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Production function analysis of paddy farming in Sri Lanka Abeysekara, W. A. Terrence 1976

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A PRODUCTION FUNCTION ANALYSIS OF PADDY FARMING IN SRI LANKA by W. A. TERRENCE ABEYSEKARA .Sc. ( A g r i c ) , The U n i v e r s i t y o f S r i Lanka, 1972 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department o f A g r i c u l t u r a l Economics We accept t h i s t he s i s as conforming to the requ i red standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1976 W. A. Terrence Abeysekara, 1976 In p resent ing t h i s t he s i s in p a r t i a l f u l f i l m e n t o f the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree tha t permiss ion fo r ex tens i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r ep re sen ta t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l gain s h a l l not be a l lowed without my w r i t t e n permi s s ion . Department of A f t " ^ ' C u t / ^ t m X f^js^tr^u^ The U n i v e r s i t y of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1WS Date AP fyr) / l^fX, i ABSTRACT The primary purpose of t h i s t he s i s was to analyse under l y ing input -output r e l a t i o n s h i p s in paddy farming in S r i Lanka. C r o s s - s e c t i on study data invo lved 107 paddy farms from f i v e major paddy d i s t r i c t s . The' per iod under study was the 1972-73 Maha paddy season. Data c o l l e c -t i o n was based on farm record keeping. P roduct ion f unc t i on a n a l y s i s was app l i ed in the study. Factor shares and l ea s t squares regres s ion methods were used to es t imate produc-t i o n f unc t i on s . Resu l t s .from the f a c t o r shares method were not completely s a t i s f a c t o r y in the context of the study. Acco rd ing l y the l ea s t squares method assumed most importance in the a n a l y s i s . Both m u l t i - l i n e a r and Cobb-Douglas funct ions were f i t t e d to the data and the l a t t e r gave the best s t a t i s t i c a l f i t . Funct iona l a n a l y s i s was a l s o used at the reg iona l l e v e l . The dummy v a r i a b l e technique and d i s c r im i nan t a n a l y s i s i d e n t i f i e d two regions w i t h i n the main sample. P r o d u c t i v i t y index comparisons were made among d i s t r i c t s composing the two reg ions. The ana l y s i s w i t h respect to the o v e r - a l l sample i nd i ca ted the presence of resource m i s - a l l o c a t i o n on paddy farms. T yp i c a l paddy farmers were found to be employing land and d r a f t s e r v i ce s e f f i c i e n t l y when a l l o ther resources remained at geometric mean l e v e l s of use. Never-the less , under s i m i l a r - c o n d i t i o n s of geometric mean l e ve l resource use, f e r t i l i z e r and labour were not used i n t e n s i v e l y enough. In p a r t i c u l a r f e r t i l i z e r was s e r i o u s l y u n d e r - u t i l i z e d . C a l c u l a t i o n of expansion path resource combinations and var ious p r o d u c t i v i t y est imates conf irmed these r e s u l t s . Therefore , the ana l y s i s showed that paddy output can be i i increased by more i n t en s i v e a p p l i c a t i o n of f e r t i l i z e r and labour. The l a t t e r c a l l s f o r i n t en s i v e p r a c t i c e s such as t r a n s p l a n t i n g and manual weeding. But study f i nd i n g s a l s o suggested the ex i s tence of labour shortages dur ing peak per iods of paddy farming. Marginal p r o d u c t i v i t i e s of f e r t i l i z e r and labour in both low and high response des ignated reg ions , showed once again that at geo-metr i c mean l e ve l s of resource a p p l i c a t i o n , they were s u b s t a n t i a l l y higher than t h e i r p r i c e s . In the reg iona l a n a l y s i s the d r a f t s e r v i ce input ( i n c l ud i n g animal and t r a c t o r s e r v i ce s ) was found to be t y p i c a l l y o v e r - u t i l i z e d in the low response region and u n d e r - u t i l i z e d in the high response reg i on . The l a t t e r po in t s to a shortage of d r a f t s e r v i ce s in the high response reg ion which can act as a c o n s t r a i n t to increased paddy p r oduc t i on . Expansion path resource combinations were a l s o c a l c u l a t e d fo r each reg ion to act as g u i d e - l i n e s fo r e f f i c i e n t resource app1i cat i on . A n a l y s i s a t the d i s t r i c t l e ve l f o r a s c e r t a i n i n g the p r o d u c t i v i t y of a l l inputs other than land in paddy farming, showed that Polonnaruwa d i s t r i c t was twice as p roduct i ve as Kurunegala d i s t r i c t . In the same context Hambantota came c l o s e to Polonnaruwa, whereas, Kandy and Colombo c l o s e l y matched Kurunegala. TABLE OF CONTENTS Page ABSTRACT ACKNOWLEDGEMENTS CHAPTER I INTRODUCTION 1 A. Problem Se t t i n g 1 1. The Ag ra r i an Sector and Economic Development in S r i Lanka 1 2. Role of the Rice Industry in the Economy of S r i Lanka ^ B. Objec t i ve s 6 C. Thes is O rgan i za t i on 7 I I LITERATURE REVIEW 9 A. Ea r l y Developments in P roduct ion Funct ion Ana l y s i s 9 B. Developments in Product ion Funct ion Ana l y s i s in A g r i c u l t u r e 12 C. Recent I nve s t i ga t i on s i n to Resource A l l o c a t i v e E f f i c i e n c y in Subs i stence A g r i c u l t u r e 17 III THEORETICAL CONSIDERATIONS . 22 A. 1. P roduct ion Functions and the Law of D imin i sh ing Returns 22 A. 2. C r i t e r i a f o r E f f i c i e n t Resource A l l o c a t i o n . . 25 a . Necessary Cond i t i ons 30 b. S u f f i c i e n t Condi t ions 31 c . Relevance of Average and Marginal P r o d u c t i v i t y Est imates 31 i v CHAPTER Page B. S e l e c t i o n and Appropr iateness o f Methodology . . 32 IV CONCEPTUAL MODEL AND DATA 36 A. Technique of Paddy P roduct ion 36 B. Conceptual Model of Paddy Product ion 37 C. Input and Output Va r i ab l e s 38 D. Source and Method of C o l l e c t i o n o f Data k3 V ESTIMATION OF PADDY PRODUCTION FUNCTIONS AND INTERPRETATION OF RESULTS k7 A. Ana l y s i s of the Tota l Farm Sample 48 1. E s t ima t i on o f P roduc t i on Funct ions kS a. Factor Shares Est imates h8 b. Least Squares Est imates 57 2. Resource P r o d u c t i v i t y Ana l y s i s 68 a . Returns to Sca le on Paddy Farms 68 b. Pa t te rns of Resource Use on Paddy Farms . . 69 c. Marginal P r o d u c t i v i t i e s of Inputs 71 d. D i s t r i b u t i v e Shares of I nd i v i dua l Inputs of P roduct ion 76 e. Average Apport ioned Value P r o d u c t i v i t i e s and Farm Net Value P r o d u c t i v i t i e s of Farm Inputs 78 f . Assessment of Input A l l o c a t i v e E f f i c i e n c y . 81 B. Ana l y s i s of Resource P r o d u c t i v i t i e s in Paddy Product ion a t the Regional Level 89 1. Need f o r I d e n t i f y i n g D i f f e r e n t P r o d u c t i v i t y Regions in Paddy Product ion 90 2. I d e n t i f i c a t i o n of Regions 91 V CHAPTER Page a . Dummy V a r i a b l e Method 92 b. D i s c r im inant Ana l y s i s Method 93 3. E s t imat i on of Regional P roduct ion Funct ions f o r High and Low Response Farming Regions . . 97 k. Assessment of Resource P r o d u c t i v i t i e s at the Regional Level 101 a . MVP's of Inputs in Low and High Response Regions . . . . . 102 b. E f f e c t s of Changing Input Levels on Tota l Paddy Output 107 c . I n t e n s i t i e s of Resource Use in Low and High Response Regions 108 5- Resource P r o d u c t i v i t y Ana l y s i s at the D i s t r i c t Level 109 VI SUMMARY, IMPLICATIONS AND RECOMMENDATIONS OF THE STUDY . 112 A. Summary of F ind ings 112 B. Imp l i ca t ions and P o l i c y Recommendations of the Study . . • 117 1. Need f o r P r o d u c t i v i t y Increases in the Paddy Sector 117 2. Output Expansion through Approp r i a te Product P r i c i n g 119 3. Increased Supp l ie s of F e r t i l i z e r 120 4. Expansion of Farm C red i t F a c i l i t i e s 121 5. Investments in Farmer Educat ion 122 C. Areas f o r Further Research 123 1. Labour Use in Paddy C u l t i v a t i o n 123 2. Imp l i ca t i on s of R ice P o l i c y on the Domestic Paddy Sector 125 v i CHAPTER Page 3 . Studies on Economic Responses from the Farmer 127 SELECTED BIBLIOGRAPHY 129 APPENDIXES 1 Procedure f o r C a l c u l a t i n g MVP's 1 3 ^ 2 Computation o f Returns to Scale 135 3 Method of D i s t r i b u t i n g Tota l Product to I nd i v i dua l Factors of P roduct ion 137 k Comparative Data on S r i Lanka 's Major Crops, 1 9 6 7 ; Acreage, Output and Exports 1 3 8 5 Comparative Data on S r i Lanka 's Major Crops, 1 9 6 7 ; Employment and Value Added 1 3 9 6 D i s t r i b u t i o n of Sample Farms accord ing to D i s t r i c t s . . . 140 7 Simple C o r r e l a t i o n C o e f f i c i e n t s f o r Va r i ab l e s Included in Paddy Regression Ana lys i s - -Tota 1 Farm D a t a -Low Response Region ( 6 3 Farms) 1^1 8 Simple C o r r e l a t i o n C o e f f i c i e n t s f o r Va r i ab l e s Included in Paddy Regress ion Anal ys i s - -Tota 1 Farm D a t a -High Response Region (kk Farms) 1^2 v i i LIST OF TABLES TABLE Page 5.1. Factor Shares Est imates of C o e f f i c i e n t s of Farm Based Cobb-Douglas Product ion Funct ion at Geometric and A r i t h m e t i c Mean Leve l s o f Output and Inputs f o r the Maha Paddy Season 55 5.2. Simple C o r r e l a t i o n C o e f f i c i e n t s f o r L o g a r i t h m i c a l l y Transformed Va r i ab l e s Included in Paddy Regression A n a l y s i s — T o t a l Farm D a t a — A l l Survey Farms 60 5.3. M u l t i - l i n e a r P roduct ion Funct ion C o e f f i c i e n t s — Total Farm Data—A l 1 Survey Farms 63 5.4. Cobb-Douglas P roduct ion Funct ion C o e f f i c i e n t s -Tota l Farm Data—Al 1 Survey Farms 65 5.5. Levels of Inputs and Output in Paddy P roduct ion on Per Farm and Per Acre Bases; 1972-73 Maha Season— A l l Survey Farms 70 5.6. E f f e c t s of Increas ing (a) A l l Inputs, (b) Some Inputs on Marginal Value P r o d u c t i v i t i e s and Tota l Ou tpu t— Based on Equation R^  72 5.7. E s t imat ion of MVP's of Resource Inputs a t D i f f e r e n t Levels of A p p l i c a t i o n (Assuming Geometric Mean Leve l s fo r Other Resources)--Based on Equation R^  75 5.8. Amounts of Value Product Cont r ibu ted by Resource Inputs to Tota l Paddy Output ( A l l Resources a t Geometric Leve l s )—Based on Equation R^  77 5.9- Average Apport ioned Value P r o d u c t i v i t i e s and Farm Net Value P r o d u c t i v i t i e s of Inputs in Paddy P roduct ion a t Geometric Mean Input Leve l s—Based on Equat ion R^ . . . 73 5.10. Comparison o f Marginal Value P r o d u c t i v i t i e s and Marg inal Factor Costs o f Inputs in Paddy Farming at Geometric Mean Leve l s of A p p l i c a t i o n — A l l Survey Farms — Based on Equation R^ 82 3-11 - Comparison of Actua l and Optimal Levels of Inputs at the Geometric Mean Output of R s . l S ^ - SO and the Geometric Mean Input of 1.8 Ac res—Based on Equat ion R^ 86 v i i i TABLE Page 5-12. Cobb-Douglas Product ion Funct ion C o e f f i c i e n t s — T o t a l Farm D a t a — A l l Survey Farms (Regional Dummy V a r i a b l e Included) 93 5.13. A r i t h m e t i c Mean Leve l s of Input A p p l i c a t i o n on Paddy Farms in Low and High Response Reg i on s— Inco rpo ra t i ng Tota l Survey Data Sk 5.14. C l a s s i f i c a t i o n Funct ions f o r Rice Farms in Low and High Response Reg i on s— Inco rpo ra t i ng Tota l Survey Data 95 5.15. M u l t i - l i n e a r P roduct ion Funct ions f o r Paddy Farms in Low and High Response Reg i on s— Inco rpo ra t i ng Tota l Survey Data 98 5.16. Cobb-Douglas Product ion Funct ions f o r Paddy Farms in Low and High Response R e g i o n s — l n c o r p o r a t i ng Tota l Survey Data 99 5.17. Marginal Value P r o d u c t i v i t i e s and Corresponding Geometric Mean Levels of Inputs per Farm in Low and High Response Regions 102 5.18. Expansion Path Resource Combinations f o r Low and High Response Regions a t Geometric Mean Levels of Output - - I nco rpo ra t i ng Tota l Survey Data 105 5.19. Product ion E l a s t i c i t i e s of D i f f e r e n t Inputs in Low and High Response Regions--Based on Cobb-Douglas Funct ions 107 5.20. Geometric Mean Levels of Per Acre Inputs and Outputs on Paddy Farms in Low and High Response Reg ions— Incorporat ing Tota l Survey Data . . . 108 5.21. O v e r a l l Input P r o d u c t i v i t y Measures and Corresponding Levels of Input A p p l i c a t i o n on Paddy Farms Accord ing to D i s t r i c t s 110 i x LIST OF FIGURES FIGURE Page 3 . 1 . Stages of P roduct ion and Rat iona l Resource Use 2 3 X ACKNOWLEDGEMENTS I wish to extend my deepest a p p r e c i a t i o n to my the s i s supei— v i s o r , Dr. M. J . Dor l i ng f o r h i s pa t i en t guidance and continuous encouragement dur ing a l l stages of the t h e s i s . I acknowledge the h e l p -f u l c r i t i c i s m s from Pro fes so r s J . D. Graham, R. B a r i c h e l l o , J . Richards and A. D. Woodland, members o f my the s i s committee. I would l i k e to express my g r a t i t u d e to the D i r e c t o r , Mr. C. Narayanasamy and Ch ief A d v i s e r , Mr. F. G. Saunders of the Ag ra r i an Research and T r a i n i n g I n s t i t u t e , Colombo, f o r p rov i d i ng me w i th the oppo r tun i t y of s tudy ing a t The U n i v e r s i t y of B r i t i s h Columbia. In a d d i t i o n I am indebted to the F.A.O. of the United Nat ions f o r p r o v i d -ing me w i t h the necessary f i n a n c i a l a s s i s t a n c e . I am s i n c e r e l y g r a t e f u l f o r the help of Mr. A. S. Ranatunga and other members of the Ag ra r i an Research and T r a i n i n g I n s t i t u t e , C o l -ombo, in making study data a v a i l a b l e . I a l s o wish to thank the many farmers, who, w i l l i n g l y co-operated in supp ly ing data and the d i s t r i c t a g r i c u l t u r a l ex tens ion s t a f f fo r t h e i r a s s i s t ance in c o l l e c t i n g i n f o r -mat ion. I take personal r e s p o n s i b i l i t y f o r any e r r o r s and omiss ions in the s tudy. CHAPTER I INTRODUCTION A. PROBLEM SETTING 1. The Agra r i an Sector and Economic Development in S r i Lanka The a g r i c u l t u r a l indust ry con t r i bu te s about o n e - t h i r d of S r i Lanka 's Gross Domestic Product and prov ides employment f o r h a l f the c o u n t r y ' s t o t a l labour f o r c e . This study deals w i t h an economic a n a l y s i s of resource use in r i c e p roduc t i on , a major a g r i c u l t u r a l a c t i v i t y in S r i Lanka. Along w i th the three main export c r o p s - - t e a , rubber, coconut - -r i c e occupies a predominant p lace in the economy of the i s l a n d . The output o f these four a g r i c u l t u r a l crops i s s t i l l the major i n f l uence in S r i Lanka 's c r u c i a l balance of payments problem. There fo re , concern has been repeated ly expressed by the planners over the lagg ing rates of a g r i c u l t u r a l development, and t h i s has been p a r t i c u l a r l y true of the subs i s tence s e c t o r . The task of supp ly ing domestic food requirements i s s o l e l y dependent on the subs i s tance or peasant s e c t o r , in which r i c e farming is the most important e n t e r p r i s e . In s p i t e of a l l the e f f o r t s to develop the subs i s tence sector i t s response has been f a r from s a t i s f a c t o r y . As i s common in other developing c o u n t r i e s , slow improvement in the economic we l f a re of the peasantry has caused f r u s t r a t i o n among p lanner s . The f a i l u r e of t h i s sec to r i s c l e a r l y demonstrated by recur rent food s c a r c i t y c r i s e s . The 1 2 d i s appo i n t i n g performance of subs i s tence a g r i c u l t u r e has c reated a tremendously large burden on the a l ready s t r a i ned economy. As a r e s u l t the government has been fo rced to c u r t a i l or postpone other high p r i o r i t y development programmes in the non-farm sec to r of the economy. Although some degree of cont roversy s t i l l e x i s t s as to whether emphasis should be p laced on a g r i c u l t u r e or i ndu s t r y , i t i s g ene ra l l y agreed that the former has a c r i t i c a l r o l e to p lay in the process of economic development in c oun t r i e s l i k e S r i Lanka, p a r t i c u l a r l y in the i n i t i a l stages of growth. In a develop ing economy, a growing a g r i c u l -t u r a l i ndus t ry can be an important source o f food supply f o r the popu la -t i o n and i t can a l s o c o n t r i b u t e much to the growth of indust ry by supp ly -ing raw m a t e r i a l s , labour and c a p i t a l . ' Furthermore, in an economy c h a r a c t e r i z e d by l o w - p r o d u c t i v i t y labour and an extreme shortage of c a p i t a l , a g r i c u l t u r e can p lay a c r u c i a l r o l e in the o v e r a l l development e f f o r t by p rov i d i n g an oppo r tun i t y f o r economic growth w i th r e l a t i v e l y l i t t l e phy s i ca l c a p i t a l . Emp i r i c a l ev idence seems to suggest that the income e l a s t i c i t y of demand f o r a g r i c u l t u r a l products in develop ing coun t r i e s i s so h i g h — three to four times more than in developed c o u n t r i e s — t h a t a s tagnat ing a g r i c u l t u r a l i ndus t ry can r e s t r a i n economic growth by causing food s ho r t -2 ages. Th is s i t u a t i o n can a l s o lead to i n f l a t i o n a r y food p r i c e s or Peter T. Bauer and B a s i l Yamey, The Economics of Underdevelop-ing Count r i e s , Chicago U n i v e r s i t y P re s s , 1971, pp. 235 -36• 2 Ea r l 0. Heady, A Primer on Food, A g r i c u l t u r e and P u b l i c P o l i c y , New York, Random House, 1967, pp. 9-10. 3 u t i l i z a t i o n of f o r e i g n exchange f o r importat ion o f food. If the l a t t e r takes p lace i t w i l l be at the expense of c a p i t a l goods and raw m a t e r i a l s needed fo r the i n d u s t r i a l s e c t o r . Many i n v e s t i g a t i o n s i n t o f a c t o r s c o n t r i b u t i n g to the a g r i c u l t u r a l 3 lag in developing coun t r i e s have y i e l d e d a wide v a r i e t y of r e s u l t s . In gene ra l , these analyses have tended to show at l e a s t four major sources of problems—economic, t e c h n o l o g i c a l , s o c i o - c u l t u r a l and p o l i t i c a l — c o n -t r i b u t i n g to the s i t u a t i o n . The economic f a c t o r s i nvo l ve c on s i de r a t i on s such as inadequate c r e d i t f a c i l i t i e s , improper market ing mechanisms, d e f i c i e n t supply of inputs and i n e f f i c i e n t a l l o c a t i o n of a v a i l a b l e r e -sources. The q u a l i t y of inputs and outputs , the ease w i th which inputs can be s u b s t i t u t e d fo r another, and the e x i s t i n g stock of p roduct ion techn iques, can be cons idered as some of the t e chno l o g i c a l f a c t o r s . The s o c i o - cu l t u r a1 aspects inc lude the response and a t t i t u d e s of people t o -wards change, tenure and ownership pat terns of t r a d i t i o n a l s o c i e t i e s and s i m i l a r i n s t i t u t i o n a l a spect s . The f i n a l category dea l i n g w i t h p o l i t i c a l f a c t o r s , inc ludes types and e f f i c i e n c y of t a x a t i o n , q u a l i t y o f s o c i a l s e r v i ce s such as t r a n s p o r t a t i o n , h e a l t h , and a g r i c u l t u r a l extens ion s e r -v i c e s , e t c . , and a l s o the e f f i c i e n c y and responsiveness of the c i v i l s e r v i c e and p o l i t i c a l leaders to the needs and a s p i r a t i o n s of the people. Whi le admi t t i ng that t h i s l i s t does not prov ide an e l abo ra te and c l e a r -cut c l a s s i f i c a t i o n , i t , neve r t he l e s s , i nd i ca te s some of the v a r i e t y and For an i n t e r e s t i n g d i s c u s s i o n see R. Wharton C l i f t o n , J r . , Subs i s tence A g r i c u l t u r e and Economic Development, Chicago, A l d i ne P u b l i s h ing Co., 1970. k complex i ty of problems of a g r i c u l t u r a l development in a developing economy l i k e S r i Lankas. Thus, i t i s apparent that there can be numerous approaches to development of the peasant a g r i c u l t u r a l sec to r in a growing economy. Broadly speaking, these approaches can be d i v i d e d i n t o two c a t e g o r i e s , economic and non-economic. Whi le the non-economic c o n s i d e r a t i o n might e n t a i l a l t e r i n g the e x i s t i n g s o c i a l and p o l i t i c a l framework of s o c i e t y , the economic f a c t o r s would b a s i c a l l y invo lve the man ipu la t ion and r e -s h u f f l i n g of e x i s t i n g stocks of resources in the most e f f i c i e n t manner and supply ing a d d i t i o n a l resources wherever i t was deemed necessary. Economic development i s p r imar i1y connected w i th i nc rea s ing the number of permanent annual income streams produced by the economy. With regard to r i c e p roduc t i on , t h i s can be accomplished by s h i f t i n g the p ro -duct ion p o s s i b i l i t y f r o n t i e r of the indust ry outwards and more e f f i c i e n t a l l o c a t i o n of the e x i s t i n g resource i npu t s , or by some combination of both. The former method invo lves a p p l i c a t i o n of more convent iona l and non-convent ional resources as we l l as i n t r oduc t i on of modern r i c e p r o -duct ion techno log ie s , e i t h e r s epa ra te l y or in combinat ion. The l a t t e r method invo l ves opt imal resource and output combinations in the context of marginal rates o f s u b s t i t u t i o n and marginal ra tes o f t r an s fo rmat i on . 2. Role of the Rice Industry in the Economy of S r i Lanka S r i Lanka can be descr ibed as having a dual a g r i c u l t u r a l economy in which a commercial, e xpo r t - o r i e n t ed p l a n t a t i o n sec to r e x i s t s a l ong -s ide a t r a d i t i o n a l , s u b s i s t e n c e - o r i e n t e d , peasant s e c t o r . The p l a n t a -t i o n sec to r deals w i th the three major export c rops , wh i l e the subs i s tence 5 sec to r i s a s soc i a ted w i t h domestic food supply and i s mainly concerned w i t h r i c e p roduc t i on . P r i o r to independence in 1 9 4 8 , r i c e p roduct ion had been neg lected in favour of the export c rops . But s ince independence, success ive governments have taken steps to increase domestic r i c e ou tput . The importance o f r i c e in the economy of S r i Lanka i s ev ident from data presented in Appendices 4 and 5 . Appendix 4 shows a t o t a l c u l t i v a t e d area of 3 - 5 m i l l i o n acres under four major crops namely r i c e , t e a , coconut and rubber, of which r i c e alone occupies 1.3 m i l l i o n a c re s . Appendix 5 shows that employment generated by the r i c e i ndus t ry accounted f o r 41 per cent o f t o t a l employment prov ided by the four major c rops . Hence, r i c e occupies a predominant p o s i t i o n in the land-use pa t te rn and i t i s a major source of employment in S r i Lanka. The s i g n i f i c a n c e of r i c e in the economy stems from the f a c t that i t c o n s t i t u t e s the s t ap l e d i e t of a popu la t i on of 13 m i l l i o n . Food consumption data f o r S r i Lanka shows that in the per iod 1 9 6 3 - 6 4 , r i c e and wheat j o i n t l y accounted f o r 9 7 - 5 per cent of g r a i n consumption and 5 5 per cent of t o t a l c a l o r i e i n -take. As the c a l o r i f i c va lue by weight of these two g ra in s i s almost i d e n t i c a l , a high degree of s u b s t i t u t i o n in consumption can e x i s t be-tween them. However, at the usual r e l a t i v e p r i c e s r i c e i s p r e fe r r ed to wheat a t a l l income l e v e l s . Th i s f a c t i s c l e a r l y ev ident from the r e -l a t i v e per c a p i t a consumption f i g u r e s of wheat and r i c e . In 1966-67 t o t a l per c a p i t a consumption of both r i c e and wheat was 1 2 3 . 