e s of a wage increase depend, i n p a r t , upon the l e v e l of p r o f i t s of B r i t i s h Columbia's mining i n d u s t r y , then the p o s s i b i l i t i e s of a wage increase depend upon metal p r i c e s as w e l l as c o s t s - p e r - u n i t of output. Suppose labour's p r o d u c t i v i t y changes, then the p o s s i b i l i t i e s of an increase i n wage r a t e s may be completely a l t e r e d by a change i n metal p r i c e s . Therefore, the permissive nature of a change i n mining labour's p r o d u c t i v i t y i n B r i t i s h Columbia may be dominated by changes i n metal p r i c e s . The p o s i t i v e nature of changes i n mining labour's p r o d u c t i v i -t y , while not dominated by changes of metal p r i c e s , may be hidden or d i s t o r t e d i n the trends of wage rates by changes i n metal p r i c e s . The in f l u e n c e s of changes i n metal p r i c e s upon changes i n wage r a t e s was described i n Chapter I I . The close r e l a t i o n -ship between the trends of the d i f f e r e n t i a l s of metal p r i c e s and the d i f f e r e n t i a l s of wage ra t e s of B r i t i s h Columbia's mining labour suggests that changes of metal p r i c e s may be a dominant 78 2 t3 2 Z -2 o ^ ^ U-> O O 2 w> O o 0 o 3 8 o o vo o 8 8 o o O 8 I ko 3 O. o —> t— 2 > O O £ > 2 CO >-— i -a 2 O 2 2 iu b-S i VXI O 2 <1 5 3 -x. i l C O VA-S i 3 : 5 d 6 3D <£ 2 6 o ° o o o O O ° O O O o o o o 6 o o 6 O O 6 6 7 9 TABLE V Productivity Wage Rates 1949 1,063.8 106.2 1.28 .04 1950 1,170.0 -237.9 1 . 3 2 .14 1951 932.1 201*4 1.46 .22 1952 1,133.5 55H.2 1.68 .08 1953 1,684.7 -36.0 1.76 .04 1954 1,648.7 134.9 1.80 .03 1955 1,783.6 —128.1 1.83 .18 1956 1,615.5 -110.9 2.01 .06 1957 1,504.6 212.7 2.07 -.01 1958 1,717.3 173.2 2.06 .13 1959 1,890.5 312.8 2.19 .16 I960 2,203.3 2.35 Sources: Minister of Mines and Petroleum Resources, Annual Report, 1960, B r i t i s h Columbia, p. A49, A50. Review of Man-Hours and Hourly Earnings, Dominion Bureau of S t a t i s t i c s , 1955, 1956, 1957, 1958, 1959, I960. 80 f o r c e of the changes of wage r a t e s . The wage r a t e s of mining labour i n B r i t i s h Columbia may increase with an increase i n labour's p r o d u c t i v i t y . Nevertheless, the trends of the d i f -f e r e n t i a l s of wage rat e s and p r o d u c t i v i t y of labour need not be associated. The- increase of wage rat e s may be caused by a change i n labour's p r o d u c t i v i t y , but the degree of the change i n wage ra t e s may be dominated by metal p r i c e changes* For example, i n 1952, output-per-man-per-year increased by more than the increase i n output-per-man-per-year i n 1951. While wage rat e s increased i n 1952, the wage rat e d i f f e r e n t i a l of t h i s year was lower than the wage rate d i f f e r e n t i a l of 1951. Metal p r i c e s decreased i n 1951. I f the p r o d u c t i v i t y increase caused the wage inc r e a s e , the i n f l u e n c e of the change i n l a -bour's p r o d u c t i v i t y was not great enough to cause the trends of the d i f f e r e n t i a l s of wage rat e s and the d i f f e r e n t i a l s of labour's p r o d u c t i v i t y to move i n the same d i r e c t i o n . While changes i n labour's p r o d u c t i v i t y influenced wage r a t e s , t h i s i n f l u e n c e i s not revealed i n Chart VI. The impact of a change of metal p r i c e s i s not confined to the trends of changes i n wage r a t e s . Metal p r i c e changes pro-bably have a major i n f l u e n c e on the changing number of mines i n B r i t i s h Columbia's mining i n d u s t r y . The e f f e c t of a change i n the number of mines upon the marginal product and the p r o d u c t i v i t y of mining labour i n B r i t i s h Columbia was described e a r l i e r i n t h i s chapter. I f metal p r i c e s change and the number of mines changes i n the same d i r e c t i o n , then labour's p r o d u c t i v i t y tends 81 to change i n the opposite d i r e c t i o n . Therefore a change i n metal p r i c e s i n f l u e n c e s a change i n labour's p r o d u c t i v i t y i n one d i r e c t i o n , and a change i n wage r a t e s i n the other d i r e c -t i o n . The i n f l u e n c e of v a r i a b l e metal