UBC Theses and Dissertations

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UBC Theses and Dissertations

Study of the income elasticity of demand in Canada for selected food products. Prinhar, Surendra Sing 1956

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A STUDY OP THE INCOME ELASTICITY OP DEMAND IN CANADA FOR SELECTED POOD PRODUCTS by SURENDRA SINGH PRIHAR A THESIS SUBMITTED IN PARTIAL FULFILMENT OP THE REQUIREMENTS FOR THE DEGREE OP MASTER OP SCIENCE IN AGRICULTURE I n the Department of ATRICULTURAE ECONOMICS  We accept t h i s t h e s i s a s conforming t o the standard r e q u i r e d f r o m candidates f o r tha degree o f MASTER OP SCIENCE IN AGRICULTURE.  Members o f the Department o f A g r i c u l t u r a l Economics.  THE UNIVERSITY OP BRITISH COLUMBIA A p r i l , 1956  ACKNOWLEDGMENT Tha author i s v e r y t h a n k f u l  t o Dr. W.J.  Anderson f o r the guidance I n the f i e l d . The t h e s i s has been r e a d by the members o f the Committee. The author I s t h a n k f u l  t o Dr. C l a r k , D r . K I t t s , D r .  Hornby, Mr. Menzie and Mr. M^tuszewki f o r t h e i r c r i t i c i s m towards improvement o f t h e t e x t . The author i s g r a t e f u l f o r the c o o p e r a t i o n and help o f the members o f the U n i v e r s i t y staff.  Library  A B S T R A C T  A n a l y s i s o f income e l a s t i c i t y o f demand was c a r r i e d out f o r b e e f , pork, eggs, t e a , and c o f f e e .  Prices f o r  b e e f and pork were t a k e n a t the wholesale l e v e l , w h i l e those f o r eggs, t e a and c o f f e e were t a k e n a t the r e t a i l l e v e l . P r i c e s and d i s p o s a b l e income were o b t a i n e d from the N a t i o n a l Accounts and were d e f l a t e d by the I m p l i c i t P r i c e D e f l a t o r o b t a i n e d from the same source. The e f f e c t o f the time v a r i a b l e was e l i m i n a t e d , i n the case o f b e e f , pork, and eggs, by t a k i n g the f i r s t ferences.  dif-  S t r a i g h t l i n e r e g r e s s i o n s were f i t t e d t o t h e con-  sumption d a t a o f a l l 5 commodities. iable equation, estimated values o f f o r each y e a r were computed.  From the m u l t i p l e varand the r e s i d u a l s  The r e s i d u a l s were p l o t t e d  around the p a r t i a l r e g r e s s i o n e q u a t i o n ( o b t a i n e d by subs t i t u t i n g the a r i t h m e t i c mean f o r the value o f the e t h e r v a r i a b l e s ) a c c o r d i n g t o the s i g n o f the r e s i d u a l s f o r tho year.  Free-hand l i n e s were f i t t e d t o t h i s s c a t t e r diagram  and from these l i n e s the degree o f v a r i a t i o n was c a l c u l a t e d . The r e g r e s s i o n c o e f f i c i e n t s ware used i n c a l c u l a t i n g e l a s ticities. The income e l a s t i c i t y o f the demand f o r b e e f v a r i e d from + 0 . 8 1 5 t o + 1 . 1 7 8 from 1929 t i l l  19i|i|..  For the p e r i o d  1945-52, lars.  the average i n c r e a s e i n income was o n l y  There was a decrease I n the p e r c a p i t a  0.875  dol-  consumption  o f b e e f as c a l c u l a t e d from the p a r t i a l r e g r e s s i o n e q u a t i o n (removing tho o f f e e t o f changes I n p r i c e o f b e e f and p r i c e o f pork).  Thus income e l a s t i c i t y was  1945~52.  -0.199  -  0.02  during  When tho y e a r s o f extreme v a r i a t i o n I n b e e f con-  (1934>-35>-43.-44>-48) were o m i t t e d from the s e r i e s , tho income e l a s t i c i t y was + 0.34$ f o r the p e r i o d 1929-33 and 0.00, -0.0063 for the p e r i o d s 1939-1*2 and 1946-52. Thus i n sumption  r e c e n t y e a r s the income e l a s t i c i t y o f demand f o r b e e f has been d e c r e a s i n g and has approached 0.00.  However, i n con-  s i d e r i n g these r e s u l t s , one s h o u l d remember t h a t t h e m u l t i p l e r e g r e s s i o n e q u a t i o n e x p l a i n e d o n l y 26  p e r cent o f the t o t a l  variation. Tho r e g r e s s i o n c o e f f i c i e n t f i t t e d t o pork consumpt i o n e x p l a i n e d only 19  p e r cent o f the t o t a l v a r i a t i o n . Even  out o f t h i s t o t a l e x p l a i n e d v a r i a t i o n the p r i c e o f pork oxp l a i n e d 80  per cent.  pork came out t o be  The Income e l a s t i c i t y o f demand f o r  +0.053 *© +0.090.  I n the a n a l y s i s o f tho demand f o r eggs, the p r i c e c o e f f i c i e n t was not s t a t i s t i c a l l y s i g n i f i c a n t . e l a s t i c i t y o f demand f o r oggs v a r i e d from  The income  +0.403 t o +0.657.  The consumption o f t e a has been d e c r e a s i n g and t h a t o f c o f f e e I n c r e a s i n g s i n c e 1926.  Tho r e s u l t s o f tho  m u l t i p l e r e g r e s s i o n a n a l y s i s were i n f l u e n c e d by t h i s time trend.  When income e l a s t i c i t y o f demand f o r c o f f e e  was  c a l c u l a t e d over the whole p e r i o d i t decreased from +1.120 t o +1.068.  The  income e l a s t i c i t y o f demand f o r tea was found t o  vary from -0.530 - 0.133 to -1.438 - 0.362.  When s e p a r a t e ,  r e g r e s s i o n l i n e s were f i t t e d f o r the p e r i o d s 1926-lj.l and 19i|.2-52, none o f the r e g r e s s i o n c o e f f i c i e n t s was s i g n i f i c a n t i n the l a t t e r p e r i o d and only the p r i c e of t e a c o e f f i c i e n t i n the f i r s t period.'  As has a l r e a d y been p o i n t e d out, t h e r e  been a t r e n d In the consumption o f t e a and p o s s i b l e t h a t because o f Increases  coffee.  i n disposable  has  It i s  Income and  i n c o f f e e consumption the income e l a s t i c i t y o f demand I s p o s i t i v e f o r c o f f e e and negative  f o r tea.  c i t y o f demand has been d e c r e a s i n g and  The  income e l a s t i -  i n the case o f b o t h t e a  c o f f e e but the r e a s o n seems t o be d i f f e r e n t In the two  cases.  The income e l a s t i c i t y o f demand f o r t e a d e c l i n e d  at a f a s t e r r a t e than the Income e l a s t i c i t y o f demand f o r coffee•  TABLE OF CONTENTS CHAPTER  Page INTRODUCTION  I.  1  THE THEORY OF DEMAND  •  ^  F a o t o r s c a u s i n g changes i n demand T a s t e s and t h e laws e f t h e i r change F u n c t i o n i n g o f the market mechanism Four types o f dynamic r e l a t i o n s h i p s between supply and demand curves Variables determining  supply  Lag i n adjustment II.  SURVEY OF STATISTICAL MATERIALS . . . .  10  Time s e r i e s on p r i c e s , Income and quantities Commodities  selected  The problem e f d e t e r m i n i n g Time s e r i e s and budget The time III.  weights  studies  variable  METHOD OF CALCULATION D e r i v a t i o n o f demand r e l a t i o n s h i p s from the time The  supply  series  function  The income e q u a t i o n The  s i n g l e e q u a t i o n and t h e m u l t i p l e  e q u a t i o n model S t o c k s , imports and e x p o r t s  lij.  TABLE OP CONTENTS  (Continued) Page  CHAPTER J u s t i f i c a t i o n o f the s i n g l e e q u a t i o n approach F r e s h p r o d u c t s and s t o c k s B u i l d i n g a model The method used IV.  RESULTS  21  Beef Pork Eggs Coffee Tea APPENDICES BIBLIOGRAPHY  28 103  EIST GP FIGURES Figure  Page  1.  Price and Consumption of Beef  4°  2.  Price of Pork and Beef Consumption  3.  Disposable Income and Beef Consumption  4.  Real Price and Consumption of Pork  . . . .  JLj.1  . .  42  • • • •  54  5*  Price of Beef and Consumption of Pork . . .  55  6.  Disposable Income and Consumption of Pork .  56  7.  Real Price and Consumption of Eggs  . . . .  64  8.  Disposable Income and Egg Consumption • • •  64  9.  Disposable Income and Coffee Consumption  •  82  10*  Disposable Income and Tea Consumption . . .  82  11.  Ratios of the Prices and the Consumptions of Tea and Coffee  87  12.  Price of Tea and Consumption of Coffee  . .  13.  Price and Consumption of Coffee  90  14*  Disposable Income and Consumption of Coffee  91  15•  Per Capita Disappearance of Coffee  92  • • • •  89  16-18.Graphic Analysis f o r Coffee  93  19-25.Graphic Analysis f o r Tea  96  INTRODUCTION A study of the income e l a s t i c i t y of demand Involves the measurement of s h i f t s i n the consumption function. These s h i f t s are Important economic phenomena because consumption determines the Income going to resources as a remuneration f o r t h e i r use and thus the amount of resources used i n the production o f a p a r t i c u l a r commodity.  The quantity of a  commodity demanded at any p a r t i c u l a r time depends upon I t s p r i c e , the p r i c e of the other commodities that can be used as substitutes, the disposable income of the consumers, and a number ef other factors grouped as "tastes and preferences".  These l a t t e r include the habits of Individuals,  r e l i g i o n , a t t i t u d e s , race, age differences, sex and others which cannot be measured q u a n t i t a t i v e l y .  Aggregate move-  ments are forecast from a knowledge of the response of the i n d i v i d u a l consuming unit which i s the household. Determination of the relationship of the various variables a f f e c t i n g demand can be made from the budget studies of these households or the time series data of p r i c e s , i n come and quantities consumed.  The records f o r most time  series do not go baek beyond the present century. The s t a t i s t i c a l derivation of demand curves f a l l s under the f i e l d of econometrics. 1  The development of  2 s t a t i s t i c a l analysis of demand has been slow because economics and s t a t i s t i c s were not related u n t i l  recent  decades and time series were not a v a i l a b l e . Demand analysis has been carried on by the following methods:  1)  single-equation  The single-equation  2)  Tho  approach supplemented by the s e l e c t i o n of  useful variables. has been discovered single-equation  approach.  3)  Tho multiple-equation  approach.  It  that regression c o - e f f i c i e n t s from the  approach have a downward bias when there  are errors or disturbances i n the independent variables. Sampling errors were recognized by Mordecai Ezekiel" * and 1  he gave the t e s t s of significance by the end of 1930. 2 Schultz's l a t e r work  Is another monument to the s i n g l e -  equation approach. A refinement of the single equation approach represented by (2) was developed by Ragnar P r l s c h during the period 1929-34 i n h i s method of " S t a t i s t i c a l confluence analysis by means of complete regression systems" to cope with the problem of spurious c o r r e l a t i o n when random errors and high i n t e r - c o r r e l a t i o n between independent variables were present. The f i r s t major a r t i c l e dealing with the •a  multiple equation approach was published by Haavelmo-' 1 E z o k i e l , Mordecai, Methods of Correlation Analysis. 2d.ed. New York, J . Wiley and Sons, Inc.; London, Chapman & H a l l , 1941* 2 Schultz, Henry, The Theory and Measurement of Demand, Chicago, University of Chicago Press, 1938. 3 Haavelmo, T., S t a t i s t i c a l Implications of a System of Simultaneous Equations. Econometrica XI, pp. 1-12.  3  i n 1943*  The t h e o r e t i c a l background o r t h i s approach has  been covered thoroughly i n the Cowles Commission Monograph Ho.  10 . 1  The b a s i c assumption  o f t h i s approach i s t h a t  economic data a r e generated by systems o f r e l a t i o n s t h a t a r e ,  2 i n general, stochastic,  dynamic, and simultaneous.  There i s a d i f f e r e n c e o f o p i n i o n over the accuracy gained by r e s o r t i n g t o the simultaneous, m u l t i p l e e q u a t i o n approach.  A c c o r d i n g t o Fox,3 t h e r e i s n o t much  d i f f e r e n c e i n the r e s u l t s o b t a i n e d by u s i n g a  simultaneous  e q u a t i o n approach and the s i n g l e - e q u a t i o n approach, b u t a c o n t r a r y view-point f a v o r i n g t h e m u l t i p l e - e q u a t i o n approach i s expressed by Rojko.^-  The evidence  o f the two a r t i c l e s  suggests t h a t when a commodity i s p u t t o many uses o r when there are many s u b s t i t u t e s a v a i l a b l e , the m u l t i p l e e q u a t i o n approach g i v e s more a c c u r a t e r e s u l t s .  Koopmans, T. J a i l i n g , S t a t i s t i c a l I n f e r e n c e i n Dynamic Economic Models, New York, Wiley, 1 9 5 0 . x  2 S t o c h a s t i c v a r i a b l e s a r e those whose p r o p e r t i e s a r e a c c u r a t e l y d e s c r i b e d by p r o b a b i l i t y d i s t r i b u t i o n s . 3 Fox, K.A., A n a l y s i s o f Demand f o r Farm P r o d u c t s . T e c h n i c a l B u l l e t i n No. 1081 U.S.D.A., 1953. k Rojko, Anthony S., Economic Models and D a i r y I n d u s t r y , J o u r n a l o f Farm Economics, pp. S 3 8 , December 1 9 5 3 *  CHAPTER I THE THEORY OP DEMAND Factors  Causing Changes I n Demand  The demand f o r a commodity may be c o n s i d e r e d as mainly a f u n c t i o n o f the p r i c e o f the commodity, the p r i c e s o f other commodities, the d i s p o s a b l e consumer, and consumer t a s t e s . time there may be c o n s i d e r a b l e  income o f the  I n any short p e r i o d o f v a r i a t i o n i n the amount o f  a commodity consumed by consumers.  