6 kgs., of which r i c e accounted f o r 1 0 3 - 5 kgs. The present s t a te o f under product ion of r i c e has become a sub-s t a n t i a l burden on the na t i ona l economy. For instance in 1 9 6 9 - 7 0 , t o t a l 6 d i r e c t and i n d i r e c t s ub s i d i e s towards p r o v i s i o n of r i c e to consumers amounted to Rs. 556.8 m i l l i o n , which was 19 per cent of t o t a l government revenue. This inc luded a d i r e c t subsidy of Rs. 219-6 m i l l i o n to producers and Rs. 237.2 m i l l i o n f o r consumers. There fo re , these f a c t s i n d i c a t e the nece s s i t y of expanding domestic r i c e output by way of s u i t -ab le adjustments in the i ndu s t r y . An increase in r i c e output would r e s u l t in the sav ing of a cons ide rab le amount of f o r e i g n exchange through import s u b s t i t u t i o n . This sav ing could be used f o r import ing the c a p i t a l goods necessary f o r i n d u s t r i a l development. Therefore, an i n v e s t i g a t i o n of resource-use e f f i c i e n c y in r i c e product ion in S r i Lanka i s of major i n t e r e s t . Through economic a n a l y s i s i t i s po s s i b l e to make resource adjustment recommendations f o r t h i s commodity, and t h i s i n fo rmat ion helps to form a bas i s f o r p o l i c y d i r e c t i v e s . In t h i s regard, i n t e r e s t would mainly centre on measures of marginal con-t r i b u t i o n to t o t a l output by d i f f e r e n t resources, e l a s t i c i t y of output w i t h respect to i n d i v i d u a l inputs employed and the p r o d u c t i v i t y d i f f e r -ences between a g r o - c l i m a t i c a reas . B. OBJECTIVES The pr imary purpose of the study i s to ana ly se the economics of product ion on paddy farms in S r i Lanka and a s c e r t a i n the nature of c o r r e c t i v e measures f o r i nc rea s i ng paddy output in the major a reas . The a n a l y s i s is based on the hypothes is that a g r i c u l t u r a l resources were not S p e c i f i c areas are g iven in Chapter IV. 7 being used e f f i c i e n t l y in these a reas . In other words i t was po s tu l a ted that a g r i c u l t u r a l resources could be reorganized to generate a g reate r output of paddy w i t h the same l e v e l s of i nput s , o r , conve r se l y , the same output could be obta ined w i th fewer resources . The other o b j e c t i v e s of the study are to i d e n t i f y resource u t i l i z a t i o n pa t te rn s and to prov ide g u i d e l i n e s f o r the e f f i c i e n t use of a g r i c u l t u r a l inputs in the areas under c o n s i d e r a t i o n . More s p e c i f i c a l l y these ob jec t i ves can b'e def ined as: i . to determine p r o d u c t i v i t y c o e f f i c i e n t s f o r re levant resources in paddy product ion in s e l ec ted areas ; i i . to measure the gap between e x i s t i n g and opt imal l e v e l s of resource use on sample farms and, thereby show the degree of economic e f f i c i e n c y of resource u t i l i z a t i o n in 1973 at the farm l eve l ; i i i . to determine app rop r i a te economic adjustments in the e x i s t -ing stock of resources on farms in the areas s t u d i e d , from the s tandpo int of p r o f i t max imizat ion . The study f o r a t t a i n i n g these o b j e c t i v e s was based on farm records mainta ined by 107 paddy farmers f o r the 1 9 7 2 - 7 3 Maha season r i c e crop in f i v e s e l e c ted d i s t r i c t s . The main research technique employed was product ion f u n c t i o n a n a l y s i s , using f a c t o r shares and m u l t i p l e reg re s -s i o n , whereby, the a s s o c i a t i v e e f f e c t s of inputs are expressed in terms of reg res s ion c o e f f i c i e n t s . C. THESIS ORGANIZATION The study is d i v i ded i n t o s i x chapte r s . The present chapter prov ides i n t r oduc to r y in format ion f o r the a n a l y s i s , w h i l e the second 8 chapter surveys re levant l i t e r a t u r e . Chapter III dea l s w i t h fundamental t h e o r e t i c a l concepts r e l a t i n g to resource a l l o c a t i o n and appropr ia tenes s of methodology. Chapter IV d i scusses the conceptual model, the nature of v a r i a b l e s and the source and c o l l e c t i o n o f da ta . Chapter V repor t s on the research a n a l y s i s and r e s u l t s . The l a s t chapter presents a sum-mary of f i n d i n g s and d i scusses t h e i r re levance to cu r ren t problems. It a l s o makes recommendations to p o l i c y makers and suggests areas f o r f u t u r e re sea rch . CHAPTER I I LITERATURE REVIEW A. EARLY DEVELOPMENTS IN PRODUCTION FUNCTION ANALYSIS A number of e a r l y economists such as Smith, R icardo and Malthus hypothes ized the general nature of the product ion f u n c t i o n . S ince then much l i t e r a t u r e has been added regard ing a p p l i c a t i o n of formal produc-t i o n f unc t i on s to farm s t u d i e s , both a t the micro and macro l e v e l . One of the f i r s t economists to hypothes ize an a l b e g r a i c form fo r the phy s i ca l a g r i c u l t u r a l product ion f unc t i on was Knut W i c k s e l l . He i n f e r r e d that i n c rea s i ng returns to c a p i t a l and labour inputs were p o s s i b l e when f e r -t i l i z e r i s added to n u t r i t i o n a l l y d e f i c i e n t s o i l s . Thus, he showed that a g r i c u l t u r a l output i s dependent on the quan t i t y and q u a l i t y of resources used to o b t a i n i t . He f u r t h e r showed that a g r i c u l t u r a l o u t -put was c l e a r l y dependent on land, labour and c a p i t a l inputs and the r e l a t i o n s h i p could be expressed i n terms of a mathematical equa t i on . He demonstrated that i f the inputs f o r a g iven pe r iod of time are de-noted by X j , X^, X^ and the corresponding t o t a l output by P, the p r o -duct ion f unc t i on can be de f ined as: P = f (X,, X 2 , X 3 ) [2.1] Although W i c k s e l l was the f i r s t to hypothes ize the mathematical bas i s of p roduct ion f u n c t i o n s , the f i r s t emp i r i c a l e s t i m a t i o n of the 9 10 parameters of a product ion f u n c t i o n was attempted by Char les W. Cobb and Paul H. Douglas in 1928. ^ The type of f unc t i on used in t h e i r study i s g ene ra l l y known as the Cobb-Douglas product ion f u n c t i o n . However, the o r i g i n of t h i s p a r t i c u l a r f unc t i on can be t raced to W i c k s e l l who mentioned i t in a footnote as having the f o l l o w i n g f o rmu l a t i o n : P = X™ W i c k s e l l goes on to s t a te that the c o e f f i c i e n t s f o r t h i s type of f unc t i on might add up to u n i t y , imply ing a s t a te of constant returns to s c a l e . In t h e i r study, Cobb and Douglas f i t t e d a f u n c t i o n , s i m i l a r to that of Wick-s e l l ' s to the data on American manufactur ing indust ry f o r the pe r i od 1899 to 1922. This work c o n s t i t u t e d the f i r s t formal e s t ima t i on of a p roduct ion f unc t i on us ing time s e r i e s da ta . The form of the f i t t e d k k-1 f unc t i on was P = b L C , where P was the p r ed i c t ed output over the p e r i o d , L was labour employment and C was the c a p i t a l input in the i n -•75 .25 du s t r y . The f unc t i on der i ved from the data was P = 1.01 L' C ' The s e l e c t i o n of t h i s p a r t i c u l a r f u n c t i o n a l form, sub ject to the c o n s t r a i n t that the c o e f f i c i e n t s add up to u n i t y , was presumably due to t h e i r wish to as s ign the t o t a l product to the two f a c t o r s of p r oduc t i on . I f the sum of the c o e f f i c i e n t s were g rea te r or less than u n i t y , the t o t a l product would be greater or less than the t o t a l amount inputed to the two f a c t o r s by way of marginal p r o d u c t i v i t i e s . A complete d i s t r i b u t i o n of product among inputs can be exp la i ned in terms of E u l e r ' s theorem of product Char les W. Cobb and Paul H. Douglas, "A Theory of P r o d u c t i o n , " Am. Econ. Rev., 18: 1928, pp. 139-156. 11 exhaus t ion , which s ta te s that under cond i t i on s of l i n e a r homogeneity the t o t a l product w i l l be j u s t exhausted when marginal products are inputed to the resources . In t h e i r l a t e r s t u d i e s , however, Douglas and co-workers re l axed the r e s t r a i n t of f o r c i n g the sum of e l a s t i c i t i e s of the i n d i v i d u a l r e -sources in the f unc t i on to be equal to one and employed the f u n c t i o n a l k i form, P = b L C , where the c o e f f i c i e n t s j and k cou ld take any non-zero va l ue . It i s t h i s type of l o g - l i n e a r power f unc t i on which is commonly r e f e r r e d to as the Cobb-Douglas p roduct ion f u n c t i o n . The l a t t e r i s w ide l y used in product ion f unc t i on a n a l y s i s and in numerous other q u a n t i t a t i v e e s t ima t i on procedures in economics. The p o p u l a r i t y of t h i s s p e c i f i c f u n c t i o n a l form can be a t t r i b u t e d to the r e l a t i v e ease w i th which c o e f f i c i e n t s are computed, convenience of i n t e r p r e t i n g the e l a s t i -c i t i e s of product ion and a l s o the f a c t that the e s t ima t i on of parameters permits more degrees of freedom than some other a l g e b r a i c forms. A major attempt a t determining a p roduct ion f unc t i on from farm 2 data was reported in 1942. In t h i s study T o l l e y , Black and E z k i e l , based t h e i r e s t ima t i on on c r o s s - s e c t i o n a l observat ions of e n t e r p r i s e s . The input ca tego r i e s were s p e c i f i e d as l abour , f e r t i l i z e r and f eed . The un i t s of measurement were both in phy s i c a l and value terms. The data were used to es t imate a hog product ion f unc t i on and l i n e a r f u n c t i o n a l forms were used. From the r e s u l t s they concluded that d im in i s h i ng mar-g i n a l p r o d u c t i v i t i e s of resources p r e v a i l e d . H. R. T o l l e y , J . D. B lack and M. J . E z k i e l , Inputs as Related  to Output in Farm Organ i za t i on and Cost of Product ion S t ud i e s . Techn ica l B u l l e t i n 1277, USDA, Washington, D.C., 19^2. 12 A study by T i n t ne r in 1942 used data from 6 0 9 farms in Iowa S t a t e . S i x independent v a r i a b l e s were s e l e c ted as a f f e c t i n g farm output . In a d d i -t i on to land and labour T i n tne r inc luded farm improvement expend i tu re , l i q u i d a s se t s , working as set s and cash opera t ing expenses as v a r i a b l e s to e x p l a i n output . The est imated func t i on was not cons t ra ined w i t h respect to the sum of the e l a s t i c i t i e s . Decreasing returns to s ca le were shown by the est imated Cobb-Douglas f u n c t i o n , the sum of the input c o e f f i c i e n t s coming to . 8 6 . Heady pub l i shed h i s f i r s t study on product ion f unc t i on a n a l y s i s in 1 9 ^ 6 . This was based on survey data from a random sample. The design of the sample was such as to g ive unbiased est imates of c e r t a i n l i v e s t o c k and crop i n v e n t o r i e s . The input v a r i a b l e s used by Heady were r ea l e s t a t e , labour, machinery and equipment and l i v e s t o c k expenses. Both phy s i c a l and monetary values were used in measuring v a r i a b l e s as in the case of T i n t n e r . To obta in the best r e s u l t s Heady po inted out that p r e l im i na r y research should be c a r r i e d out to determine c o r r e l a t i o n s among the f a c t o r i nput s . He mentioned that i f high c o r r e l a t i o n s are present between f a c t o r inputs they may lend themselves to combinat ional assessment and t o t a l l i n g . Heady used a Cobb-Douglas f unc t i on in h i s a n a l y s i s which exp la ined about 7 7 per cent of the va r i ance o f output . B. DEVELOPMENTS IN PRODUCTION FUNCTION ANALYSIS IN AGRICULTURE An important development in recent p roduct ion s tud ie s has been the concept of d u a l i t y . Dua l i t y in r e l a t i o n to product ion theory i s 3 G. T i n t n e r , "A Note on the De r i va t i on of P roduct ion Funct ions from Farm Records. " Econometrica 16 : 1 9 4 4 , pp. 2 9 5 - 3 0 4 . E. 0 . Heady, " P r oduc t i on Funct ions from a Random Sample of Farms." J . Farm. Econ: 2 8 : 1 9 4 6 , pp. 9 8 9 - 1 0 0 4 . 13 analogous to dual and pr imal problems and s o l u t i o n s in mathematical p r o -gramming. In r e l a t i o n to product ion f unc t i on s d u a l i t y can be exp la i ned as f o l l o w s : g iven e i t h e r the minimum cost f unc t i on or the product ion f unc t i on and c e r t a i n r e g u l a r i t y assumptions, one can be un iquely d e t e r -mined from the o t he r . This impl ies that producers operate as though p r i c e s are given and they attempt to minimize cos t s of producing a c e r t a i n s p e c i f i e d l e ve l of ou tput . Recent p u b l i c a t i o n s by Diewert" ' and Dan ie l son^ exp lo re a p p l i c a t i o n s of d u a l i t y theory f o r the purpose of i d e n t i f y i n g and d e r i v i n g product ion f u n c t i o n r e l a t i o n s h i p s . It i s s u f f i c i e n t to note here that the present study was not conceived as working from farm cost m in im i za -t i on assumptions towards d e f i n i n g the a s soc i a ted dual p roduct ion f u n c t i o n . Work pub l i shed on t h i s type of approach leads one to th ink that data problems q u i c k l y become p r o h i b i t i v e . Another major advancement in product ion f u n c t i o n s tud ies i s the development o f a l t e r n a t i v e f u n c t i o n a l forms that can be used in e m p i r i c a l e s t i m a t i o n s . Important examples are the CES^ (constant e l a s t i c i t y of g s u b s t i t u t i o n ) and other f l e x i b l e gene ra l i z ed f unc t i on forms. These 0 See: W. E. Diewert, " A p p l i c a t i o n of Dua l i t y Theory. " D i scuss ion paper, No. 8 9 , The U n i v e r s i t y o f B r i t i s h Columbia, 1 9 7 3 -^ R. Dan ie l son, Three Stud ies in Canadian A g r i c u l t u r e . M.Sc. t h e s i s , The U n i v e r s i t y of B r i t i s h Columbia, 1974. ^ For an important d i s c u s s i o n o f the CES f u n c t i o n see: K. J . Arrow, H.B. Chenery, B.S. Minhas and R. M. Solow, " C a p i t a l - L a b o r S u b s t i -t u t i o n and Economic E f f i c i e n c y . " Rev. Econ. S t a t . , V o l . 43, No. 3, Aug. 1961, pp. 225-249. A l a i n De Janvry , "The Genera l i zed Power Product ion F u n c t i o n , " Am. J . Agr. Econ. 54: 1972, pp. 234-237. 14 s p e c i f i c types of product ion f unc t i on are very usefu l under c e r t a i n c i r -cumstances and they o f ten inc lude the more s imple f u n c t i o n a l forms as t h e i r s p e c i a l cases. For example the CES and gene ra l i z ed power ( e . g . , t ranscendenta l ) f unc t i on s inc lude the Cobb-Douglas as t h e i r s p e c i a l cases . The CES and other gene ra l i z ed f unc t i on s can have c l e a r advantages over s impler ones but in c e r t a i n respects they can have l i m i t i n g f ea tu re s too. For example the CES model a l l ows the assumption o f un i t a r y e l a s t i -c i t y of s u b s t i t u t i o n in a Cobb-Douglas f unc t i on to be r e l a xed . Neverthe-less the CES f u n c t i o n s t i l l imposes constant e l a s t i c i t y of s u b s t i t u t i o n between p a i r s o f independent v a r i a b l e s . With respect to the use of a l t e r n a t i v e f un c t i o na l forms a study 9 of cons ide rab le i n t e r e s t was conducted by S a l k i n in 1970, us ing a sample of paddy farms in Vietnam. He est imated Cobb-Douglas, CES and two other gene ra l i z ed forms of product ion f unc t i on f o r h i s da ta . On the bas i s of r e s u l t s he concluded that the major d i f f i c u l t y in s p e c i f y i n g product ion f unc t i on s w i t h s o p h i s t i c a t e d p r ope r t i e s was that they may on ly be e s t i -mated approx imate ly or by us ing very compl icated techn iques . Hence i t can be noted that the product ion f unc t i on models employed in the present study were of the s impler type. With the c r o s s - s e c t i o n a l data a v a i l a b l e there seemed to be no d i s t i n c t advantage in employing the more complex regress ion models. J . S. S a l k i n , On the S p e c i f i c a t i o n and E s t imat ion o f A l t e r n a t i v e  Funct iona l Forms in the Theory of P r oduc t i on . The Case of Rice Product ion  in South Vietman. Unpublished Ph.D. Thes i s , North Western U n i v e r s i t y , 1970, p. 190. 15 Examination of recent l i t e r a t u r e prov ides c l e a r ev idence that the product ion f u n c t i o n technique as a too l f o r ana l y z i n g farm problems has been cont inuous l y improved upon. S ince the e a r l y f i f t i e s many s tud ie s have been pub l i shed by Heady and other research workers in v a r -ious aspects of product ion f u n c t i o n a n a l y s i s , i n co rpo ra t i ng more and more t h e o r e t i c a l concepts . As a r e s u l t , the o b j e c t i v e s , a n a l y t i c a l t oo l s and research methodology of the technique are h i g h l y developed and r e -l a ted f i n d i n g s o f t en prov ide a g reate r bas i s fo r a c t i o n than r e s u l t s from many other areas in app l i ed economic s . ' ^ This has been made po s s i b l e by the use of advanced s t a t i s t i c s , mathematics and computers. A remarkable featu re of recent developments in product ion f unc t i on a n a l y s i s has been the broadening of research o b j e c t i v e s . The e a r l y s tud ie s seem to have been mainly concerned w i th i n d i v i d u a l farm a n a l y s i s . Now the recogn i t i on of m u l t i p l e o b j e c t i v e s f o r p roduct ion f unc t i on a n a l y -s i s has increased i t s use. M u l t i p l e o b j e c t i v e s of p roduct ion f unc t i on a n a l y s i s have con-c e r n e d ' ' ( l ) p r o v i d i n g g u i de l i n e s to i n d i v i d u a l farmers f o r the e f f i -c i e n t combination of resources , (2) ana l y z i n g the impact of p u b l i c and p r i v a t e p o l i c i e s on the use of farm resources, (3) des ign ing programmes l u For a d i s cu s s i on of recent trends of development of the p ro -duct ion f unc t i on method see, G.L. Johnson, " S t r e s s on Product ion Economics" in A.E.A. Readings in the Economics o f A g r i c u l t u r e , Kar l A. Fox and Gale D. Johnson ( e d s j , R ichard D. I rw in , Inc. , 1969, pp. 203-20. W. W. W i l cox , "Research in Economics of Farm P r o d u c t i o n , " J . Farm Econ., August, 19^7. 16 12 of adjustment in farming a reas . S i m i l a r l y , Warren has s ta ted the dual o b j e c t i v e of product ion f u n c t i o n ana l y s i s to be one of gu id ing i n d i v i d u a l entrepreneurs and a c q u i r i n g broader understanding of the a g r i c u l t u r e i ndu s t r y . S ince product ion f unc t i on s have been t r a d i t i o n a l l y a s s oc i a ted w i th i n d i v i d u a l farm u n i t s , t h e i r a p p l i c a t i o n to indus t ry -w ide problems has sometimes been over looked. Viewed in i t s e n t i r e t y , a g r i c u l t u r e is a compet i t i ve indus t ry p rov id i ng a s i t u a t i o n where o p t i m i z a t i o n of r e -source use by i n d i v i d u a l s leads to o p t i m i z a t i o n c ond i t i o n s being achieved f o r s o c i e t y , which in turn impl ies a p a r t i c u l a r income d i s t r i -b u t i o n . This f o l l ows from the fundamentals of s o c i a l we l f a re a n a l y s i s ' ' which s t a t e that under compet i t i ve cond i t i on s the s o c i a l product would be maximized i f , and on ly i f , consumers maximize t h e i r u t i l i t y and p ro -ducers maximize t h e i r p r o f i t s . Problems w i l l e x i s t in app ly ing the above o p t i m i z i n g c r i t e r i a in cases where p r i c e s do not r e f l e c t compet i t i ve demand and supply cond i t i on s f o r products and f a c t o r s . As a consequence, d ivergence w i l l occur between the ac tua l and f r ee market p r i c e s in any segment of a g r i -c u l t u r e which is not c o m p e t i t i v e . In such cases s p e c i a l a n a l y t i c a l approaches are requ i red to eva luate cos t s and bene f i t s in the p r i v a t e and p u b l i c sec to r s of the economy. However, w i t h i n the l i m i t s of these S.W. Warren, S t a t i s t i c a l Ana l y s i s in Farm Management, J . Farm. Econ ., February, 1 9 3 6 . 1 3 J.M. Henderson and Richard E. Quandt, M icro Economic Theory, New York, McGraw-Hi l l Book Company, 1 9 5 8 , pp. 2 5 4 - 2 9 2 . 17 c o n d i t i o n a l f o r c e s , more e f f i c i e n t combinations of resources on i n d i -v i dua l farms augment s o c i a l net product . C. RECENT INVESTIGATIONS INTO RESOURCE ALLOCATIVE EFFICIENCY IN SUBSISTENCE AGRICULTURE Attempts to study resource a l l o c a t i o n by farmers in les s developed coun t r i e s (LDC's) are rather 1 i m i t e d , a lthough i n t e r e s t in t h i s subject has been growing. The purpose of t h i s s e c t i on is to review the more important s tud ie s on t h i s s ub j e c t . In doing t h i s s p e c i f i c a t t e n t i o n w i l l be paid to the bas ic assumptions under ly ing such s t u d i e s , t h e i r general methodology and recent attempts to es t imate a l l o c a t i v e e f f i c i e n c y in subs i s tence a g r i c u l t u r e . Several important s tud ie s on a l l o c a t i v e behaviour of farmers in t r a d i t i o n a l a g r i c u l t u r e have concluded that r e s u l t s are in conformity 14 w i t h S c h u l t z hypothes i s : " t h e r e are few s i g n i f i c a n t i n e f f i c i e n c i e s in a l l o c a t i o n of f a c t o r s of product ion in t r a d i t i o n a l a g r i c u l t u r e . " In these s tud ie s the measurement of a l l o c a t i v e e f f i c i e n c y i s based on the assumption of p r o f i t maximizing behaviour on the par t of peasant farmers. P r o f i t maximizing approaches have been c r i t i c i z e d by some econ-15 1 6 omists and s o c i o l o g i s t s . ' The i r arguments are based on two cons ide ra t T.W. S chu l t z , "Transforming T r a d i t i o n a l A g r i c u l t u r e , " New Haven, Ya le U n i v e r s i t y P res s , 1 9 6 3 , p. 3 7 . 15 See: G. Myrda l , Economic Theory and Underdeveloped Regions. London, Duckworth, 1 9 5 7 ; D. Seers, "The L i m i t a t i o n s of the Spec ia l Case , " B u l l e t i n of Oxford I n s t i t u t e of Economics and S t a t i s t i c s 2 5 : May, 1 9 6 3 , pp. 7 7 - 9 8 . [16 H. My int , "Economic Theory and the Underdeveloped C o u n t r i e s , " Jour . P o l . Econ., Oct. 1 9 6 5 , pp. 4 7 7 - 4 9 1 . 