p r i c e s and v a r i a b l e r e -turns to other f a c t o r s of production are only two reasons f o r the l a c k of a s s o c i a t i o n between the trends of the d i f f e r e n -t i a l s of p r o d u c t i v i t y and the d i f f e r e n t i a l s of wage r a t e s of mining labour i n B r i t i s h Columbia. There are other f o r c e s — such as the forces of the supply of mining labour i n B r i t i s h Columbia—which d i s t o r t the a c t u a l r e l a t i o n s h i p s of the trends between the p r o d u c t i v i t y and wage r a t e s of B r i t i s h Columbia's mining labour. However, these other f o r c e s w i l l not be de-s c r i b e d as the o b j e c t i v e s of t h i s part of the t h e s i s are to describe the r e l a t i o n s h i p s between the changes of labour's p r o d u c t i v i t y and the changes of wage r a t e s . The a n a l y s i s of the r e l a t i o n s h i p s between the trends of the d i f f e r e n t i a l s of wage r a t e s and the d i f f e r e n t i a l s of pro-d u c t i v i t y of B r i t i s h Columbia mining labour assumed that i n -creases i n wage rates should vary d i r e c t l y with changes i n the p o s s i b i l i t i e s of a wage rat e increase. This assumption may be tr u e , but a change i n the p o s s i b i l i t i e s of an. increase i n wage r a t e s i n one year may lead to an increase i n wage r a t e s i n the same year, i n some other year, or i n a number of years. Thus, the impact of a change i n labour's p r o d u c t i v i t y of B r i t i s h Columbia's mining i n d u s t r y upon the wage rates of the in d u s t r y 82 may be re l e a s e d immediately, i t may be lagged f o r one or more periods, or i t may be d i f f u s e d over a number of periods. Chart V I I shows the trends of wage r a t e s and p r o d u c t i v i t y f o r mining labour i n B r i t i s h Columbia f o r the per i o d 1949-1960. In g eneral, both v a r i a b l e s move i n the same d i r e c t i o n . When the trends of wage ra t e s and p r o d u c t i v i t y of mining labour were studied f o r a longer p e r i o d (25 y e a r s ) , the r e s u l t a n t r e l a t i o n -ship between the v a r i a b l e s was s i m i l a r to the trends shown i n Chart VII- The influence of changes of mining labour's produc-t i v i t y i n B r i t i s h Columbia upon the wage r a t e s of the i n d u s t r y might be revealed as a for c e underlying long run wage move-ments. However, the impact of changes of the p r o d u c t i v i t y of mining labour upon the wage ra t e s of B r i t i s h Columbia's mining i n d u s t r y f o r the per i o d 1949-1960 cannot be determined. The p o s i t i v e nature of mining labour's p r o d u c t i v i t y changes may cause some changes i n wage r a t e s . But the permissive nature of mining labour's p r o d u c t i v i t y changes are probably dominated by metal p r i c e changes or other v a r i a b l e s . In c o n c l u s i o n , p r o d u c t i v i t y and p r o d u c t i v i t y changes of B r i t i s h Columbia's mining labour i s an i n t e r e s t i n g but r e s t r i c t e d subject f o r a n a l y s i s . L i t t l e evidence can be found cf any i n -fluence of changes i n the aggregate marginal p h y s i c a l product curve upon the wage r a t e s and employment of mining labour i n B r i t i s h Columbia. No r e l a t i o n s h i p s can be found between the trends of the changes of mining labour's p r o d u c t i v i t y and the changes of wage rates f o r the per i o d 1949-1960. While the trends of c w A e y 7 T26U0S OF OUTPUT PEZ MAW P62 VeAf2 AMD AveEAGG \VA<5£ OF BEITI^H COLUMBIA'S MINIU6 lUOUSTey: 84 wage r a t e s and p r o d u c t i v i t y of mining labour i n B r i t i s h Colum-b i a moved i n the same general d i r e c t i o n i n a long run p e r i o d , t h i s observation does not provide any conclusions f o r the period 1949-1960. The only p o s i t i v e c o n c l u s i o n which was based on a s t a t i s t i c a l a s s o c i a t i o n concerned employment. The trends of the changes of employment and changes of p r o d u c t i v i t y of B r i t i s h Columbia mining labour were shown to be s i m i l a r to movements on an aggregate average product curve f o r mining