The causes o f v a r i a -  t i o n among i n d i v i d u a l s and over time can be c l a s s i f i e d as the p r i c e o f the commodity, the p r i c e s o f the s u b s t i t u t e s and  complements and consumers  1  incomes and t a s t e s .  The p r i c e e l a s t i c i t y o f demand f o r a commodity usually  increases  w i t h the l e n g t h  under c o n s i d e r a t i o n .  o f the p e r i o d o f time  Almost a l l l o n g - r u n demand curves  are e l a s t i c because the p o t e n t i a l s u b s t i t u t e s f o r most products are numerous.  Two  commodities may be  defined  as s u b s t i t u t e s when a r i s e i n the p r i c e o f one l e a d s the consumer t o buy more of the o t h e r , and as complements I f a r i s e i n the p r i c e o f one leads the consumer to buy l e s s o f the o t h e r . the  The r e a c t i o n o f the i n d i v i d u a l i s not  same t o temporary changes i n p r i c e s and incomes as  i t i s t o permanent changes.  5 T a s t e s and the Laws o f Changes In T a s t e s I n most demand a n a l y s e s , a l l f a c t o r s o t h e r than p r i c e s and Incomes are lumped t o g e t h e r as t a s t e s . T a s t e s thus embrace a l l non-monetary determinants  of  con-  sumption such as o c c u p a t i o n , age, f a m i l y composition, community s i z e , r a c e and n a t i o n a l i t y . o f t h i s procedure  The  justification  I s t h a t much the g r e a t e s t p a r t o f s h o r t -  r u n changes i n consumption are e x p l a i n e d i n terms o f monetary f a c t o r s , o r , t h a t f o r l a r g e b o d i e s o f consumers, t a s t e s . a r e r e l a t i v e l y s t a b l e e s p e c i a l l y i n the s h o r t r u n . Even f o r the I n d i v i d u a l consumer a c e r t a i n s t a b i l i t y o r p e r s i s t e n c e e x i s t s because most persons do not  shift  q u i c k l y ( o r o f t e n ) between o c c u p a t i o n s or types o f comm u n i t i e s o r make o t h e r changes t h a t a l t e r t h e i r Furthermore,  tastes.  t a s t e s which are a s s o c i a t e d w i t h n a t i o n a l  and c u l t u r a l t r a d i t i o n s are even more s t a b l e . T h e r e f o r e , the assumption  t h a t consumers* t a s t e s are s t a b l e i n the  s h o r t r u n and do not a f f e c t demand, i s not an  unreasonable  one. I n order to study the p r i c e and income a s p e c t s o f demand one must e i t h e r assume t h a t t a s t e s remain f i x e d over the p e r i o d s d e a l t w i t h o r d i s c o v e r the laws o f t h e i r change.  The f i r s t assumption  i s commonly made because  t a s t e s are w i d e l y b e l i e v e d to be r e l a t i v e l y s t a b l e , t h a t i s , f l u c t u a t i o n s i n incomes and p r i c e s a f f e c t changes i n consumption more than do changes i n t a s t e s .  Moreover,  6  changes i n t a s t e s are o f t e n non-economic i n o r i g i n and can o n l y he e x p l a i n e d by i n v e s t i g a t o r s i n other than economics.  disciplines  Thus the t o t a l demand f o r the commodity  may be c o n s i d e r e d  a f u n c t i o n o f a l l p r i c e s and o f t o t a l  d i s p o s a b l e income o f a l l consumers. F u n c t i o n i n g o f the Market Mechanism A study o f demand f u n c t i o n s i n v o l v e s the study o f the r e a c t i o n s o f the consumers t o changes i n p r i c e s and l e v e l s o f incomes.  The o b s e r v a t i o n s  f o r the d e r i v a t i o n  o f demand f u n c t i o n s are a v a i l a b l e i n the form o f time s e r i e s on the consumption, p r i c e s and Incomes and the problem i s one o f d e v i s i n g a s a t i s f a c t o r y s t a t i s t i c a l technique f o r a n a l y s i n g these market I t i s impossible  data.  t o d e r i v e s t a t i s t i c a l l y the  demand from market data without s p e c i f i c a t i o n s o f the supply f u n c t i o n s i n v o l v e d .  The p r i c e and q u a n t i t y  demanded, and the p r i c e and q u a n t i t y o f f e r e d determine between themselves the e q u i l i b r i u m p r i c e and the e q u i librium quantity.  One must a l l o w f o r the economic  f a c t o r s a f f e c t i n g supply and those d e t e r m i n i n g before  demand  one can determine the nature o f e i t h e r the demand  or the supply f u n c t i o n , f o r time s e r i e s o f p r i c e s and q u a n t i t i e s a r e e q u i l i b r i u m p o i n t s produced b y the i n t e r a c t i o n o f demand and supply  forces.  7  Pour types o f dynamic r e l a t i o n s h i p s Pour main types o f dynamic r e l a t i o n s between the demand and the supply curves may e x i s t : supply curve, and s h i f t i n g demand curve.  2)  1) F i x e d F i x e d demand  curve, and s h i f t i n g supply curve.  3)  curve, and s h i f t i n g supply curve.  I f ) F i x e d demand c u r v e ,  and f i x e d supply curve.  S h i f t i n g demand  Thus one must determine i f i t i s  p o s s i b l e t o deduce s t a t i s t i c a l l y the demand curve when o n l y the c o - o r d i n a t e s o f the p o i n t s o f i n t e r s e c t i o n o f the demand and the supply curve a t d i f f e r e n t p o i n t s o f time are known. I f the supply curve i s f i x e d and the demand curve s h i f t s , one gets the supply curve by p l o t t i n g the o r i g i n a l data o f p r i c e and q u a n t i t y .  I f the demand curve  i s f i x e d and supply curve s h i f t s , one o b t a i n s the demand curve by the same method.  I f b o t h the curves s h i f t , an  e n d l e s s v a r i e t y o f p r i c e - t i m e curves and q u a n t i t y - t i m e curves i s p o s s i b l e and i t may not be p o s s i b l e t o deduce any o f the curves from the market d a t a .  Except i n the  v e r y s h o r t r u n , the s h i f t i n g o f the one curve while the other remains f i x e d i s not a p l a u s i b l e assumption because o f the inter-dependence curves.  o f the demand and the supply  N e i t h e r i s the i m p l i c i t assumption t h a t t h e r e i s  no time l a g and t h a t a l l changes i n supply o c c u r s i m u l t aneously w i t h the changes i n p r i c e s which c a l l them f o r t h .  8  For many commodities, subsequent  changes i n supply which occur a t a  p e r i o d are more Important  than those which o c c u r  s i m u l t a n e o u s l y w i t h the p r i c e change.  T h i s i s t r u e because  i n the case of many farm p r o d u c t s the p r o d u c t i o n I n the c u r r e n t y e a r i s not determined p r i m a r i l y by the p r i c e s p r e v a i l i n g i n t h a t y e a r , because p r o d u c t i o n d e c i s i o n s must be made i n seme cases s e v e r a l y e a r s i n advance.  For example,  the v a r i a t i o n s i n l i v e s t o c k p r o d u c t i o n from one y e a r t o another are determined by p r i c e - c o s t r e l a t i o n s h i p s p r e v a i l i n g 2 to 4 years previous. V a r i a b l e s d e t e r m i n i n g supply Thus I n a s t a t i s t i c a l f o r meat one must c o n s i d e r : -  a n a l y s i s o f the s u p p l y  1)  V a r i a b l e s whose v a l u e s  were a c t u a l l y known p r i o r to the b e g i n n i n g o f the c u r r e n t p e r i o d e.g.,  the then p r e v a i l i n g p r i c e s o f v a r i o u s k i n d s  of meats and the p r i c e s of f e e d s , e t c .  2)  V a r i a b l e s whose  v a l u e , though not known i n advance, must c l e a r l y have been determined p r i o r to the c u r r e n t p e r i o d , e.g.,  changes i n  I n v e n t o r i e s and s t o c k s which a f f e c t the q u a n t i t y o f meat put on the consumer market.  3)  Exogenous o r  non-  economic v a r i a b l e s such as weather and d i s e a s e , of measurement. I f by such a procedure  I j . ) Errors  the f a c t o r s  chosen  e x p l a i n 9 5 p e r cent o f the observed v a r i a t i o n i n p r o d u c t i o n , i t may  be concluded t h a t f o r p r a c t i c a l purposes, p r o d u c t i o n  i s determined by those v a r i a b l e s .  9  For  perishable food products, production i s very  n e a r l y e q u a l t o domestic consumption.  I f the p r o d u c t i o n  of a p e r i s h a b l e commodity i s pre-determined, and i f consumption i s e q u a l t o p r o d u c t i o n , consumption  I t s e l f can  be t r e a t e d as a pre-determined v a r i a b l e i n the s h o r t r u n . L a g i n adjustment The l a g I n adjustment  o f s u p p l y t o changes i n  demand s i m p l i f i e s the study o f supply because  i t reduces  the v a r i a t i o n o f the t h e o r e t i c a l demand and s u p p l y c u r v e s . I f the curves are assumed t o r e t a i n t h e i r shapes, i f the s h i f t i s i n some r e g u l a r manner and i f t h e r e e x i s t s a time i n t e r v a l between changes i n demand and changes i n supply, then b o t h these curves can be deduced  statistically.  CHAPTER I I SURVEY OP STATISTICAL, MATERIALS Time S e r i e s on P r i c e s . Income and  Quantities  Market s t a t i s t i c s i n the form o f time s e r i e s are the p r i n c i p a l m a t e r i a l income and  f o r the e s t i m a t i o n  cross e l a s t i c i t i e s .  purchased by the  The  quantities actually  consumer must be used.  f i g u r e s o f consumption were not  of p r i c e ,  Because d i r e c t  a v a i l a b l e , the  quantities  purchased were estimated by a d j u s t i n g the t o t a l p r o d u c t i o n t o a l l o w f o r f o r e i g n t r a d e and  changes i n  inventories.  I f the wastages i n tho m a r k e t i n g channels were c o n s i d e r e d , the a c t u a l i n t a k e would be l e s s than the par appearance f i g u r e s . for  capita d i s -  However, t h e r e i s no way  of  allowing  this. Sources o f the The  sumed and  Series  s e r i e s of n a t i o n a l t o t a l s o f q u a n t i t i e s  a c t u a l p r i c e s o f the f o o d s t u f f s  constitute  market s t a t i s t i c s of, p r i n c i p a l Importance i n the  conthe  study.  P r i c e d a t a are r e l a t i v e l y f r e e from o b s e r v a t i o n a l  errors.  The  National  disposable  Accounts.  The  income f i g u r e s were taken from the par  c a p i t a disposable  f o r the v a r i o u s y e a r s by u s i n g estimates f o r these y e a r s .  10  Income was  the t o t a l  computed  population  For the e v a l u a t i o n  of r e a l  p r i c e s and r e a l incomes the a c t u a l money p r i c e s were adj u s t e d by u s i n g the i m p l i c i t p r i c e d e f l a t o r from the National Accounts. Commodities The commodities  selected  s e l e c t e d f o r the study were  b e e f , pork, eggs, c o f f e e and t e a .  T h i s c h o i c e was  based  on the a v a i l a b i l i t y o f the s e r i e s o f q u a n t i t i e s and p r i c e s from 1926  t o 1952  and on the assumption t h a t the demand  e q u a t i o n f o r these commodities  can be approximated by the  a p p l i c a t i o n o f the s i n g l e - e q u a t i o n approach.  None o f  these commodities, t a k e n i n d i v i d u a l l y , i n f l u e n c e s  sub-  s t a n t i a l l y income o f a l l the s e c t o r s i n the economy. Thus, n a t i o n a l income becomes an exogenous f a c t o r i n the system.  T h i s would not have been so i n the case o f a  commodity such as wheat. commodities  Another r e a s o n i s t h a t these  have a s i n g l e major use and the t o t a l demand  can be e s t i m a t e d from a s i n g l e - e q u a t i o n r e g r e s s i o n .  If  m i l k had been chosen, f o r example, l t would have been n e c e s s a r y t o e s t i m a t e the demand f o r m i l k f o r making b u t t e r , cheese, and other manufactured p r o d u c t s and the demand f o r f r e s h m i l k . multiple-equation  T h i s would i n v o l v e the use o f a  model.  The  problem o f d e t e r m i n i n g weights  For  beef and pork, tha a v a i l a b l e f i g u r e s f o r  q u a n t i t i e s are not c l a s s i f i e d a c c o r d i n g t o c u t s but are t o t a l c a r c a s s weights i n pounds. of  Though the r e t a i l  prices  some o f tha c u t s ware a v a i l a b l e , i t was d i f f i c u l t t o  c a l c u l a t e the average p r i c e because o f v a r i a t i o n s i n the q u a l i t y o f the c u t s from the d i f f e r e n t animals and over a number o f y e a r s .  Moreover, the s e r i e s was  discontinued  i n the case o f p o r k a f t e r 1 9 4 2 and a g a i n i n 1 9 4 6 .  