18 F i r s t l y , the Economic theory used in such a n a l y s i s i s e s t a b l i s h e d in r e l a t i o n to the p a r t i c u l a r s o c i a l and i n s t i t u t i o n a l s e t t i n g of the i n d u s t r i a l l y developed c o u n t r i e s . Therefore , i t i s argued that a p p l i c a -t i o n of p r o f i t maximizing theory to underdeveloped subs i s tence economies has l i t t l e mean ing . ' ^ Secondly, in view of the important i n f l uence of r i s k f a c t o r s in peasant farming systems, i t i s thought that p r o f i t max i -mizat ion does not hold t r u e . Most o b j e c t i o n s to the assumption of p r o f i t maximizat ion seem to be based on casual emp i r i c i sm and ob se r va t i on s . Arguing in favour of 18 using hypotheses in economic research Friedman s ta te s t ha t : The evidence fo r a hypothesis always c on s i s t s of i t s repeated f a i l u r e to be c o n t r a d i c t e d , cont inues to accumulate as long as the hypothes is i s used, and i t by very nature i s d i f f i c u l t to document at a l l comprehens ively. It tends to become part of the t r a d i t i o n and f o l k l o r e of a sc ience revealed in the t e n a c i t y w i th which hypotheses are held ra ther than in any textbook l i s t of instances in which the hypothesis has f a i l e d to be c o n t r a d i c t e d . Therefore , qu i t e apart from i t s acceptance or c o n t r a d i c t i o n , i t would seem that p r o f i t maximizat ion can serve as a usefu l po s t u l a t e on the bas i s of which research can proceed and be extended. In view of the above c r i t i c i s m s i t i s important to d i scus s some of the s tud ie s which have shown that standard economic theory i s r e l e -vant to the farmers in subs i s tence a g r i c u l t u r e . See: Michael L i p t o n , "The Theory of Opt imiz ing Peasant . " Jou r . Dev. S tud i e s , 1968, pp. 327-351. 18 M i l t o n Friedman, "The Methodology of P o s i t i v e Economics, " in Essays on Economics, M. Friedman, e d i t o r , Chicago, Univ. Chicago P res s , 1953, p. 23. 19 19 Wise and Yotopoulous conducted a r i gorous e m p i r i c a l t e s t of the economic r a t i o n a l i t y of subs i s tence farmers in Greece. By employ-ing a number o f econometric techn iques, they re laxed the usual major assumptions under l y ing such a n a l y s i s . They assumed that the farms d i d not have the same product ion f u n c t i o n . The Cobb-Douglas type of product ion f u n c t i o n employed had constant input c o e f f i c i e n t s , yet e x -p l i c i t l y a l lowed f o r farm to farm v a r i a t i o n in e f f i c i e n c y , t e c h n i c a l knowledge and volume and q u a l i t y of f i x e d f a c t o r s . On the ba s i s of t h e i r f i n d i n g s the researchers concluded t ha t : . . . the idea i t s e l f of app l y i ng such a framework to t r a d i t i o n a l s e l f - s u b s i s t e n c e a g r i c u l t u r e may sound qua in t or e c c e n t r i c ! S t i l l , the r e s u l t s a re h i gh l y s a t i s f a c t o r y and are in keeping w i th accepted economic theory: a t l ea s t two - th i rd s of the v a r i a t i o n in observed behaviour in our random sample of farms can be exp la i ned by a p r i o r i t h e o r e t i c a l not ions on p r o f i t max im i za t i on .^ The methodology employed in two major s t ud i e s o f resource a l l o c a -21 t i v e behaviour of farmers in LDC 's, shows that both of them used cross s e c t i o n a l data and reg res s ion techn iques . The exact methodology used in such s tud ie s v a r i e s w i t h s p e c i f i c approaches to handl ing d i f f e r e n t s i t u a t i o n s . 19 John Wise and Pan A. Yotopoulous, "The Emp i r i ca l Content of Economic R a t i o n a l i t y : A Test f o r a Less Developed Economy," J . P o l . Econ. 77: Nov.-Dec. 1969, pp. 876-IOO3. 2 0 I b i d . , p. 999. 21 D.E. Welsch, "Response to Economic Incent ive by A b a k a l i k i R ice Farmers in Eastern N i g e r i a , " J . Farm Econ. 47: Nov, 1965, pp. 900-914, and V. Chennereddy, " P r oduc t i on E f f i c i e n c y in South Indian A g r i c u l t u r e , " J . Farm Econ. 49: Nov. 1967, pp. 816-820. 20 22 For example, Sahota in h is study i n vo l v i n g three bodies of cross s e c t i o n a l data f o r three years , r e l a t i n g to s i x areas in India and e i g h t farm groups, used a number of i n t e r cep t and s lope changing v a r i a b l e s in the regres s ion a n a l y s i s . His study was l i m i t e d to per acre data , s i n ce 23 t o t a l farm data were u n a v a i l a b l e . Hopper s e l e c ted 43 farms to observe resource a l l o c a t i o n behaviour of t r a d i t i o n a l farms in I nd i a . The data were c o l l e c t e d at the peak pe r iod o f farming when f a c t o r markets faced the most compet i t i ve c o n d i t i o n s . The usual approach to judg ing e f f i c i e n c y of resource use from c r o s s - s e c t i o n a l samples has been to employ techniques which do not con-s i de r r i s k f a c t o r s a s soc i a ted w i t h peasant fa rming. D i l l o n and Ander-24 son were probably amongst the f i r s t to incorporate r i s k c o n s i d e r a t i o n i n to the a p p r a i s a l of resource use. In r epo r t i ng t h e i r study, they s t a ted that " r i s k a t t i t u d e s must be an important element in understand-ing farmer behaviour in undeveloped a g r i c u l t u r e . " They presented a d e c i -s ion theory a p p l i c a t i o n of c ross s e c t i o n a l p roduct ion f unc t i on es t imates f o r assessment of a l l o c a t i v e e f f i c i e n c y , ma in ta in ing that "What i s needed i s a measure of p r o f i t maximizing e f f i c i e n c y that has a d i r e c t economic i n t e r p r e t a t i o n yet depends on the s t a t i s t i c a l q u a l i t y of under l y ing 22 Gian S. Sahota, " E f f i c i e n c y of Resource A l l o c a t i o n in Indian A g r i c u l t u r e , " Am. J . A g r i c . Econ. 50: Aug, 1968, pp. 584-605-23 David W. Hopper, " A l l o c a t i o n E f f i c i e n c y in a T r a d i t i o n a l Indian A g r i c u l t u r e , " J . Farm Econ. 47: Aug, 1965, pp. 611-624. 24 J . L. D i l l o n and J . R. Anderson, " A l l o c a t i v e E f f i c i e n c y , T r a -d i t i o n a l A g r i c u l t u r e and R i s k , " Am. J . A g r i c . Econ., 53: 1971, PP- 26-32. 21 product ion f u n c t i o n . " In t h i s s tudy, the measure of a l l o c a t i v e e f f i c i e n c y invo lved the expected oppo r tun i t y lo s s o f the average input a l l o c a t i o n r e l a t i v e to the most p r o f i t a b l e a l l o c a t i o n under constant t o t a l expend i -t u r e . D i l l o n and Anderson ' s con s i de ra t i on s regard ing unce r t a i n t y about the product ion f unc t i on have two main a spec t s . F i r s t l y , even i f a t rue f unc t i on represented a l l farms the est imated f unc t i on might d i f f e r from the true one owing to "pure no i s e " or unsystematic v a r i a t i o n s in the independent v a r i a b l e s . Secondly, unce r t a i n t y a f f e c t s the product ion f unc t i on in the sense that es t imated c o e f f i c i e n t s can be thought of as not being r i g i d l y f i x e d . The study by D i l l o n and Anderson was based on the f a c t that these c o e f f i c i e n t s are not f i x e d , but only sample e s t i -mates having a p a r t i c u l a r p r o b a b i l i t y d i s t r i b u t i o n . In a d d i t i o n to being a va luab le c o n t r i b u t i o n to research methodology the study a l s o prov ided p a r t i a l support f o r the hypothes is o f p r o f i t maximizing behaviour among farmers in subs i s tence a g r i c u l t u r e . Furthermore, they concluded that t h e i r r e s u l t s a re more favourab le to the hypothes i s o f expected p r o f i t maximizat ion than expected. CHAPTER I I I THEORETICAL CONSIDERATIONS This chapter i s d i v i ded i n to two s e c t i o n s . Sect ion A i s devoted to the more bas i c t h e o r e t i c a l concepts of product ion and cos t s r e l e van t to the present a n a l y s i s . Sec t ion B deals w i th t h e o r e t i c a l aspects i n -vo lved in the s e l e c t i o n and appropr ia teness of methodology used in the study. A - l . PRODUCTION FUNCTIONS AND THE LAW OF DIMINISHING RETURNS The theory o f product ion in economics c o n s i s t s of an a n a l y s i s of how ent repreneurs , under a given " s t a t e o f a r t " or technology, combine var ious inputs to produce a s t i p u l a t e d output in an e f f i c i e n t manner. The core of p roduct ion theory r e l evan t to e f f i c i e n t resource a l l o c a t i o n is based on the concept of the product ion f unc t i on and the law of d i m i n -i sh ing r e t u r n s . A p roduct ion f unc t i on in general i s an expres s ion o f the r e l a t i o n s h i p between the phy s i ca l inputs and output . The law o f d im in i s h i n g marginal returns i s a c t u a l l y an e m p i r i c a l a s s e r t i o n of r e a l i t y and i t s ta te s that as the amount o f a v a r i a b l e i n -put is i nc reased, w i th other inputs held cons tant , a po in t i s reached beyond which the marginal product d e c l i n e s . This law is v a l i d under the f o l l o w i n g c o n d i t i o n s : (a) the s t a t e of technology i s g i ven , (b) the p o s s i b i l i t y e x i s t s f o r va ry ing a s i n g l e i nput , (c) there e x i s t other p r o -duc t i ve s e r v i c e s whose q u a n t i t i e s can be he ld cons tant . 22 23 A Product ion f unc t i on of the c l a s s i c a l type inc ludes ranges of i n c r ea s i n g , decreas ing and negat ive marginal r e t u r n s . In terms of the t o t a l product curve these ranges help de f i ne the three stages of p r o -d u c t i o n , i l l u s t r a t e d w i th respect to a s i n g l e v a r i a b l e input in the f o l l o w i n g diagram: 0 output (Y) / Input (Xj) F igure 3-1. Stages of P roduct ion and Rat iona l Resource Use Any l e ve l of resource u t i 1 i z a t i o n in Stage I of product ion i s c l e a r l y uneconomic s i nce i nc rea s ing average returns to the v a r i a b l e input are a s soc i a ted w i th under u t i l i z e d f i x e d i nput s . A r a t i o n a l producer would never operate in t h i s reg ion , s i n ce a p p l i c a t i o n o f a d d i t i o n a l v a r -i a b l e inputs could always b r ing about higher average p r o d u c t i v i t y . In t h i s s tage, the f i x e d inputs are present in too large a p ropo r t i on r e l a t i v e to the v a r i a b l e i nput . There fo re , a g reate r product from g iven resources cou ld be a t t a i n e d by d i s c a r d i n g or leav ing i d l e some of the f i x e d f a c t o r s . However, in the extreme s h o r t - r u n , i t may be necessary f o r the producer to operate in stage I i f there i s no p o s s i b i l i t y of 2k app ly ing more v a r i a b l e input or a l l ow i ng some of the f i x e d inputs to remain i d l e . I t must be remembered that as the length of run under con s i de ra t i on inc reases , more and more of the f i x e d f a c t o r s become v a r i a b l e u n t i l in the extreme long run a l l f a c t o r s can be sa id to be var i a b l e . Stage III covers the other area of i r r a t i o n a l p r oduc t i on . Here, the marginal product of the v a r i a b l e input i s nega t i ve imply ing a de-c l i n i n g t o t a l product . In stage III the resource input i s combined w i t h f i x e d inputs in uneconomical ly large p ropor t i ons and the v a r i a b l e input is used beyond the po in t of zero marginal product . Under these c i r cum-stances, withdrawal of some of the v a r i a b l e inputs w i l l always lead to an increase in t o t a l output . It i s t h e o r e t i c a l l y po s s i b l e f o r farmers to operate i n such regions due to lack of in format ion and resource ad -justment problems. Nonetheless, instances of i t happening are l i k e l y to be i s o l a t e d and r a r e . Thus, under cond i t i on s o f r a t i o n a l dec i s i on making stages I and III are e l im i na t ed from a product ion process . P roduct ion must occur in stage l l - - be tween the ex tens i ve and i n t en s i v e p r o d u c t i v i t y margins of the v a r i a b l e input . In other words, product ion must take p lace w i t h i n the range o f v a r i a b l e input a p p l i c a t i o n which runs from maximum average product to zero marginal product . Therefore the l e ve l a t which a v a r i a b l e input i s app l i ed to f i x e d f a c t o r s can never f a l l o u t s i de t h i s stage i f the goal i s to maximize p r o f i t . However, t h i s c o n d i t i o n determines on ly a range of economic o p e r a t i o n . S t i p u l a t i o n of the exact po in t of opt imal resource a l l o c a t i o n would i nvo l ve c o n s i d e r a t i o n of p r i c e s of input and output . This development is d i scussed in the f o l l o w i n g s e c t i o n . 25 A -2 . CRITERIA FOR EFFICIENT RESOURCE ALLOCATION If t o t a l p r o f i t whether f o r the a g r i c u l t u r a l indust ry as a whole or f o r a farm, i s to be maximized, resources must be a l l o c a t e d among d i f f e r e n t t e chn i c a l un i t s in such a manner that t h e i r marginal va lue p r o d u c t i v i t i e s per rupee of inputs are equal in a l l cases. Maximum a l l o c a t i v e e f f i c i e n c y i s . ob ta i ned on ly when i t becomes impossi ble to r e a l l o c a t e resources wi thout decreas ing t o t a l product. of resources to use in p roduc t i on , i t i s necessary to apply the concepts of marginal f a c t o r cos t (MFC) and marginal va lue product (MVP). Marginal f a c t o r cos t r e f e r s to the co s t of a c q u i r i n g a un i t of an a d d i t i o n a l i n -put wh i l e MVP r e f e r s to the a d d i t i o n a l gross income r e s u l t i n g from a un i t increase in the inputs c e t e r i s pa r i bu s . As w i l l be shown l a t e r in t h i s chapter , the c r i t e r i a f o r determin ing e f f i c i e n t resource use are based on marginal values a l one . i n vo l ved , the optimum u t i l i z a t i o n of the resource i s achieved when i t s marginal va lue p r o d u c t i v i t y equals i t s c o s t . Mathemat ica l l y i f the pro duct ion f u n c t i o n i s represented by, In order to a s c e r t a i n p r o f i t maximizing p ropor t i ons and amounts In a s i t u a t i o n where one v a r i a b l e resource and one output are Y = f (X. X. — X ) where X n -I 2 n z X are f i x e d n then the marginal product (MP.) i s g iven by, MP, = 3f(X) [3.1] 26 Denoting the p r i c e s of output and input by and P^ , i t can be seen that the f i r s t order c ond i t i on f o r maximizing the p r o f i t f u n c t i o n , i s g iven by, n = Max P .Y - P .X, y x ] 1 and t he re f o r e , P .8X, P =—I [3.3] y 8y Equation [3.2] shows that the va lue of the marginal product of the input is equal to i t s p r i c e and equat ion [3-3] i nd i ca te s that product p r i c e equals marginal c o s t , a t the p r o f i t maximizing l e v e l o f resource a l l o c a -t i o n . In the same manner, when severa l v a r i a b l e resources are being cons idered, the f unc t i on can be represented as , y = f ( X r X 2 , X 3 X n ) [3.4] and MP. = , i = (1,2, ...n) [3.4] i The opt imal combination of inputs occurs when the f o l l o w i n g f i r s t order cond i t i on s hold f o r a l l inputs X., P y . f , (X) = PX ] [3.5] P . f (X) = PX y n n 27 from which i t f o l l ows t ha t , P . f . (X) P f (X) P f (X) Y 1 - V 2 = V n = i [ 3 6 ] PX. P X 0 • • • PX 1 1 3 J 1 2 n The above equat ions show that the necessary c o n d i t i o n f o r p r o f i t maximizat ion s t i p u l a t e s that the r a t i o of marginal va lue product to marginal f a c t o r cos t must be equal to one f o r a l l v a r i a b l e resources . However, in s i t u a t i o n s of c a p i t a l c o n s t r a i n t , i t w i l l not be po s s i b l e to u t i l i z e product ion inputs up to the po in t where MVP's equal MFC's. Hence under t h i s c o n d i t i o n r a t i o s in equat ion [3-6] w i l l be g reater than un i t y f o r p r o f i t max imizat ion . Consequently, f o r maximum economic e f f i -c iency to e x i s t in a l i m i t e d c a p i t a l s i t u a t i o n , resources must be a l l o -cated in such a manner that corresponding MVP's and MFC's show on ly the same r a t i o s . If c a p i t a l i s u n l im i t ed the r a t i o s must be equal to un i t y to achieve p r o f i t max imizat ion . The a n a l y s i s so f a r i s based on assumptions that farmers are p r o f i t maximizers , the l e ve l s o f c e r t a i n input f a c t o r s are v a r i a b l e and the r i s k and u n c e r t a i n t i e s invo lved in p roduct ion and marketing are min ima l . I t i s sometimes necessary to r e l a x these assumptions. Incorporat ing r i s k and unce r t a i n t y con s i de ra t i on s f o r r e s o l v i n g quest ions of p r o f i t maximizing behaviour in peasant farming, requ i res complex methods which are beyond the scope of t h i s t h e s i s . The c o n t r o l o f f a c t o r inputs by farmers i s of d i r e c t i n t e r e s t when dea l i ng w i th r e -source a l l o c a t i o n on the farms in the present s tudy. Observed l e v e l s of a p p l i c a t i o n of most input s , a l though va r y i ng , do not cover very wide ranges due to f a c t o r s such as c a p i t a l c o n s t r a i n t s . Therefore , a few 28 comments on the i m p l i c a t i o n s of c o n t r o l o f f a c t o r inputs by farmers are des i r a b l e . U sua l l y , c e r t a i n f a c t o r s o f product ion in farming cannot be i n -creased in the short run. Th i s is p a r t i c u l a r l y true in the case o f land, However these f a c t o r s can be decreased e a s i l y by non-use. For example labour, which i s supposedly in exces s i ve supply in develop ing economies, could be reduced i f i t d id not earn i t s marginal f a c t o r co s t . Any labour regarded as f r e e , e . g . , f am i l y labour, could be employed up to zero marginal p r o d u c t i v i t y w i thout reduct ion being necessary. The ex i s t ence of inputs which cannot be increased in the short run, can c reate cond i t i on s of cons t ra ined p r o f i t max imiza t ion . This s i t u a t i o n can be formulated in mathematical terms as f o l l o w s . Assuming P to be the p r i c e of output and P. and P. to be the p r i c e of f a c t o r s X. y . 1 J 1 and Xy r e s p e c t i v e l y , then f i r m ' s revenue f unc t i on i s g iven as: T.R. = P . f (X.,X.) [3-7] y ' J and i t s t o t a l cos t as , T.C. = P. X. + P. X. [3.8] 1 1 j j There fo re , p r o f i t II i s g iven by: n = P f (X., X.) - P. X. - P. X. Y 1 J 1 1 J J and from the f i r s t order cond i t i on s f o r a maximum we get , P f. - P. = 0 [3.9] y 1 1 P f . - P. = 0 [3.10] y j J 2 9 From equat ions [ 3 . 9 ] and [ 3 - 1 0 ] ' i t i s seen that a t opt imal l e v e l s the f a c t o r p r i c e r a t i o s should equal the marginal rates of sub-s t i t u t i o n when the two resources are v a r i a b l e . However, in the case cons idered the optimum l e ve l of cannot be achieved because of i t s cons t ra ined nature. There fo re , instead of [ 3 . 1 0 ] the f o l l o w i n g c o n d i -t i o n ho lds . P . f . > P. [ 3 . 1 1 ] Y J J Therefore equat ions [ 3 - 9 ] and [ 3 . 1 1 ] g ive the c o n d i t i o n , P. P. 1J - < 1 L [ 3 . 1 2 ] J ' or in terms of the marginal r a te of s u b s t i t u t i o n , 3X. f. P. ± = T ± < * L [ 3 - 1 3 ] 3X. f . P ' J J or f . f. [ 3 - 1 4 ] ' J This i l l u s t r a t e s that when a f a c t o r i s l i m i t e d below the l e ve l requ i red f o r unconstra ined p r o f i t max imizat ion , the marginal cond i t i on s (or cons t ra ined p r o f i t maximizat ion) e a s i l y f i t in w i th the theory f j and f . r e f e r to f i r s t d e r i v a t i v e s (marginal p r o d u c t i v i t i e s ) w i th respect to X . J and X j . In s t a t i n g equat ions [ 3 - 9 ] and [ 3 . 1 0 ] i t i s assumed that second order cond i t i on s are s a t i s f i e d . 30 p rev i ou s l y e xp l a i ned . Thus the farmer w i l l on ly maximize in so f a r as he can ad ju s t v a r i a b l e f a c t o r s under the p r i n c i p l e o f equi-margina1 re tu rn s . S ince paddy farmers are o f t en cons t ra ined by cash resources and other r i g i d i t i e s , they f i n d themselves f r equen t l y t r y i n g to maximize p r o f i t in the sho r t - run under sub-opt imal c o n d i t i o n s . a . Necessary Condi t ions 2 Heady po in t s out that c e r t a i n necessary c o n d i t i o n s must be met before maximum e f f i c i e n c y of farm resources can be a t t a i n e d . He s ta te s them as f o l l o w s : 1. The marginal ra te at which f a c t o r is transformed i n t o product must be the same fo r any p a i r o f farms us ing the same f a c t o r s and producing the same product . 2. The marginal ra te of s u b s t i t u t i o n between any p a i r of f a c t o r s must be the same fo r any two farms using both to produce the same product.3 3. The marginal rate of s u b s t i t u t i o n between two f a c t o r s must be the same f o r every product in which they are used. k. The marginal ra te of s u b s t i t u t i o n between any two products must be the same fo r any two farms producing bo th .^ 5. The marginal rate a t which two crops s u b s t i t u t e as products on one farm must be equal to the marginal r a te a t which they sub-s t i t u t e as f a c t o r s on another (or the same) farm. ^ E. 0. Heady, Economics o f A g r i c u l t u r a l P roduct ion and Resource  Use, New York, P r e n t i c e - H a l l , Inc., 1952, pp. 708-710. Two other c o n d i -t i on s are de f ined besides those quoted. These concern income and u t i l i t y of a resource in p roduct ion and consumption as we l l as an adaptat ion o f cond i t i on s p r e v i ou s l y s t a t e d . 3 For d e t a i l e d d i s cu s s i on of the f a c t o r - f a c t o r r e l a t i o n s h i p and the f a c t o r s u b s t i t u t i o n r e l a t i o n s h i p see I b i d . , Chs. 5, 6, and 7. For d i s cu s s i on o f the product-product r e l a t i o n s h i p see I b i d . , Ch. 7. 31 6. P r i c e r a t i o s must equal s u b s t i t u t i o n and t rans fo rmat ion ra tes in a l l cases such that (2) the f a c t o r - p r oduc t p r i c e r a t i o equa l s the marginal r a te a t which the f a c t o r is transformed i n to p r o -duct , (b) the product -product p r i c e r a t i o i s equal to the mar-g i n a l ra te of s u b s t i t u t i o n of any two commodities', (c) the f a c t o r - f a c t o r p r i c e r a t i o i s equal to the marginal rate of sub-s t i t u t i o n between any p a i r of f a c t o r s , (d) the d i scounted p r i c e r a t i o i s equal to the s u b s t i t u t i o n r a t i o f o r one product p ro -duced at two po in t s in t ime, and (e) the compounded p r i c e r a t i o i s equal to the s u b s t i t u t i o n r a t i o f o r two resources extending i n to t ime. b. S u f f i c i e n t Cond i t ions The p r opo s i t i on s enunciated above i n d i c a t e the economic and t echn i ca l product ion cond i t i on s which are necessary f o r (a) maximizat ion of output from given resources or (b) m in im iza t i on of resource inputs to produce a given l e ve l of output . Taken by themselves these c ond i t i o n s do not guarantee the most e f f i c i e n t resource a l l o c a t i o n . S u f f i c i e n t c ond i t i on s f o r opt imal resource a l l o c a t i o n requ i re that products are produced under decreas ing returns ( i n c r ea s i n g c o s t s ) . They a l s o s t i p u l a t e that resources s u b s t i t u t e a t decreas ing rates and commodities in combination are produced w i t h i n the complementing and supplementary ranges of oppor tun i t y curves . c . Relevance of Average and Marginal P r o d u c t i v i t y Est imates It can be shown that es t imates of marginal p r o d u c t i v i t y serve b e t t e r than those f o r average p r o d u c t i v i t y as a bas i s fo r making na t i ona l resource adjustment. The on l y instance where average p r o d u c t i v i t y of resources can be used as a r e l i a b l e bas i s f o r resource a l l o c a t i o n , w i t h -out re ference to marginal p r o d u c t i v i t y , i s in the extremely s i m p l i f i e d case where the product ion f u n c t i o n i s homogeneous o f degree one ( i . e . , 32 constant returns to sca le ) i n vo l v i n g on ly one input v a r i a b l e . When t h i s c ond i t i o n ho lds , marginal p r o d u c t i v i t y o f a resource i s constant and i s equal to average p r o d u c t i v i t y a t a l l l e v e l s of resource use. In homogeneous func t i on s of degree one w i t h more than one independent v a r i a b l e , marginal and average value products do not c o i n c i d e . How-ever , even though.there may be on ly one input v a r i a b l e , i f the product ion f unc t i on inc ludes both i nc rea s i ng and decreas ing marginal r e t u rn s , as i s the case in the c l a s s i c a l product ion f u n c t i o n , average p r o d u c t i v i t y est imates do not serve as a use fu l c r i t e r i a of e f f i c i e n t a l l o c a t i o n . B. SELECTION AND APPROPRIATENESS OF METHODOLOGY Recent developments in q u a n t i t a t i v e research in the m i c r o -economics of farm product ion are c h a r a c t e r i z e d by a v a r i e t y of mathe-mat i ca l research models. The techniques f o r i n v e s t i g a t i n g economic a d j u s t -ment p o s s i b i l i t i e s o f farm product ion are numerous and they can be c l a s s i -f i e d under three broad c a t e g o r i e s , namely: 1. budgeting 2. programming techniques 3. f u n c t i o n a l a n a l y s i s Budgeting has been a t r a d i t i o n a l method of e s t ima t i n g gains and losses in farm management s t u d i e s . A farm budget can be def ined as a set of expec ta t i on s f o r resource use of the farm. A plan p ro jec ted f o r the e n t i r e mix of products and input s , i n c l ud i ng marketing and f i n a n c i n g , i s descr ibed as a complete budget, wh i l e a plan i n v o l v i n g on ly par t of the p roduct ion process i s r e f e r r e d to as a p a r t i a l budget. In a p a r t i a l budget 33 a small change i s made in the quan t i t y and k ind of resources used, and the gain or less in net revenue i s e s t imated. A c a p i t a l budget i s f r equen t l y used when dea l i ng w i t h a l l o c a t i o n of farm c a p i t a l w i th or wi thout in ter tempora l s p e c i f i c a t i o n s . It i s in f a c t another form of p a r t i a l budget. Programming models have been w ide l y used in a g r i c u l t u r e f o r the past two decades. These serve as important management and p o l i c y t oo l s f o r the a n a l y s i s of i n d i v i d u a l or aggregate farms, reg iona l p roduct ion pat te rns and i n t e r r e g i o n a l c ompet i t i on . The most common programming technique i s l i n e a r programming.