labour. CONCLUSION The o b j e c t i v e s of t h i s t h e s i s were to describe and to analyse the in f l u e n c e s of the determinants of the de r i v e d de-mand f o r mining labour upon the trends of wage rates and em-ployment of B r i t i s h Columbia's mining i n d u s t r y . The concept of an upper wage bound f o r a mine and f o r the i n d u s t r y as a whole was given i n the I n t r o d u c t i o n . This con-cept was used f o r a d e s c r i p t i o n of the p o s s i b l e i n f l u e n c e s of two aspects of the market s t r u c t u r e of B r i t i s h Columbia's min-ing i n d u s t r y upon the wage rates and employment of the i n d u s t r y . The competitive determination of metal p r i c e s probably r e s t r i c t s the p r o f i t s of the i n d u s t r y more than other methods of p r i c e determination. Furthermore, the number of a l t e r n a t i v e wage l e v e l s above the e x i s t i n g wage l e v e l v a r i e s with the amount of p r o f i t s i n the i n d u s t r y . I f the p r o f i t s of B r i t i s h Columbia's mining i n d u s t r y have been r e s t r i c t e d by the competitive d e t e r -mination of metal p r i c e s , then the i n d u s t r y ' s upper wage bound w i l l be lower than i t would be i f metal p r i c e s had been det e r -mined i n some other f a s h i o n . I f the upper wage bound of B r i t i s h Columbia's mining i n d u s t r y has tended to be low, wage r a t e i n -creases w i l l depend l a r g e l y upon changes of the i n d u s t r y ' s upper wage bound. The basing point system of p r i c e s was the other aspect of market s t r u c t u r e studied i n Chapter I. The inf l u e n c e of base p r i c e s upon the upper wage bound of the i n d u s t r y could not be determined. However, i f the system of base p r i c e s has encour-aged a gr e a t e r output i n B r i t i s h Columbia's mining i n d u s t r y 86 than any other system of p r i c i n g , the amount of employment i n the i n d u s t r y w i l l probably be l a r g e r . There are other elements of market s t r u c t u r e which i n f l u e n c e the p o s i t i o n of the mining i n d u s t r y ' s upper wage bound. However, the i n f l u e n c e s of the other elements of market s t r u c t u r e were not considered as im-portant as the competitive determination of metal p r i c e s and the basing point system of p r i c e s . The b r i e f a n a l y s i s of the competitive determination of p r i c e s implied that changes i n the wage r a t e s of B r i t i s h Colum-b i a mining labour would be r e l a t e d to changes i n the ind u s t r y ' s upper wage bound. Metal p r i c e s and the marginal product of mining labour were defined as determinants of both the upper wage bound and the derived demand f o r mining. I f the derived demand f o r mining labour changes, then the upper wage bound must a l s o change. The concept of the derived demand f o r mining labour was employed f o r much of the d e s c r i p t i v e a n a l y s i s of the t h e s i s i The trends of wage ra t e s and metal p r i c e s were not a s s o c i -ated—wage r a t e s increased i n every sub-period except one and metal p r i c e s f l u c t u a t e d over the e n t i r e p e riod. Therefore, i f metal p r i c e s and wage r a t e s were r e l a t e d , other wage forces caused the d i s c r e p a n c i e s between the trends. A theory was de-veloped to show that the supply curve of B r i t i s h Columbia's min-ing labour must s h i f t upwards over the period 1949-1960. The close a s s o c i a t i o n between the trends of y e a r l y abso-l u t e wage d i f f e r e n t i a l s and one year lagged absolute metal 87 p r i c e d i f f e r e n t i a l s permitted the co n c l u s i o n that metal p r i c e s and wage rat e s of B r i t i s h Columbia's mining i n d u s t r y are r e -l a t e d . The degree of wage rate i n c r e a s e s of B r i t i s h Columbia's mining hdustry i s dependent upon the degree and d i r e c t i o n of lagged metal p r i c e changes. A change i n the number of mines probably changes the average aggregate wage rat e s of B r i t i s h Columbia's mining l a -bour. I f the labourers of a marginal mine receive the lowest wage r a t e s of a l l mining