For  t h i s r e a s o n wholesale p r i c e s per pound o f d r e s s e d c a r c a s s ware u s e d . The a v a i l a b l e wholesale p r i c e f i g u r e s ware f o r "Good S t e e r Beef", "Good Cow Beef", and d r e s s e d porkc a r c a s s f o r the f o u r c a t t l e markets l o c a t e d i n Toronto, M o n t r e a l , Winnipeg and Vancouver.  Even i n t h i s case,  average weight p a r animal was needed to compute the average v a l u e .  Tha average weight used would be t h a t o f  c a t t l e s o l d on the v a r i o u s markets.  As there Is an i n t e r -  p r o v i n c i a l movement i t i s p o s s i b l e t h a t t h e r e was double c o u n t i n g . A simple average was  some  computed from the  wholesale p r i c e s a t the f o u r markets.' ' 1  Tha domestic disappearance o f t e a and c o f f e e computed from imports and e x p o r t s o f these two  was  commodities.  The o r i g i n a l s e r i e s o f p r i c e s ware taken from P r i c e s and P r i c e Indexes, Dominion Bureau o f S t a t i s t i c s , Ottawa. 1  T o t a l p o p u l a t i o n e s t i m a t e s were used t o compute p e r  c a p i t a domestic disappearance and per  capita  d i s p o s a b l e income. Time S e r i e s and Both income and can be  Budget S t u d i e s  p r i c e e l a s t i c i t i e s o f demand  c a l c u l a t e d e i t h e r from time s e r i e s o f p r i c e s  q u a n t i t i e s or from budget s t u d i e s . cross-section time and may  Budget s t u d i e s  o f the economic c o n d i t i o n s  and are  a  at a p a r t i c u l a r  p r o v i d e a more r e l i a b l e e s t i m a t e o f income  e l a s t i c i t y than the  regression  technique a p p l i e d  to time  series. The  Time  When the p e r i o d ened, the  Variable  covered by  the  study i s  time v a r i a b l e becomes important.  length-  Over a number  o f y e a r s , the average l e v e l and  d i s t r i b u t i o n of income,  the  composition of the  geographic l o c a t i o n and  the  u l a t i o n , r e l a t i v e s u p p l i e s o f commodities and of l i v i n g a l l change.  the manner  H i s t o r i c r e c o r d s on these f a c t o r s  of changes i n demand are d i f f i c u l t t o o b t a i n and f i c u l t i e s are  encountered i n the  ment o f these v a r i a b l e s .  quantitative  dif-  measure-  Even i f the h i s t o r i c s e r i e s  these v a r i a b l e s were a v a i l a b l e , one  c o u l d not  them a l l because c a l c u l a t i o n s m u l t i p l y i n the number of  pop-  variables.  on  allow f o r  w i t h the  increase  CHAPTER I I I METHOD OF CALCULATION D e r i v a t i o n o f Demand R e l a t i o n s h i p from Time S e r i e s Time s e r i e s data r e p r e s e n t tho i n t e r - a c t i o n o f supply and demand f o r c e s . f o r c e s i s necessary  Consideration of both  t o understand  how  o b s e r v a t i o n s f o r demand f u n c t i o n are The  these  the d a t a or tho generated.  supply f u n c t i o n  In order to d e r i v e the demand r e l a t i o n s h i p , have t o make c e r t a i n assumptions r e g a r d i n g the function.  For many p r o d u c t s  v a r i a b l e i n the s h o r t r u n .  output  is a  supply  predetermined  I f the p r o d u c t s  cannot be  s t o r e d , the time d i s t r i b u t i o n o f marketings by  farmers  i s determined by the t i m i n g of the a c t u a l p r o d u c t i o n supply, t h e r e f o r e , may  we  and  be d i s c o n t i n u o u s as i n the case  hogs f o r which tho heavy r u n occurs i n tho l a t e f a l l  and  e a r l y winter months. The  income  equation  A s i d e from the d i f f i c u l t y of a d i s c o n t i n u o u s supply f u n c t i o n , there i s the Income e q u a t i o n .  14  of  I f the  demand f o r the commodity i n f l u e n c e s the income o f the consumers, i t has t o be I n c l u d e d i n the model. for  However,  the i n d i v i d u a l commodity, the expenditure I s t r i f l i n g  i n I t s i n f l u e n c e on the income o f consumers. able income i s determined  I f dispos-  j o i n t l y w i t h t h e p r i c e o f the  g i v e n commodity, there w i l l be two s t r u c t u r a l e q u a t i o n s , the demand and t h e income e q u a t i o n .  Changes i n d i s p o s -  able income depend upon i n c r e a s e s i n p r o d u c t i v i t y which are i n f l u e n c e d by d e c i s i o n s o f businessmen  (including  farm o p e r a t o r s ) and f e d e r a l , p r o v i n c i a l and l o c a l ments.  govern-  Thus i n the demand a n a l y s i s f o r i n d i v i d u a l farm  p r o d u c t s , the income e q u a t i o n can be ignored."'' The  S i n g l e E q u a t i o n and the M u l t i p l e E q u a t i o n Model A s i n g l e l e a s t - s q u a r e s demand e q u a t i o n g i v e s an  unbiased estimate o f the e l a s t i c i t y o f demand f o r a g i v e n farm product i f the marketable  p r o d u c t , consumer incomes,  and i n seme cases, s u p p l i e s o f the competing p r o d u c t s , are not measurably a f f e c t e d by the p r i c e o f the commodity d u r i n g the marketing  season.  D i s p o s a b l e income o f con-  sumers i s not i n f l u e n c e d t o a s t a t i s t i c a l l y measurable e x t e n t by the changes i n the demand f o r groups o f comm o d i t i e s such as a l l l i v e s t o c k p r o d u c t s .  Fox, K.A., Measurement o f Demand f o r Farm P r o d u c t s , Review o f Economics and S t a t i s t i c s . V o l . XXXVI, pp. 6 1 , fn. 13.  The p r i c e and the supply i n the c u r r e n t y e a r The  supply f o r the e n t i r e y e a r i s determined  mainly  by p r i c e s i n the p e r i o d p r i o r t o the time o f h a r v e s t or m a r k e t i n g and by non-economic f a c t o r s such as weather. Consumption u s u a l l y depends upon the c u r r e n t p r i c e . For many commodities, consumption f o r a marketing  year  i s h i g h l y c o r r e l a t e d w i t h p r o d u c t i o n which i s not  affected  by p r i c e d u r i n g the p e r i o d of marketing.  This i s true  f o r a l l p e r i s h a b l e p r o d u c t s but not f o r those which  may  be s t o r e d . I f the supply t o the consumer of a g i v e n commodity i s a f f e c t e d by c u r r e n t p r i c e , a second s t r u c t u r a l i s p r e s e n t i n the model. approach can be  I f n o t , the s i n g l e  equation  equation  used.  S t o c k s , Imports and  exports  Consumption o f a g i v e n commodity may  b©  signi-  f i c a n t l y a f f e c t e d by c u r r e n t p r i c e or by demand f o r export o r s t o r a g e . more supply c u r v e s .  E x i s t e n c e o f imports suggests one Where s t o c k s , exports and  or  Imports  o f a commodity are b e i n g c o n s i d e r e d a m u l t i p l e e q u a t i o n model i s r e q u i r e d .  I f consumer income i s s i g n i f i c a n t l y  a f f e c t e d by changes i n p r i c e or consumption o f the g i v e n commodity an e q u a t i o n e x p l a i n i n g consumer income as a f u n c t i o n o f c e r t a i n o t h e r v a r i a b l e s would bo r e q u i r e d I n a complete model f o r the  commodity.  I f the supply o f any competing commodity i s not s i g n i f i c a n t l y a f f e c t e d by c u r r e n t p r i c e o f the commodity the s u p p l i e s o f c o m p e t i t i v e items  given  can be  i n c l u d e d as an independent v a r i a b l e i n a l e a s t - s q u a r e s demand equation w i t h the p r i c e o f the g i v e n commodity as a dependent v a r i a b l e .  I f more than one major domestic  o u t l e t i s a v a i l a b l e f o r the g i v e n commodity, equations  separate  are needed to measure demand i n each o u t l e t .  I f v a r i e t i e s grown f o r f r e s h and processed they can be  t r e a t e d as separate  use  commodities.  s t a n t i a l p a r t o f the supply moves i n t o e i t h e r the simultaneous  equation approach must be  differ, I f a suboutlet,  used.  J u s t i f i c a t i o n o f the S i n g l e - E q u a t i o n Approach F r e s h products  and  stocks  Gn the average 5 m i l l i o n pounds o f boef, v e a l , lamb, and pork are consumed d a i l y i n Canada* " almost a l l 1  i n the form o f f r e s h meat.  Thus the whole amount o f meat  d o m e s t i c a l l y consumed has to bo put on the market w i t h i n 10  to 15  days.  Peak storage stocks o f b e e f are 2 . 5  P©r  cent of the t o t a l amount o f b e e f s l a u g h t e r e d i n a y e a r . I n the case o f pork the h i g h l y seasonal nature o f  hog  marketings l e a d s t o peak f r o z e n - s t o r a g e s t o c k s o f  4.2  per cont o f a y e a r ' s p r o d u c t i o n .  2  Thus the market f o r  S w i f t Company, A g r i c u l t u r a l Research Department, L i v e s t o c k P r i c e s and What Causes Them t o Change, May 1 9 5 5 , pp. 6 . 1  2  Ibid.  f r e s h pork absorbs  n e a r l y a l l o f the p o r k p r o d u c t i o n .  A l m o s t t h e whole o f t h e e g g p r o d u c t i o n i s a l s o a t home.  Canada h a s b e e n b o t h  o f eggs.  Except  large relative table.  an importer  f o r t h e war y e a r s  Average  Average  19??~ W  19^3-47  212,523  Imports  291  7,223  Exports  be  have n o t b e e n  1  Production  and c o f f e e a r ewholly  source  and e x p o r t e r  t o p r o d u c t i o n a s i s shown b y t h e f o l l o w i n g  '000  Tea  exports  consumed  o f supply  1952  Dozens  366,llf3  329,519  341,512  10!+  If ,6 7lf  1,550  73,086  7,103  13,1*20  imported,  and s i n g l e  1951  and there i s a s i n g l e  outlet.  Stocks  a r e assumed t o  unimportant.  B u i l d i n g a Model  The m o d e l f o r a n a g r i c u l t u r a l s i n g l e major use i s b u i l t  commodity h a v i n g a  a s f o l l o w s : t h e volume o f  p r o d u c t i o n i s i n f l u e n c e d b y weather and economic prior income  factors  t o h a r v e s t ; p r o d u c t i o n along w i t h the d i s p o s a b l e determines  the r e t a i l p r i c e .  Farm p r i c e  i s also  C u r r e n t Review o f A g r i c u l t u r a l C o n d i t i o n s i n Canada, Canada, D e p t . o f A g r i c u l t u r e , O t t a w a , Nov. 1953, P» 6. 1  is it  2 Consumer's d e s i r e t o s p e n d t h i s d i s p o s a b l e income a l s o i m p o r t a n t b u t l t i s h a r d t o measure i t . Here i s assumed t h a t t h e r e i s no h o a r d i n g .  a f f e c t e d by the e x t e n t o f c o m p e t i t i o n i n the market. S i m i l a r l y a model can be c o n s t r u c t e d when there are two independent markets f o r a commodity: one f o r the f r e s h p r o d u c t and the o t h e r f o r the p r o c e s s e d p r o d u c t , the o n l y d i f f e r e n c e b e i n g t h a t there are two o u t l e t s .  Econ-  omic i n f l u e n c e s p r i o r to marketing and non-economic i n f l u e n c e s such as weather determine product.  the output of the  T h i s product i s p r o c e s s e d and i s a l s o  sold  f r e s h , and o f the t o t a l p r o d u c t i o n , the p r o p o r t i o n g o i n g i n t o each o f these uses, a l o n g w i t h the d i s p o s a b l e income, h e l p to determine  the r e t a i l p r i c e s i n the two u s e s . Farm  p r i c e s then depend upon the r e t a i l p r i c e and the marketing  margin. There  system.  can be many s t r u c t u r a l equations i n the  I n order t h a t s t a t i s t i c a l d e r i v a t i o n may  be  pos-  s i b l e , the number of v a r i a b l e s and r e l a t i o n s h i p s must be l i m i t e d t o the v e r y important ones. the number o f v a r i a b l e s may difficulty  The l i m i t a t i o n o f  be necessary due t o the  o f f i n d i n g r e l i a b l e d a t a or t o the n e c e s s i t y  of keeping the c a l c u l a t i o n s w i t h i n manageable l i m i t s but by the method o f m u l t i p l e c o r r e l a t i o n , more than two v a r i a b l e s may  be  considered simultaneously. The Method Used  In t h i s study, a l i n e a r p a r t i a l r e g r e s s i o n has been f i t t e d t o the p e r c a p i t a disappearance o f s e v e r a l  commodities u s i n g  price  d e f l a t e d by appropriate variables.  o f the s u b s t i t u t e price  The r e g r e s s i o n  deflators  and income,  as independent  o f the dependent  variable  (amount consumed) o n income was c a l c u l a t e d b y k e e p i n g t h e values o f the independent v a r i a b l e s their respective estimating  means.  the  The r e s i d u a l s  e q u a t i o n were a d d e d t o t h i s  f i g u r e s were p l o t t e d Lines  o t h e r t h a n income a t  were f i t t e d  elasticity  against  full  regression.  These  income t a k e n on t h e X - a x i s .  t o tho s c a t t e r diagram and from  was  this  c a l c u l a t e d by tho f o r m u l a : 1  Income e l a s t i c i t y When t h e p o i n t s  from the  = b x ^  .  i n t h e s c a t t e r d i a g r a m wore  m a i n l y i n two p l a c e s ,  separate multiple  congregated  regression  e q u a t i o n s were f i t t e d t o e a c h o f t h e c o n g r e g a t i o n s i n order  to avoid  the e r r o r  e q u a t i o n s i n one  1  D e r i v e d as  o f combining  iso-regrossion  equation.  