^ This technique invo lves o p t i m i z a t i o n of an o b j e c t i v e f unc t i on sub ject to a set o f l i n e a r resource c o n s t r a i n t s . The major under l y ing assumptions a re : l i n e a r p roduct ion technology, a d d i t i v i t y of a c t i v i t i e s and d i v i s i b i l i t y of products and resources . A number of o ther programming techniques such as quad ra t i c in teger and mixed in teger programming a l s o e x i s t , but t h e i r use i s not widespread due to comp lex i t i e s in a p p l i c a t i o n . Quadrat ic programming invo lves a non-l i n e a r o b j e c t i v e f u n c t i o n wh i l e integer programming attempts to so lve a problem w i t h a l l integer v a r i a b l e s . In the mixed in teger programming technique on ly s e l e c ted v a r i a b l e s need to s a t i s f y the in teger requirement. Budgeting and l i n e a r programming are fundamental ly s i m i l a r t e c h -niques used f o r gu id ing the a l l o c a t i o n of re sources . The d i f f e r e n c e be-tween them l i e s in the number o f a c t i v i t i e s that can be handled and the For a d e t a i l e d account o f l i n e a r programming technique see E.O. Heady and W. Candler , L inear Programming Methods, Ames, Iowa State Co l lege P re s s , 1958. 34 method of s o l v i n g the product ion problems. Although budgeting i s com-monly used in s imple p lann ing problems, i t f i n d s l i m i t e d a p p l i c a t i o n to s i t u a t i o n s w i t h a la rge number of resource c o n s t r a i n t s and a c t i v i t i e s . Another advantage o f l i n e a r programming over budgeting i s that i t compels the researcher to e x p l i c i t l y s t a t e the value judgements and product ion r e l a t i o n s h i p that are assumed to hold good in the model i t s e l f . L inear programming has another advantage in that i t can be used as a procedure f o r p rov i d i ng normative s o l u t i o n s to fundamental problems. By normative we r e f e r to the course of a c t i o n which ought to be taken by an i n d i v i d u a l or economic u n i t (a) when i t s o b j e c t i v e takes a p a r t i c u l a r form and (b) the r e s t r a i n t cond i t i on s surrounding the a c t i o n or cho ice are o f a pa r -t i c u l a r form. Genera l l y speak ing, l i n e a r programming i s not a too l f o r p o s i t i v e a n a l y s i s . In con t r a s t to normat ive, the term p o s i t i v e desc r ibes a n a l y s i s which exp l a i n s phenomena as they e x i s t and not as they ought to be. For example, l i n e a r programming might be used t o de r i ve a normative supply f unc t i on f o r farmers which would i n d i c a t e the amounts which should be produced at d i f f e r e n t p r i c e s , i f farmers had p e r f e c t knowledge and a c t u a l l y maximized p r o f i t s . On the other hand reg re s s i on a n a l y s i s can be used to de r i ve a p o s i t i v e supply f u n c t i o n . This would descr ibe or p r e d i c t how farmers a c t u a l l y respond to p r i c e changes and would probably d i f f e r from the normative supply f u n c t i o n . L inear programming and budget-ing are not techniques f o r e s t ima t i n g product ion f unc t i on s by themselves; instead they represent methods of determin ing p roduct ion values based on given input -output r e l a t i o n s h i p s . In essence they are p lann ing techniques 35 which prov ide a method of s y s t e m a t i c a l l y ana l y z i ng a p roduct ion s i t u a -t i o n . Funct iona l a na l y s i s based on regress ion methodology, i s used in the present study. As w i th any other a n a l y t i c a l t o o l , f u n c t i o n a l a n a l y s i s a l s o has i t s l i m i t a t i o n s . However, i t has c e r t a i n c h a r a c t e r -i s t i c s that make i t app rop r i a te f o r s tudy ing the e f f i c i e n c y of resource use and po s s i b l e adjustments. These are s ta ted below: 1. P r o d u c t i v i t y c o e f f i c i e n t s o f inputs can be r e a d i l y est imated d i r e c t l y from data used in a n a l y s i s . 2. E f f e c t s of d i f f e r e n t l e v e l s of input c a tego r i e s can be measured by t h i s method. Marginal va lue p r o d u c t i v i t y e s t i -mates f o r d i f f e r e n t l e v e l s of inputs show such in format ion because the c o n t r i b u t i o n in p roduct ion of any l e ve l o f a s i n g l e input i s cont ingent upon the l e ve l a t which other inputs are employed. 3. Funct iona l a n a l y s i s i s app rop r i a te f o r hand l ing adjustment p o s s i b i l i t i e s w i t h i n an e x i s t i n g technology because i t pe r -mits es t imates to be made of resource marginal p r o d u c t i v i t i e s . These are c a l c u l a t e d from the p roduct ion f u n c t i o n which i s est imated d i r e c t l y in the a n a l y s i s . A c t u a l l y , s p e c i f i c com-modity product ion f unc t i on a n a l y s i s u s ua l l y assumes that the same ba s i c technology i s used by a l l farms, but a t d i f f e r e n t input l e v e l s . CHAPTER IV CONCEPTUAL MODEL AND DATA The f i r s t s e c t i on in t h i s chapter deals w i t h the nature of r i c e p roduct ion from an operat ions s t andpo in t . The second s ec t i on i s concerned w i t h the fo rmu la t ion of a conceptual model of p roduc t i on . The t h i r d s e c t i o n deals w i th the c a t e g o r i z a t i o n and measurement of ex-p lanatory v a r i a b l e s . The l a s t s e c t i on d i scusses the procedure f o r c o l l e c t i n g data from farmers. A. TECHNIQUE OF PADDY PRODUCTION Rice p roduct ion i s a complex and v a r i ed phenomenon in S r i Lanka. Complexity a r i s e s out of the numerous steps i n vo l ved , va r i ou s k inds of inputs r equ i r ed , t iming of i nput s , d i f f e r e n t v a r i e t i e s of r i c e adaptable to d i f f e r e n t environmental c o n d i t i o n s , and reg iona l v a r i a b i l i t y in c u l t u r a l p r a c t i c e s . Land p repa ra t i on i s a c r i t i c a l ope ra t i on in paddy c u l t i v a t i o n . At the beginning of the season land i s prepared thoroughly to make i t s u i t a b l e f o r sowing seeds or f o r t r an sp l an t i n g s eed l i n g s . Land p re -pa ra t i on i s done by manual l abour , bu f f a l oe s or t r a c t o r s . Seed sowing and t r an sp l an t i n g are performed e x c l u s i v e l y by manual labour. Trans-p l a n t i n g i s cons idered to be a management p r a c t i c e r e q u i r i n g r e l a t i v e l y la rge amounts of labour. Once the es tab l i shment o f the r i c e stand i s completed, the range of p re -harves t opera t ions inc ludes weed and pest 36 37 c o n t r o l , i r r i g a t i o n and a p p l i c a t i o n of f e r t i l i z e r s . Harves t ing i s u sua l l y c a r r i e d out three to four months a f t e r es tab l i shment of the c rop . It i s done by manual labour a l one . The harvested crop i s threshed to the f i n a l product, paddy, and t h i s ope ra t i on i s performed by manual labour , bu f fa loes and t r a c t o r s . Paddy farming in general invo lves a labour i n t en s i v e system of p roduc t i on . The usual labour requirement f o r farming an acre of paddy ranges from about 55 to 90 man days. Instances where some farmers use more labour u n i t s than others can u s u a l l y be exp la ined by the f a c t that they employ more labour i n -tens i ve p r a c t i c e s such as t r an sp l an t i n g and hand weeding. In a d d i t i o n to manual labour, most farmers use t r a c t o r s or bu f fa l oe s f o r land p r e -pa ra t i on and thresh ing ope ra t i on s . It i s a f a c t that high y i e l d s of paddy can be obta ined by us ing n o n - t r a d i t i o n a l i nput s , p a r t i c u l a r l y f e r t i 1 i z e r . B. CONCEPTUAL MODEL OF PADDY PRODUCTION On the bas i s of t h i s d e s c r i p t i o n of paddy farming ope r a t i on s , i t i s p o s s i b l e to hypothes ize the general form of the paddy product ion f unc t i on as f o l l o w s ; Y = f ( X r X 2 , X 3 , Xk, X 5 , X 6 , X y , S) [4.1] where, Y i s the t o t a l output , X^ i s l and, i s l abour , X^ i s f e r t i l i z e r , X^ i s ag ro -chemica l s , X^ i s t r a c t o r s e r v i c e s , X^ i s b u f f a l o s e r v i c e s , X^ is seed mate r i a l and S represents a random v a r i a b l e , c o n s i s t i n g of a whole a r ray of i n f l uences such as c l i m a t i c , geog raph i ca l , s o c i a l and p o l i t i c a l f a c t o r s , which i s exceed ing ly d i f f i c u l t to measure in e n t i r e t y . Even when i t i s not measured, as i s f r equen t l y the case, reg re s s i on a n a l y s i s s t i l l permits s t a t i s t i c a l est imates to be made of Y through the assumption of normal ly d i s t r i b u t e d mean-zero e r r o r terms around the l i n e of r e g r e s s i o n . When S is omi t ted under f a c t o r shares est imates the assumption i s again the same w i t h regard to the s t a t i s t i c a l model. C. INPUT AND OUTPUT VARIABLES The concepts , d e f i n i t i o n s and major d i f f i c u l t i e s connected w i t h the s e l e c t i o n and measurement of v a r i a b l e s inc luded in the a n a l y s i s , w i l l be d i scussed in the f o l l o w i n g s e c t i o n . A l l va lue measures r e f e r r e d to are in 1973 rupees . ' Output The independent v a r i a b l e used in the study was the va lue measures of t o t a l r i c e output on farms in the 1972-73 Maha season. The output data obta ined from the i n d i v i d u a l farm un i t s were in phy s i c a l u n i t s , namely bushels of paddy, which inc luded t o t a l domestic consumption, sa le s and payments in k ind f o r rents and wages. The value of output was obta ined by p r i c i n g the phy s i c a l output a t the government guaranteed p r i c e , which a t the time o f survey was Rs.16.00 a bushe l . One Rupee was equ i va len t to .1506 Canadian Do l l a r s a t the o f f i c i a l exchange ra te in 1973-2 One bushel of paddy i s equal to k$ l b s . 39 A p r i c e o f Rs.16.00 a bushel was used in v a l u i n g the output of a l l farms f o r two main reasons. F i r s t l y , most of the farmers were in f a c t subs i s tence o r i e n t e d , so that very l i t t l e or no marketable r i c e surp lus i s produced. Secondly, in S r i Lanka, the scheme of paddy pur -chas ing implemented by the government s t i p u l a t e s that there w i l l be no paddy sa le s by producers to ou t s i de sources other than the Paddy Market-ing Board. The use of an unique p r i c e l e ve l might be ob jec ted to on the grounds that i t d i s rega rds q u a l i t y d i f f e r e n c e s in the product . How-ever , an examinat ion of the v a r i e t i e s of r i c e grown by the sample of farmers revealed that there were no app rec i ab le q u a l i t y d i f f e r e n c e s , which f o r t u n a t e l y makes the a p p l i c a t i o n o f product ion f u n c t i o n a n a l y s i s s t r a i g h t -forward from the dependent v a r i a b l e s tandpo in t . Almost a l l the farmers in the sample grew high y i e l d i n g v a r i e t i e s of r i c e which d i d not show marked d i f f e r e n c e s in q u a l i t y and hence, one can expect the government p r i c e to be c l o s e l y r ep re sen ta t i ve of the homogeneous output . This of course would not be the case i f t r a d i t i o n a l v a r i e t i e s were being c u l t i v a t e d . Land The measure of land input used in the a n a l y s i s is in terms of farm area under paddy c u l t i v a t i o n . An a l t e r n a t i v e and perhaps be t te r s u i t ed measure of land input would be the value o f land under n ice p ro -d u c t i o n . But in t h i s case the assumption that the p r o d u c t i v i t y of land i s impl ied by i t s p r i c e i s c r u i c i a l , and i t has to be remembered that apar t from the p r o d u c t i v i t y c o n s i d e r a t i o n , the p r i c e of land can be a f f e c t e d by a number of other f a c t o r s . If any of these app l y , then value o f land becomes that much les s s a t i s f a c t o r y as a measure. Furthermore, AO in r u r a l areas there does not e x i s t an a c t i v e market f o r paddy land and t h i s again leads to d i f f i c u l t i e s in a s ses s ing land va l ue s . In view of these con s i de ra t i on s i t was decided to use the phy s i c a l area as the most s a t i s f a c t o r y measure of land input a v a i l a b l e . Labour Labour input was expressed in terms of man-days, where a pe r iod of e i g h t hours o f work was cons idered to be a man-day. This invo lved measurement of t o t a l labour input used d i r e c t l y f o r p roduct ion of paddy, exc lud ing that used fo r d r i v i n g t r a c t o r s and b u f f a l o e s . The e n t i r e system of labour u t i l i z a t i o n in paddy c u l t i v a t i o n is r e l a t i v e l y complex. Three c a tego r i e s of l abou i—men, women and c h i l d r e n — are used. Labour commitment i s h i gh l y seasonal in nature and dur ing c e r -t a i n c r i t i c a l phases of requirements, such as p l a n t i n g , ha rve s t i ng and t h re sh i ng , the f am i l y labour supply is o f ten inadequate, and the re fo re has to be augmented by h i r ed or exchange labour ( a t t a n ) . In gene ra l , r i c e farming i s not a system o f farming which can make do on the supply of f am i l y labour a l one . In f a c t , i t has been shown that the share o f h i r ed labour in t o t a l labour requirements i s as high as 85 per cent in 3 c e r t a i n d i s t r i c t s . In view of the d i f f e r e n t ca tegor ie s of labour employed in r i c e c u l t i v a t i o n , i t was necessary to b r ing a l l labour i n to an a p p r o p r i a t e l y 3 K. Izumi and A.S. Ranatunga, Cost o f Product ion o f Paddy Y a l a , 1972; Ag ra r i an Research and T r a i n i n g I n s t i t u t e , S r i Lanka, Research p u b l i c a t i o n No. 1, J u l y , 1973. equ i v a l en t form. This was accomplished by conver t ing woman and c h i l d labour days to man-day e q u i v a l e n t s , us ing the f o l l o w i n g index of con-v e r s i o n : one woman-day and one c h i l d - d a y equ i va l en t to .75 and .5 man-days r e s p e c t i v e l y . These i nd i ce s of convers ion were based on the average wage ra tes p r e v a i l i n g at the time of survey. It i s assumed that the average wage rates of the ca tego r i e s of labour adequately r e f l e c t t h e i r d i f f e r e n t p r o d u c t i v i t i e s . F e r t i 1 i zer The f e r t i l i z e r v a r i a b l e was def ined as the t o t a l va lue of f e r -t i l i z e r s used in producing r i c e output on a farm. The p r i c e s are those at which f e r t i l i z e r s were purchased by the farmers a f t e r a government subsidy of 50 per cent of t o t a l cos t had been deducted. Gene ra l l y speak-ing farmers were observed to keep the combinat ion of f e r t i l i z e r i n g red -ient s reasonably cons tant . This a l lowed t o t a l value to act as the v a r -i a b l e measure. Chemicals A number of chemicals are used in r i c e c u l t i v a t i o n . These take the form of va r ious seed d re s s i ng s , he rb i c i de s and i n s e c t i c i d e s . Owing to the heterogeneous nature o f i n d i v i d u a l chemica l s , an aggregate va lue of chemicals used on each farm was obta ined fo r measuring the c o r r e s -ponding v a r i a b l e . For a s i m i l a r s i t u a t i o n in Ind ia , Chenareddy uses the f o l l o w -ing i nd i ce s : one woman-day equ i v a l en t to .8 man-day and one c h i l d - d a y equ i va l en t to .5 man-day. See: V. Chenereddy, " P roduc t i on E f f i c i e n c y in South Indian Agr i c u l t u r e , " J . Farm Econ. hS, 1967, pp. 816-20. B u f f a l o Se rv i ce s This v a r i a b l e represents animal power u t i l i z e d f o r p loughing land p r i o r to p l an t es tab l i shment and th resh ing the harves t . Measure-ment was made in value terms and inc ludes the expense of h i r i n g bu f fa l oe s as we l l as t h e i r a t tend ing labour. U s ua l l y , a b u f f a l o s e r v i c e u n i t used in r i c e farming c o n s i s t s of two animals and the a t tend ing b u f f a l o d r i v e r . The t y p i c a l approach to measuring t h i s v a r i a b l e has been to assess the b u f f a l o s e r v i c e independently from a t tend ing labour. However, i t seems l o g i c a l to cons ider the s e r v i ce s of both b u f f a l o and d r i v e r as a s i n g l e u n i t , each complementing the o the r . Machinery Se rv i ce s Machine power represents a major input in r i c e product ion and i s used fo r f i e l d p repa ra t i on and fo r t h re sh ing . The types of machines used are e i t h e r "two whee l " or " f o u r whee l " t r a c t o r s . As in the case of animal s e r v i c e s , the measure o f machinery input inc ludes the cost of h i r i n g both t r a c t o r s and d r i v e r s . Even though t r a c t o r usage i s f a i r l y common among the paddy c u l t i v a t o r s , a m a j o r i t y of farmers do not own them. In instances where farmers used t h e i r own t r a c t o r s computation of the cos t s of t r a c t o r inputs was based on the normal t r a c t o r h i r i n g charges p r e v a i l i n g in the a rea . The cost of using p roduct ion equipment i s a l s o incorporated in the machinery s e r v i c e s v a r i a b l e . Apart from t r a c t o r -c u l t i v a t o r attachments, equipment items are i n f r e q u e n t l y used by sample farmers and when present might comprise spray ing machines, r o ta ry weeders and water pumps. A h i r i n g equ i va len t cost was charged f o r these items which excluded labour. 43 Seed Ma te r i a l The measure f o r t h i s v a r i a b l e invo lved a va lue assessment of the seed paddy used on each farm, at Rs.18.00 per bushe l . D ra f t Se rv i ce s Th is v a r i a b l e i s a summation of Machinery s e r v i c e s ' and animal s e r v i c e s ' v a r i a b l e s o u t l i n e d above. Regional Dummy Va r i ab l e Regional f a c t o r s can i n f l uence l e v e l s of p roduct ion and t h e r e -fore the p roduct ion f u n c t i o n . It was thought u se fu l to de f i ne a z e r o -one dummy v a r i a b l e f o r the purpose of i n d i c a t i n g the presence of reg iona l e f f e c t s in one par t of the a n a l y s i s . D. SOURCE AND METHOD OF COLLECTION OF DATA The present study is based on input -output data p r e v i o u s l y c o l l e c t e d from 107 r i c e farms in f i v e major r i c e c u l t i v a t i n g d i s t r i c t s in S r i Lanka, namely: Polonnaruwa, Hambantota, Kurunegala, Colombo and 5 Kandy. The time per iod r e f e r r e d to in t h i s study is the 1972-73 Maha season. Maha or wet season, extending from September to March, i s the major r i c e growing season in S r i Lanka. The method employed f o r c o l l e c t i n g data was that of superv i sed farm record keeping. The usual approach f o r ga ther ing farm data in r u r a l areas in developing coun t r i e s has been the f i e l d survey, where a ^ The d i s t r i c t sample breakdown of farm numbers i s g iven in Appendix 6. once-and-for-a11 i n te r v i ew i s conducted by a t r a i ned enumerator us ing an a p p r o p r i a t e l y designed i n te r v i ew schedule. However, t h i s technique seemed to be c l e a r l y u n s a t i s f a c t o r y f o r c o l l e c t i n g in format ion in view of the e r r o r s that could creep i n t o the da ta . In a farm s i t u a t i o n where r i c e product ion extends fo r a per iod o f k-5 months, and where no record of the farming e n t e r p r i s e i s mainta ined at a l l , the r e c a l l lapses of a farmer can be s u b s t a n t i a l and s e r i o u s l y a f f e c t the accuracy of in forma-t i on ob ta i ned . Since r u r a l farmers are not used in ma in ta in ing produc-t i o n records by themselves, a superv i sed record keeping method had to be adopted. Th is invo lved sy s temat ic maintenance of records by farmers w i t h the a s s i s t ance o f a g r i c u l t u r a l extens ion per sonne l , who superv i sed them at regu la r i n t e r v a l s , p a r t i c u l a r l y dur ing the peak per iods of farm-ing . S e l e c t i o n of the farm sample in t h i s study was made on a judge-ment bas i s and a l l the farmers inc luded i n the sample had the r i c e crop as t h e i r major source of income. On the bas i s of l o c a l exper ience i t was thought that farm un i t s inc luded in the sample represented a t y p i c a l c r o s s - s e c t i o n of r i c e farming in the areas under study. There fo re , de sp i t e the f a c t that the o r i g i n a l sample was not chosen under a random s e l e c t i o n procedure, the data rep re sen ta t i on was cons idered to be ade-quate f o r e s t ima t i n g v a l i d f u n c t i o n a l r e l a t i o n s h i p s between inputs and output . Hence i t should be made c l e a r that a l though the sample was not taken a t the time w i th the express purpose of performing f u n c t i o n a l a n a l y s i s , the fundamental input -output data which i t was meant to p ro -v ide a l s o ensured i t s re levancy f o r product ion f unc t i on e s t i m a t i o n . 