labourers i n the i n d u s t r y , then the re d u c t i o n ( a d d i t i o n ) of a marginal mine w i l l r a i s e (lower) average aggregate wage r a t e s of B r i t i s h Columbia mining labour. U n f o r t u n a t e l y t h i s i n f l u e n c e on wage r a t e s could not be iden-t i f i e d i n the a v a i l a b l e s t a t i s t i c s . A change i n the number of mines i n the in d u s t r y changes the amount of employment of B r i t i s h Columbia's mining labour. However, the t h e o r e t i c a l marginal p h y s i c a l product curve f o r mining labour s h i f t s w i t h a change i n the number of mines. The s h i f t of the curve dampens the change of labour's marginal pro-duct which would r e s u l t from a movement along the aggregate curve i f employment had changed, but the f i x e d f a c t o r remained constant. I f there were a s i n g l e wage r a t e f o r a l l mining l a -bour of B r i t i s h Columbia, then the s h i f t of the aggregate curve could i n f l u e n c e wage r a t e s through a change i n the l e v e l of mining labour's marginal product. However, the v a r y i n g wage r a t e s between mines allow," the wage e f f e c t of a change i n the number of mines to be i n t e r p r e t e d as a s t a t i s t i c a l phenomenon. 88 The study of the i n f l u e n c e s of changes of labour's produc-t i v i t y upon wage rates d i d not provide any p o s i t i v e c o n c l u s i o n s . I t was suggested that the p o s s i b l e i n f l u e n c e upon a t h e o r e t i c a l s i n g l e wage rate f o r the i n d u s t r y by a change i n the number of mines would be sma l l . A r e d u c t i o n or a d d i t i o n of a sm a l l num-ber of mines would not app r e c i a b l y a f f e c t the t h e o r e t i c a l average marginal product curve f o r B r i t i s h Columbia's mining labour. Changes i n the amount or form of c a p i t a l may have a f f e c t e d wage rates of the ind u s t r y ' s mining labour, but no evidence of these i n f l u e n c e s could be found i n the given s t a t i s t i c s . The trends of y e a r l y absolute wage r a t e d i f f e r e n t i a l s and y e a r l y absolute output-per-man-per-year d i f f e r e n t i a l s provided no in f o r m a t i o n of the r e l a t i o n s h i p between these v a r i a b l e s . However, long run trends of wage rates and output-per-man-per-year suggested that the p r o d u c t i v i t y and wage r a t e s of B r i t i s h Columbia's mining l a -bour tended to move i n the same d i r e c t i o n . Therefore, i t i s p o s s i b l e that p r o d u c t i v i t y changes are broad, long run f o r c e s u n d e r l y i n g the i n d u s t r y ' s wage r a t e s . Nevertheless, i t was concluded that i f the changes of labour's p r o d u c t i v i t y i n B r i t i s h Columbia's mining i n d u s t r y have had an i n f l u e n c e upon the i n -dustry's wage r a t e s , t h i s i n f l u e n c e was dominated by other wage rate determining v a r i a b l e s . The r a t e of output of B r i t i s h Columbia's mining i n d u s t r y was shown to be s e n s i t i v e to changes of metal p r i c e s . I f the rate of output of B r i t i s h Columbia's mining i n d u s t r y v a r i e d , employment would be expected to vary i n the same d i r e c t i o n , i f other f a c t o r s were not s u b s t i t u t e d f o r mining labour. Very 89 l i t t l e evidence could be found to suggest that c a p i t a l has been s u b s t i t u t e d f o r labour i n B r i t i s h Columbia's mining i n d u s t r y . A l a c k of s t a t i s t i c a l evidence does not disprove the hypothesis that c a p i t a l has been s u b s t i t u t e d f o r l a b o u r . Nevertheless, the given a n a l y s i s plus the information s u p p l i e d by Mr. C. M i t c h e l l permits the c o n c l u s i o n that, i f c a p i t a l has been sub-s t i t u t e d f o r mining labour, t h i s e f f e c t has had l i t t l e i n f l u e n c e upon employment. Therefore, i t i s f a i r l y safe to conclude that employment does vary d i r e c t l y with changes i n the r a t e of the mining i n d u s t r y ' s output• I f the r a t e of i n d u s t r y output v a r i e s with metal p r i c e changes, then the amount of employment would