follows:  Elasticity  dX  T  dY  /  dY whore Y = Income, X =  Consumption  T  X  X  CHAPTER IV RESULTS Beef  The  period  goes b a c k a s quantities  f a r as  o f the  t h i s a n a l y s i s , 1926  c o v e r e d by the  s e r i e s on  the p r i c e s and  (X4) the  of beef  (X )»  were q u i t e  2  and  the per  important  consumption o f b e e f .  The  explain a significant part  of  the  three  Furthermore,  the  X4 e x p l a i n e d  variables  4 1 . 6 4 3 and  together  The  1935,  1943,  1948  total  of 930.0476.  removed and  1944,  was  explained  total variation.  total  not  did  regression  (X^)  2  240.1674  co-  o  u  signi-  by  the  t o f which  178.66529 r e s p e c t i v e l y .  only  Thus the  26 'per  showed t h a t  contributed  cent  total  of  21  The  the  the years  734*^92 out  explained  X  three  1934,  of  E v e n when t h e s e e x t r e m e y e a r s  20 y e a r s ,  with  not  statistically  +0.513.  In  variation in  a multiple regression equation  r e s t o f the  changes  v a r i a t i o n explained  i n d e p e n d e n t v a r i a b l e s was  correlation co-efficient  the  increased,  consumption of b e e f because the  ficant.  the  the  income  s u b s t i t u t i o n of beef  e f f i c i e n t b ^ ^ g l j . ~ + 0 . 1 8 0 5 was  and  capita disposable  (X3)  The  that period  i n determining  p o r k , when t h e p r i c e o f p o r k  the  the  f o o d s t u f f s consumed were a v a i l a b l e .  r e s u l t s o f t h i s a n a l y s i s show t h a t d u r i n g price  1952,  to  fitted  the were to  variation  2  (43«543)  was  (172.579). tho  regression.  The  period  35,  43*  sion co-efficient  tho  44,  tho  elasticities was  wore v e r y  -0.0,  period  1929-1933 was  ticity  of  give  and the  low.  f r o m +0.811+8  i n 1939-1+4,  1945-52. out,  When and  For  1939-44,  an  w i t h an  exception  the  regression  i t was  as  low  groups meats, p o u l t r y  1  Income e l a s t i c i t y  l e s s at  the  retail  and  tho regres-  equation of  demand,  income  -0.0063 b u t income  the  elas-  i n c l u d i n g eggs  of expenditure  level).  W a i t e and  foods Trelogan  following results B e e f Chuck r o a s t  -0.037  Beef Roast, b o i l i n g  -0.211  Boef Salt side  -0.185  Beef S i r l o i n  2  o f demand f o r  f o r 1946-52,  B o e f Round s t e a k  New  affect  income e l a s t i c i t y  B e e f Ground  1  not  variation  +0.3489.  Schultz  (0.25  period  0.118  f r o m the m u l t i p l e  used f o r c a l c u l a t i o n of  fish  total  years,  4°* were l e f t  was  elasticity  o f 27  to +1.1781 -  0.020 during  y e a r s 1934,  and  o f the  Income e l a s t i c i t y  over the  0 . 0 8 2 i n 1929-33,  -0.1991 -  cent  Thus t h e s e e x t r e m e y e a r s do  beef varied -  25.23 p e r  only  0.00 0.206 1.32  S c h u l t z , T.W., Economic O r g a n i s a t i o n Y o r k , M c G r a w - H i l l , 1953, p. 71. I b i d . . pp.  74.  of  Agriculture.  2  From t h e s e d i f f e r e n t c u t s what t h e a v e r a g e  o f meat i t i s h a r d t o s a y  income e l a s t i c i t y  whole c a r c a s s w o u l d  o f demand f o r t h e  be. Pork  The r e g r e s s i o n lines fitted the  co-efficients calculated  t o the s c a t t e r diagrams  demand f o r p o r k were a s  b  b  12.34 "  "  13.24 *  +  2  « 5 2  i n the a n a l y s i s  °*622 X  2  = Price  of  ~ 0 . 5 2 2 X3 = P r i c e  c o r r e l a t i o n c o e f f i c i e n t , +0.4343,  three variables  namely, p r i c e  and p e r c a p i t a d i s p o s a b l e per  Pork  of Beef Income  i s quite  low.  iation, price  income e x p l a i n e d  per  Even out o f the t o t a l  the p r i c e o f pork e x p l a i n e d  o f b e e f and d i s p o s a b l e  cent r e s p e c t i v e l y .  The  18.87  only  and T r e l o g a n Pork Bacon  1  Ibid.. p.  i s + 0.053  gave  sausage  0.151  sliced  0.137  sliced  0.607  7 and  varthe 14  o f demand  to +0.090.  the f o l l o w i n g  0.522  24.  79 p e r c e n t a n d  income e l a s t i c i t y  chops  Pork Ham  1  con-  explained  income e x p l a i n e d  f o r pork a t the wholesale l e v e l Waite  The  of pork, p r i c e o f beef,  cent o f the t o t a l v a r i a t i o n i n the p e r c a p i t a  sumption o f pork.  of  follows:  ^11+.23 * + 0 . 0 7 5 * 0 . 0 6 5 X^ • D i s p o s a b l e The  from the  results:  Eggs  In t h i s analysis of the demand f o r eggs, the two variables taken wore changes i n the p r i c e o f eggs at the r e t a i l l e v e l and changes i n tho per capita disposable income i n the current year from the previous year. The regression c o - e f f i c i e n t s , with t h e i r standard errors o f estimates were:b  12.3 (  b  13.2  p r l c e  >  +0.0369603 - 0.092318  =  (Incom®)" +0.0283201 - O.OIO72I+9 11  Tho above errors show that the p r i c e regression c o - e f f i c i e n t was not s i g n i f i c a n t . Tho analysis of variance also showed that the price of eggs d i d not explain a s t a t i s t i c a l l y s i g n i f i c a n t part of tho t o t a l v a r i a t i o n .  The income var-  i a b l e , however, was highly s i g n i f i c a n t . Tho income e l a s t i c i t y of demand f o r eggs varied from +O.I4.O3 * 0.153 during 1929-33 to +0.503 - 0.191 i n 1939-1+1+ and +0.657 -  0.21+9 i n 191+5-52.  Tho e l a s t i c i t y of physical consumption with respect to the income of U.S. non-relief non-farm f a m i l i e s , March-November,  1936 was found to bo 0.1625 and 0.1457  for family Income ranges of #1233-$1707 and $17P7-#2396 respectively.  1  1  Ibid., p. 71  C o f f e e and Tea Four were t h e p r i c e (X3), p r i c e  variables  taken i n the a n a l y s i s  o f coffee ( X ) , per capita disposable 2  o f t e a (Xj^) a n d t i m e  co-efficients the  independent  with their  (Xcj).  standard  income  The r e g r e s s i o n  errors o f estimates i n  c a s e o f c o f f e e were:b  2  = -0.015988 ± 0.045954  b  3  = +0.011298 -  0.002272  b^ » -0.074936 *  0.055197  b ^ - +0.076626 - 0.038753 The  co-efficient  o f d e t e r m i n a t i o n was f o u n d  Thus t h e c o - e f f i c i e n t income e l a s t i c i t y years  1929-33,  1.082 -  t o be  o f c o r r e l a t i o n was 0 . 8 9 7 .  o f demand f o r c o f f e e v a r i e d  1939-44,  1945-52 from +1.120 -  0 . 2 1 8 and + 1 . 0 6 8 -  0.8042. The  over the 0.225 to  0.215. p  S z a r f and P l g n a l o s a  found  t h e income  elasticity  o f demand f o r c o f f e e t o b e 0 . 5 4 1 t o 0 . 5 6 4 when p r i c e from  60 c e n t s t o 110 The  cents p e r kilogram.  four regression co-efficients b  2  * +0.0515574 -  0.02149  b  3  • -0.0069244 -  0.00174  b\± •  varied  +0.132982  -  0.03062  b ^ « +0.045514  -  0.01648  f o r t e a were:-  S z a r f , A., and P l g n a l o s a , F . , F a c t o r s a f f e c t i n g U.S. c o f f e e consumption, Monthly B u l l e t i n o f A g r i c u l t u r a l E c o n o m i c s a n d S t a t i s t i c s . F.A.Q.. O c t o b e r 1954, P. 6 . x  The c o - e f f i c i e n t of determination  was 0 . 2 7 .  Income elas-  t i c i t y of demand f o r tea calculated from the regression c o - e f f i c i e n t was -O.53O to - 0 . 1 3 3  i n 1 9 2 9 - 3 3 and  -0.976  - 0 . 2 4 5 and - 1 . 4 3 8 * 0 . 3 6 2 i n the periods 1939-44 and 1945-52.  Regression  l i n e s were f i t t e d to the two  periods  from 1926-41 and 1 9 4 2 - 5 2 separately i n the case of tea. 1.  2.  1926-41 +0.0076 -  0.01593  (Price of tea)  =  (Income)  « -0.0171  -  0.00397  (Price of coffee* + 0 . 2 2 2 7  -  0.04647  1942-52 =  -0.01787  -  0.04843  «  -0.00007 -  0.01054  =  +0.00102 -  0.02286  Thus i n the f i r s t period, 1926-41, p r i c e of tea c o - e f f i c i e n t i s not s i g n i f i c a n t and i n second period none of the regression c o - e f f i c i e n t s were s i g n i f i c a n t .  This meant that the  income e l a s t i c i t y of demand f o r tea was  negative i n the  period 1926-41 and 0 . 0 0 i n the period 1 9 4 2 - 5 2 .  This r e s u l t  i s confirmed by tho graphic analysis which does not show any r e l a t i o n s h i p between income and the consumption of tea and coffee.  However, X£ and X^ showed a trend i n the  graphic analysis.  To v e r i f y t h i s change i n the consumption  of tea and coffee with a change i n t h e i r p r i c e s , r a t i o s of p r i c e s and consumption were computed.  A straight l i n e  27  regression  fitted X  y  was  as  _  to the  ratios  Per c a p i t a consumption o f t e a  1  Per c a p i t a consumption of  _ 2 ~  P r i c e o f c o f f e e p e r pound P r i c e o f t e a p e r pound  follows:  x  1  = o.104405 + 1.0865122  Even here the second p e r i o d first period  coffee  period,  x  (1949-52)  2  stood  out.  m  there i s s u b s t i t u t i o n but i n the second  the l i n e  was  horizontal.  the  A P P E N D I X  A  28  TABLE I PERSONAL, DISPOSABLE INCOME IN CANADA 1926-1953 Implicit Year Total Disposable Price Deflator2 Income 1 (*000.0Q0#)  Total dePopulation3 Per Capita f l a t e d Inc. («000) Disposable disposable Income (»0Q0.0Q0$) (Constant j 193539 » 1 0 0 B  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953  4,039 4,246 4,559 4,589 4,292 3,629 3,ooi 2,774 3,089 3,293 3,482 3,930 3,975 4,208 4,808 5,600 6,980 7,478 8,164 8,430 8,965 9,599 11,121 11,968 12,682 14,663 15,809 16,664  Sourees:-  120.7 118.1 118.3 119.2 118.2 107.7 98.6 94.5 95.8 96.1 97.7 100.8 102.6 102.2 106.6 116.0 119.3 122.4 123.0 12k.5 128.9 141.6 158.8 165.8 171.3 190.2 194.5 194.2  3,346 3,595 3,854 3,850 3,631 3,370 3,044 2,935 3,224 3,427 3,564 3,899 3,874 4,117 4,510 4,912 5,851 6,109 6,637 6,771 6,955 6,779 7,003 7,218 7,399 7,709 8,128 8,581  9,451 9,637 9,835 10,029 10,208 10,376 10,510 10,633 10,741 10,845 10,950 11,045 11,152 11,267 11,381 11,507 11,654 11,795 11,946 12,072 12,292 12,551 12,823 13,447 13,712 14,009 14,430 14,781  a  S  Q  354 373 392  $  325 290 276 300 316 325 353 347 365 396 427 502 518 556 561 566 540 546 537 540 550 563 581  1) National Accounts, Dominion Bureau of S t a t i s t i c s . 2) National Accounts, Dominion Bureau of S t a t i s t i c s . 3) Population Memorandum, D.B.S., Cen. S.A.S. 1 3 .  TABLE I I CONSUMPTION OP B E E P AND PORK,  CANADA, Beaf Yaar  Total Consumption  »000 l b s .  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 Source:  657,823 653,188 6k9,121 667,461 671,426 600,988 588,510 599,146 743,914 607,381 631,042 629,583 661,814 633,331 670,343 719,612 741,748 855,818 786,212 917,316 925,354 900,084 766,937 800,929 735,522 669,939 679,695 Livestock  1926-52 Pork  Per Capita  lbs. 69.60 67.77 66.00 16.55 65.77 57.92 55.90 56.35 69.26 56.01 57.63 57.00 59.34 56.21 58.90 62.54 63.65 72.56 65.18 75.99 75.28 71.71 59.81 59.56 53.64 47.82 47.10  Total Consumption  ?000 l b s .  706,392 775,130 796,595 798,639 744,328 862,981 899,394 796,541 718,998 428,968 444,109 465,167 460,533 493,439 518,772 568,575 667,713 779,409 822,994 665,355 687,787 707,922 738,618 838,187 888,544 988,988 1,069,783  and A n i m a l P r o d u c t s  Per Capita  lbs. 74*74 80.43 80.99 79.63 72.92 83.17 85.58 74.91 66.94 39.55 40.56 42.11 41.30 43.80 45.58 49.41 57.29 66.08 68.89 55.12 55.95 56.40 57.60 62.33 64.80 70.60 74.14  Statistics  30  TABLE I I I CONSUMPTION AND PRICE OP EGGS IN CANADA Year  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938: 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  Total Disappearance (Dozens)  264,783,655 282,405,692 295,484,271 302,470,239 307,147,408 311,396,473 251,933,710 242,00k,5l9 239,686,928 2%,576,368 238,269,532 238,941,743 233,471,546 240,%4,596 245,560,935 234,006,649 256,788,735 279,754,361 291,681,000 283,226,000 285,410,000 302,518,000 301,552,000 294,299,000 309,842,000 315,833,000 329,015,000  ±  Per Capita Price Eggs Constant Consumption 'A* Large & Med. Price (Dozens) {<i per dog.) (t^ per doz.) Base 1 9 3 5 39 = 1 0 0 28.02 29.30 30.04 30.16 30.09 30.01 23.97 22.76 22.32 22.55 21.76 21.63 20.94 21.38 21.58 20.34 22.03 23.72 24.42 23.46 23.22 24.10 23.52 21.89 22.60 22.55 22.80  46.8 48.7 47.8 47.5 45.7 33.7 29.4 28.1 31.9 31.2 33.8 33.3 34.5 33.5 33.7 36.9 43.6 49.0 45.7 47.9 49.6 5i.i 60.6 62.5 57.1 73.2 60.8  38.77 41.24 40.41 39.84 38.66 31.29 29.82 29.74 33.30 32.k7 34.60 33.04 33.63 32.78 31.61 31.81 36.55 40.03 37.15 38.47 38.48 36.09 38.16 37.70 33.33 38.49 31.26  Sources: 1) Production o f Poultry and Eggs, Dominion Bureau of S t a t i s t i c s , Ag. Div., Quarterly B u l l e t i n of A g r i c u l t u r a l S t a t i s t i c s , D.B.S. 2) Prices and Price Indexes, Dominion Bureau o f Statistics.  