45 Heady^ has po inted out that a l though a random sample i s most s u i t a b l e fo r d e r i v i n g popu lat ion parameters i t i s o f ten c l e a r l y u n s a t i s -f a c t o r y f o r e s t imat i ng regres s ion c o e f f i c i e n t s . He proposed that e s t ima t i on of reg res s ion c o e f f i c i e n t s be based on an equal d i s t r i b u t i o n of v a r i a b l e observat ions through the e n t i r e range of study da ta . Thus we see that data f o r regres s ion a n a l y s i s should be r e p r e s e n t a t i v e l y s ca t te red w i t h respect to the plane or su r face r e l a t i o n s h i p being e s t i -mated. The use of sample data from a group of record keeping farmers may perhaps lead to some d i f f i c u l t i e s in regress ion e s t i m a t i o n . For in s tance, a paddy farmer who is keeping records might be expected to operate a more e f f i c i e n t and be t te r ad jus ted farm. If t h i s were t rue the inputs from such farms would tend to c l u s t e r around s ca le l i n e s , imply ing high i n t e r c o r r e l a t i o n s among independent v a r i a b l e s which would reduce the r e l i a b i l i t y of est imated regress ion c o e f f i c i e n t s . ^ g In order to avo id t h i s problem Johnson suggests that s e l e c t i o n of farms be done on a purpos ive bas i s w i t h two o b j e c t i v e s in mind. F i r s t l y , the i n t e r c o r r e l a t i o n between the input f a c t o r s be kept as near to zero as po s s i b l e and secondly, maximizat ion of the var iances be achieved in the 6 E.O. Heady, "E lementary Models in Product ion Economic Research, " J . Farm Econ., 3 0 : 1 9 4 8 , pp. 2 0 1 - 2 6 . ^ For a d i s cu s s i on of t h i s sub jec t see: H.S. K o n j i n , " E s t ima t i on of an Average Product ion Funct ion from Surveys , " Economic Record 3 5 : 1 9 5 9 , pp. 1 1 8 - 2 5 . g E.O. Heady, Glen Johnson and Lowell S. Ha rd in , Resource P ro - d u c t i v i t y , Returns to Sca le and Farm S i z e , Iowa State Co l l ege Pres s , Iowa, 1 9 5 6 , p. 9 5 - In t h i s reference Johnson a l s o po int s out that random samples can s u f f e r from lack of resource combination v a r i a b i l i t y . f a c t o r dimension wi thout drawing observat ions in stage I o r I I I , where, Cobb-Douglas f unc t i on s would encounter c e r t a i n i n t e rp re ta t i ona1 d i f f i -c u l t i e s . There fo re , in us ing the data f o r the study, the w r i t e r who was a s soc i a ted in i t s comp i l a t i on in S r i Lanka, i s s a t i s f i e d that such sampling cond i t i on s were met to a reasonable degree. The data i s thought to permit v a l i d reg res s ion c o e f f i c i e n t e s t ima te s . CHAPTER V ESTIMATION OF PADDY PRODUCTION FUNCTIONS AND INTERPRETATION OF RESULTS Before saying anything about e s t imat i on procedures i t i s necessary to s t a t e the reason f o r dea l i ng w i t h the t o t a l farm sample f i r s t of a l l and then proceeding to the reg iona l a n a l y s i s , rather than the other way round. Ea r l y on i t was thought that any a n a l y s i s of the data c o l l e c t e d should inc lude both a t o t a l and reg iona l farm sample approach. While there was prima f a c i e evidence suggest ing that the dry c l i m a t e areas showed higher response to inputs in the Maha season, t h i s p o s i t i o n was s u f f i c i e n t l y i n t e r e s t i n g f o r a comparison of the two approaches to be rendered necessary. With that d e c i s i o n taken i t seems l o g i c a l to proceed w i th the t o t a l farm sample a n a l y s i s f i r s t , because i t permits a focus s ing of a t t e n t i o n from a broad context to narrower ones. In t h i s way f a c t o r shares est imates can be a p p l i e d and appra i sed without d u p l i c a t i o n , because i t was omit ted f o r the reg iona l da ta . In us ing the order of a n a l y s i s i n d i c a t e d , having decided that the comprehensive approach was r e l e van t , the author f e l t q u i t e uncom-promised as to making c o r r e c t judgements on the bas i s of a c tua l r e s u l t s . This chapter then i s d i v i d e d i n to two major p a r t s . Pa r t A i s concerned w i th the e s t ima t i on o f p roduct ion f unc t i on s and a n a l y s i s of resource p r o d u c t i v i t y f o r the o v e r a l l sample of farmers s e l ec ted for the study. Par t B invo lves e s t ima t i on of product ion f unc t i on s and resource func t i on s p r o d u c t i v i t y a n a l y s i s f o r reg iona l farm samples w i t h i n the 47 4 8 main sample and p r o d u c t i v i t y index comparisons between the d i s t r i c t s composing the reg ions . A. ANALYSIS OF THE TOTAL FARM SAMPLE 1. E s t imat ion of Product ion Funct ions A number of econometric techniques are a v a i l a b l e f o r e s t imat i ng product ion f unc t i on s and these can be ca tego r i zed under four main head-ings. They a re : ( i ) the f a c t o r shares method, ( i i ) the s i n g l e equat ion l e a s t squares method, ( i i i ) the covar iance mat r i x method and ( i v ) the instrumental v a r i a b l e s method. The f i r s t two methods r ece i ve a p p l i c a -t i o n in the study and w i l l be d i scussed at l ength . The covar iance mat r i x and inst rumenta l v a r i a b l e s methods are not w ide l y used, p a r t i c u l a r l y on c r o s s - s e c t i o n data , and w i l l not be d i scussed f u r t h e r . ' a . Factor Shares Est imates An attempt was made to de r i v e the p r o d u c t i v i t y c o e f f i c i e n t s of the product ion f unc t i on f o r t o t a l sample data by use of a r e l a t i v e l y s imple method c a l l e d " f a c t o r shares " which has been descr ibed by 2 K l e i n . This method in con junct ion w i th l ea s t squares has been used 3 • by Mundlak. f o r d e r i v i n g a p roduct ion f u n c t i o n from a combination ' For a d e t a i l e d d i s cu s s i on of these methods see Ronald J . Wonnacott and Thomas J . Wonnacott, Econometr ics, London, John Wi ley and Sons, Inc. , 1969, pp. 237 -383 . 2 Lawrence R. K l e i n , A Text Book of Econometr ics , Evanston, Row Peter son, 1 9 5 3 , p. 206. 3 Y a i r Mundlak, " E s t ima t i on of Product ion and Behav iora l Funct ions from a Combination of C r o s s - s e c t i on and Time Se r ie s Da ta , " in Ca r l F. C h r i s t , et a 1., Measurements in_Economics, S tan fo rd , C a l i f o r n i a : S tanford U n i v e r s i t y P res s , 1 9 6 3 , pp. 1 6 3 - 1 6 5 . k of c r o s s - s e c t i o n a l and t ime - s e r i e s data . Recent ly , K i s l e v has es t imated a product ion f unc t i on f o r U.S. a g r i c u l t u r e us ing the f a c t o r shares method. ( i ) Technique o f E s t imat ing Product ion  C o e f f i c i e n t s by Factor Shares Method Factor shares est imates are by f a r the s imp le s t method o f d e r i v -ing s t r u c t u r a l c o e f f i c i e n t s of a Cobb-Douglas p roduct ion f u n c t i o n f o r a sec to r c h a r a c t e r i z e d by c ompe t i t i o n . The fundamental p r i n c i p l e under-l y i n g t h i s method can be i l l u s t r a t e d as f o l l o w s : Given a f unc t i on o f the form, n b i Y = a n X. [ 5 - 1 ] o . , 1 i = l then under compet i t i ve e q u i l i b r i u m , the marginal va lue product of the i t h input w i l l be equal to i t s market p r i c e or market earn ing ra te W. . If Y in equat ion [ 5 . 1 ] i s expressed in terms of va lue o f output , then fo r each input i , 1 In the Cobb-Douglas f unc t i on the output e l a s t i c i t y o f the i t h resource i s g iven by, BY X. e . = i ax. Y I [5.3] S u b s t i t u t i n g equat ion [ 5 . 2 ] in [ 5 - 3 ] we o b t a i n , Yoav K i s l e v , E s t imat ing a Product ion Funct ion from 1959 U.S. Census of A g r i c u l t u r e Data, Unpublished Ph.D. The s i s , U n i v e r s i t y o f Chicago, 1 9 6 5 -50 W. X. e. =-^—L- [5.4] Y W. X. where, v 1 represents the share of the ou t l a y on the i th f a c t o r as a p ropor t i on of t o t a l output , which i s equal to the f a c t o r ' s c o -e f f i c i e n t in the Cobb-Douglas product ion f unc t i on [5.1] . A major assumption in the f a c t o r shares est imates method i s the e x i s t ence of a compet i t i ve e q u i l i b r i u m . Therefore , the use of t h i s method in the present a n a l y s i s r a i s e s the important quest ion as to whether the paddy sector in S r i Lanka was in e q u i l i b r i u m dur ing the per iod of s tudy, and i f i t was, whether i t achieved t h i s under compet i -t i v e c o n d i t i o n s . The concept of e q u i l i b r i u m can be t rea ted from s ho r t -run and long-run s tandpo in t s . W i th in the l a s t ten years the paddy producing sector has witnessed s i g n i f i c a n t changes w i t h respect to t e c h n o l o g i c a l , economic and s o c i a l f a c t o r s . Owing to these changes and r e l a t i v e l y s low d i s seminat ion o f i n fo rmat ion to fa rmers , i t is q u i t e po s s i b l e that the sho r t - run obse rva t ion data used in the study w i l l not represent a long-run e q u i l i b r i u m p o s i t i o n . One way of at tempt-ing to overcome such a problem would be to average observat ions over a long per iod of t ime. That was not po s s i b l e in the s tudy, so p ro -ceeding on the assumption that sho r t - run e q u i l i b r i u m cond i t i on s in paddy farming e x i s t e d , i t is usefu l to e s t a b l i s h j u s t how much compe-t i t i o n wqs present in the f a c t o r and product markets to a l l o w compe-t i t i v e e q u i l i b r i u m to app l y . 51 Another major c r i t i c i s m o f the f a c t o r shares technique i s that i t does not a l l ow much scope f o r t e s t i n g hypotheses about econ-omies of s c a l e . If the method i s used to est imate the c o e f f i c i e n t s of a l l f a c t o r s of p roduc t i on , t h e i r sum should be un i t y imply ing the assumption of constant returns to s c a l e . On the other hand, i f the indus t ry being s tud ied i s c ha r a c t e r i z ed c l o s e l y by p e r f e c t c ompe t i t i on , then, there w i l l be no nece s s i t y f o r t e s t i n g the presence of i n c r ea s -ing or decreas ing returns to s c a l e . In t h i s case, the f a c t o r shares method w i l l g i ve the most s a t i s f a c t o r y est imates of p roduct ion co -e f f i c i e n t s . Despite these l i m i t a t i o n s the use of f a c t o r shares est imates f o r d e r i v i n g product ion c o e f f i c i e n t s prov ides some advantage. For i n s tance , the product ion c o e f f i c i e n t est imated by t h i s method f o r a p a r t i c u l a r i nput , u n l i k e that obta ined from l e a s t squares, i s inde-pendently determined from those f o r the other f a c t o r s of p roduc t i on . Hence, an e r r o r in e s t imat i ng a p a r t i c u l a r p roduct ion c o e f f i c i e n t by the f a c t o r shares method w i l l not cause e r r o r s in e s t ima t i n g other c o e f f i c i e n t s . Never the le s s , f a c t o r shares est imates are i n f l uenced by the p r i c e s of inputs and output and, t h e r e f o r e , any e r r o r in de-termin ing these can cause e r r o r s in the c o e f f i c i e n t s ob ta i ned . Factor shares est imates can be made f o r d i f f e r e n t resource and output combinat ion l e v e l s . For the sake of r ep re sen ta t i on in the study, 52 they were est imated at the a r i t h m e t i c and geometric mean combinations f o r the t o t a l farm sample. A d i s t i n c t advantage o f the f a c t o r shares method as suggested by 5 Mundlak i s that i t can be used along w i th the l ea s t squares method f o r e s t ima t i n g product ion f unc t i on c o e f f i c i e n t s f r ee of s i m u l t a n e i t y b i a s . Accord ing to h i s suggest ion the c o e f f i c i e n t s o f inputs which are found to be c o r r e l a t e d w i t h observed output data are est imated by the f a c t o r shares method. The remaining c o e f f i c i e n t s are der i ved from regres s ion in which f a c t o r shares determined c o e f f i c i e n t s o f v a r i a b l e s a re a l s o imposed. For the data in the present study i t was not ev ident that use of t h i s composite technique would r e s u l t in be t te r e s t ima t i on procedure, and so i t was not app1 ied . ( i i ) Models Used in Factor Shares E s t imat i on The s t a t i s t i c a l models used in Factor Shares E s t imat i on are as fo11ows: (a) at the a r i t h m e t i c mean l e v e l s of inputs and output , S. = a. + u. ( i = 1 n) [5.5] where S. i s the share of i t h input , a . i s the p roduct ion e l a s t i c i t y co -e f f i c i e n t o f the i t h input and u. i s the random e r r o r term. Assuming the mean o f u. to be ze ro , then a. = S". i i 5 Y a i r Mundlak, " E s t ima t i on of P roduct ion and Behav iora l Funct ions from a Combination o f C r o s s - s e c t i on and Time Se r i e s Data" in Car l F. C h r i s t e t a l . , Measurements in Economics, S tan fo rd ; C a l i f o r n i a , Stanford Un i ve r -s i t y P re s s , 1963, pp. 163-165. Hence, 53 (b) S i m i l a r l y , at the geometric mean l e v e l s o f inputs and output , us ing the same n o t a t i o n , u. S. = a. e 1 [5.6] i i Jin S. = IT] a. + u. i i i Again the u. are assumed to have a mean of zero Therefore, and Jin. a. = Jin. S. i i a. = a n t i l o g (£n a.) It has been shown that c o e f f i c i e n t s determined under f a c t o r shares in model (b) u n l i k e those in model (a ) , are sub ject to b ias a r i s i n g from the l oga r i t hm ic t rans fo rmat ion i n vo l v ed . ^ The r e l a t i v e b ias in model (b) i s g iven by the term, 2 [5.7] a r 2n 2 where, o i s the va r iance of the c o e f f i c i e n t b and n i s the sample r r s i z e . From the above express ion i t i s c l e a r that sma l l e r samples w i l l have g reate r b ia s of t h i s nature . However, w i th a t o t a l farm sample s i z e ^ P. J . Dhrymes, "On Dev i s ing Unbiased Es t imator fo r the Parameters of the Cobb-Douglas Product ion F u n c t i o n , " Econometr ica, 31, J anua r y -Ap r i l 1963, P. 297. 5h of 107, i t can be observed that c o e f f i c i e n t es t imates w i l l not be b iased s u b s t a n t i a l l y , even i f model (b) i s used. A f t e r con s i de r i ng a l l these f a c t o r s i t can be concluded that the f a c t o r shares est imates method o f d e r i v i n g product ion func t i on s is a va l uab le a n a l y t i c a l t o o l , i n s o f a r as i t prov ides an oppor tun i t y to com-pare i t s r e s u l t s , under compet i t i ve e q u i l i b r i u m assumptions, w i t h those der i ved from l ea s t squares r e g re s s i on . ( i i i ) Emp i r i c a l Resu l t s of Factor Shares E s t imat i on Model The computed f a c t o r shares est imates fo r the o v e r a l l sample along w i th corresponding mean values o f output and inputs are reported in Table 5.1. The f i g u r e s i nd i ca ted in column (3) are geometric means wh i l e those in column (5) a re a r i t h m e t i c means. It i s seen that corresponding a r i t h m e t i c means and geometric means d i f f e r from one another . These d i f -ferences are a f unc t i on of the skewness of d i s t r i b u t i o n s . Columns (4) and (6) i n d i c a t e the f a c t o r shares est imates computed at geometric and a r i t h m e t i c input l e v e l s , r e s p e c t i v e l y . In s p i t e of the marked d i f f e r -ences observed in the inputs at the geometr ic and a r i t h m e t i c mean l e v e l s , the a s soc i a ted f a c t o r shares est imates do not show s u b s t a n t i a l d i f f e r e n c e s . However, i t i s more app rop r i a te to concent rate on the p roduct ion c o -e f f i c i e n t s w i t h regard to geometric means because these are c l o s e r to the " t y p i c a l " farm s i t u a t i o n . The mean values given f o r the d r a f t power v a r i a b l e , Xg, represent an aggregat ion of both animal and machine power v a r i a b l e s . These v a r i -ab les were t rea ted together here because they were subsequently handled t h i s way in regress ion a n a l y s i s . 55 Table 5.1. Factor Shares Est imates of C o e f f i c i e n t s of Farm Based Cobb-Douglas Product ion Funct ion at Geometric and A r i t h m e t i c Mean Leve l s of Output and Inputs f o r the Maha Paddy Season (6 months) Farm Farm Farm V a r i a b l e ' ( 0 Value Uni ts (2) Geometric Mean Value (3) Factor Sha re (4) A r i thmet i c Mean Value (5) Factor Share (6) Rupees Y Output Rs. 1638.00 1 .000 2442.00 1 .000 X l a Land2 (a) Rs. 409.50 0.250 540.00 0.221 X l b Land 2 (b) Rs. 486.00 0.297 673-00 0.276 X 2 Labour Rs. 634.40 0.387 835.70 0.342 X 4 F e r t i 1 i zer Rs. 80.50 0.049 136.00 0.056 X 6 Agro-chemicals Rs. 32.00 0.019 46.00 0.019 X 7 Seed Ma te r i a l Rs. 55.40 0.034 62.60 0.026 X 8 Draf t Se rv i ces Rs. 199.00 0.121 334.00 0.137 Sum of Factor Shares (a) - 0.860 - 0.801 (b) - 0.907 - 0.856 ' V a r i ab l e s are de f i ned in Chapter IV. ^ Value of land was c a l c u l a t e d us ing two d i f f e r e n t approaches: (a) average rent payment was c a p i t a l i z e d to g ive the t o t a l va lue o f land, (b) paddy land was valued a t Rs.3000 per a c r e . For the purpose of e s t ima t i n g the f a c t o r share to land, i t was necessary to apply a 9 per cent semi-annual i n t e r e s t rate to each farm ' s land i n -vestment va l ue . Therefore the geometric and a r i t h m e t i c mean t o t a l s f o r v a r i a b l e s and i n d i c a t e the app rop r i a te semi-annual oppo r tun i t y co s t s on the r e spec t i ve land investment v a r i a b l e s . 56 The f a c t o r shares es t imate a t the geometric mean f o r the d r a f t s e r v i c e v a r i a b l e , Xg, i s .121. The labour v a r i a b l e , X^, shows the h ighest f a c t o r share es t imate o f .387. The lowest c o e f f i c i e n t e s t imate i s .019 which a p p l i e s to ag ro -chemica l s . The f e r t i l i z e r v a r i a b l e , a l s o shows a rather low est imate o f .0^9. The small f a c t o r shares est imates f o r the two most important n o n - t r a d i t i o n a l i nput s , f e r t i l i z e r and agro-chem-i c a l s , seem rather p u z z l i n g a t f i r s t . But the reason i s almost c e r t a i n l y caused by p r i c e s which underest imate marginal va lue p r o d u c t i v i t i e s . Two a l t e r n a t i v e f a c t o r share es t imates f o r land were computed. The f i r s t was based on the average va lue o f land r en t a l payments wh i l e the second was based on the average assessed land va lue . In the l a t t e r case the average land value was set at Rs.3000.00 per a c r e . If we assume that these two value bases represent high and low assessments, then the corresponding f a c t o r shares est imates of .250 and .297 can be taken as upper and lower l i m i t s o f the t rue c o e f f i c i e n t f o r the land v a r i a b l e . The sums of the f a c t o r shares est imates f o r the two a l t e r n a t i v e geometric mean l e v e l p roduct ion f u n c t i o n s , (a) and (b) , are .860 and .907 r e s p e c t i v e l y . These are not g r e a t l y d ivergent from 1, and wh i l e they suggest that a compet i t i ve e q u i l i b r i u m s i t u a t i o n was not complete ly ach ieved, they do come c l o se enough, assuming small data measurement e r r o r , f o r us to expect that paddy farmers ' use o f resources i s i n f l u -enced by compet i t i ve f o r ce s . A l so the f a c t o r shares est imates prov ide a usefu l a l t e r n a t i v e bas i s from which to compare regress ion c o e f f i c i e n t e s t imate s . 5 7 b. Least Squares Est imates The usual approach to e s t ima t i n g a p roduct ion f unc t i on i s by reg res s ing the output , or some monotonic t r an s fo rmat ion of output , on a set o f app rop r i a t e input v a r i a b l e s . The e s t ima t i on in t h i s study i s l i m i t e d to s i n g l e equat ion procedure. Th is i s based on the assumption that inputs are independently, and not s imu l taneous l y , determined. These cond i t i on s probably apply be t te r to inputs whose l e v e l s are decided e a r l y in the process o f p roduc t i on . Inputs app l i ed a t a l a t e r s tage, such as harvest labour , can be c o r r e l a t e d w i t h a c tua l l e ve l of output . A s i t u a t i o n where v a r i a b l e s are r e l a t e d to one another by more than one equat ion cannot u s u a l l y be t r ea ted s a t i s f a c t o r i l y by s i n g l e equat ion r e -g r e s s i o n . Marschak and Andrew's^ have shown that t h i s type of problem connected w i t h the e s t ima t i on of p roduct ion func t i on s i s s i m i l a r to that faced in the e s t ima t i on of supply and demand equat ions . A s i n g l e equat ion model f o r the paddy product ion f unc t i on can be j u s t i f i e d on the bas i s that l e v e l s o f most inputs are decided before the a c tua l y i e l d outcome i s known. If t h i s i s the case, they can be s a i d to be determined accord ing to the expected l eve l o f output and, the re fo re w i l l not be c o r r e l a t e d w i t h e r r o r s in the ac tua l output . Under these c o n d i t i o n s , s i n g l e equa-t i o n l e a s t squares es t imates are not sub ject to b ias caused by s i m u l t a -n e i t y r e l a t i o n s h i p s and t h i s was the s i t u a t i o n assumed in the a n a l y s i s . Jacob Marschak and W i l l i a m H. Andrew, J r . , "Random Simultaneous Equations and the Theory of P r o d u c t i o n , " Econometrica 1 2 : J u l y - O c t . , 1 9 4 4 , pp. 1 4 3 - 2 0 5 . 58 ( i ) S t a t i s t i c a l Model o f Paddy Product ion Funct ion Using the v a r i a b l e s i nd i ca ted in the conceptual model presented in Chapter IV we can now hypothes ize the general form of the paddy p r o -duct ion f unc t i on f o r the i t h farm, Y. = f ( X u , X 2 . , . . . X 7 . , u.) where, Y. i s the output, X. are the inputs and u. i s the random d i s -turbance term, which i s assumed to be normal ly d i s t r i b u t e d w i t h mean ze ro . In the l i n e a r from the f unc t i on can be expressed as , Y. = a + b. X.. + b „ X „ . + . . . b, X^. + u. [5.8] i 1 1 1 2 2i 7 7' i where a i s the popu la t i on constant term and b. are the popu la t ion p r o -duct ion c o e f f i c i e n t s . S i m i l a r l y , in the Cobb-Douglas form the equat ion can be w r i t t e n as , Y. - a X^! X, b 2 . . . X ^ J eU] [5.9] i 1i 21 7i Express ing equation [5.9] f o r each farm in l o ga r i t hm i c form we o b t a i n , £n Y. = Jin a + b] £n X ] . + b 2 In X^ ... b^ SLr\ X^. + u. [5-10] In order to es t imate equat ion [5 .10] , the r a t i o n a l e and assumptions g used by Z e l l n e r , Kmenta and Dreze are adopted. These hold that the p r o -duct ion func t i on s of f i rms are i d e n t i c a l in form and parameters. There fo re , A. Z e l l n e r , J . Kmenta, and P. Dreze, " S p e c i f i c a t i o n and mation o f Cobb-Douglas Product ion Funct ion Model s , " Econometr ica, Oct. 1966, pp. 784-795. E s t i -34: 59 in the l o ga r i t hm i c form the est imated product ion f u n c t i o n f o r the sample i s given as , £n Y = £n a + b Jin X ] + b 2 An X 2+...+b 7 Jin X^ [5.11] where a , b^ . . . . b^ are c o e f f i c i e n t e s t imate s ; or a l t e r n a t i v e l y in the na tu ra l form as , S i m i l a r l y , in the l i n e a r form the est imated product ion f unc t i on can be expressed as Y = a + b ] Xj + b 2 X 2+...