be expected to vary w i t h metal p r i c e changes. The s t a t i s t i c a l a n a l y s i s of the trends of metal p r i c e s and employment of B r i t i s h Columbia's mining labour suggested these v a r i a b l e s have v a r i e d i n the expected manner. Moreover, i t was considered as a f a c t that employment of B r i t i s h Columbia's mining labour was a v a r i a b l e dependent upon metal p r i c e s and metal p r i c e changes. Wage r a t e s of B r i t i s h Columbia's mining labour are c l o s e l y r e l a t e d to lagged metal p r i c e s , and as employment and wage r a t e s are f u n c t i o n a l l y r e l a t e d i n the same p e r i o d , employment must be r e l a t e d to lagged metal p r i c e s . The c l o s e r e l a t i o n s h i p between the y e a r l y ab-solute d i f f e r e n t i a l s of employment of B r i t i s h Columbia's mining labour and the y e a r l y absolute metal p r i c e s enforces the con-c l u s i o n that changes of metal p r i c e s have been an important i n -fluence upon the trends of employment i n B r i t i s h Columbia's mining i n d u s t r y f o r the p e r i o d 1949-1960. 90 F i n a l l y , l i t t l e s t a t i s t i c a l evidence could be found of any i n f l u e n c e s of changes i n the amount or form of c a p i t a l upon B r i t i s h Columbia's mining labour. The i n d u s t r y ' s trends of the y e a r l y absolute employment d i f f e r e n t i a l s and the y e a r l y abso-l u t e d i f f e r e n t i a l s of p r o d u c t i v i t y d i d seem to be r e l a t e d . The r e l a t i o n s h i p was s i m i l a r to the expected r e l a t i o n s h i p given by a number of p o i n t s on a t h e o r e t i c a l average product curve f o r B r i t i s h Columbia mining labour. The v a r y i n g number of mines has an employment e f f e c t which i s s i m i l a r to a movement along an aggregate marginal p h y s i c a l product curve f o r B r i t i s h Columbia's mining labour. Therefore, the r e l a t i o n s h i p between output-per-man-per-year and employment i s to be expected. In summary, the f o r c e s of the demand f o r mining labour have had a considerable impact upon the wage r a t e s and employ-ment of B r i t i s h Columbia's mining i n d u s t r y f o r the p e r i o d 1949-1960. Wage ra t e s and employment are both r e l a t e d to metal p r i c e changes. Employment v a r i e s d i r e c t l y with metal p r i c e s but wage rates do not seem to vary at a l l w i t h metal prices." Both employment and wage d i f f e r e n t i a l s vary d i r e c t l y with lagged metal p r i c e d i f f e r e n t i a l s . The degree and d i r e c t i o n of metal p r i c e changes i n f l u e n c e the degree of wage rate changes. P r o d u c t i v i t y changes of labour vary i n v e r s e l y with em-ployment changes but l i t t l e evidence can be found that changes of labour's p r o d u c t i v i t y i n f l u e n c e e i t h e r wage r a t e s or employ-ment. There may be a long run r e l a t i o n s h i p between labour's p r o d u c t i v i t y and wage r a t e s , but t h i s r e l a t i o n s h i p i s not per-t i n e n t to the p e r i o d 1949-1960. 91 BIBLIOGRAPHY Bakke, E. Wight and Kerr, C l a r k , ed., Unions Management and the P u b l i c , New York, Harcourt Brace and Company, 1948. Bakke, E. Wight; K e r r , Clark; and Anrod, Charles W.; ed., Unions  Management and the P u b l i c , Burlingame, New York, Harcourt Brace and Company, I960, 2nd ed. Baumol, W i l l i a m J . , Economic Theory and Operations A n a l y s i s , Englewood C l i f f s , N. J . , P r e n t i c e H a l l Inc., 1961. Bloom, G. P., "A Reconsideration of the Theory of E x p l o i t a t i o n " , Quarterly J o u r n a l of Economics, V.55, 1940-41, pp.413-442. B r i t i s h Columbia, Annual Report of The M i n i s t e r of Mines and  Petroleum Products, I960. Bronfenbrenner, M., "The Incidence of C o l l e c t i v e Bargaining", Papers and Proceedings, American Economic Review, V.44, 1954, pp. 293-307. C a r l i s l e , Donald, "The Economics of a Fund Resource With Par-t i c u l a r Reference to Mining", The American Economic Review, V.44, 1954, pp. 595-616. C l a r k , J . 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