TABLE IV DOMESTIC DISAPPEARANCE OP COFFEE IN CANADA Year  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  Imports (lbs.)  2k,837,0l8 26,621,548 28,242,490 28,598,510 31,281,375 33,035,538 31,263,271 34,141,820 34,736,108 35,074,793 40,471,266 38,268,430 43,019,706 47,174,985 42,278,928 56,330,489 46,291,152 60,754,828 96,815,535 55,407,726 85,756,712 52,449,658 88,102,958 98,646,509 83,772,329 89,516,726 99,395,384  Exports (lbs.)  41,029 58,184 46,749 83,516 66,162 44,152 42,961 51,278 57,787 175,231 246,709 358,897 319,177 533,053 478,284 913,702 404,531 273,715 225,679  114,638 132,416  264,70k 423,388 147,654 92,103 106,198 147,512  Total Domestic Disappearance (lbs.)  24,795,989  26,557,296 28,159,741 28,514,994 31,215,213 32,991,386 31,220,310 34,090,542 34,678,321 34,899,562 40,224,557 37,909,583 42,700,529 46,641,932 41,800,644 55,416,787 45,886,621 60,481,113 96,589,856 55,293,088 85,624,296 52,184,954 87,679,570 98,k98,855 83,681,226 89,410,528 99,247,872  Source: Trade of Canada V o l . I l l - Imports Vol. I I - Exports  Per Capita (lbs.) 2.62 2.75 2.92 2.6% 3.06 3.18 2.97 3.21 3.20 3.22 3.67 3.43 3.83 4.14 3.67 4.82 3.94 5.13 8.09 4.58 6.97  H 6.84 6  7.32 6.10 6.38 6.88  TABLE V DOMESTIC DISAPPEARANCE OP TEA IN CANADA Year  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  Source:  Imports (lbs.)  37,629,652 38,116,897 39,526,653 38,676,724 50,885,670 33,115,482 40,417,747 39,414,116 38,538,795 35,176,462 39,739,189 40,122,186 37,591,064 43,393,607 42,682,730 38,633,446 31,166,990 38,581,584 41,470,437 53,454,367 29,851,837 47,390,998 36,206,451 43,193,575 55,198,271 45,456,287 45,908,126  Exports (lbs.)  616,920 635,550 720,551 678,404 483,190 456,076 424,682 435,796 499,498 494,976  415,170  645,684 591,674 929,297 599,953 591,730 2,281,771 2,257,630 2,835,982 2,635,055 1,468,504 972,550 322,415 368,792 418,333  Total Per Domestic Capita Disappearance ( l b s . ) (lbs.) 37,012,732 37,481,347 39,526,653 38,676,724 50,165,119 32,437,078 39,934,557 38,958,040 38,114,113 34,740,666 39,239,691 39,627,210 37,175,894 42,747,923 42,091,056 37,704,149 30,567,037 37,989,854 39,188,666 51,196,737 27,015,855 44,755,943 34,737,947 42,221,025 54,875,856 45,087,495 45,489,793  Trade o f Canada V o l . I l l - Imports Vol. I I - Exports  3.92 3.88 4.02 3.86 4.91 3.13 3.80 3.66 3.55 3.20 3.58 3.59 3-33 3.79 3.70 3.28 2.62 3.22 3.28 4.24 2.20 3.57 2.71 3.14 4-00 3.22 3.15  TABLE V I  P R I C E OP TEA AMD 1  Year  Actual Tea  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  GOPPEE I N CANADA  71.7 71.6 71.3 7O.4 62.8 55.2 47.2 42.4 50.4 52.1 52.0 53.7 58.4 59.3 66.7 84.7 77.3 77.4 77.4 77.4 91.6  IO2.4  103.6 105.4 107.5 108.9  i  Price Coffee p o u nd per  61.2 61.2 60.7 60.4 57.2 49.2 42.8 40.0 39.2 37.4 35.8 35.5 34.8 35.9 44.8 46.8 46.8 44.2 i»4.3  44.4  44.7 51.1 61.4 65.7 96.7 105.1 106.0  S o u r c e : P r i c e s and P r i c e Indexes, Labour Gazette 1949-52.  Deflated Price Tea Coffee <l p e r p o u n d  59.40 60.63 60.27 59.06 53.13 51.25 47.87 44.86 52.61 54.21 53.22 53.27 56.92 58.02 62.57 63.97 71.00 63.15 62.93 62.17 60.05 64.69 64.48 62.48 61.53 56.51 55.98  D.B.S. 1 9 2 6 - 4 8 .  50.70 51.82 51.31 50.67 48.39 45.68 43.40 42.32 40.92 38.91 36.64 35.22 33.92 35.13 42.03 40.34 40.15 36.11 36.02 35.66 34.68 36.09 38.66 19.63 56.45 54.49  A P P E N D I X  B  APPENDIX B  CALCULATION OP INCOME-ELASTICITY  OP  DEMAND FOR B E E F  Year  Consumption Per Capita Lbs.  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 Total Av.  69.60 67.77 66.00 66.55 65.77 57.92 55.90 56.35 69.26 56.01 57.63 57.00 59.34 56.21 58.90 62.54 63.65 72.56 65.18 75.99 75.28 71.71 59.81 59.56 53.64 47.82 47.10 1675.050 62.039  Real Beef  Price  Cents p e r lb.  Real Pork  Price (Base  1935-39=100) Cents p e r lb.  Real Income  Dollars  9.747 11.498 14.551 14.562 12.870 9.622 9.242 7.870 8.064 9.222 8.534 10.913 9.698 10.763 11.187 12.069 12.888 14.808 15.183 15.080 14.769 14.107 19.033 19.911 24.008 27.668 21.497  17.433 34.'886 14.258 16.653 15.998 11.165 7.733 9.402 13.165 13.814 13.357 13.418 14.693 13.625 12.500 13.638 15.004 14.984 15.020 14.960 15.729 16.402 21.316 21.366 19.177 20.492 15.758  354 373 392 38k 356 325 290 276 300 316 326 353 347 365 396 427 502 518 556 561 566 540 546 537 540 550 583  369.364  403.946  n,559  13.68015  14.961  428.111  Year  Consumption Price Beef tl-to t l - to  Price Pork tl-to X  1927 1928  1929  1930 1931 1932  1933 1934 1935 1936  1937  1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  - 1.83 - 1.77 + 0.55 + 0.22 - 7.85 - 2.02 + 0.45 +12.91 -13.25 + 1.62 - 0.63 + 2.34 - 3.13 + 2.69 + 3.64 + 1.11 + 8.91 - 7.38 +10.81 - 0.71 - 3.57 -11.90 - 0.25 - 5.92 - 5.82  -  0.72  -21.50  + 1.751 + 3.053 + 0.011  -  1.692 3.248 O.38O  1.372  + 0.194 + 1.158  + -  0.688  2.379  Real Income t l - •to  3  x  + 19 + 19  -  + 16 + 10 + 27  mm  -  + 1.669 + 3.763 + 0.649 0.457  + 0.061 + 1.275  Mi  -  8 28 31 35 14 ^  -  0.103 0.311 0.662 4 + .926 + 0.878 + 4.097 3.660 6.171  -  .0.060 0.769 0.673 4.914 0.050 2.189 + 1.315 4.734  -  6 + 18 31 ^31 + 75 + 16 + 38 + 5 + 5 26 + 6 9 + 3 + 10 + 13  +11.750  - 1.705  +209  1.215 1.065 O.424 O.882 0.819  + + + + + 1.920 + 0.375  -  -  -  1.068 1.125  + 1.138 + 1.336 mm*  0.020  + O.O36 + + + +  2  X  2 3 X  4  2.547 0.628 + 2.395 0.655 4.833 3.432  _  x,x  -  + 4.66101 + 1.11156  -  - 3.20433 - 5.40381 + 0.00605 - 0.37224 +25.49680 + 0.76760 - 0.61740 + 2.50454 -15.34350 - 1.11456 - I.49877 - 2.84310 - 3.33345 + I.14056 + 3.21048 + 0.90909 +17.10720 - 2.77150 - 1.11343 + 0.22081 + 2.36334 -58.61940 - 0.21950 -24.25424 -21.30120 + 4.44312  1.31725 0.14410 +37.93905 + 6.93264 + 0.75105 +48.58033 8.59925 0.74034 0.03843 + 2.98350 + 3.34284 - 3.02625 + 4.14232 + 1.38296 0.17820 0.26568 - 0.64860 0.54599 2.40261 -58.47660 0.01250 +12.95888 7.65330 + 3.40848  +15.607584 + 1.304160 -2.289868 0.730022 0.751542 + 0.314416 + 0.145119 1.549125 1.137420 0.487000 + 1.003716 + 1.094184 0.038400 0.013500 + 0.006180 0.239159 - 0.445526 +24.206364 + 0.043900 8.968333 4.812900 29.213514  -83.84084  +46.78002  + 8.494266  -  -  -  mm  mm  -  4.459797 1.917284 + 0.026245  + 1.108260  -  Year  X_ X. 2 k  1927  33.269 58.007 -0.088 47.376 100.688 13.300 19.208 k.656 18.528  1928  1929  1930 1931 1932  1933 193k 1935  1936 1937  1938 1939  19k0 19kl 19k2 1943  19kk  1945 1946 1947 1948 1949 1950 1951 1952  X  3 k X  ^"k • 34.77 • 33.63  64.233 7.280 19.170 13.1kk 27.342 61.425 30.720 14.250 -0.515 -1.555 17.212 29.556 -7.902 12.291 36.600 -80.223  -48.393 -11.932 -19.160 18.340 149.823 120.120 -23.366 90.312 10.384 - 4.570 1.647 - 7.650 -19.224 -34.885 35.278 100.202 - 0.320 1.368 - 0.300 3.845 -17.498 29.484 O.450 - 6.567 13.150 -61.542  +531.092  +318.996  +375.89  -6.880  •  k.40  • 6.16 243.35 70.70 • 6.30 309.84 •212.00 16.20 • 17.01 • 14.04 • 56.34 83.39 112.84 83.25 132.56 •280.44 54.05 • 3.55 92.82 • 71.40 2.25 • 17.76 • 58.20 • 9.36  (X )2  (x )  361 361 64 784 961 1,225 196 576 256 100  3.3489 3.1329 0.3025 0.0484 61.6225 4.0804 0.2025 166.6681 175.5625 2.6244 0.3969 5.4756 9.7969 7.2361 13.2496 1.2321 79.3881  k  729  36 324 961 961 5,625 256  2  16,341  3  3.066001  0.5041 12.7449 141.6100 0.0625 35.0464 33.8724 0.5184  0.096721 0.438244 24.265476 0.770884 16.785409 13.395600 38.081241  6.487209 0.394384 4.736025 0.429025 23.357889 11.778624 2.785561 14.160169 0.421201 0 . 2 0 8849 0.003721 1.625625 I.140624 1.265625 1.295044 1.784896 0.000400 0.001296 0.003600 0.591361 0.452929 24.147396 0.002500 4.791721 1.729225 22.410756  930.0476  137.247788  126.005655  1,444  25 25, 676 36 81 9 100 169  (X )2  x  9.320809 0.000121 2.862864 10.549504 O.14440O 1.882384 O.O37636 1.340964 0.k7334k 5.659641 1.476225 1.134225 . 0.179776 0.777924 0.670764  3.686kOO O.140625  0.010609  VJJ  DOOLITOE SOLUTION L. I n e  Reciprocal  a. 1.234 +26.00  I  b  12.34  +11.75 +137.247788  .11 III  l3.24  V.23  -1.705  +209.00  b  +26.00 - 1.00  +21.50  +8.494266  +531.092  +83.84084  +126.005655  +318.996  -46.78002  +16,341.00  -375.89  IV 1 2  Check  -1.705 +0.065576923 +8.494266  +209.00 -5.0384615 +531.092  +21.50 +266.545 -0.82692307 - 1 0 . 2 5 1 7 3 0 7  3  #11.75 -0.45192307 +137.247788  +83.84084  +760.674894  4  -5.3100961  +0.77052884  -94.451923  -9.7163461  -108.70783636  5 6  +131.9376919 +9.26479484 -1.00 -0.070143725  +436.640077  +74.1244939  +651.9670576  -0.038461538  -0.007570933  +3.3094416  -0.561196589  -4.94147697  7 8  +126.005655  +318.996  -46.78002  +398.221635  -0.649866987  -30.6275614  -5.199367  -36.476795387  9  -0.111808654  +13.70557692  +1.40990378  +15.00367205  10  +125.2439794 -1.00  +302.0740153 -2.411884521  -50.56948322 +376.7485116 +0.399925722  -3.00811673  12  +16,341.00  -375.89  +15,965.11  13  -728.567598  +121.9677522  15 16 17  -1,445.03458 -1,680.03845 +12.487.3594 -1.00  -245.3105654 -1,690.34514 -172.826922 -1,852.865375 -672.0597352 +11,815.2996 +0.053819203 -0.94618079  11  -0.OO79O84415  -  -0.000080081  -606.59988  BACK SOLUTION  *1.234  b  +0.342673068 +0.017713638 -0.432623569 - 0 . 826923077 -0.899159940  12.34  b  -0.0189472230 -O.178III4993 -0.5611965895 . -O.7582553II8  13.2k  b  -0.129805694 +0.399925722  l4»23 +0.0538192  ' +0.270120028  ESTIMATING- EQUATION; X-L =  -0.89915994 -0.758255 X  x  =  -0.48425  -0.758255  x  =  -0.8092093  +0.270120  X  =  -1.2595465  +0.0538192  X  R  x  X  2 1.234  =  b  2  X  l  x  2  +  b  =  3  x  5 (xf)  +0.270120 X  2  X  K  2  3  x x  +0.0538192  3  k  x  +  b  k  x  x  x  k  ~—*  = 56.205268 +12.255344 +29.531456 912.268756 = 0.1074158  VjJ CD  Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  b  12.34  X  2  -1.32770451 -2.31495252 -0.00834081 +1.28296746 +2.46281224 +0.28813690 +1.04032586 -0.14710147 -0.87805929 +0.52167944 -I.80388865 +0.92127983 -0.80754157 -0.32150012 -0.66878091 -0.62101084 -1.45585960 -0.28434562 +0.07810026 +0.23581730 +0.50196481 -3.73516413 -0.66574789 -3.10657073 -2.77521330 +4.67919160  b  13.2k  X  3  -0.68799564 -0.16963536 +0.64693740 -0.17692860 -1.30548996 -0.92705184 +0.45083028 +1.01646156 +0.17530788 -0.12344484 +0.01647732 +0.34440300 -O.28848816 -O.30388500 +0.30739656 +0.36088032 -0.00540240 +0.00972432 -0.01620720 +0.20772228 +0.18179076 +1.32736968 +0.01350600 -0.59129268 +0.35520780 -1.27874808  b  l4.23  X  4  +1.0225648 +1.0225648 -0.4305536 -1.5069376 -1.6683952 -I.883672O -0.7534688 +1.2916608 +0.8611072 +0.5381920 +1.4531184 -0.3229152 +0.9687456 +1.6683952 +1.6683952 +4.0364400 +0.8611072 +2.0451296 +0.2690960 +0.2690960 -1.3992992 +0.3229152 -0.4843728 +0.1614576 +0.5381920 +0.6996496  -1.89229529 -2.36II8302 -0.69111695 -1.30005868 -1.41023286 -3.42174688 -O.I614726O +1.26186095  -0.74080415 +0.03726666 -1.23345287 +0.04360769 -I.02644407 +O.14385014 +0.40785091 +2.87714954 -I.49930474 +O.87134836 -0.56817088 -O.I865243O  -1.61470357 -2.98403919 -2.03577463 -4-43556575 -2.78097344 +3.20093318  0.0036 0.3481 1.5376 2.3104 41.4736 1.9600 0.3721 135.7225 156.5001 2.4964 O.36OO 5.2900 4.4100 6.5025 10.4329 3.1329 IO8.368I 68.0625 129.5044 O.2704 3.8kl6 79.5664 3.2041 2.1904 9.2416 15.3664  792.4686  +0.06 +0.59 +1.24 +1.52  -6.44 +I.40  +0.61 +11.65 -12.51 +1.58 +0.60 +2.30 -2.10 +2.55 +3.23 -1.77  +10.4l  -8.25 +11.38 -0.52 -1.96 -8.92 +1.79 ^1.48 -3.04 -3.92  FiG.a  CHANGES  OF  INTHEPR»C£ OF  BEE.F ^  IN  PO^K'^AND CANADA .  THE  WlS-'Sl.  CONSUMPTION  C H A N G E S IN T H E PER CRPITA D I S P O S A B L E - | N C Q M E A N D T H E CONSUMPTION °T BEEF?CANADA, I^ZFE J*SZ. V  vi^*—  -K)  Ck^yi^es \n J>er cii|3>ta. d i s p o s a b l e t kc v e s i d u d - f s regression  SoUfcCES:-  weve  as  d'vie. To t k e s . C & t t e >  t; NATlO/v/iL i>  jotted  +30  *S»  fcaiten  as 6\.fc3c»ss&e JVnd  .4*  income ovc*<YiOtes  u/cre  above dud b e l o w  { v e e kav\c( {'ivies (jucye /  ACCOUNTS, (OTT7UV/», boniNtau  LIVESTOCK ^  ANIMAL  PZO&UCTS  the  fsarciaC  fitted  BUREAU o f STATISTICS).  STATISTICS,  (DB.S).  ESTIMATING THE RATE OP CHANGE PROM THE SCATTER DIAGRAMS: 1.  Price  o f B e e f and Consumption X  Pitting  9.50 7.25 5.50 if.00 2.75 1.75 0.75  0 7.20 11.00 12.00 11.10 8.75 4.50  0 1 4 9 16 25 i6  21  31.50  54.55  91  a straight line  b a Price  x  y  0 1 2 3 4 5 _6  31.5 54.55  2.  o f Beef  =  7a 21a  + +  2  trend: 21b 91b  = -1.427 = +8.781  o f Pork and Consumption Straight  line  o f Beef  from the p a r t i a l  e q u a t i o n h a s t h e same s l o p e a s t h e l i n e scatter. 3.  Income a n d C o n s u m p t i o n X 6 10 14 18 22 26 _J0 126  y 1.00 2.00 3.00 4.00 5.25 6.50 7.75 29.50  o f Beef xy  6.0 20.0 42.0 72.0 115.5 169.0 232.5 657.0  2 X 36 100 196 324 484 676 900 2716  regression f i t t e d t o the  29.5 =  7a + 126b  657  = 126a + 2716b  b  = +0.28125  a  = -0.848214  Prom the l i n e s f i t t e d t o the s c a t t e r s :  bl2.34 = -1.427 bl3.24 • +0.1805 bl4.23 = +0.28125 al.234 = M _ M b X  2  1 2 < 3  - M3 b  ^  1 3 # 2 i +  -  b - ^  = -2.138942 R  2  =  b  2  (x x ) + b x  1.234  2  3  (x x ) + ^ ( x  <*l)  3  b  X lx  ^)  2  + 105.775647 + 8.18930666 + 126.2025 912.268754  = 0.263264  TESTING-  X-^ and  X  SIGNIFICANCE  2  Estimating equation  -21.5  =  26  -83.84 = a b  X-^ = a + b  11.75  a +  11.75a+  b  X  = -0.56181  2  and  2  X  2  = -74.1245  X  Taking  l  41.643144  equation  =  a  1.23  =  b  12.3  X  2  =  l  x  2  =  b  12.3  x  2  x  l  x  3  =  b  12.3  x  2  2 +  x  b  3  13.2 +  b  x  2  3  +45.37012 =  1  >  2  12.3  = =  7.723737 b  |  x  1 2  b  X  2  3  x  13.2  -74.12449 = 131.937692 b  3  l3.2  b  t h e o r i g i n a t t h e means  x  1  (-0.5618)  3  Estimating  b  2  -0.57302817  =  =  lt  2  2  137.247788b  V a r i a t i o n e x p l a i n e d by X  X  X  + >  7.723737  b  1  3  >  2  +124.887569  3  +0.39948007  "°.58520023  V a r i a t i o n e x p l a i n e d by X  2  and X  3  = b  2  x^x  2  +b  3  = 61.50210704  x-jX  ANALYSIS OF VARIANCE FOR TESTING THE SIGNIFICANCE Source o f V a r i a t i o n  Amount o f Variation  Degrees o f Freedom  Estimated Variation  Total Explained by X ^ X ^ X ^  912.26875 2k0.167^0  36.k9075 80.05580  Unexplained  6 72.10135  25 3 22  2k0.l67k0  3  80.05580  61.502107  2  30.751053  178.665293  1  178.665293  61.502107  2  30.751053  kl.6k31kk  1  kl.6k31kk  19.858963  1  19.858963  E x p l a i n e d by X , X , X 2  3  k  E x p l a i n e d by X ^ X ^ Net  Explained by X  Explained by X  2  k  & X3  Gross E x p l a i n e d by X Net  e x p l a i n e d b y X3  . *lk.23  l j >  is  -  "^  .  ^  s  36.k075  value  percent  178.665293 36.k9075  »13 2 k  The  2  30.55006  f o r F,,  or  . f a l l s b e t w e e n one p e r c e n t  levels of variation ratio.  significant.  Therefore,  and f i v e the b ^  ^3  STANDARD ERRORS OF THE REGRESSION C O - E F F I C I E N T S =  912.26875  •»  25  =  36.49075  =  131.937692  *  25  =  5.2775076  V a r i a n c e o f X-  =  12k.887569  *  25  =  4.995502  V a r i a n c e o f X^  =  14,661  t  25  =  563.8846  Variance of X  1  Variance of X  S.E.(b)  2  s» y n-l.  =  S.  = s 2 - 2. y  s»2 y  b  1.  s  2 x  (  s^ =  5.07387  S.E.(b2)=  5.07378 5.277507  x  25  0.570543 2.  S  y  =  6  '02716  S.E.(b3) = 6.02716 4.995502 x  25  0.539343 3.  S» = - 3 . 3 5 6 7 2 y s.E.(b4) » -3.35672 5 563.88 = -0.028279  x  x  =  Period 1929-33 1939-44 1945-52 1  -1.482211 +0.28125  x  k  A v . Change i n Change i n income consumption! -23.20 -8.00721 +34.83 +8.31373 -1.2361 +0.875  Computed f r o m t h e p a r t i a l  Income  elasticity  +O.8148 * 0 . 0 8 2 +1.1781 ± 0.118 -0.1991 * 0.020  regression equation.  (  A P P E N D I X  C  APPENDIX C CALCULATION OP INCOME-ELASTICITY OP DEMAND FOR PORK Year  Consumption t-. - t ' 1 o l Y  x  1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  P r i c e Pork ti - t •x 2 r t 0  x  +5.69 +0.56 -1.36 -6.71 +10.25 +2.41 -10.67 -7.97 -27.39 +1.01 +1.55 -0.81 +2.50 +1.78 +3.83 +7.88 +8. 79 +2.81 -13.77 +0. 83 +0.45 +0.80 +4.73 +2.k7 +5.80 +3.54  -2.547 -0.628 +2.395 -0.655 -4.833 -3.432 +1.669 +3.763 +0.649 -0.457 +0.061 +1.275 -1.068 -1.125 +1.138 +1.336 -0.020 +0.036 -0.060 +0.769 +0.673 +4/914 +0.050 -2.189 +1.315 -4.734  -1.00  -1.705  7  7  P r i c e Beef x  \  3  +1.751 +3.053 +0.011 -1.692 .  R e a l Income *i V  +0.882 +0.819 +1.920 +0.375 -0.103 -0.311 -0.662 +4.926 +0.878 +4.097 +3.660 -6.171  +19 +19 - 8 -28 -31 -35 -14 +24 +16 +10 +27 - 6 +18 +31 +31 +75 +16 +38 + 5 + 5 -26 + 6 - 9 + 3 +10 +13  +11.750  +209  -3-4  8  -O.38O -1.372 +0.194 +1.158 -0.688 +2.379 -1.215 +1.065  +0.424  49  Year 1927 1928 1929 1930 1931 1932  1933  1934 1935 1936 1937 1938  1939  1940 1941 1942 1943 1944 1945 1946 1947 1948  1949  1950 1951 1952  x  l 2 x  X  1 3 X  x  i 4 x  A  l  -14.49243 - 0.35168 - 3.25720 + 4.39505 -49.53825 - 8.27112 -17.80823 -29.99111 -17.77611 - 0.46157 + 0.09455 - 1.03275 - 2.67000 - 2.00250 + 4.35854 +10.52768 -0.17580 + 0.10116 + 0.82620 + 0.63827 + 0.30285 + 3.93120 + 0.23650 - 5.40683 + 7.62700 -16.75836  +9.96319 +1.70968 -0.01496 +11.35332 -33.29200 -0.91580 +14.63924 -1.54618 -31.71762 -0.69488 +3.68745 +0.98415 +2.66250 +0.75472 +3.37806 +6.45372 +1.68768 +1.05375 +1.41831 -0.25813 -0.29790 +3.94080 +4.15294 +10.11959 +21.22800 -21.84534  +108.11 + IO.64 + 10.88 +187.88 -317.75 - 84.35 +149.38 -191.28 -438.24 + 10.10 + 41.85 + 4.86 + 45.00 + 55.18 +118.73 +591.00 +140.64 +106.78 - 68.85 + 4.15 - 11.70 + 4.80 + 42.57 + 7.41 + 58.00 + 46.02  +32.3761 + 0.3136 + 1.8496 +45.0241 +105.0625 + 5.8081 +113.8489 +71.2518 +750.2121 + 1.0201 + 2.4025 + 0.6561 + 6.2500 + 3.1684 +14.6689 +62.0944 +77.26kl + 7.8961 +189.6129 + 0.6889 + 0.2025 + 0.6400 +22.3729 + 6.1009 +33.6400 +12.5316  -136.95494  + 8.60429  +546.67  +1566.9571  50  --  X X  12  vy = W • h  2  X2 2  =  =  -136.95454  X X =  +8.604290  X  +546.67  X  -=  1,566.9571  .  126.005655  -1.00 = 26a -136.95494  88  23 34 X  =  24  =  X  x  +8.494266 +531.092 +318.996 137.247788  3 2 _ 4 "  y x  16,341  1.705 D12.34  b  -1.705A + 126.005655 b  i3.24  1 2 # 3 k  +  2  0  9 b  i4.23  + 8.494266 b  1 3 # 2 k +  318.996 b ^ . ^ +8.60249 = 11.75a + 8.494266 b  1 2 # 3 k  + 137.247788  b  1 3 i 2 k  . 531.092 b ^ +546.67 = 209a + 318.996 b  + 1 2 # 3 k  531.092 b i . 2 4 3  + l 6  »  3 k l b  -  2  + 3  i4.23  DOOKC.TTLB SOLUTION Reciprocal  a  1  1.234  b  +26.00  II  i2.34  b  -1.705 +126.005655 •  III iv;  1  j  i!-~  1  2 -O.O38461538 1 3. 1  k\ 5i 6 1-0.0079432 7 8 : 9i 10 r 11 -0.007618747 12 ! 13 I 14 i15 ! 16 17 -0.000092212  1 !  I 1 ;  i !  ;  +26.00 -1.00  i3.24  V 2 3  +11.75  +209.00  Check +1.00  +8.494266  +318.996  +136.95494  +137.247788  +531.092  -8.60429  +16,341.00  -546.67  |  +209.00 +246.045 +1.00 -1.705 +11.75 -9.463269230 +0.065576923 -0.45192307 -8.0384615 -0.03846154 +590.450861 +318.996 +126.005655 +8.494266 +136.95494 -0.11180 8654 i+0.770528845 +13.7055769 +0.065576923 ;+14.42987401 +332.7015769!. +137.0205169 +604.88073501 1+125.8938463 i +9.26955445 i -1.00 :-4.804688666 -0.073629925 -2.64271517 -1.08838137 1 +659.735498 +137.247788 +531.092 -8.60429 -0.682516599 -24.496676O -10.0988091 -35.26129745 i -94.4519216 -0.45192307 -100.2139407 -5.31009607 +524.2602599 -19.15502217 ! +131.25517533!+412.143402 -1.00 -3.1400164 +0.145937099 -3.9942063 1+16,341.00 -546.67 +15,794.33 : j-1,294.13028 +60.1467628 -1,233.983525 : 1-879.2312805 -362.1061306 -1,241.341455 j-1,680.0625 -8.0384615 -1,688.0769 +12,487.57594 -856.6678293 +11,630.928125 -1.00 +0.06860161 +0.9313999 :  ;  H  BACK SOLUTION a  1.23k  b  12.34  b  13.24  -0.05911+8522  +0.0051152126  -O.215409024  +0.03139596k  +0.1812944890  +0.145937099  -0.551451323  -I.O8838137OO  b  +0.0686016  -O.038461540 -0.901971668  -0.617665421  -0.069471925  ESTIMATING EQUATION: X  x  X  1  R  2  = -0.6176654-0.90197  X  2  - 0 . 0 6 9 4 7 1 9 X^ + 0 . 0 6 8 6 0 1 6 X  = - 0 . 7 0 8 2 0 9 8 +0.0686016 X b  =  =  2  x-^g  +b  3  x ^  k  +b  k  2 3 . 4 6 9 7 7 - 0 . 6 2 8 9 9 +38.05331 +1566.91864 = +160.89409 +1566.91864 + 1  = 0.102683  x ^  l4.23  k  Year  b x  1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  +2.2973176 +0.5664372 -2.1602181 +0.5907903 +4.3592210 +3.0955610 -1.5G53879 -3.3941131 -0.5853785 +O.4122003 -0.0550202 -1.1500117 +O.9633040 +1.0147162 -1.0264419 -1.2050319? +0.0180394: -O.0324709 +0.0541182 -0.6936149 -0.6070258 -4.4322806 -0.0450985 +1.9744123 -1.1860905 +4.2699260  2  2  b  :  3  X  X  3  +0.1216455 +0.2120980 +0.0007642 -0.1175466 -0.2256451 -0.0263994 -0.0953156 +0.0134776 +0.0804486 -0.0477967 +0.1652739 -0.0844085 +0.0739877 +0.0294561 +0.0612743 +0.0568975 -0.1333862 +O.O26052O +0.0071556 -0.0216058 -0.0459905 +0.3422191 +0.060996k +0.2846268 +0.2542675 -0.4287117  +1.3034304 +I.3034304 -0.5488128 -1.9208448 -2.1266496 -2.4010560 -0.9604224 +1.6464384 +1.0976256 +0.6860160 +1.8522432 -0.4116096 +1.2348288 +2.1266496 +2.1266496 +5.1451200 +1.0976256 +2.6068608 +0.3430080 +0.3430080 -1.7836416 +0.4ll6096 -0.6174144 +0.2058048  +0.6860160 +0.8918208  i  +3.104728 +1.464300 -3.325932 -2.065266 +1.389261 +0.050440 -3.178791 -2.351862 -0.024970 +0.432754 +1.344831 -2.263695 +1.654455 +2.553156 +0.543817 +3.379320 +0.364613 +1.982776 -O.213384 -0.989878 -3.054323  -4.296117 -1.219182 +1.847179 -0.863472 +4.115370  X + 2.59 - 0.90 - 1.97 - 4.64 + 8.86 + 2.36 - 7.49 - 5.62 -27.36 + 0.58 + 0.21 + 1.45 + 0.85 - 0.77 + 3.29 + 4.50 + 8.63 + 0.83 -13.56 + 1.82 - 3.50 5.10 5.95 0.62 6.66 0.58  6.7081 0.8100  3.8809  21.5296 78.4996 5.5696 56.1001 31.5844 748.5696 0.3364 0.0441 2.1025 0.7225  0.5929  10.8241 20.2500 744769  0.6889  183.8736 3.3124 12.2500 26.0100 35.4025 0.3844 44.3556 0.3364 1369.2151  FlG»6  CHANGES A N D TH£  W  INCOM^  THE R E R C A P ' T / I D I S P O S A B L E  CoNSUMPTJON^Of  PoRK . C A N A D A . I 9 2 £ - ' S 2 .  fneri/t L .46 so  -40  •3i  -5<s  -10  ResV<J.uaU -fvom t k e Qvouvid Source:-  5i 2*'  rto  t2,  °  1 4 0  + s e  _»CH«IU«£.  ^ct fife v e ^ r e ^ r i o o ^ j u ^ t / o n  i/w IrtCONE  UJcrc  ^(c^ted  Hr*. t a v t i ^ l Y<?£-resS(OVi ( O n e . Q  NATIONAL  i)  LIVESTOCK  AccoU/V/TS , ( O t t a w a , Dowi'm'oi fiuiMfiL  PRODUCTS  6urea.il  Statistics).  STATISTICS , (b-&s}.  The three slopes calculated from the scatter diagrams are as follows:-  a  i.23i|  =  M  1  b  l2.34  b  l4.23 "  ~ 2 2 b  M  -  =  1  +  " 3 3 b  '  ° -  7  0  0  7  5  - \ \  M  = 1/26 ( - 1 . 0 0 + 2 . 8 9 8 5 - 26.1+375 - 15.675) = 1/26 (-1+0.2U+0) = -1.51+669 Estimating Equation f o r demand f o r Pork:X  x  x  1  R  2 1.234  = -1.54669 - 1 . 7 0 X  3  + 0 . 0 7 5 X^  2 3 2 . 7 1 1 3 + 2 0 . 3 7 1 2 7 5 +1+1.6031 1566.91864  s  = 0.188681 1.234  +2.25 X  = -0.1+1838 + 0 . 0 7 5 X^  = 294.6857 1566.91864  R  2  =  0  - ^  3  TESTING 1.  R e g r e s s i o n o f X-^ on X  -  1.00  = 26a  SIGNIFICANCE  2  -1.705b  2  -136.95454 = -l.705a+l26.005655b  2  b  = -1.088378  2  = -0.109834  a  V a r i a t i o n e x p l a i n e d by X =  0  b,  X  l 2 x  = 1.088378 (136.88936) = li|8.988338 2.  Regression o f X  1  on X  & X^  g  -137.020517 = 125.893847b  +  + 9.05621 =  +  12#3  13.2  =  12.3  =  b  b  9.26k795b  +0  12.3  9.26k795b  13<2  131.937692b  g  - 45829 1  - »°9911231 1  V a r i a t i o n e x p l a i n e d by X  2  & X^  = 150.4547 + 1.320338 = 151.775038 ANALYSIS OF VARIANCE Source o f V a r i a t i o n Amount o f V a r i a - D.F. tion Total 1566.9186k 2T E x p l a i n e d by X ,X-  & X>,  d  5  Unexplained E x p l a i n e d by Xp,Xo  & X^  ^  Gross E x p l a i n e d by  x &x 2  Net  3  E x p l a i n e d by X  k  62.676745"  3  1272.23294  22  98.22856 57.828770  294.6857  3  98.22856  151.775038 lk2.910662  2 75.887519 1 lk2.910662  294.6857  5  Estimated Variance  Source of  Amount o f V a r i a tion  Variation  E x p l a i n e d b y X & X3 G r o s s e x p l a i n e d by X N e t e x p l a i n e d b y X3  151.775038  2  Thus X  2  & X  2.786700  k  o f X^ = of X =  62.676745 4.995502  Variance Variance  o f X3 = o f X^ =  5.277508 563.8846  2  2.  12.34  b  13.2k  +2.2500  b  i4.23  +0.075 b  2  62.676745 - 2 . 8 9 48.239745  2  Standard e r r o r of  =  6.9455  =  6.9455 5/4.995502 0.62210  62.676745 -5.0625 35.9594 y  S.E.(b ) 3  3.  (4.995502)  b.  y s»  CO-EFFICIENTS  -1.7099  b  S . E . (Sp)  explaining  variation.  Variance Variance  S« y s»  Estimated Variance 75.887519 lk8.988338 2.786700  a r e t h e two v a r i a b l e s  STANDARD ERRORS OF THE REGRESSION  Standard e r r o r of  2 1 1  Lk8.988338  2  almost a l l the e x p l a i n e d  1.  D.F.  Standard e r r o r of b 4* St2 y  (5.2775076)  5.996 5.996 5/5.27750 0.52207  62.676745 -0.005625  (603.76)  60  S' y S.E.(b ) k  X  =  Period  =  59.28  =  7.7  =  7.7  5/563.88k6 0.06k85  - 0 . k l 8 3 8 +0.075 X  k  Av. change income  Ave. change consumption  1929-33  -23.20  -2.1584  369*78.27 +0.353  1939-44  +34.83  +2.1939  382*43.49 +0.659 - 0 . 5 6 9  1945-52  +0.875  -0.3528  5 5 7 * 6 8 5 4 +0.609 ± 0 . 5 2 7  As t h e p o s s i b i l i t y  X  j i /  z  X  l  I  n  c  o  m  e  elasticity -0.300  o f income e l a s t i c i t y b e i n g e q u a l  to 1 i s remote, t h e above c o r r e c t i o n would be n e g a t i v e . Thus income e l a s t i c i t y f o r t h e 3 p e r i o d s i s : 1929-33  +0.053  1939-44  +0.090  1945-52  +0.082  A P P E N D I X  D  61 APPENDIX  D  CAIiCTJLATION OP INCOME-ELASTICITY OP DEMAND FOR EGGS  Year  1926 1927 1928  1929 1930 1931 1932  1933 1931+  1935 1936  1937 1938  1939  1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  Total  Consumption (doz.) 28.02 29.30 30.04 30.16 30.09 30.01 23.97 22.76 22.32 22.55 21.76 21.63 20.94 21.38 21.58 20.34 22.03 23.72  Real Real Price Income (cts.) (#)  22.55 22.80  38.77 41.24 40.41 39.84 38.66 31.29 29.82 29.74 33.30 32.47 34-60 33.04 33.63 32.78 31.61 31.81 36.55 40.03 37.15 38.47 38.48 36.09 38.16 37.70 33.33 38.49 31.26  276 300 316 326 353 347 365 396 427 502 518 556 561 566 540 546 537 540 550 56,3  651.16  958.72  11559  24.42  23.46 23.22 24.10 23.52 21.89  22.60  354 373  392  384 356 325  290  X  +1.28 +0.74 +0.12 -0.07 -0.08 -6.04 -1.21  -0.44  x  P  c.  +2.47 -0.83 -0.57 -1.18 -7.37 -1-47  -o:;08  +0.20 -1.24 +1.69 +1.69 +0.70 -0.96 -O.24 +0.88 -0.58 -1.73 +0.71 -0.05 +0.25  +3.56 -0.83 +2.13 -1.56 +0.59 -0.85 -1.17 +0.20 +4.74 +3.48 -2.88 +1.32 +0.01 -2.39 +2.07 -0.46 -4.37 +5.16 -7.23  -5.32  -7.51  +0.23 -0.79 -0.13  -0.69  +0.1+4  X. j  +19  +19 - 8 -28 -31 -35 -14 +24 +16 +10 +27 - 6 +18 +31 +31 +75  +16  +38 + 5 + 5 -26 + 6 - 9 + 3 +10 +1?  +209  62  x x  Year  1  2  h h  + 3.1616  1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  X X  + 24.32 + 14.06  Xl  2 3  + 46.93  0.96 1.26 2.48 +211.40 + 16.94 10.56 + 3.68 - 7.90 + 3.51 + 4.14 + 7.92 + 6.20 38.44 + +126.75 + ^.8812 + 27.04 - 2.0160 + 26.60 - 1.2672 - 4.80 - 0.0024 - 1.20 - 2.1032 - 22.88 - 1.2006 3.48 + 0.7958 + 15.57 - 3.1027 + 2.13 - 0.2580 - 0.50 1.8075 + 3.25 399.51 +10.5565 1.53666c 42.76  -  + 9.01984 +442.27  +732.38  54.05785  14,661  + + + +  -  -  + +  -  -  -  =  -  -  26 a - 7.51  D  i2.  +10.5565 = -7.51&+240.6027 b =  +392.76  209 a+672.02  b  1  3  1 2  .  2  3  #  +  1.23 1 3  ^  2  =  =  -°-4211797 ,  b  i2.3  =  2  + 3  S o l v i n g these e q u a t i o n s by D o o l i t t l e ' s  ±  3  361 361 64 784 961 1225 196 576 256 100 729 36 324 961 961 5625 256 1444 25. 25 676 36 81 9 100 169 16,341 -1.680  0.6lk2 0.0684 0.0826 0.5896 8.8788 0.0968 1.5664 0.1909 1.6827 0.2028 0.4071 0.3740 0.2340 0.2480 8.0106  - 5.32  x  2  2  1.6384 * 6.1009 0.5476 0.6889 0.0144 0.3249 0.0049 1.3924 0.006k 54.3169 36.4816 2.1609 0.0064 1.4641 0.1936 12.6736 0.0529 0.6889 O.6241 4.5369 2.4136 0.0169 0.4761 0.3481 0.1936 0.7225 0.0400 1.3689 O.0400 1.5376 2.8561 22.4676 12.1104 2.8561 0.4900 8.2944 0.9216 1.7424 0.0001 0.0576 5.7121 0.7744 4.2849 0.3364 0.2116 2.9929 0.5041 19.0969 26.6256 0.0025 0.0625 52.2729 55.14640 240.6027 -1.08855 - 2.1692  -  b  X  2  15.77 + 4.56 + 21.24 +228.47 + 51.45 + 1.12 + 85.44 - 13.28 + 21.30 - 42.12 - 3.54 15.30 - 36.27 + 6.20 +355.50 + 55.68 109.44 + 6.-60 + 0.05 + 62.l4 + 12.42 + 4.14 - 13.11 + 51.60 - 93.99 +<b72.02 + 60.36  -  a  X  2  A  238.4335  0  9  b  672.02b  + l6,34lb  2  1 3 < 2  1 3  method, +0.0369603,  +0.0283201  = -0.4211797 + 0.0369603 X  13.2  + 0.0283201 x  3  [  2  Year 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945  1946 1947 1948 1949 1950 1951 1952  b  12.3  X  2  b  -0.0912919 +0.0306770 +0.0210674 +0.0436132 +0.2723974 +0.0543316 +0.0029568 -0.1315787 +0.0306770 -0.0787254 +0.0576581 -0.0218066 +0.0314163 +O.0432436 -0.0073921 -0.1751918 -0.1286218 +0.1064457 -0.0487876  13.2  X  3  X  +0.5380819 +O.5380819 -0.2265608 -0.7929628 -0.8779231 -0.9912035 -0.3964814 +0.6796824 +O.45312I6 +0.2832010 +0.7646427 -0.1699206 +0.5097618 +0.8779231 +0.8779231 +2.1240075 +0.4531216 +1.0761638 +0.1416005 +0.1416005 -O.7363226 +0.1699206 -0.2548809 +0.0849603 +0.2832010 +O.368I613  -O.OOO3696  +0.0883351 -0.0765078 +0.0170017 +0.1615165 1,-0.1907151 +0.2672229  l  +0.0256103 +0.1475792 -O.626673I -1.1702930 -1.0267054 -1.3580516 -0.8147043 +O.1269240 +0.0626189 -0.2167041 +0.4011211 -0.6129069 +0.1199984 +0.4999869 +0.4493513 +1.5276360 -0.0966799 +0.7614298 -O.3283668 -0.2799488 -1.0691672 -0.3277669 -0.6590589 -0.1747029 -0.3286938  +0.2142045  +1.25 +0.59 +0.79 +1.10 +0.95 -4.68 -0.30 -0.57 +0.17 -0.57 -0.53 -0.08 +0.32 -0.30 -1.69 +0.16 +1.79 -0.06 -O.63 +0.04 +1.95 -0.25 -1.07 +0.88 +0.28 +0.04  1.5625 0.3481 0.6241 1.2100 0.9025 21.9024 0.0900 0.32k9 0.0289 0.3249 0.2809 0.0064 0.1024 0.0900 2.8561 0.0256 3.204l O.OO36 0.3969 0.0016 3.8025 0.0625 1.1449 0.7744 0.0784 0.0016 40.1502  1.23  -  b  2  (  x  l  x  2>  +  (*l)  R  J  1.23 xl  3  b  (  x  !  x  j  2  =  +0.3333732864 + 12.5250864 = 54.05785  =  0.4877  =  40.1502 26  =  1.^238  =  +0.2378648  1.2427  FIE,.7. C H A N G E S  IN R E A L P R I C E " A N D rue CONSUMPTION*'** £G«S,  •30  -10  ,M» "*  V i —  U N {  2 a «l £  *'+  —}CH*NG£ IN INCOME  65  TESTING SIGNIFICANCE 1.  Simple r e g r e s s i o n o f X-^ on - 5.32  =26  +10.5565  = -7.51  b  X  2  a - 7.51  b  2  a + 240.6027  b  2  = -0.0359064  2  a  =  -0.255302683  V a r i a t i o n e x p l a i n e d by X  2  =  b  x 2  i 2 x  = 0.0359064  (9.01984)  = 0.32386998 2.  Simple r e g r e s s i o n o f X-^ on -  X  3  5.32  =  +392.76  =  b  =  +0.0278256  =  -0.39939458  3  a  26 a +182  b  3  182 a + 1 6 , 3 6 8  V a r i a t i o n e x p l a i n e d by X  3  b  3  =  +0.0278256  (442.27)  -  +12.306428112  ANALYSIS OF VARIANCE Source of V a r i a t i o n  Amt.  Total E x p l a i n e d by X  of Variation  &  X  3  Un-explained E x p l a i n e d by X & X Gross e x p l a i n e d by X Net e x p l a i n e d by X3 2  Net e x p l a i n e d by  3  X  2  2  Estimated  Var.  2.1623140  12.8584597  25 2  41.1993903  22  1.87269955  12.8584597 0.32386998 12.53458972  2 1 1  6.42922985 0.32386998 12.53458972  0.55203159  1  0.55203159  54.05785 2  D.F.  6.42922985  Multiple  Correlation _  P  6.42922985 1.87269955  K23)  _  , . ^  „  3  3  3  Prom the Table o f V a r i a n c e R a t i o : P at 5 $ l e v e l * 3 . 0 P at 1% l e v e l = k.6 The m u l t i p l e c o r r e l a t i o n Partial  coefficient  i s just  significant.  Correlation p L  d  t  .  0.55203159 1.87269955  =  12.53458972 1.87269955  i  p 13.2 F  =  0  =  6  #  2  6  *  Q  9  k  8  , 9  3  The r e q u i r e d values a t 5% and 1% l e v e l s o f v a r i a n c e are  3.8 and 6.6  T h e r e f o r e , the Income V a r i a b l e  very s i g n i f i c a n t r e l a t i o n s h i p whereas p r i c e  relationship  ratio  (X^) has  w i t h t h e consumption o f eggs,  i s not s i g n i f i c a n t .  STANDARD ERRORS OF THE COEFFICIENTS OF REGRESSION Variance o f X  x  =  2.16231k  Variance of X  2  =  9.53734  V a r i a n c e o f X^ 1.  = 586.44  Standard e r r o r o f b : 2  S» y  2  = 2.162314 -  0.1302792348  = 2.0320347652 6* S. .(b ) E  2  2  7  =  1.42549  , 5/9.53734 = 0.092318  2.  Standard e r r o r o f b^: S«  2  =  2.162314 -0.00080220224 (586.44)  = 1.691976 s' y S.E.(b) 3 x  =  =  1.30076  = 1O0076— 5/586.44  = 0.0107429  -0.431854 +0.0283201  Period  x  3  Ave.Change i n Change i n income consumption  X./X  2  ^  4  Income e l a s t i city  1929-33  -23.20  -1.0889  +14.25  +O.403 -  0.153  1939-44  +34.83  +0.5545  +17.77  +0.503 -  0.191  1945-52  +0.875  -0.4071  +23.21  +0.657 -  0.249  1)  Computed from the p a r t i a l r e g r e s s i o n e q u a t i o n .  2)  X^ and X^ were o b t a i n e d by adding or s u b t r a c t i n g the change from the income and the p r i c e i n 1 9 2 8 , 1944.  1938  and  A P P E N D I X  E  A P P E N D I X  C A L C U L A T I O N  Year  1928  1929  2.75  51.82  2.92  1939 1940 1941 1942 1943 1944 1945 1946  5 5 4 4  2.84 3.18  1938  2  50.70  3.06  1937  x  2.62  1931 1932 1934 1935 1936  Real Price Cents p e r pound  l  1930  1933  I N C O M E - E L A S T I C I T Y  Consumption Per Capita (lbs.) X  1926 1927  O P  1.31 0 . 6 7 8 . 3 9 5 . 6 8  43.40 4 2 . 3 2  2.97 3.21 3.20  40.92 38.91  3 . 2 2 3.67  4.14 3.67 4 . 8 2 .  O P  D E M A N D  Income  (•)  X  3  354 373  392  F O R  C O P P E E  Price of tea <V p e r l b . X  Time  4  59.40 6 0 . 6 3  60.27  X  5  -13 -12 - 1 1 -10  384  59.06  356  53.13  325 290  51.25 4 7 . 8 7 4 4 . 8 6  -  9 8  -  7 6  276 300  52.61  -  5  316 326  5 4 . 2 1 5 3 . 2 2  53.27 56.92  4 3 2  33.92  353 347  -  35.13 4 2 . 0 3  365 396  5 8 . 0 2  1 0  6 2 . 5 7  +  1  4 0 . 3 4 4 0 . 1 5 36.11  427 502  6 3 . 9 7 71.00  +  2  +  3  518  3 6 . 0 2 35.66  556 561  6 3 . 1 5 6 2 . 9 3 62.17  + + +  4 5 6 7 8  3 6 . 6 4 3 5 . 2 2  3.43 3.83  3.94 5.13 8.09 4 - 5 8  E  3 4 . 6 8  566  4.16  36.09  60.05 64.69  + +  1949 1950  6.84 7.32 6.10  540 546  39.63  6 4 . 4 8 6 2 . 4 8  + 9 +10  61.53  1951 1952  6 . 3 8 6.88  +11 +12  1947 1948  Total Mean  6.97  119.92 4 . 4 4 1 4 8 1  38.66 5 6 . 4 5 5 5 . 2 5 54.59  537 540 550 563  56.51 55.98  +13  1150.59  11,559  1576.23  0  42.61444  4 2 8 . 1 1 1 1  58.37888  0  Year  XX.  XX.  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 19I+I 191+2 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  3011.5800 31i|1.8k66 3092.4537 2992.5702 2570.9607 2341.1000 2077.5580 I898.k752 2152.8012 2109.3111 191+9.9808 1876.1694 1930.726k 2038.2426 2620.8171 2580.5498 2850.6500 2280.3465 2266.7386 2216.9822 2082.5340 2334.6621 2492.7968 2476.0824 3473.3685 3122.1775 3050.3502  21,027.60 22,614.99 23,625.8k 22,670.0k l8,91k.28 16,656.25 13,882.30 12,381.36 15,783.00 17,130.36 17,349.72 18,804.31 19,751.24 21,177.20 24,777.82 27,315.19 35,642.00 32,711.70 34,989.08 34,877.37 33,988.30 34,932.60 35,206.08 33,551.76 33,226.20 31,080.50 31,516.74  1_4  A  Total  67040.8316  685,592.83  Adj.  67170.1491  674,801.577  -129.3175  +10,791.253  XX, 2J>  XX 3 5  XX, k5  -659.10 -621.8k -56k.kl -506.70 -435-51 - 3 6 5 . kk -303.80 -253.92 -204.60  -4602 -4476 -4312 -38kO -320k -2600 -2030 -1656 -1500 -126k - 978 - 706 - 347 0 + 396 + 854 +1506. +2072 +2780 +3366 +3962 +4320 +4914 +5370 +5940 +6600 +7319  -772.20 -727-56 -662.97 -590.60 -ij.78.17 -1J10.00 -335.09 -269.16 -263.05 -216.81+ -159.66  -155.61+  -109.92 - 70.44 - 33.92 0 +42.30 + 80.68 +120.45  +144.44 +180.10 +213.96  +242.76 +288.72 +347.94 +396.30 +620.95 +663.00 +708.37  -235.27 + 1 7 , 8 8 4 0  0  - 2 3 5 . 2 7 +17,884  -106.54  - 56.92 0 + 62.57 +127.94 +213.00  +252.60  +314.65 +373.02 +420.35 +517.52 +580.32 +624.8O +676.83 +678.12 +727.74 +520.70 0 +520.70  Year  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  132.8340 142.5050 149.8252 143.9028 148.0734 145.2624 128.8980 135.8472 130.9440 125.2902 134.4688 120.8046 129.9136 145.4382 154.2501 194.4388 158.1910 185.2443 291.4018 163.3228 241.7196 150.1344 264.4344 290.0916 344.3450 352.4950 374.8912  927.48 1025.75 1144.64 1090.56 1089.36 1033.50 861.30 885.96 960.00 1017.52 1196.42 1210.79 1329.01 1511.10 1453.32 2058.1k 1977.88 2657.34 4498.04 2569.38 3945.02 2246.40 3734.64 3930.84 3294.00 3509.00 3873.44  Total 5,078.9674 55,030.830 Adj.  X X  X X l 3  5,109.1322  51,339.084  -30.1648 +3,691.746  i  X  5  o  X  o  2 3  -34.06 -33.00 -32.12 -28.40 -27.54 -25.44 -20.79 -19.26 -16.00 -12.88 -11.01 - 6.86 - 3.83 0 + 3.67 + 9.64 +11.82 +20.52 +40.45 +27.48 +48.79 +33.28 +61.56 +73.20 +67.10 +76.56 +89.44  17,947.80 19,328.86 20,113.52 19,457.28 17,226.84 14,846.00 12,586.00 11,680 . 32 12,276.00 12,295.56 11,944.64 12,432.66 11,770.24 12,822.45 16,643.88 17,225.18 20,155.30 18,704.98 20,027.12 20,005.26 19,628.88 19,488.60 21,108.36 21,281.31 30,483.00 30,387.50 30,677.87  7099.5287 +292.32  492,545.41  7000.79463  492,580.36  155.6280 166.7325 175.9884 167.730k 162.5778 162.9750 142.1739 144.OOO6 168.3520 174-5562 195.3174 182.7161 218.0036 240.2028 229.6319 308.3354 279.7400 323.9595 509.1037 284.7386 418.5485 269.1104 44L0432 457.3536 375.3330 360.5338 385.1424  0  + 9 8 . 7 3 4 0 7 +292.32  -34.95  71  Year  (x )  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 -1944 1945 1946 1947 1948 1949 1950 1951 1952  6.8644  2  x  2  2  2  (x )  2  k  (x ) 5  169 144 121 100 81  50,372.3353 £225417.00  92887.7165  +I638  532.6221  49,031.7435 4S43536.33  92018.2032  0  +71.1181  + 1 3 4 0 . 5 9 1 8 +276,980.67  7.5625 8.5264 8.0656 9.3636 10.1124 8.8209 10.3041 10.2400 10.3684 13.4689 11.7649 14.6689 17.1396 13.4689 23.2324 15.5236 26.3169 65.4481 20.9764 48.5809 17.3056  46.7856  53.5824 37.2100 40.7044  47.3344  2570.4900 2685.3124 2632.7161 2567.4489 2341.5921 2O86.6624 1883.5600 1790.9824 1674.4464 1513.9881 1342.4896 1240.4484 1150.5664 1234.1169 1766.5209 1627.3156 1612.0225 1303.9321  (X3)  3528.3600 3675.9969 3632.4729 3488.O836 2822.7969 2626.5625 2291.5369 2012.L196 2767.8121 2938.7241 2832.3684 2837.6929 3239.8864 3366.3204 3915.0049 4092.1609 5041.0000 3987.9225 3960.I849 3865.1089 36O6.0025 4184.7961 4157.6704 3903.7504 3785.9409 3193.3801 3133.7604  Total 603.7402 Adj.  (X )  1297.4404  1271.6356 1202.7024 1302.4881 1494.5956 1570.5369 3186.6025 3052.5625 2969.1601  125316 139129 153664 147456 126736 105625  s4ioo  76176 90000  99856  106276 124609 120409 133225  156816  182329 252004 268324 309136 314721 320356  291600  298116 288369 291600 302500 316969  64 49 36 25 16 9  4 1 0 1  4  9 16 25  36 49 64  81 100 121 144 169  +869.5133 +I638  2  ( x ^ )  (x  iV  (x x_J l 5 ( x ^ j  -30.1648 = +1,340.5918  =  -30.1648  »  +3,691.746  ( x  2 4 x  = -129.3175  )  = +98.73407  (x x^)  = -235.27  =  (xyt^)  = +17,884  +292.32  = +10,791.253  D  = -34.95  (XgXJ  1  2  >  3  U  + 3,691.746 = - 34.95 *>i2.345  (  x  4 5 x  = +520.70  }  34.95 ^3.245 - 129.3175  -  5  2  276,980.67 ^13.245  +  +  - 235.27 b ^  10,791.253 ^14.235  +  17,884 b  + 98.73407 = - 129.3175 t> .345 12  +  10,791.253 b  + 869.5133 i4.235 b  1 3 # 2 i ; 5  +  234  l5.234  520.70 l5.234  b  + 292.32  = - 235.27 b . ^5 12  3  +  17,884 bn.3.245  +  520.70 b^.235 + 1*638 b ^  234  ->3  ro  x  x  x  l 2 =  -30.161+8  l 3  =  +3691.71+6  l 4  =  +  x  x  x  x ^  =  -30.1648  9 8  -34.95  x x^ = -129.3175  x x^ =  -235.27  x x ^ = +10,791.253  x x^ =  +17,884  x ^  x  2*3 * 2  * 73407  3  3  = +520.70  +292.32. = +1340.5918 h  +3691.746 = - 3 4 . 9 5  b  1  2  t  3  k  s  i2.345 2  = -235.27  -  34.95 *>  fcn.2.31^  " 129.3175 t>i4.235 ~ 35.27 b ^ . 2 3 4 2  1 3 < 2 j + 5  +276,980.67b  + 9 8 . 7 3 4 0 7 = -129.3175 t > i . 3 4 5 +292.32  2  +I0,791.253b  1 3 #  1 3 <  ^10,791.253b j 1  ^+869.5133  +17,884 ^13.245  +£20.70  4 i 2 3  ^  17,884  bi.5.234  &14.235+ 5 2 0 . 7 0 bi.5.234 ^.23?  >1  1  6  Q  b  l5.234  S o l v i n g these E s q u a t i o n s : b  b  a  12.345 l4.*235 i.2345  =  -0.015987956  = -0.074935726 =  4.441481  :M  2  = 42.61444  ±  45  =  =  +°'  0 1 1 2  9845  + «076626 0  :M  = 428.111  ^  =  3  4.441481  +0.681313 - 4 . 