+b 7 X^ The s imple c o r r e l a t i o n mat r i x fo r l o g a r i t h m i c a l l y transformed v a r i a b l e s u t i l i z e d in the a n a l y s i s f o r a l l survey farms i s presented in Table 5-2. Th i s shows that a l l p a i r s o f v a r i a b l e s are p o s i t i v e l y c o r -r e l a t e d except in the case o f animal s e r v i ce s and machinery s e r v i c e s . The reason f o r t h i s negat ive c o r r e l a t i o n i s the s u b s t i t u t i o n of machinery s e r v i c e s fo r animal s e r v i c e s on farms. The magnitudes of the c o e f f i c i e n t s in the c o r r e l a t i o n are usefu l q f o r i n v e s t i g a t i n g the presence o f co l l i n e a r i t y between independent v a r i a b l e s . Gene ra l l y , a high c o r r e l a t i o n between two independent v a r i a b l e s For an i n t e r e s t i n g d i s cu s s i on o f t h i s sub jec t see: D.E. F a r r a r , and R.R. Glauber, " M u l t i c o l 1 i n e a r i t y in Regress ion A n a l y s i s : the Problem R e v i s i t e d , " Rev, o f Econ. S t a t s . , kS: 1967, pp. 92-107. 60 Table 5 - 2 . Simple C o r r e l a t i o n C o e f f i c i e n t s f o r L o g a r i t h m i c a l l y Transformed Va r i ab l e s inc luded in Paddy Regression A n a l y s i s — T o t a l Farm D a t a — A l l Survey Farms. Farm V a r i a b l e 2 Y X, X„ X 0 X. X r X, X., X Q I 2 i H p b / o Y Output (Rs.) 1 . 0 0 X ] Land (Acres) .82 1 . 0 0 X 2 Labour (Man days) . 8 4 . 6 9 1 . 0 0 X 3 F e r t i l i z e r (Rs.) . 8 8 .72 . 3 2 1 . 0 0 X. Machine Serv i ces (Rs.) . 4 2 . 7 7 . 3 8 . 7 4 1 . 0 0 Xj. Animal 5 Se rv ices (Rs.) . 3 8 .27 . 7 3 . 7 8 - . 8 3 1 . 0 0 X. Agro-chemicals (Rs.) . 5 9 . 6 4 . 6 3 . 7 3 . 1 0 .76 1 . 0 0 X 7 Seed 1 Ma te r i a l (Rs.) . 8 4 . 8 6 .81 . 7 7 . 1 8 . 7 4 .67 1 . 00 X f i Dra f t Se rv i ces (Rs.) .71 .71 . 7 7 . 7 8 .51 . 7 0 .71 . 6 2 1 . 0 0 1 H : p = 0 , r e j e c t ed i f c a l c u l a t e d r > . 1 9 0 ( . 0 5 L.O.S.) o 2 r > . 2 4 8 ( .01 L.O.S.) For the d e f i n i t i o n o f v a r i a b l e s see Chapter IV. is i n d i c a t i v e of m u l t i c o l 1 i n e a r i t y in regress ion e s t i m a t i o n . ' ^ On a_ p r i o r i grounds i t might be expected that some c o r r e l a t i o n would e x i s t among v a r i a b l e s in a p roduct i ve process . The c o r r e l a t i o n mat r i x in The l i m i t a t i o n s of a p p l i c a b i l i t y of t h i s c r i t e r i a f o r d e t e c t i o n o f m u l t i c o l 1 i n e a r i t y i s d i scussed in P. Rao and R.L. Mi 1 l e r , App l i ed  Econometr ics , C a l i f o r n i a , Wadsworth P u b l i s h i n g Co., 1 9 7 1 , pp. 4 6 - 5 2 . 61 Table 5-2. i n d i c a t e s the presence o f reasonably high and s i g n i f i c a n t c o r r e l a t i o n s among the exp lanatory v a r i a b l e s . However, on ly in the cases o f seed mate r i a l and land (r=.86), animal s e r v i c e s and machine se r v i ce s (r=-.83) and seed mate r i a l and labour (r=.8l) do the c o e f f i -c i e n t s exceed .8. From research exper ience the s i z e of the c o r r e l a t i o n s between the independent v a r i a b l e s i nd i ca te s that wh i l e m u l t i c o l 1 i n e a r i t y can occur among c e r t a i n v a r i a b l e s , i t i s not l i k e l y to be a l l that s e r i ou s . Furthermore the forming of a composite v a r i a b l e from machinery and animal s e r v i ce s can on ly serve to reduce whatever mu11icol 1 i n e a r i t y i s introduced by the separate v a r i a b l e s . Some s t u d i e s ' ' have shown that the use of per acre data rather than t o t a l farm data tends to reduce c o r r e l a t i o n s between the independent v a r i a b l e s . Th i s r e d e f i n i t i o n was attempted in the present study and the r e s u l t i n g c o r r e l a t i o n mat r i x d i d not show important d i f f e r e n c e s from the c o r r e l a t i o n mat r i x in Table 5.2. In f a c t the c o r r e l a t i o n between labour and chemicals increased to (r=.89) . Consequently, i t was decided to use t o t a l farm data rather than per acre da ta , s ince the former had the bene f i t o f being ab le to d i s c l o s e in format ion on returns to s ca le in paddy farming. ( i i ) E s t imat ion of L inear Product ion Funct ions On the assumption that a l i n e a r product ion r e l a t i o n s h i p e x i s t e d between output and f a c t o r s of p roduc t i on , two m u l t i - l i n e a r reg res s ion equat ions were est imated us ing t o t a l farm data from a l l survey farms, and Delane E. Welsch, "Response to Economic Incent ive by A b a k a l i k i R ice farms in Eastern N i g e r i a , " Jou r . Farm Econ. , 47: 1965, p~p. 900-914. 62 the r e s u l t s o f these s p e c i f i c a t i o n s are presented in Table 5.3-2 The c o e f f i c i e n t of m u l t i p l e determinat ion (R ) f o r the two regres s ions show high va lues , .911 and .839, i n d i c a t i n g that the f unc -t i on s e x p l a i n a large par t of the output v a r i a b i l i t y . However, a s t a t i s t i c a l e v a l u a t i o n of the est imated c o e f f i c i e n t s revea l s that the assumption of a l i n e a r product ion r e l a t i o n s h i p f o r the popu la t i on i s not s a t i s f a c t o r y . Regress ion Rj incorporates a l l input f a c t o r s employed in the conceptual model of paddy p roduc t i on , but the seed m a t e r i a l , animal s e r v i c e s and agro-chemica l s v a r i a b l e s show n o n - s i g n i f i c a n t co -e f f i c i e n t s a t the .05 l e ve l of s i g n i f i c a n c e (L .O.S. ) . The n o n - s i g n i f i c a n c e o f the c o e f f i c i e n t s i s due to the r e l a t i v e l y low values o f the c o e f f i c i e n t s in con junc t ion w i t h t h e i r high standard e r r o r s . It i s a l s o important to note that the marginal p r o d u c t i v i t y o f agro-chemica l s i s shown to be negat ive in the f i r s t reg res s ion equat i on . Therefore , in equat ion seed ma te r i a l and agro-chemica l s v a r -i ab le s were de le ted and the model r e s p e c i f i e d to use a d r a f t s e r v i ce s v a r i a b l e in p lace of separate machine and animal s e r v i c e v a r i a b l e s . 2 The e f f e c t of these changes was to reduce the R va lue s l i g h t l y and to render the land and f e r t i l i z e r r eg re s s i on c o e f f i c i e n t s n o n - s i g n i f i c a n t at the .05 L.O.S. The constant terms fo r the two reg re s s i on equat ions show s t a t i s t i c a l l y s i g n i f i c a n t negative, va lues . These may w e l l i n d i c a t e non - l i n ea r r e l a t i o n s h i p s under l y ing the da ta . In f a c t the general un-s u i t a b i l i t y o f the l i n e a r p roduct ion f unc t i on in the na tu ra l form would a l s o suggest that a t t e n t i o n be d i r e c t e d towards a Cobb-Douglas type of f u n c t i o n . Table 5 . 3 . M u l t i - l i n e a r Product ion Funct ion C o e f f i c i e n t s — T o t a l Farm D a t a — A l l Survey Farms Regress ion R^  R 2 R 2 .911 .839 Y t o t a l Output (Rs.) X, Land (Acres) 2 9 6 . 2 2 7 - 9 6 . 0 4 9 ' ( 9 2 . 4 4 6 ) ( 9 9 . 2 8 7 ) X Labour (Man days) 8 . 3 3 1 * 1 0 . 6 0 3 * ( 1 . 1 4 0 ) ( 1 . 3 5 2 ) X F e r t i l i z e r (Rs.) 2 . 1 4 1 * . 5 9 8 5 (.811) ( 1 . 0 3 9 ) X, Machinery s e r v i ce s (Rs.) 3 - 4 6 7 * ( . 6 0 7 ) Xj. Animal s e r v i ce s (Rs.) .298 B ( . 6 9 1 ) X/- Agro-chemicals (Rs.) - 6 . 5 4 8 ( 5 . 8 5 6 ) X., Seed mate r i a l (Rs.) 4.235 (3.089) 7 <8 2 X Q Draft s e r v i ce s (Rs.) 3 . 1 0 4 * ( . 5 9 7 ) Constant Term - 2 0 6 . 6 6 5 * * - 3 4 8 . 8 7 3 * ( 9 2 . 4 4 6 ) ( 1 0 1 . 5 6 0 ) ' F igures in parenthes i s i n d i c a t e standard e r r o r s . 2 Composite of machinery and animal s e r v i c e s . * S i g n i f i c a n t at 1 per cent l e ve l .-. H : 8=0, r e j e c t e d * * S i g n i f i c a n t a t 5 per cent l e ve l 6 4 ( i i i ) E s t imat i on of Non - l i nea r P roduct ion Funct ions S ince the l i n e a r i t y assumption regard ing the t rue product ion f unc t i on was c a l l e d in to ques t ion by the forego ing a n a l y s i s , an attempt was made to f i t a n on - l i n ea r f unc t i on to the t o t a l farm sample da ta . The most w ide ly used non - l i nea r f unc t i on in a g r i c u l t u r a l p roduct ion a n a l y s i s i s the Cobb-Douglas f o r m u l a t i o n . The more important reasons f o r s e l e c t i n g t h i s s p e c i f i c form can be summarized as f o l l o w s : ( i ) Ease o f computing product ion e l a s t i c i t y w i t h respect to a p a r t i c u l a r i nput . P roduct ion e l a s t i c i t y o f an input r e f e r s to the percentage change in output in response to a one per cent change in i npu t ; ( i i ) I t permits d im in i s h i n g marginal returns to occur in the est imated f unc t i on wi thout us ing up too many degrees of freedom. ( i i i ) If the random e r r o r terms f o r the o r i g i n a l data are small and normal ly d i s t r i b u t e d , log t rans fo rmat ions of the v a r -i ab l e s w i l l preserve no rma l i t y of e r r o r terms in the r e -de f ined data . It should be noted that even i f the e r r o r terms are not normal ly d i s t r i b u t e d , i t i s s t i l l p o s s i b l e to ob t a i n best l i n e a r unbiased est imates by the a p p l i c a t i o n of the l e a s t squares method. However, in such a case s t a t i s -t i c a l t e s t s of s i g n i f i c a n c e are no longer v a l i d . The est imated Cobb-Douglas product ion f unc t i on c o e f f i c i e n t s are presented in Table 5 - 4 . The regress ion equat ions R^  to R^  i n d i c a t e c o -e f f i c i e n t s f o r p r o g r e s s i v e l y s e l e c ted set s of v a r i a b l e s . The seed v a r i a b l e 65 Table 5.4. Cobb-Douglas P roduct ion Funct ion C o e f f i c i e n t s — T o t a l Farm D a t a - - A l l Survey Farms Regression number R 3 R 4 R 5 R 6 R2 Y Tota l Output (Rs.) .953 . 9 4 2 .933 .922 X 1 Land (Acres) .322* ( . 1 0 4 ) . 392* (.072) .275* (.080) .257* (.084) Labour (Man-days) .569* (.084) .564*. (.079) .594* (.083) .599* (.082) F e r t i 1 i zer (Rs.) .243* (.037) .231* (.022) .223* ( . 0 3 4 ) .203* (.035) X^ Machinery se r v i ce s (Rs.) .003 (.011) .002 (.015) - -X,- Animal s e r v i ce s (Rs.) . 0 1 4 (.016) .013 (.012) - -X^ Agro-chemicals (Rs.) - . 0 4 4 (.034) -.035 (.033) - . 0 4 9 (.030) -Seed mate r i a l (Rs.) .087 (.094) - - -2 Xg Draft s e r v i ce s (Rs.) - - .125** (.061) .127** (.062) Constant Term 25.028* ( 0 . 4 66 ) 33.685* ( 0 . 3 4 0 ) 19.068* ( 0 . 4 3 3 ) 17.2194 ( 0 . 4 3 3 ) Sum of e l a s t i c i t i es 1 .194 1.179 1 .168 1.186 1 F igures in parenthes i s i n d i c a t e standard e r r o r s (those f o r cons tant~term r e f e r to l o g - l i n e a r equa t i on ) . 2 Composite of machinery and animal s e r v i c e s . * S i g n i f i c a n t at .01 L.O.S. * * S i g n i f i c a n t a t .05 L.O.S. 66 c o e f f i c i e n t i s again seen to be a n o n - s i g n i f i c a n t in a l l the reg re s s i on s . The machinery s e r v i ce s and animal s e r v i c e s c o e f f i c i e n t s are n o n - s i g n i -f i c a n t a t the .05 L.O.S. The r e - s p e c i f i c a t i o n of these two v a r i a b l e s in the form of a s i n g l e d r a f t s e r v i c e s v a r i a b l e i s seen to g i ve s i g n i -f i c a n t c o e f f i c i e n t s in and R^. In equat ion R^ the agro-chemica l s c o e f f i c i e n t i s n o n - s i g n i f i c a n t a t the .05 L.O.S. and i t a l s o shows a negat ive p roduct ion e l a s t i c i t y . Consequently, a f t e r r e t a i n i n g t h i s v a r i a b l e in equat ions R^  and R^  and s t i l l not a ch i ev i ng any d i f f e r e n t r e s u l t , i t was dropped in the case o f Rg. Thus R^  leaves out agro-chemica l s and seed mate r i a l and inc ludes the d r a f t s e r v i c e s input in p lace o f machinery and animal s e r v i c e s . In R^  a l l reg res s ion c o e f f i c i e n t s prove s i g n i f i c a n t at the .05 L.O.S. and a 2 high R va lue of .922 i s ob ta i ned . There fo re , equat ion R^ can be s a i d to g i ve a good f i t to the observed output and input data us ing l and , labour, f e r t i l i z e r and d r a f t s e r v i ce s as independent v a r i a b l e s . As seen from Table 5.4 (p. 65) the reg res s ion equat ion R^  d i f f e r s from the conceptual model of p roduct ion descr ibed e a r l i e r . The d i f -ference invo l ves the e x c l u s i o n of the agro-chemica l s (X^) and seed mater-i a l (X^) v a r i a b l e s in R .^ On a p r i o r i grounds one might expect these to be var i iab les w i th s i g n i f i c a n t c o e f f i c i e n t s . As regards seed mate r i a l the reason f o r i t s e x c l u s i on may be exp la i ned by the f a c t that c o r r e s -ponding data v a r i a t i o n in the farm sample was too s m a l l . On the other hand i t i s po s s i b l e a l s o that d i f f e r e n c e s in seeding ra tes on farms were not s y s t e m a t i c a l l y r e l a t e d to output . 67 Exc lu s i on of agro-chemica l s in R^  may have r e s u l t ed from a measurement problem. Farmers used a wide range o f ag ro -chemica l s . There fo re , the use of a va lue measure f o r t h i s v a r i a b l e might have caused i n s u f f i c i e n t s p e c i f i c a t i o n . r e n d e r i n g i t n o n - s i g n i f i c a n t . i It i s a l s o po s s i b l e that the use of agro-chemicals by farmers in the sample showed i n s u f f i c i e n t v a r i a t i o n or no sy s temat ic e f f e c t on y i e l d s , in which case the regres s ion c o e f f i c i e n t would be judged n o n - s i g n i f i c a n t . The important f a c t , however, is that even a f t e r exc l ud i ng seed ma te r i a l and ag ro -chemica l s , the R^ f unc t i on ex -p l a i ned 92 per cent of the v a r i a t i o n in output , which i s a good f i t to the da ta . At t h i s stage we can compare the r e s u l t s of e s t ima t i n g produc-t i on c o e f f i c i e n t s f o r the v a r i a b l e inputs by reg re s s i on and f a c t o r shares methods. It i s seen that the f a c t o r shares est imates f o r geo-met r i c mean input l e v e l s of land and d r a f t s e r v i ce s v a r i a b l e s come reasonably c l o se to corresponding regress ion c o e f f i c i e n t s in R .^ How-ever , a d i f f e r e n c e between the r e s u l t s o f the two methods e x i s t s r e -garding labour and f e r t i l i z e r . The f a c t o r shares e s t imate f o r the labour c o e f f i c i e n t i s .387 wh i l e the corresponding R^ regres s ion c o e f f i c i e n t es t imate i s .599- The f a c t o r shares est imated fo r the f e r t i 1 i z e r co -e f f i c i e n t i s .0^9 and the corresponding reg res s ion es t imate i s .203. The d i f f e r e n c e in the c o e f f i c i e n t es t imates from the two methods f o r both labour and f e r t i l i z e r can be exp la i ned s imply in terms o f t h e i r marginal value p r o d u c t i v i t i e s exceeding p r i c e s of the resources at geo-met r i c mean l e ve l s of a p p l i c a t i o n . Th is po int w i l l be expanded on l a t e r in the chapte r . 68 2. Resource P r o d u c t i v i t y A n a l y s i s As d i scussed above, the most s a t i s f a c t o r y f i t to the t o t a l farm sample data was g iven by product ion f unc t i on R^  in Table 5-4., which in the na tu ra l form i s as f o l l o w s : .2570 .5987 .2030 .1272 Y = 17-2187 X ] X 2 X 3 X g [5.12] This f unc t i on is cons idered s u i t a b l e f o r conduct ing resource p r o d u c t i v i t y a n a l y s i s a t a t o t a l farm sample l e v e l . Th is i s not to say that i t con -s t i t u t e s an e n t i r e l y s a t i s f a c t o r y r e l a t i o n s h i p f o r a l l the d i f f e r e n t areas covered by the t o t a l sample o f farms. Never the le s s , pending r e f i n e -ment, i t does seem to o f f e r a very usefu l g l oba l f unc t i on to work w i t h in the absence of more s u i t a b l e reg iona l f u n c t i o n s . Based on t h i s paddy p roduct ion f unc t i on a number of a n a l y t i c a l c r i t e r i a f o r i d e n t i f y i n g and e v a l u a t i n g the p r o d u c t i v i t y o f d i f f e r e n t resource inputs w i l l now be d e a l t w i t h . They a r e , r e t u r n s - t o s c a l e , : pa t te rn of resource use, average and marginal va lue p r o d u c t i v i t i e s o f i npu t s , c o n t r i b u t i o n o f each input to t o t a l product and the degree o f a l l o c a t i v e e f f i c i e n c y in o v e r a l l p roduc t i on , a . Returns to Sca le on Paddy Farms Returns to s ca l e represent an important economic c h a r a c t e r i s t i c of a product ion process . They are def ined as the p r opo r t i ona l change in the dependent v a r i a b l e in response to a s imultaneous and s i m i l a r propor -t i o n a l change in a l l the inputs en te r i n g i n to p roduc t i on . If the input e l a s t i c i t i e s sum to g reater than one, i n c rea s i ng returns to s ca l e are i n d i c a t e d . If they sum to less than one i t represents a s i t u a t i o n of 69 decreas ing returns to s c a l e . On the o the r hand i f t h e i r sum equals one, then i t impl ies constant returns to s c a l e . In a Cobb-Douglas f unc t i on returns to s ca le a re i nd i c a ted r e a d i l y by i t s f u n c t i o n c o e f f i c i e n t (e) which i s obta ined by summing the output e l a s t i c i t i e s (exponents) o f the i n d i v i d u a l f a c t o r s o f p roduct ion (see Appendix 2 ) . The sum of the p ro -duct ion e l a s t i c i t i e s f o r the inc luded v a r i a b l e s in equat ion i s 1.186. This impl ies that a s imultaneous change of one per cent in a l l inputs w i l l lead to a 1.186 per cent change in the t o t a l output . Bearing in mind that the equat ion does not e x p l i c i t l y i nc lude a l l u t i l i z e d input s , e s p e c i a l l y management, as we l l as the f a c t that the c o e f f i c i e n t i s q u i t e c l o s e to one, i t i s reasonable not to p lace too much emphasis on the i n d i c a t i o n that i nc rea s i ng returns to s ca le e x i s t s . Rather i t is probably 12 s a fe r to th ink more in terms o f constant returns to s c a l e , b. Pat te rns of Resource Use on Paddy Farms Before proceeding to a d e t a i l e d a n a l y s i s of p r o d u c t i v i t i e s and e f f i c i e n c y in resource use, i t i s h e l p f u l to cons ider l e v e l s o f input employed by the farmers. Acco rd i ng l y the mean farm l e v e l s of input f a c t o r s and output f o r the t o t a l sample a re reported in Table 5-5. Com-par i son of the input and output geometric and a r i t h m e t i c mean farm data revea l s s u b s t a n t i a l d i f f e r e n c e s between the two. In the case of land 13 the average farm acreage under paddy was 2.45 ac re s . The average 12 Nu l l hypothes i s that sum of e l a s t i c i t i e s ( e ) equa l l ed 1 was accepted a t 1 per cent L.O.S. 1 3 Unless s ta ted otherwise the term mean or average r e f e r s to the a r i t h m e t i c mean. Whenever geometric mean i s used the term w i l l be s p e c i f i c a l l y s t a t e d . 70 Table 5 . 5 . Levels o f Inputs and Output in Paddy Product ion on per Farm and per Acre Ba s i s ; 1972-73 Maha Season--Al1 Survey Farms V a r i a b l e Per Farm Per Acre Geometric A r i t h m e t i c Geometric A r i t h m e t i c mean mean mean mean Y Output (Bushels) 102 .37 152.62 56 .81 62.29 X l Land (Acres) 1 .8 2.45 -Farm labour (Man-days) 41 • 38 55.91 22 .99 22.82 Non-farm labour(Man-days) 63 • 77 81.92 35 .43 33.43 X 2 Tota l l abou r ' (Man-days) 104 .00 137.83 57 .77" 56.25 X 3 F e r t i 1 i zer (Rs.) 80 .50 136.00 44 .72 55.51 x 4 Agro-chem i ca1s (Rs.) 32 .00 46 .00 17 .78 18.77 h 2 Draf t s e r v i c e s (Rs.) 199 .00 334.00 110 .00 136.33 X 2 inc ludes farm labour and non-farm labour . X Q inc ludes both animal and machinery s e r v i c e s labour requirement per farm fo r a Maha paddy crop amounted to I38 man-days, i n d i c a t i n g a per acre labour u t i l i z a t i o n of 56 man-days. It was found that the f am i l y labour supply on ly accounted fo r 56 man-days o f the t o t a l labour requirement w i t h the re s t represented by h i r ed and e x -change labour. The average farm expenditure on f e r t i l i z e r use was Rs.i36.OO which amounted to Rs.55-51 per a c r e . The geometric mean f e r t i l i z e r cos t was s t i l l lower; the r e spec t i v e f i g u re s per farm and per acre being Rs.80.50 and 44.72 r e s p e c t i v e l y . At an average p r i c e of Rs.23.00 per cwt. 71 the amount of f e r t i l i z e r used per ac re on a " t y p i c a l " farm was 1.9 14 cwts. The survey showed that a l l the farmers grew high y i e l d i n g v a r i e t i e s of r i c e , which u s ua l l y r equ i re 3 - 4 cwts. of f e r t i l i z e r per acre f o r ob t a i n i n g best y i e l d s . This s t r a i g h t away i nd i c a te s an under use o f f e r t i l i z e r by farmers. The t ab l e a l s o shows the average expen-d i t u r e on animal and machinery s e r v i c e s per farm was R s . 3 3 4 . 0 0 , ranking as the second h ighest item of expend i ture in paddy p roduc t i on . The average expenses on agro-chemica l s input,, e . g . , h e r b i c i d e s , i n s e c t i -c ides and f u n g i c i d e s , were on l y R s . 1 8 . 7 7 per a c r e , c. Marginal P r o d u c t i v i t i e s of Inputs Of the three p r o d u c t i v i t y measures the most r e l i a b l e and usefu l in gu id ing resource a l l o c a t i o n dec i s i on s i s marginal va lue p r o d u c t i v i t y (MVP). It i s def ined as the a d d i t i o n . t o t o t a l va lue product r e s u l t i n g from the a d d i t i o n of one u n i t of an input to the product ion process , c e t e r i s pa r i bu s . The est imates of input MVP's in paddy product ion a t geometr ic mean l e v e l s and four other input 1 eve 1scombinations a re i n d i -cated in Table 5 . 6 . The l a t t e r input combinations inc luded (a) geometric mean input l e v e l s r a i sed 5 0 per cen t , (b) on l y d r a f t s e r v i ce s input i n -creased 5 0 per cent , keeping o ther s a t geometric mean l e v e l s , (c) on ly f e r t i l i z e r input increased 5 0 per cen t , other inputs held a t geometric mean l e v e l s and (d) f e r t i l i z e r and labour each increased by 5 0 per cent ho ld ing other inputs a t geometric mean. A c c o r d i n g l y , the MVP's o f inputs Implies geometric mean l e v e l s of i nput s . One cwt. equals 112 l b s . Table 5 . 6 . E f f e c t s of Increas ing (a) A l l Inputs, (b) Some Inputs on Marginal Value P r o d u c t i v i t i e s and Tota l Output—Based on Equation R^  Resource Inputs Geometr i c mean input l e v e l s ( 0 MVP's of i nputs (Rs.) ( 2 ) Input l eve l at 50 per cent above geometr i c mean ( 3 ) Marginal Value P r o d u c t i v i t i e s (Rs.) A l l inputs at 50 per cent above geometr ic mean ( 4 ) Only d r a f t se rv i ce s at 50 per cent above geo-met r i c mean ( 5 ) Only f e r -t i l i z e r at 50 per cent above geo-met r i c mean ( 6 ) Only f e r -t i 1 i zer and labour a t 50 per cent above geo-metr i c mean ( 7 ) X] Land (Acres) X 2 Labour (Man-days) X^ F e r t i 1 i z e r (Rs.) Xg Draft Serv ices (Rs.) 1.80 1 0 4 . 0 0 80.50 1 9 9 - 0 0 (per ac.) 2 2 0 . 4 3 (per m-d) 8 . 8 9 (per Rs.) 3 . 8 9 (per Rs.) . 9 9 2.70 1 5 6 . 0 0 1 2 0 . 7 5 298 .50 (per i jcre) 237.72 2 3 2 . 0 9 (per mar 239.33 l-day) 3 0 3 . 7 0 9 . 5 9 9 . 3 6 (per 9 . 6 5 -upee) 8.16 4 . 2 0 4 . 1 0 (per 2 .81 -upee) 3 . 5 7 1 . 0 6 . 6 9 1 . 0 6 1 . 35 Value o f Output (Rs.) 1 , 5 4 3 . 8 3 2 , 4 9 7 . 4 2 1 , 6 2 5 . 2 1 1 , 6 7 6 . 2 9 2 , 1 3 7 . 1 0 73 c a l c u l a t e d show what changes take p lace when resources are combined in d i f f e r e n t ways. Thus in r e l a t i o n to resource p r i ce s the MVP's po in t to p r o f i t a b l e adjustments. Columns (1) and (2) in Table 5.6. (p. 72) i n d i c a t e geometric mean l e v e l s of inputs used on the survey farms and the corresponding input marginal va lue p r o d u c t i v i t i e s , r e s p e c t i v e l y . Column (2) shows that the va lue p r o d u c t i v i t y of an acre o f paddy land a t the margin i s Rs.220.A3, wh i l e the marginal re tu rn from a man-day i s Rs.8.89. Column (2) a l s o i n d i c a t e s that an e x t r a rupee used in e i t h e r f e r t i l i z e r or d r a f t s e r v i ce s would have brought an a d d i t i o n a l Rs.3.89 and Rs.-0.99 respec-t i v e l y . The l e v e l s o f inputs shown in column (3) represent a h ypo the t i c a l input combinat ion, where a l l input l e v e l s are s imul taneous ly increased 50 per cent above t h e i r geometric means. The corresponding marginal va lue p r o d u c t i v i t i e s of inputs a t these l e v e l s are given in column (A), which shows that a l l MVP's have now increased. The increase of a l l i n -puts by 50 per cent a l s o increased the est imated t o t a l output from Rs.15A3.83 to Rs.2A97.A2. Columns (5) and (6) o f Tab le "5 -6 i l l u s t r a t e the po in t that increase in one input , keeping a l l other inputs at prev ious l e v e l s , serves to inc rease MVP's of the other inputs wh i l e decreas ing i t s own MVP. For i n s tance , a s o l i t a r y increase in expend i ture on d r a f t s e r v i ce s (column 5) by 50 per cent would lower i t s MVP from Rs.0.99 to 0.69, wh i l e i n -c reas ing the MVP's of the other input s . Thus, i t i s c l e a r l y seen that employing more d r a f t s e r v i ce s under the s i t u a t i o n de s c r i bed , on l y serves 74 to move f u r t h e r away from opt imal a l l o c a t i o n , because the MVP's of the inputs d i ve rge f u r t h e r from t h e i r p r i c e s (see Table 5 - 7 . ) . From column ( 6 ) (Table 5 . 6 . p. 7 2 ) i t i s seen that i f f e r t i l i z e r cost per farm alone i s increased from Rs .80 .50 to R s . 1 2 0 . 7 5 , the MVP o f d r a f t s e r v i ce s i s increased to R s . 1 . 0 6 from Rs.0.99 wh i l e that of i t s e l f i s reduced to R s . 2 . 8 l from Rs.3-89. Therefore, the f i g u r e s shown in columns ( 5 ) and ( 6 ) demonstrate that increased a p p l i c a t i o n s of a s i n g l e input do not a l t e r output as much as would occur i f more resources were inc reased. Th i s i s c l e a r l y seen from the r e s u l t s in column ( 7 ) , where both labour and f e r t i l i z e r are increased s imu l taneous l y . Here, the i n -crease in output i s much higher than when e i t h e r f e r t i l i z e r or d r a f t s e r v i ce s a lone was inc reased. In summary i t can be s a i d that the demon-s t r a t e d changes in MVP's p rov ide u se fu l d i r e c t i o n s f o r resource a d j u s t -ments under cond i t i on s p o s i t e d . S ince the MVP of any resource decreases w i t h h igher l e v e l s of a p p l i c a t i o n , c e t e r i s pa r i bu s , i t i s necessary to observe what happens at resource l e v e l s o ther than geometric means i f opt imal resource a l l o c a -t i o n i s to be ach ieved. Never the le s s , MVP obse rva t ions a t geometric mean resource l e v e l s are o f great use in he lp ing farmers and extens ion pe r -sonnel recogn ize t y p i c a l needs f o r resource adjustments. To extend the a n a l y s i s , MVP's were est imated at d i f f e r e n t l e v e l s of a p p l i c a t i o n , ho ld ing other inputs constant at t h e i r geometric means. The r e s u l t s a re presented in Table 5 . 7 -From Table 5 - 7 - i t i s seen that by i nc reas ing the f e r t i l i z e r i n -put per farm from Rs .80.50 to R s . 1 4 0 . 0 0 (other resources held a t geometr ic 75 Table 5-7. E s t imat ion o f MVP's of Resource Inputs a t D i f f e r e n t Levels of A p p l i c a t i o n (Assuming Geometric Mean Levels f o r Other Resources)—Based on Equation R^  Resource 1nput Unit P r i c e (Cost) Input l e ve l MVP e s t i mates (rupees) Tota l product e s t imates (rupees) Land 227.50 (Rs./Ac.) (acres) 1 .00 1 .50 1 . 80 * 2.00 2.50 341 .96 307.40 2 2 0 . 4 3 * 203.83 172.64 per acre 1,327.43 1,473.22 1,543.83* 1,586.27 1,679-39 Labour 6.10 (Rs./man-day) (Man-days) 80.00 100.00 1 0 4 . 0 0 * 120.00 140.00 9.90 9.06 8.89* 8.39 7.88 per man-day 1,322.25 1,512.61 1,543.83* 1,681.88 1,844.58 Fert i 1 i zer 1 .00 (Rs.) (Rs.) 60.00 80.50* 100.00 120.00 140.00 4.92 3.89* 3.27 2.81 2.50 . per Rupee 1,454.42 1,543.83* 1,612.14 1,674.17 1,727.39 Draft Se rv i ces 1 .00 (Rs.) (Rs.) 100.00 150.00 199•00* 200.00 250.00 2.08 1.38 0.99* O.98 0.83 per Rupee 1 , 4 1 4 . 4 2 1,489.28 1,543.83* 1,544.92 1,589.27 * Ind icates geometric means, a l s o MVP's and t o t a l products a t geometric mean input l e v e l s . 76 mean l e v e l s ) , the t o t a l output increased but the MVP dropped to Rs2.50. Even a f t e r the increase the MVP o f f e r t i l i z e r was s t i l l c l e a r l y above input p r i c e . S i m i l a r l y , by i nc rea s i ng farm labour input from 104 to 140 man-days, t o t a l p r o d u c t i v i t y increased w i t h an accompanying decrease in MVP to Rs.7.88, which i s s t i l l above input p r i c e . In c on t r a s t a co s t increment f o r d r a f t s e r v i ce s from Rs.199-00 to Rs.250.00 r e s u l t e d in an output increase which was i n s u f f i c i e n t to pay fo r the e x t r a input . In t h i s case the MVP became lower and even more d i ve rgent from p r i c e , d. D i s t r i b u t i v e Shares of I nd i v i dua l Inputs of P roduct ion An a n a l y s i s i n vo l v i n g the a l l o c a t i o n of the t o t a l product to i n d i v i d u a l input f a c t o r s i s usefu l f o r i d e n t i f y i n g the r e l a t i v e c o n t r i -but ion of inputs to t o t a l paddy output . Such an a l l o c a t i o n of the t o t a l product to d i f f e r e n t input f a c t o r s can be undertaken by using E u l e r ' s theorem. The theorem s t a te s that under c o n d i t i o n s o f l i n e a r homogeneity, the t o t a l product w i l l be exhausted by the d i s t r i b u t i v e shares f o r a l l the input f a c t o r s i f each f a c t o r of p roduct ion i s pa id the amount of i t s marginal p r o d u c t i v i t y . The R^ product ion f unc t i on e s t imate in the present study shows returns to s ca le of 1.186. There fo re , an extens ion of E u l e r ' s theorem was used f o r ob t a i n i n g the c o n t r i b u t i o n o f each input f a c t o r to the t o t a l p r o d u c t . ' ^ In the c a l c u l a t i o n s , resources were assumed to be combined a t geometr ic mean l e v e l s . See Appendix 3 f o r account of method. Table 5 . 8 i l l u s t r a t e s that in the paddy product ion under s tudy, labour accounts f o r the l a r ge s t farm share of p r oduc t i on , namely 5 0 . 6 per cent of t o t a l farm output . The land input share of t o t a l paddy output amounts to 2 1 . 6 per cent . The c o n t r i b u t i o n of f e r t i l i z e r and d r a f t s e r v i ce s v a r i a b l e s are 1 7 . 0 and 1 0 . 8 per cent of the t o t a l output , Table 5 - 8 . Amounts o f Value Product Cont r ibuted by Resource Inputs to Tota l Paddy Output ( A l l Resources at Geometric Leve l s )—Based on Equation R, Resource 1nput Resource Level Amount of Value Product C o n t r i -buted (Rs.) Percentage Value Product -Contr i buted X ] Land (Acres) 1.8 3 3 3 - 9 0 2 1 . 6 5 Labour (Man-days) 1 0 4 . 0 7 7 9 - 5 4 5 0 . 5 6 X^ F e r t i 1 i z e r (Rs.) 80 . 50 2 6 4 . 0 5 1 7 . 0 2 Xg Draft s e r v i c e s (Rs.) 1 9 9 . 0 0 1 6 6 . 1 1 1 0 . 7 7 Tota l 1 , 5 4 3 . 6 0 1 0 0 . 0 0 r e s p e c t i v e l y . A d i r e c t comparison between the costs of resources (see Tables 5 - 5 . ( p . 7 0 ) and 5 - 7 . (p. 7 5 ) ) and t h e i r value c o n t r i b u t i o n s to t o t a l product ion (see Table 5 .8 . ) can a l s o be made. At the geometric mean l e v e l , the t o t a l co s t o f labour input per farm was R s . 6 3 4 . 4 0 , wh i l e i t s c o n t r i b u t i o n to t o t a l output was R s . 7 7 9 . 5 4 . The cos t s o f f e r t i l i z e r and d r a f t s e r v i ce s were Rs .80.50 and R s . 1 9 9 . 0 0 r e s p e c t i v e l y and t h e i r corresponding value c o n t r i b u t i o n s to t o t a l output were R s . 2 6 4 . 0 3 and 1 6 6 . 1 1 . 78 e. Average Apport ioned Value P r o d u c t i v i t i e s and Farm Net  Value P r o d u c t i v i t i e s of Farm Inputs The average apport ioned value p r o d u c t i v i t y o f a resource can be determined by d i v i d i n g i t s l e ve l o f a p p l i c a t i o n i n to i t s a l l o t t e d va lue p r o d u c t i v i t y (see Table 5.8, p. 77). The average apport ioned produc-t i v i t i e s o f the paddy inputs are g iven in column (3) o f Table 5.9- The t ab l e i nd i ca te s that the average apport ioned p r o d u c t i v i t y of an acre o f paddy land f o r a c u l t i v a t i n g season was Rs.185-50 S i m i l a r l y the average apport ioned p r o d u c t i v i t y f o r a man-day o f labour and Rs.1.00 of f e r t i l i z e r was Rs.7-49 and Rs.3-28 r e s p e c t i v e l y . The corresponding va lue f o r Rs.1.00 o f d r a f t s e r v i c e s was Rs.0.83- Thus in r e l a t i o n to t h e i r p r i c e s the average apport ioned p r o d u c t i v i t i e s o f labour and f e r t i l i z e r are sub-s t a n t i a l l y h igher than t h e i r per u n i t c o s t s . On the other hand the average apport ioned p r o d u c t i v i t y of d r a f t s e r v i ce s i s le s s than i t s c o s t . Having determined the average apport ioned value p r o d u c t i v i t y of an input used in paddy p roduc t i on , i t i s now po s s i b l e to compute i t s farm net value p r o d u c t i v i t y . Thus, on m u l t i p l y i n g average apport ioned va lue p r o d u c t i v i t y f o r an input by i t s geometric mean l e v e l of a p p l i c a -t i o n and deduct ing a s soc i a ted c o s t s , i t i s p o s s i b l e to ob ta i n the farm net value p r o d u c t i v i t y . However, t h i s computation faces the problem of va l u i ng farm inputs . Cos t ing of inputs can adhere to d i f f e r e n t p roced-ures. An economist may use oppor tun i t y cos t as the ba s i s , wh i l e a farmer may cons ider the cost to be h i s a c tua l cash expend i ture on the input . To overcome the problem of v a l u a t i o n , two types of cos t assessment were used. 79 Table 5.9. Average Apport ioned Value P r o d u c t i v i t i e s and Farm Net Value P r o d u c t i v i t i e s of Inputs in Paddy Product ion at Geometric Mean Input Levels — Based on Equation R^ Resource (1) Ave rage apport ioned Geometric va lue p ro -mean l e v e l d u c t i v i t y o f input on farms on farms (Rs.) (2) (3) Farm Net Valued P r o d u c t i v i t i e s o f Inputs  Farm Farm Market^ based 2 Market based cost o f cost o f cos t s co s t s resource Resource deducted deducted (Rs.) (Rs.) (Rs.) (Rs.) (4) (5) (6) (7) x l Land (Acres) 1. 8 185 .50 227.50 165. 00 -75.10 36.90 X 2 Labour (Man-days) 1 0 4 . 00 7 .49 6.10 3. 74 144.56 390.00 X 3 F e r t i 1 i z e r (Rs.) 80. 50 3 .28 2.00 1 . 00 103.93 183.54 X 8 Dra f t Se rv i ces (Rs.) 199. ,00 0 . 8 3 1.00 0. 62 - 3 3 . 8 3 41 .79 Tota l 139.56 652.23 Determined under f u l l oppo r tun i t y cos t c on s i de r a t i on s ( e . g . , Rs.6.10 per man-day of labour; f e r t i l i z e r w i thout subs idy ) . Costs r e l a t e r t o geometr ic mean l e v e l s o f i npu t s . 2 R e f l e c t s e s t a b l i s h e d land r en t , mix of h i red and f am i l y labour , sub-s i d i z e d f e r t i l i z e r , and mix o f h i red and farm prov ided d r a f t s e r v i c e s . Costs r e l a t e to geometric mean l e v e l s of i nput s . 3 Farm Net va lue p r o d u c t i v i t i e s are der i ved by deduct ing cos t s from input va lue p r o d u c t i v i t y shares (see: Table 5.8. p. 77). 80 These types of cos t s a re r e f e r r ed to as market cost and farm based cost de te rminat ions . The corresponding costs f o r an input are i nd i ca ted in columns (4) and (5) of Table 5-9- (p- 79). The farm based cost of an input represents the t o t a l cash ou t l a y invo lved in a c q u i r i n g ( h i r i n g and purchasing) an input f o r paddy p r oduc t i on , d i v i d e d by the t o t a l number o f un i t s used. Here no charge i s made f o r resources a l ready on the farm, e . g . , f am i l y labour . Market cost of an input r e f l e c t s oppor tun i t y c o s t , which in the case of f e r t i l i z e r was assessed at the unsubs id ized r a t e . Columns (6) and (7) of Table 5-9 present the computed farm net va lue p r o d u c t i v i t i e s from i n d i v i d u a l inputs based on the d i f f e r e n t cost assessments. The land and d r a f t s e r v i ce s v a r i a b l e s when valued at market cost r e s u l t in negat ive farm net va lue p r o d u c t i v i t i e s o f Rs.75.10 and Rs.33-83 r e s p e c t i v e l y , w i th regard to geometric mean l e v e l s of a p p l i c a -t i o n . However, i f farm based costs are used fo r v a l u a t i o n , they y i e l d p o s i t i v e farm net value p r o d u c t i v i t i e s of Rs.36.90 and Rs.41.79 r e s -p e c t i v e l y . In c o n t r a s t , the f e r t i l i z e r and labour v a r i a b l e s show p o s i t i v e farm net va lue p r o d u c t i v i t i e s f o r both types of co s t s . F e r t l i z e r at market cost y i e l d s a f i g u r e of Rs.103-93, wh i l e at the farm based cost ( i . e . , a f t e r deduct ing subsidy) i t y i e l d s Rs.183-54. This i l l u s t r a t e s the bene f i t of the f e r t i l i z e r subs idy to a farm, a l b e i t at geometric mean l e ve l s o f i nput s . In summary, Table 5.9- shows that farm net va lue p r o d u c t i v i t i e s fo r a l l inputs in equat ion R^, added up to Rs.139-56 when valued at market cost and Rs.652.23 when valued accord ing to farm based co s t s . The e f f e c t of f u l l oppo r tun i t y cost assessment i s the re fo re c l e a r -l y demonstrated. 81 f . Assessment o f Input A l l o c a t i v e E f f i c i e n c y The a n a l y t i c a l procedure fo l lowed in t h i s s e c t i on def ines input a l l o c a t i v e e f f i c i e n c y in terms o f p r o f i t maximizing behaviour of paddy farmers. Two ways o f a s ses s ing the e f f i c i e n c y o f input a l l o c a t i o n w i l l be cons idered. F i r s t l y , the marginal va lue p r o d u c t i v i t i e s (MVP's) o f inputs at geometric mean l e v e l s in the sample w i l l be compared w i th corresponding marginal f a c t o r cost s (MFC 's). Secondly, opt imal resource combinations w i l l be compared w i t h ac tua l geometric mean l e v e l s of i n -put a p p l i c a t i o n . From prev ious d i s cu s s i on of theory i t i s c l e a r that these two approaches prov ide ready c r i t e r i a f o r judg ing whether opt imal resource a l l o c a t i o n has been approached c l o s e l y or not , under the assumption of un1imi ted c a p i t a 1 . ( i ) Comparison o f MVP's and MFC's of Paddy Inputs The r e s u l t s of comparing input MVP's and MFC's in paddy produc-t i o n are presented in Table 5.10. With the absence of c a p i t a l l i m i t a t i o n s or o ther r e s t r i c t i o n s on the a p p l i c a t i o n of an i nput , a r a t i o of 1 between i t s MVP and MFC would i n d i c a t e that the most e f f i c i e n t a l l o c a t i o n fo r the resource had been achieved under c e r t a i n c o n d i t i o n s . It i s very important that these c ond i t i o n s are c l e a r l y understood. The p roduct ion f unc t i on in the form of R^  shows inc reas ing returns to s ca le f o r the v a r i a b l e s inc luded in the r e l a t i o n s h i p . It i s t he re -fo re imposs ib le to have a l l inputs a l l o c a t e d in a way that t h e i r MVP's equal MFC.';s a t an opt imal output l e ve l fo r that could on ly happen i f the sum of p roduct ion e l a s t i c i t i e s o f inputs was les s than 1. There fo re , the 82 Table 5 . 1 0 . Comparison of Marginal Value P r o d u c t i v i t i e s and Marginal Factor Costs of Inputs in Paddy Farming a t Geometric Mean Levels of A p p l i c a t i o n — A l l Survey Farms—Based on Equation R^  Resource Input MVP1 (Rs.) MFC (Rs.) Rat io of MVP to MFC ( 1 ) ( 2 ) ( 3 ) ( 4 ) Xj Land (acres) 2 2 0 . 4 3 ( 1 8 . 7 1 ) 2 2 7 . 5 0 . 9 6 X 2 Labour (man-days) 8 . 8 9 ( 0 . 7 3 ) 6 . 1 0 1 . 4 6 * X^ F e r t i l i z e r (Rs.) 3 . 8 9 ( 0 . 1 4 ) 1 . 0 0 3 . 8 9 * Xg Dra f t s e r v i ce s (Rs.) 0 . 9 9 ( 0 . 6 0 ) 1 . 0 0 . 9 9 1 F igures in parenthes i s i n d i c a t e the standard e r r o r s of MVP es t ima te s . * Nu l l hypothes i s that r a t i o equals 1 was r e j e c t ed a t 1 per cent . The standard e r r o r of MVP es t imate of each product ion input was c a l c u l a t e d from the fo rmula , Y" SEP Y = - .S, X . "y b. _ i X i _ where Y i s the geometric mean value of ou tput , Xj i s the geometric mean value o f i npu t , and S^ i s standard e r r o r of the reg re s s i on c o e f f i c i e n t b. w i t h regard to X.. i See E.O. Heady and J . D i l l o n , A g r i c u l t u r a l P r o - duct ion Funct ions , Iowa State U n i v e r s i t y P res s , 1 9 6 1 , p. 2 3 1 . S ince a l l the MVP est imates were made a t the input geometric mean l e v e l s using the Cobb-Douglas f u n c t i o n , the more complex var iance formula f o r determin ing the standard e r r o r s o f e s t imate developed by Car ter and Ha r t l ey was not a p p l i e d . See H.0. Ca r te r and H.0. H a r t l e y , "A va r iance Formula f o r Marginal P r o d u c t i v i t y Est imates us ing the Cobb-Douglas F u n c t i o n , " Econometr ica, 2 6 : A p r i l , 1 9 5 8 , pp. 3 0 6 - 3 1 3 . 83 usefu lness of seeing how c l o s e MVP's are to MFC's a t geometric l e v e l s of input a p p l i c a t i o n f o r the survey farms i s somewhat r e s t r i c t e d . Under the assumption that t y p i c a l farmers are f r ee to vary an input w h i l e ho ld ing other inputs constant at the geometric mean l e v e l s , i t i s e f f i c i e n t p r a c t i c e to b r ing the MVP of the v a r i a b l e input i n to e q u a l i t y w i th i t s MFC. This i s indeed po s s i b l e even w i th the R^  equa-t i o n . Hence Table 5-10., under the c ond i t i o n s de s c r i bed , i n d i c a t e s what adjustments can be recommended. Here i t can be noted that the r a t i o of MVP to MVC, in column h of Table 5-10. f o r each f a c t o r input , was s t a t i s t i c a l l y tested w i th respect to the n u l l hypothes is that the r a t i o equa l l ed 1. The r e s u l t s of the t e s t s show that the r a t i o s f o r land and d r a f t s e r v i c e s were not r e j e c t e d as being equal to one. Therefore in the r e s t r i c t e d e q u i l i b r i u m sense desc r ibed these inputs show e f f i c i e n t a l l o c a t i o n . In the case o f labour and f e r t i l i z e r the r a t i o s were r e -j e c t e d as being equal to one. There fo re , s ince t h e i r MVP's are higher than t h e i r MFC's, i t i s c l e a r that many farmers cou ld have a f f o rded to use more of these inputs under the assumptions s p e c i f i e d . It appears that paddy farmers in S r i Lanka have been concerned w i th a ch i e v i n g e f f i c i e n t uses of land and d r a f t s e r v i c e s . In c o n t r a s t , labour and f e r t i l i z e r a l l o c a t i o n appears to present a problem. The under u t i l i z a t i o n o f f e r t i l i z e r can be e xp l i ned to a large, extent in terms of cash shortages su f fe red by most farmers, as we l l as the rather high de-gree of r i s k a s soc i a ted w i t h output in paddy farming. But, the under u t i l i z a t i o n of labour may be ra ther s u r p r i s i n g a t f i r s t s i g h t , i f the common view is held that the MVP of r u r a l labour in subs i s tence economies 84 i s zero or near z e r o . ' ^ The usual argument f o r assuming a zero MVP fo r labour i s that a surp lus of farm labour e x i s t s and a lack of a l t e r n a t i v e means of employment in subs i s tence economies ensures c o n d i t i o n s , where-by, i t i s r e a d i l y employed to the po in t of zero MVP. In the case of the S r i Lanka data i t i s obvious that farmers cannot a f f o r d to see the MVP of labour go below the wage r a te (at l e a s t f o r h i r ed l abou r ) , l e t alone see i t go to ze ro . The i n t e r e s t i n g po in t i s tha t equat ion R^  shows the MVP of labour remaining we l l above the wage r a te f o r the t y p i c a l farmer. The r e l a t i v e l y high MVP of labour in paddy c u l t i v a t i o n at geo-met r i c mean l e v e l s o f ' inputs i s exp la ined reasonably w e l l by the pa t te rn of seasonal labour d i s t r i b u t i o n . It shows c r i t i c a l per iods of heavy labour demand f o r opera t ions such as land p r e p a r a t i o n , t r a n s p l a n t i n g , ha rves t ing and t h re sh i ng . During these peak p e r i o d s , f a m i l y labour i s hard ly adequate and on most paddy farms a d d i t i o n a l labour, o f t en hard to f i n d , has to be h i r e d . This s i t u a t i o n i s ev ident from the data in the present study. As i nd i c a t ed in Table 5.5- (p. 70) nea r l y 60 per cent of labour fo r paddy product ion came from h i r ed labour. Aga in, the ex i s t ence of shortages of labour f o r paddy product ion in the sample areas are confirmed by the i n -m i g ra t i on of farm labour dur ing peak per iods of paddy f a r m i n g . 1 ^ Thus inadequate labour supp l i e s The d o c t r i n e of zero marginal p r o d u c t i v i t y of r u r a l labour in developing economies has been re fu ted by a number of economists: see, T.W. S c h u l t z , Transforming Tradi t i o n a l A g r i c u l t u r e , New Haven and London, Yale U n i v e r s i t y P res s , Chapter 4, 1969. This can be observed p a r t i c u l a r l y in the d i s t r i c t s of Hamban-to ta and Polonnaruwa. 85 dur ing c r i t i c a l per iods would help to e x p l a i n the r e l a t i v e l y high MVP of labour. ( i i ) Comparison o f Optimal and Geometric Mean  Levels of Input A p p l i c a t i o n Another way of examining the e f f i c i e n c y of resource use of the t y p i c a l paddy farmer i s to compute the opt imal combination of resources from the product ion f u n c t i o n R^, w i th regard to the geometr ic mean o u t -put l e ve l per farm of Rs.15^3.80 and the geometric mean paddy acerage of 1.8 a c re s . Land i s an input that mean ing fu l l y lends i t s e l f to con -s t r a i n t . The opt imal combinat ion o f labour, f e r t i l i z e r and d r a f t s e r v i ce s under these c ond i t i o n s can then be compared w i th the ac tua l l e v e l s of t h e i r use. When paddy land i s f i x e d at 1.8 acres per farm, the equat ion R^ becomes: .5987 .2030 .1272 Y = 20.0313 X 2 X 3 Xk [5.12] The exponents in t h i s f u n c t i o n sum to O.9289. T h e o r e t i c a l l y i t is now p o s s i b l e to determine an opt imal l e ve l of output as we l l as the c o r r e s -ponding combination of i nput s . But i t is not p r a c t i c a b l e to do that because i t means e x t r a p o l a t i n g beyond the re levant range of the da ta . This i s e a s i l y exp la ined by the f a c t that the c o e f f i c i e n t s come c l o s e to adding up to u n i t y , which means that the optimum p o s i t i o n occurs a con-s i d e r a b l e way along the expansion path. Never the le s s , under t h i s s i t u a -t i o n i t i s s t i l l p o s s i b l e to compute the opt imal p ropor t i on s of inputs to produce a des i red l e ve l of output , w i t h i n the re l evan t range of da ta . A c co rd i n g l y , i f output i s f i x e d at the geometric mean l e ve l o f Rs.15^3.80 86 and land i s held a t the geometric mean l e v e l of 1.8 a c r e s , the optimum combination of labour, f e r t i l i z e r and d r a f t s e r v i ce s i s g iven in Table 5.11 below. Table 5.11- Comparison of Actua l and Optimal Levels of Inputs a t the Geometric Mean Output of Rs.1543.80 and the Geometric Mean Input of 1.8 Ac res—Based on Equat ion R^  1 nput Current Optimal Amounts Amounts of Inputs of Inputs Current P ropor t i on s of Inputs k Optimal k Proport ions of Inputs (1) (2) (3) (4) (5) Land 1 "(Rs.) 409.50 409.50 1 .00 1 .00 X 2 Labour 2 (Rs.) 634.40 589.32 1 .55 1.44 X 3 F e r t i 1 i z e r 3 (Rs.) 80.50 165.44 .19 .40 X^ Draft Serv ices (Rs.) 199.00 125.59 .48 .30 1 Land was valued at Rs.227.50 per a c r e . 