8 3 6 8 6 6 + 4 . 3 7 4 7 4 6  2  X  3  1  1) S. E .  1 3 < 2  = 5 8 . 3 7 8 8 8 ^> $.23k  = +4.660674 E s t i m a t i n g e q u a t i o n :X = +4.660674 -0.01598796 X x  :b  = - 0 . 3 9 5 3 8 5 +0.01129845  x  + 0 . 0 1 1 2 9 8 4 5 X3 - 0 . 0 7 4 9 3 5 7 2 6 X^ + 0 . 0 7 6 6 2 6  X5  STANDARD ERRORS OP REGRESSION CO-EFFICIENTS (b2) = 0 . 0 4 5 9 5 4 , 2)-S. E . (b3) = 0 . 0 0 2 2 7 2 * 3) S.-E* ( b 4 ) = 0 . 0 5 5 1 9 7  4) s . E . (b5) = 0 . 0 3 8 7 5 2 6 ~ - • As the standard e r r o r was about as h i g h as the r e g r e s s i o n c o - e f f i c i e n t i n a l l the cases except X3, the r e g r e s s i o n c o - e f f i c i e n t s were not s t a t i s t i c a l l y s i g n i f i c a n t .  x  Year  -b  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  0.8284982 0.8203443 0.8101196 0.7736593 0.7303318 0.6938792 0.6766122 0.6542289 0.6220931 0.5858003 0.5630974 0.5423130 0.5616584 0.6719756 0.6449559 0.6419182 0.5773267 0.5758878 O.5701321 0.5544638 0.5770069 0.6180960 0.6336044 0.9025226 0.8833370 0.8711861  2  2  0.8105916  +b  3  X^  3.999492  4.214154 4.428816 4.338432 4.022088 3.671850 3.276420 3.118248 3.389400 3.570168 3.683148 3.988194 3.920406 4.123770 4.474008 4.824246 5.671596 5.852364 6.281688 6.338178 6.394668 6.100920  6.168708 6.067026 6.100920  6.213900 6.360774  -  b  4  x  4  4.4511984 4.5433697 4.5163927 4.4257202 3.9813497  3.8404700  3.5871863 3.3616290 3.9423830 4.0622806 3.9880939 3.9918407 4.2653571 4.3477867 4.6887455 4.7936559 5.3204560 4.7322084 4.7157225 4.65877H 4.4999068 4.8476098 4.8318733 4.6820013 4.6108121 4.2346334 4.1949173  x b  5  x  5  -0.996138 -0.919512 -0.842886  -0.766260 -0.689634 -O.6I3OO8  -0.536382 -0.459756 -O.38313O -0.306504 -0.229878 -0.153252 -0.076626  0 +0.076626 +0.153252 +0.229878 +0.306504 +O.383130 +0.459756 +0.536382 +O.613008 +0.689634 +O.766260 +0.842886 +0.919512 +0.996138  i  2.402238 2.583448 2.909867 2.997006 3.238119 3.148714 3.119646 3.280925 3.070332 3.239964 3.540050 3.940677 3.696784 3.874999 3.850587 4.199560 4.599774 5.510007 6.033882 6.229705 6.537353 5.949985 6.069047 6.178354 6.091145 6.676115 6.951483  +0.22  +0.17 +0.01  -0.16 -0.18 +0.03 -0.15 -0.07  +0.13 -0.02  +0.13 -0.51 +0.13 +0.27  -0.18 +0.62 -0.66  -O.38 +2.06 -1.65  +0.43 -1.79  +0.77 +1.14 +0.01 -0.29 -0.07  75  R  2  _ 0 . 4 8 2 2 7 8 +1+1.711 -7.3981+ +22.3993  I  57.194187  7  1  -  1  1  8  1  71.1181 = 0.8042 R  1.2345  X  =  °-  8  9  7  = - 0 . 3 9 5 3 8 5 +0.01129845 X  x  Year  Av.Income  3  Av. consumptionl  Xo/X-^  Income  elasticity  1929-33  326.2  3.29  99.1489  +1.120 - 0 . 2 2 5  1939-44  460.7  4.8.1  95.7796  + 1 . 0 8 2 ±0.218  1945-52  550.4  5.82  94.5704  +1.068 ± 0 . 2 1 5  Computed from the p a r t i a l r e g r e s s i o n e q u a t i o n .  A P P E N D I X  P  APPENDIX  P  CALCULATION OP INCOME-ELASTICITY OP DEMAND FOR TEA Year  Consumption Per C a p i t a (lbs.)  Real Price Cents p e r pound  x  *1  2  Income  X  3  Price of Coffee x  4  x  5  59.40 60.63 60.27 59.06 53.13 51.25 47.87 44.86 52.61 54.21 53.22 53.27 56.92 58.02 62.57 63.97 71.00 63.15 62.93 62.17 60.05 64.69 64.48 62.48 61.53 56.51 55.98  354 373  94.52  1576.23  n,559  1150.59  0  Mean 3 - 5 0 0 7 4 0 7  58.37888  428.1111  42.61/|I|4  0  1926 1927 1928  1929  1930 1931 1932  1933 1934  1935 1936  1937 1938  1939  1940 1941 1942  1943  1944 1945 1946 1947 1948 1949 1950 1951 1952  Total  3.92 3.88 4.02 3.86 4.91 3.13 3.80 3.66 3.55 3.20 3.58 3.59 3.30 3.79 3.70 3.28 2.62 3.22 3.28 4.24 2.20 3.57 2.71 3.14 4.00 3.22 3.15  ,  392  38k 356 325 290 276 300 316 326 353 347 365 396 427 502 518 556 561 566 540 546 537 540 550 565  50.70 51.82 51.31 50.67 48.39 45.68 43.40 42.32 40.92 38.91 36.64 35.22 33.92 35.13 • 42.03 40.34 40.15 36.11 36.02 35.66 34.68 36.09 38.66 39.63 56.45  Time  54.49  -13 -12 -11 -10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 0 + 1 + 2 + 3 +  4'  + 5 + 6 + 7 + 8 + 9 +10 +11 +12 +13  Year 1926  1927 1928  1929  1930 1931 1932  1933 1934 1935 1936  1937 1938  1939  1940 1941 1942  1943  1944 1945 1946 1947 1948 1949 1950 1951 1952  XX 1 2 232.8480  235.2444  242.2854 227.9716 260.8683 160.4125 181.9060 I64.I876 186.7655 173.4720 190.5276 191.2393 187.836O 219.8958 231.5090 209.8216 186.0200 203.3430 206.4140 263.6008 132.1100 230.9433 174.7408 196.1872 246.1200 181.9622 176.3370  1 3  x  X  1,387.68  1,447.24  1,575.84 1,482.24 1,747.96 1,017.25 1,102.00 1,010.16 1,065.00 1,011.20 1,167.08 1,267.27 1,145.10 1,383.35 1,465.20 1,400.56 1,315.24 1,667.96 1,823.56 2,378.64 1,245.20 1,927.80 1,479.66 1,686.18 2,160.00 1,771.00 1,773.45  198.7440 201.0616 206.2662 195.5862 237.5949 142.9784 164.9200 154.8912 145.2660 124.5120 131.1712 126.4398 111.9360 133.1427 155.5110 132.3152 105.1930 116.2742 118.1456 151.1984 76.2960 128.8413 104.7686 124.4382 225.8000 177.9050 171.6435  l 5 x  -50.96 -46.56 -44-22 -38.60  -44.19  '  -25.04 -26.60 -21.96 -17.75 -12.80 -10.74 - 7.18 - 3.30 0 + 3.70 + 6.56 + 7.86 +12.88 +16.40 +25.44 +l5.4o +28.56 +24.39 +31.40 +44.00 +38.64 +40.95  39,912.82  4,187.8402  -53.72  5,517.9726  40,465.062  4,027.9173  0  -23.4073  -552.242  +159.9229  T o t a l 5,494.5653 Adj.  X  -53.72  (x,  V •= V •=  =  -234073  (x  =  -34.95  (x,  s' •=  -53.72  (x^ x j )  x  <x  2  5  -23.4073  =  +869.1893 i . 3 k 5 b  - 552.242 =  +10,791.253 b  +159.9229 =  -129.3175 b ^ ^ ^  - 53.72  +520.70  =  + 1 0  2  b  1  2  1  -  2  3  >  k  3  5  k  5  -129.3175  (x, X 3 )  =  +159.9229  (x  2  = +520.70  •=  +17,88k  (x  2  =  -235.27  >791.253 i . 2 k 5 " b  1 2  3  +276,980.67  b  1  +17,884  b  1  3  3  >  2  ^  k  5  5  = +10,791.253  9 . 3 1 7 5 i k . 2 3 5 + 5 2 0 . 7 0 0x5.234 b  -34.95  - 34.95  V  -552.2k2  +17,881+  b ^ ^  +1340.5918  ^  - 235.27  b ^ ^  m  2  3  $  b ^ ^  _235.27 b  + 1638  l  5  <  2  3  k  x>^ ^ 2  CO  S o l v i n g the above equations by D o o l i t t l e ' s method:  a  i.2345  =  M  b  12.345  =  b  l4.235  =  + '°S ^74 1  0  +0  b  - 32982 1  b  13.245  =  l5.234  =  -0.006924416 +0.04551475  i " i2.345 2 " i3.245 3 " i4-235 4 " i5.234 5 b  M  = 3.5007407  .-  b  M  3.009921  b  +  M  b  2.96434249  M  - 5.66636302 - 0  = -2.21120083 Estimating X  equation:  -2.21120083  =  ±  = 6.4650831  x  1  +• 0 . 0 5 1 5 5 7 4 X -  2  - 0 . 0 0 6 9 2 4 4 1 X + 0.132982X^  0.00692441 x  3  + 0.04551475x^  3  vO  Year  +  b  2  X  2  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945  3.0625095 3.1259252 3.107361+5 3.041+9800 2.7392446 2.6423167 2.4680527 2.3128649 2.7124348 2.7949266 2.7438848 2.7464627 2.9346472 2.9913603 3.2259465 3.2981268 3.6605754 3.2558498 3.2445072 3.2053235  1947 1948 1949 1950 1951 1952  3.3352482 3.3244211 3.2221306 3.1723268 2.9135087 2.8861832  1946  3.0960219  X,  - b ^ X^  +b  2.4512411 2.5828049 2.7143687 2.6589734 2.4650899 2.2504332 2.0080789 1.9111371 2.0(773230 2.1881135 2.2573576 2.4443167 2.1+027703 2.5274096 2.7420663 2.9567231 3.4760538 3.58681+44 3.8499720 3.8845940 3.9192161 3.7391814 3.7808278 3.7184082 3.7391814 3.8084255 3.8984428  6.7421874 6.8911272 6.8233064 6.7381979 6.4349990 6.0746177 5.7714188 5.6277982 5.4416234 5.1743296 4.8724605  4  4  4.6836260  4.5107494 4.6716576 5.5892335 5.3644939  5.3392273  4.8019800 4.7900116 4.7421381 4.6118158 4.7993204  5.l4l084l 5.2700767 7.5068339 7.3472555 7.2461892  bcj  X» 1  -0.5916917 -O.5I+61770 -0.5006622 -0.4551475 -0.4096327 -O.3641I8O -0.3186032 -0.2730885 -0.2275737 -0.1820590 -0.1365442 -0.0910295 -0.0455147 0 +0.0455147 +0.0910295 +0.1365442 +0.1820590 +0.2275737 +0.2730885 +0.3186032 +0.3641180 +0.4096327 +0.4551475 +0.5006622 +0.5461770 +0.5916917  4.55056 4-67677 4.50444 4-45785 4.08832 3.89118 3.70159 3.54523 3.63796 3.38788 3.01124 2.68354 2.78591 2.92441 3.90743 3.58573 3.44909 2.44184 2.20092 2.12475 1.89602 2.54830 2.88321 3.01774 5.22944 4-78731 I+.61442  -0.63 -0.80 -O.48 -0.60 +0.82 -0.76 +0.10 +0.11 -0.09 -0.19 +0.57 +0.91 +0.51 +0.87 -0.21 -0.31 -0.83 +0.78 +1.08 +2.12 +0.30 +1.02 -0.17 +0.12 ~1.23 -1.57 -1.46  0.3969 0.6400 0.2304 O.36OO 0.6724 0.5776 0.0100 0.0121 0.0081 O.O36I 0.3249 0.8281 0.2601 0.7569 0.01+41 0.0961 0.6889 0.6084 1.1664 4.4944 0.0900 I.0404 0.0289 0.0144 1.5129 2.4649 2.1316  CD O  81  6 21  s. 1.2345 2  -2 R  n  1.2345  x 19.495  =  5.57  2.0592  5.57 "7.6292  =  7.6292  0.27  STANDARD ERRORS OF THE REGRESSION COEFFICIENTS Variance o f Variance o f X  2  =  7 . 6 2 9 2 / 26 = 0 . 2 9 7 2 7 7  =  33.44282  V a r i a n c e o f X^  =  Variance of X  =  k  Variance o f  10,653.10269 51.561223  = 63.0  1.  Standard e r r o r o f e s t i m a t e o f b  2.  Standard e r r o r o f e s t i m a t e o f b  2  =  0.0214912  =  0.0017418  3 3.  Standard e r r o r o f estimate o f b  k.  Standard e r r o r o f estimate o f b ^ = 0 . 0 1 6 4 8 1  k  = 0.030626  XI = 6 . 4 6 5 0 8 - 0 . 0 0 6 9 2 4 4 X^ Year  Av. Income  Av. D i s appearance  X  / X  Income e l a s t i c i t y  3  1929-33  326.2  4.26  76.57  1939-44  460.7  3.27  140.89  -0.976 -  1945-52  550.4  2.65  207.70  - I . 4 3 8 - O.362  -0.530 - 0.133 0.245  FiGj.9.  DISPOSABLE  I N C O M E " A N D THE C O N S U M P T I O N *F C O F F E E ?  I  CANADA,  l«U6-'Si.  3«»  F'Q.10. t  D i s P O S A 6 L E INCOME * 1  -1-  AND  THE. C O N S U M P T I O N OF " T E A ,  C A N A D A , H26--S2. r*»  -10  3  :  .» i * ' 7  .44  .INCOME.  -8 a -  83  Grouping a c c o r d i n g t o the s c a t t e r : 1.  1926 t o 1941 421.67518 b +38685.575 b +2954.035 b - 0 . 7 9 9 7  = 0  38685.575 b +25697  b +866.48  = 0  2954.035  b + 6 0 3 . 2 3 4 l b -145.2453=  2  k  3  2  3  b +866.48 2  b -48.593  3  k  k  0  S o l u t i o n o f the above e q u a t i o n s by Doolittle»s method give s: ( P r i c e o f Tea)  b  2  «  +0.007604958  (Income)  b  3  =  -0.0170666799  =  +0.2226877  ( P r i c e of C o f f e e ) b  k  a  -0.34071773  =  X - L = - O . 3 4 0 7 1 7 7 3 + 0.007605X - 0.017067X + 2  2.  3  1942-$2 166.4352 b  2  -  36062.17 b  3  - 3046.8025b + 3-4698 = 0  -36062.17 b  2  +  3449  b  3  - 150.948  b -l6.08  -3046.8025b  2  -  150.948  b  3  - 732.59  b -11.9796 = 0  k  S o l u t i o n o f these equations g i v e s : b b  = -0.017875923  2  =  3  -O.OOOO727389  = +0.0010233  b^  Standard e r r o r s o f R e g r e s s i o n C o e f f i c i e n t s : A.  0.2226877Xj  Group 1926-1941 1.  S.E. ( b )  =  0.015936  2.  S.E. ( b )  =  0.0039724  3.  S.E. ( b )  «  0.046470  2  3  k  k  k  = 0  84  B.  Group 1942-52 1.  S.E. ( b ) = 0.049J+592  2.  S.E. ( b ) = 0 . 0 1 0 5 4 0 4  3.  S.E. (b.) = 0.022859  2  3  As the r e s u l t s from m u l t i p l e  regression  are not s i g -  n i f i c a n t , and moreover, the g r a p h i c method does not show any r e l a t i o n s h i p w i t h p r i c e o f t e a and p e r c a p i t a d i s p o sable income, perhaps c r o s s - e l a s t i c i t y might put l i g h t the  r e l a t i o n s h i p o f change i n the r a t i o o f c o f f e e  to tea  consumption and the change i n the r a t i o o f p r i c e o f t e a to p r i c e of coffee. « l  x  _ "  In t h i s  analysis,  Per c a p i t a Consumption o f t e a Per  c a p i t a Consumption o f Coffee  on  Year  X.  1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952  1.4961832 1.4109090 1.3766712 1.3591599 1.6045751 0.9842767 1.2794612 1.1401869 1.1093750 0.9937888 0.9754768 1.0466472 0.8616137 0.9154589 1.0081743 0.6804976 0.6649746 0.6276803 0.4059388 0.9257641 0.3156384 0.8581730 0.3961988 0.6289617 0.6557377 0.5047021 0.4578488  X  0.8535353 0.8546923 0.8513356 0.8579410 0.9107848 0.8913170 0.9066221 0.9433794 0.7777989 0.7177642 0.6884629 0.6611601 0.5959241 0.6054808 0.6717276 0.6306081 0.5654929 0.5718131 0.5723820 0.5735885 0.5775187 0.5578915 0.5995657 0.6342829 0.9174386 0.9777030 0.9733833  l  X  2  1.2770451 1.2058930 1.1720092 1.1660747 1.4614226 0.8773026 1.1599878 0.0756288 0.8628706 0.7133060 0.6715796 0.6920014 0.513456k 0.5542938 0.6772857 0.4291273 0.3760384 0.3589158 0.2320659 O.5310076 0.1822871 0.4787674 0.2375472 0.2720831 0.6015991 0.4934487 0.4456624  0.7285225 0.7306989 0.7247723 0.7360628 0.8295289 0.7944460 0.8219636 0.8899647 0.6049711 0.5151854 0.4739812 0.4371327 0.3551255 0.3666070 0.4512180 0.3976666 0.3197822 0.3269702 0.3276211 0.3290038 0.3335278 0.3112429 0.3594790 O.4023148 0.8416939 0.9559031 0.9474750  2.238614 1.990639 1.895027 1.847153 2.574420 0.966784 1.637120 1.300056 1.230768 0.987618 0.951542 1.095372  0.742372 O.838O67 1.016467 0.463080 0.442185 0.393982 0.164381 0.857031 0.996286 0.736455 0.156974 0.184007 0.429982 0.254722 0.209627  x  1  =  21+.4835688  x  2  =  19.93959445  X X =  18.7187891  x|  15.3124807  X  X^  2  =  a  =  X-^X  =  2  aX  + b X 2  2  + b  2  X'  2  24.4835688  27a  + 19.93959445  b  2  18.7187891  19.93959445a  + 15.3124807  b  £  0.031976185 0.029430118 +1.0865122 +0.104405 R R  °» 92747 4.401031 6  1.234  =  0  m  l  B  l  k  +0.396  1.234  Standard e r r o r o f estimate o f b =  2  /0.169270423-1.18048225(0.0225781) 26 X 0.169270423  = -  0.18001  GRAPHIC ANALYSES  ONSUMPTiONOP  «  *  37  •  •X  COFFE  67 ST INCOM6_  ^ouieces: TRftOE. 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