2 Labour was valued at Rs.6.10 per day • 3 F e r t i 1 i z e r and d r a f t s e r v i c e s valued at Rs.1.00 per u n i t . 4 . Land was used as the numeraire. Columns (2) and (3) of the t ab l e i n d i c a t e the cu r ren t and opt imal investments in v a r i a b l e inputs f o r producing an output of Rs.1543-80 under the land s i t u a t i o n s p e c i f i e d . The r e spec t i ve input investment p ropor t i on s are g iven in columns (4) and (5) . Thus in opt imal combinat ion labour and d r a f t s e r v i ce s show a decrease over the cu r ren t amounts; whereas f e r t i l i z e r shows an i nc rease . These r e s u l t s have rea l meaning f o r resource adjustment 87 on the t y p i c a l farm. They i n d i c a t e a r e d i s t r i b u t i o n of investment; away from labour and d r a f t s e r v i c e s , i n to f e r t i l i z e r . At f i r s t s i g h t t h i s r e s u l t might seem i n con s i s t en t w i t h the e a r l i e r p a r t i a l e q u i l i b r i u m f i n d i n g s . For instance in that case i t was found tha t labour and f e r -t i l i z e r MVP's were higher than t h e i r MFC's when c a l c u l a t e d at geometric mean input l e v e l s . Now the suggest ion i s made that investment can be r e d i r e c t e d from labour and d r a f t s e r v i c e s i n to f e r t i l i z e r . The two sets of f i n d i n g s are con s i s t en t w i t h i n the s t r i c t context s of a n a l y s i s . In the l a t t e r case s imultaneous adjustment between labour , d r a f t s e r v i c e s and f e r t i l i z e r i s being sought. In the e a r l i e r a n a l y s i s statements con -ce rn ing labour were based on the f a c t that a l l other inputs were held f i x e d a t geometric mean l e v e l s . There i s s t i l l another f a ce t of resource a l l o c a t i o n which should be t rea ted fo r the survey da ta . It c a l l s s imply f o r a d e f i n i t i o n of the expansion path (resource combination) r e l a t i o n s h i p s s p e c i f i e d by the R^  product ion f unc t i on and input p r i c e s . A Cobb-Douglas p roduct ion f unc t i on in four independent v a r i a b l e s of the type used, leads to s imultaneous 18 expansion path r e l a t i o n s h i p s between resources as f o l l o w s : b 2 P x l X = , Z p X I (X ) where: X X X X f i 1 x2 are independent v a r i a b l e s ; These equat ions can be e a s i l y v e r i f i e d by s imple a l g e b r a i c i n t e r p r e t a t i o n o f product ion theory . They f o l l o w the d e f i n i t i o n given by A. B. Anderawewa in "Supply Response in Gra in Corn in S.W. O n t a r i o , " unpubl ished M.S.A. The s i s , U n i v e r s i t y of Toronto, 1961. 88 X 3 = ^ 7 T T ( X 1> ' x l ' P x2« P x 3 ' Px8> a r e t h e '1 ' x3 corresponding input p r i c e s and b 4 P x l = ^ — p . — (X^) b^ , b 2 , b^, bg, are the corresponding 1 x8 e l a s t i c i t y c o e f f i c i e n t s from the R^  f u n c t i o n . From t h i s set of equat ions i t i s po s s i b l e to so lve f o r the l eve l of X^ w i t h regard to any output l e v e l . A f t e r that a l l other input l e v e l s can be c a l c u l a t e d . Even when no p a r t i c u l a r output l e ve l i s cons idered the expansion path r e l a t i o n s h i p s s t i l l de f ine the f i x e d p ropor t i ons in which inputs w i l l be combined at a l l output l e v e l s . With regard to the R^  p roduct ion f unc t i on and input p r i c e s , the f i x e d p ropor t ions f o r input combinat ion a re : X 2 = 86.81 Xj X 3 = 179.47 X, Xg = 112.28 Xj Where, X^ i s land in a c re s , X^ i s labour in man-days, X^ i s f e r t i l i z e r in rupees and Xg i s d r a f t s e r v i ce s in rupees. There fo re , i t i s po s s i b l e to t e l l at a g lance whether resources on any farm are out of l i n e w i t h opt imal combination cond i t i on s def ined by the expansion path. Re fe r r i n g to the geometric mean input l e v e l s f o r the survey farms (Table 5.5- , P- 70), i t is c l e a r that in r e l a t i o n to land commitment there i s cons ide rab le 89 u n d e r - u t i 1 i z a t i o n of labour and f e r t i l i z e r . In f a c t the recommended l e v e l s o f inputs w i th 1.8 acres of paddy would be approx imate ly 156 man-days of labour , Rs.323.00 of f e r t i l i z e r and Rs.202.00 o f d r a f t s e r v i c e s . The ac tua l geometric mean input combination w i t h 1.8 acres of paddy was 104 man-days of labour, approx imately Rs .8 l .00 of f e r t i l i z e r and Rs.199.00 of d r a f t s e r v i c e s . If the opt imal input combination were achieved i t would g ive Rs.2606.00 of paddy output , which exceeds the geometr ic mean output l e v e l of Rs.1544.00. With the d e f i n i t i o n of the expansion path equat ions i t i s but a short step to c a l c u l a t e the best input combinat ion fo r any given l e ve l of ou tput . For example, in the case of the Rs.1544.00 (geometric mean) output l e v e l , the recommended inputs are 1.18 acres of land and approx imately 99 man-days of labour, Rs.205.00 of f e r t i l i z e r and Rs.128.00 of d r a f t s e r v i c e s . The t y p i c a l farmer in the survey was using too much l and , labour and d r a f t s e r v i c e s , and not enough f e r t i l i z e r to a t t a i n the same output . In other words he was not s u f f i c i e n t l y i n -ten s i ve in h i s use of labour and f e r t i l i z e r . It i s obvious that the forego ing a n a l y s i s cen te r i n g on the ex-pansion path input r e l a t i o n s h i p s , i s o f g reat help in measuring input e f f i c i e n c y on paddy farms and p r o v i d i n g d i r e c t i o n s f o r resource adjustments. PART B ANALYSIS OF RESOURCE PRODUCTIVITIES IN PADDY PRODUCTION AT THE REGIONAL LEVEL This s e c t i on deals w i th resource p r o d u c t i v i t y a n a l y s i s of paddy data f o r i n d i v i d u a l reg ions w i t h i n the main sample. The d i s cu s s i on i s d i v i ded i n to f i v e s e c t i o n s , dea l i n g w i t h : 90 (1) the need fo r i d e n t i f y i n g d i f f e r e n t p r o d u c t i v i t y reg ions in paddy p roduc t i on ; (2) a c tua l i d e n t i f i c a t i o n o f the reg ions ; (3) e s t ima t i on of reg iona l product ion f u n c t i o n s ; (A) assessment of resource u t i l i z a t i o n a t the reg iona l l e v e l ; (5) resource p r o d u c t i v i t y a n a l y s i s at the d i s t r i c t l e v e l . 1. Need fo r I d e n t i f y i n g D i f f e r e n t P r o d u c t i v i t y Regions in Paddy Product ion The p r o d u c t i v i t y a n a l y s i s and i n t e r p r e t a t i o n of r e s u l t s in s e c t i o n A above were based on data f o r the t o t a l sample of survey farms. S ince these farmers were o r i g i n a l l y s e l e c ted as represent ing a number of d i s t r i c t s , an important assumption impl ied in the a n a l y s i s was that a s i n g l e p roduct ion f unc t i on could represent ' them a l l . The r e s u l t s obta ined so f a r have not suggested that t h i s assumption i s s e r i o u s l y a t f a u l t . Nevertheless in view of there being two area types in the t o t a l sample, namely farms in wet and dry zones (not based on the Maha season, which is e q u a l l y wet f o r both, but depending on the re s t o f the y e a r ) , i t was thought usefu l to ca r r y out a reg iona l a n a l y s i s on s t r a t i f i e d da ta . Th is would serve the purpose o f t e s t i n g the accepted view that the dry zone i s a h igher responding area in terms o f inputs and output . Regional a n a l y s i s a l s o serves to make the study comprehensive in treatment no matter what the outcome. There fo re , in order that any heterogene i ty in q u a l i t y of inputs in the t o t a l survey data be reduced as much as p o s s i b l e , a t t e n t i o n was turned to app rop r i a te s t r a t i f i c a t i o n of the sample. In so doing i t was hoped that r e g i o n a l l y grouped data would show g reate r 91 homogeneity which would permit p roduct ion f unc t i on s to be est imated more p r e c i s e l y . Furthermore es tab l i shment of d i s t r i c t p r o d u c t i v i t y areas a l s o has an a d d i t i o n a l advantage s i nce i t a f f o r d s g rea te r l o c a l s p e c i f i c i t y in resource adjustment. However, s t r a t i f y i n g the main sample in to too many part s i s to be avoided because i t would reduce the number of observat ions f o r any p a r t i c u l a r product ion f unc t i on e s t imat i on and render i t more d i f f i c u l t to e s t a b l i s h s t a t i s t i c a l r e l a t i o n s h i p s . Even under assumed low and high response reg ion s t r a t i f i c a t i o n the farm samples become small enough to a f f e c t e s t ima t i on in t h i s way. 2. I d e n t i f i c a t i o n o f Regions D i f f e r e n t r i c e producing d i s t r i c t s in S r i Lanka can show v a r i a -t i on s in respect of q u a l i t y and quan t i t y of inputs as w e l l as in c e r t a i n c l i m a t i c c o n d i t i o n s . On the bas i s o f a v a i l a b l e in format ion on product ion techniques and observed e c o l o g i c a l c h a r a c t e r i s t i c s , i t was hypothes ized that the f i v e d i s t i n c t p r o d u c t i v i t y regions can be d i v i d e d i n t o what w i l l be termed " h i g h response" and " l ow response" reg ions. The high response region was assumed to be more p roduc t i ve and inc ludes the d i s t r i c t s of Polonnaruwa and Hambantota. The low response region inc ludes the d i s t r i c t s of Kurunegala, Colombo and Kandy. Hence the high response 19 reg ion corresponds to the " d r y " zone, wh i l e the low response reg ion 20 corresponds approx imately to the " w e t " zone of the i s l a n d . S r i Lanka can be broadly d i v i ded in to two major a g r i c u l t u r a l areas namely dry and wet zones. The l i n e of demarcation is the 75 inches annual r a i n f a l l l i n e . 20 In a s t r i c t geographical c l a s s i f i c a t i o n Kurunegala d i s t r i c t f a l l s w i t h i n the " i n t e r m e d i a t e " zone. 92 P r i o r to e s t imat i ng separate product ion func t i on s f o r the two regions i t seemed necessary to t e s t whether the two hypo the t i ca l sub-groups of farms d id in f a c t reveal s i g n i f i c a n t d i f f e r e n c e s in paddy p r o -duc t i on . Two procedures were used f o r t h i s purpose. They a re : (a) the dummy v a r i a b l e method in regres s ion a n a l y s i s , and (b) the d i s c r im i nan t a n a l y s i s method fo r s t a t i s t i c a l l y t e s t i n g any d i f f e r e n c e s observed between groups. (a) Dummy V a r i a b l e Method This method invo lves the use of a zero-one dummy v a r i a b l e in the Cobb-Douglas f unc t i on to account f o r reg iona l d i f f e r e n c e s in p r o d u c t i -21 v i t y . The value of one was used fo r farms in the des ignated high response reg ion , wh i l e zero was used f o r those in the low response reg ion . The dummy v a r i a b l e method permits the advantage o f poo l i ng farm data from a l l regions f o r the purpose of r e g re s s i on . The es t imated Cobb-Douglas product ion f unc t i on i n co rpo ra t i n g the re l evan t p roduct ion inputs and the reg iona l dummy v a r i a b l e i s reported in Table 5 . 1 2 . The r e s u l t s i n d i c a t e that a l l reg res s ion c o e f f i c i e n t s i nc l ud ing the reg iona l dummy v a r i a b l e are s t a t i s t i c a l l y s i g n i f i c a n t at the .05 L.0.S. The i n c l u s i o n of the reg iona l dummy v a r i a b l e imp l ie s that the two hypo-thes i zed regions can in f a c t be represented by the same product ion 1 1 For s t a t i s t i c a l p r ope r t i e s and a p p l i c a t i o n of the dummy v a r -i a b l e technique see: A r thu r A. Goldberger, Econometric Theory, New York, Wi ley and Sons, Inc., pp. 2 1 8 - 2 2 7 , 1 9 6 4 . For s p e c i f i c a p p l i c a t i o n to product ion f unc t i on e s t ima t i on see: Zvi G r i l i c h e s , "Research Expenditures Educat ion and the Aggregate A g r i c u l t u r a l P roduct ion F u n c t i o n , " Amer. Econ. Rev., 5 4 : D e c - 1 9 6 4 , pp. 963-974, and Daniel B. S u i t s , "Use of Dummy Va r i ab l e s in Regress ion Equa t i on s , " Jou r . Amer. S t a t . As soc. , 5 2 : 1 9 5 7 , P P . 5 4 8 - 5 5 1 . 93 e l a s t i c i t i e s o f i nput s . The f u n c t i o n the re fo re d i s c r i m i n a t e s between the regions by way of the dummy v a r i a b l e term. The l a t t e r serves to s h i f t the t o t a l product l e v e l . Table 5.12. Cobb-Douglas Product ion Funct ion C o e f f i c i e n t s — T o t a l Farm D a t a — A l l Survey Farms (Regional Dummy Va r i ab l e Included) Draf t Regional Land Labour F e r t i l i z e r Se rv i ce s Dummy „ Constant ( X ^ (X 2 ) (x 3) (Xg) (D,) R 23.665 .2601* .5592* .1875* .1013** .1743* .9451 (.0815) (.0802) (.0351) (.0502) (.0571) ^Natural va lues f o r the reg iona l dummy v a r i a b l e s are 2.71828 and 1 f o r high and low response reg ions respect i v e l y . 2 Pa renthes i s i n d i c a t e standard e r r o r s of the c o e f f i c i e n t s * H Q : 3 = 0 r e j e c t e d at .01 L. 0.S. * * HQ:e=0 r e j e c t ed a t .05 L.O.S. (b) D i s c r im inant Ana l y s i s Method This c o n s t i t u t e s a powerful s t a t i s t i c a l approach, o r i g i n a l l y suggested by F i s c h e r , " f o r sepa ra t i ng two normal ly d i s t r i b u t e d popu la -t i on s on the bas i s of a set of c h a r a c t e r i s t i c s . In t h i s method a number o f v a r i a b l e s X., i = (1,2, ...n) are hypothes ized as a s s i s t i n g in d i s -c r i m i n a t i n g between the proposed groups. A c l a s s i f i c a t i o n f unc t i on capable of d i s c r i m i n a t i n g among groups i s then de r i v ed . The l a t t e r is of the form: R. A. F i s c h e r , "The Use of M u l t i p l e Measurements in Taxonomic Problems, " Annals o f Eugenics, 13: 1936, pp. 179-188. 94 D = a, + v. X. + v . X. + v X [5.13] I 1 1 2 2 n n where, the c o e f f i c i e n t s v. o f the l i n e a r f unc t i on D = D (x) are computed so that the r a t i o of the sums of squares between group means to sums of squares w i t h i n group means i s maximized. Hence, the d i s c r i m i n a n t f unc t i on can be cons idered as the l i n e a r f unc t i on that maximizes t h i s r a t i o . There i s no other l i n e a r combination o f the n v a r i a b l e s having more d i s c r i m i n a t -ing power than the f unc t i on ob ta i ned . In t h i s way v a r i a b l e s s e l e c ted as c o n t r i b u t i n g to d i f f e r e n c e s between the two reg iona l groups o f farms were: land area (X^), labour man-days ( X ^ , f e r t i l i z e r cos t (X^), machinery s e r v i ce s (X^), and animal s e r v i c e s (X,.). The mean values of the v a r i a b l e s used fo r d i s c r i m i n a t i n g between the two regions are g iven in Table 5-13-Table 5.13. A r i t h m e t i c Mean Levels of Input A p p l i c a t i o n on Paddy Farms in Low and High Response R e g i o n s -Incorporat ing Tota l Survey Data V a r i a b l e Low response 1 reg ion High response 1 reg ion Xj Land (acres) 1.35 4.32 X 2 Labour (man-days) 87.88 215.11 X^ F e r t i l i z e r (Rs.) 57.09 274.82 X^ Machinery Serv i ces (Rs.) 96.15 426.22 X[- Animal Se rv i ces (Rs.) 76.49 181.74 High response region inc ludes the d i s t r i c t s o f Polonnaruwa and Hambantota. Low response reg ion inc ludes the d i s t r i c t s of Kurunegala, Colombo and Kandy. 95 The data in Table 5-13. (p. 94) shows that the average l e v e l s of inputs f o r paddy product ion in the high response region are substan-t i a l l y h igher than those in the low response reg i on . It i s a l s o seen that the farms in the high response region used les s animal power and more t r a c t o r power, wh i l e those in the low response region showed the oppos i te s i t u a t i o n . C l a s s i f i c a t i o n func t i on s f o r the two reg iona l groups of farms in the high and low response reg iona l were computed and the 23 r e s u l t s are g iven in Table 5.14. Table 5-14. C l a s s i f i c a t i o n Funct ions f o r R ice Farms in Low and High Response Reg ions— Incorporat ing Tota l Survey Data Reg ion M u l t i - 1 i near c l a s s i f i c a t i o n f u n c t i o n ' F va lue f o r t e s t i n g group means^ 1. Low response region D ] = -1.6851 + .0034 X ] + .0199 X 5 49.66 2. High response reg ion D 2 = 1.5923 + .0081 Xj + .0091 x 5 Xj and X,. r e f e r to land and animal s e r v i ce s v a r i a b l e s . 2 H : no d i f f e r e n c e between regions i s r e j e c t ed at .05 ' L.O.S. The computing procedure i s i l l u s t r a t e d in User Manual, UBC BMD0 7M (March, 1975, r e v i s i o n ) , Computing Centre, The U n i v e r s i t y of B r i t i s h Columbia. See a l s o T.W. Anderson, An I n t roduc t i on to Mill t i var i a t e  Analys i s, New York, John Wi ley and Sons, 1958, p. 374. 96 The computed F value f o r t e s t i n g the two reg iona l a r i t h m e t i c (D, and D c) means was s i g n i f i c a n t at the .05 L.O.S. Th i s would i n d i c a t e that the two sub-groups of farms can be judged d i s t i n c t l y separate on the bas i s of the c l a s s i f i c a t i o n f u n c t i o n s . The c l a s s i f i c a t i o n f unc t i on s i ncorporate the two most important v a r i a b l e s f o r d i s c r i m i n a t i n g between the reg ions . If the var iances of the v a r i a b l e s inc luded in a c l a s s i f i c a -t i o n f u n c t i o n are almost equa l , the values of t h e i r corresponding co -e f f i c i e n t s prov ide measures of the r e l a t i v e importance o f each v a r i a b l e to the t o t a l " d i s c r i m i n a t o r y power" of the f u n c t i o n . The d i s c r i m i n a n t a n a l y s i s a l s o i nd i ca ted that 81.65 per cent o f the farm un i t s are s u i t a b l y c l a s s i f i e d under the hypothes i s o f high and low response reg ions . Th is f i n d i n g does not n e c e s s a r i l y show that homogeneity of data i s l a ck ing when no reg iona l separat ion is used. It does po in t s p e c i f i c a l l y to d i f f e r e n c e s in resource o r g a n i z a t i o n which may o f course lead to d i f f e r e n c e s in p r o -d u c t i v i t y due to input he te rogene i t y . Using mean values o f the v a r i a b l e s in each c l a s s i f i c a t i o n f unc t i on makes i t po s s i b l e to compute mean values o f the func t i on s f o r the two reg ions . The mean values computed f o r the c l a s s i f i c a t i o n f unc t i on s f o r high and low response regions were 3.281 and .151 r e s p e c t i v e l y . The average o f these two values i s 1.716. Hence, i f the c l a s s i f i c a t i o n func t i on s were to be used f o r a s s i gn i ng farms in to low and high response reg ion s , those farms w i th a c l a s s i f i c a t i o n f unc t i on va lue g reate r than 1.716 would be c l a s s i f i e d in the former, wh i l e those below 1.716 would be placed in the l a t t e r . It i s seen that the farms most l i a b l e to be m i s c l a s s i f i e d are those w i t h a value c l o s e to 1.716. 97 3. E s t imat ion of Regional P roduct ion Funct ions  f o r High and Low Response Farming Regions S ince i t has been shown that any input heterogene i ty on the survey farms is l i k e l y to be s u c c e s s f u l l y handled by d i v i d i n g them i n to two d i s -t i n c t reg iona l groups i t now becomes re l evan t to e s t imate a separate product ion f unc t i on f o r each reg i on . A c co rd i n g l y , product ion func t i on s were est imated f o r the reg iona l data us ing a l i n e a r and non - l i n ea r p r o -duct ion r e l a t i o n s h i p s . The r e s u l t s from d i f f e r e n t s p e c i f i c a t i o n s of the m u l t i - l i n e a r regres s ion model a re presented in Table 5 . 1 5 by equat ions R ^ Q " ^ ] ^ A N C ' R 20~ R 24 ^ o r 1 o w a n c * n ' 9 n r e s P o n s i v e reg ions , r e s p e c t i v e l y . I t i s seen that product ion r e l a t i o n s h i p s in the two reg ions cannot be s a t i s f a c t o r i l y represented by these l i n e a r f u n c t i o n s . C o e f f i c i e n t s of major v a r i a b l e s such as land and f e r t i l i z e r are shown to be s t a t i s t i c a 1 1 y n o n - s i g n i f i -cant , and, furthermore, they have large standard e r r o r s . The constant terms in a l l es t imated reg re s s i on equat ions are nega t i ve , and except in Rjg and R^ they are 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 . There fo re , the reg re s s i on r e l a t i o n s h i p s were re -e s t imated on the assumption that a Cobb-Douglas f unc t i on would prove more s a t i s f a c t o r y . The r e s u l t s of t h i s approach are reported in Table 5 . 1 6 . From Table 5 - 1 6 . i t i s seen that in con t ra s t to l i n e a r f u n c t i o n s , the Cobb-Douglas type f unc t i on s f i t reasonably we l l to farm data in both low and high response reg ions . The equat ions R^-R^g and R25~^28 s ' 1 ° w 2 high R values ranging from .818 to .933- The equat ions R^-R^g in low response region show: that machinery and animal - serv ices v a r i a b l e s become s t a t i s t i c a l l y n o n - s i g n i f i c a n t when inc luded s epa ra te l y . However, T a b l e 5 .15 - M u l t i - l i n e a r P r o d u c t i o n F u n c t i o n s f o r Paddy Farms i n Low and H igh Response R e g i o n s — I n c o r p o r a t i n g T o t a l Su rvey Data Low Response Region H igh Response Reg i on R e g r e s s i o n Number R 1 0 R l , R12 R 1 3 R , 4 R 2 0 R 21 R 2 2 R 2 3 R 2 4 .943 .940 .931 .930 .921 .925 .922 .924 .920 .882 Independent V a r i a b l e ' Xj Land (Ac re s ) 48.199 (96.07) 14/.891 (82.80) 143.050 175 .902 * * ( 100 .756 ) ( 87 .448 ) 2 36 . 859 * * (98.884) 308.616 (160.765) 232.485 (147.126) 344.52 (154.047) 267.089 f 142.72 9) 121.302 (166.003) X 2 Labour (Ma n -day s ) 6.653* (1.248) 7 .246 * (1.239) 6 . 177 * 6 . 4 5 9 * (1 .358) (1.285) 6 . 8 1 1 * (1.341) 8 . 847 * (1.977) 9 . 667 * (1.852) 9.106* (1.943) 10.727* (1.803) 11.076* (1.144) X j Fer t i 1 i z e r (Rs . ) 3-715* (1.055) 2.968 (1.645) 3.649 3 .349 * (1 .555) (1.059) 3.643* (1.109) 2.072 (1.571) 2.086 (1.578) 2.054 (1.564) 2.065 (1.577) -.491 (1.744) X^ M a c h i n e r y s e r v i c e s (Rs. ) - . 2 7 6 (.672) .279 (.621) - - 3-476* (1.057) 2 . 626 * (.758) - - -Xj. An ima l s e r v i c e s (Rs. ) .983 (.710) 1 .285 (.812) • - - 4 . 016 * (1.230) 3 -265* (1.042) - - -X^ A g r o - c h e m i c a l s (Rs . ) 4 . 119 * (1.693) 4 . 5 2 4 * (1.722) 4 . 756 * 4 . 868 * (1.844) (1.826) -- 8 . 1 4 4 * * (3.743) - 9 . 2 6 3 * (3.007) 6 . 4971 * (1.052) 10.782* (2.567) -X^ Seed m a t e r i a l (Rs. ) 5.262 (4.741) - 1.866 (2.800) - 6.941 (6.041) - 9.300 * (2.799) - -Xg D r a f t s e r v i c e s (Rs . ) - - .104 .300 (.726) (.660) .438 (.694) - - - 2 . 553 * (.754) 3 . 089 * (.890) C o n s t a n t - 1 6 3 . 3 8 2 * (53.358) - 1 5 2 . 0 3 2 * (54.330) - 88 .319 -89.870 (53-290) (49.29) -93.744 (55.765) -65 .402 (270.189) -128 .099 (265.796) -38.656 (267.028). - 103 .005 (264.403) - 135 .000 (316.906) V a r i a b l e s a r e d e f i n e d in Chap te r IV. P a r e n t h e s e s i n d i c a t e s t a n d a r d e r r o r s . * S t a t i s t i c a l l y s i g n i f i c a n t a t .01 L.O.S. * * S t a t i s t i c a l l y s i g n i f i c a n t a t .05 L.O.S. T a b l e 5 .16. C o b b - D o u g l a s P r o d u c t i o n F u n c t i o n s f o r P a d d y Farms i n Low a n d H i g h R e s p o n s e R e g i o n s — I n c o r p o r a t i n g T o t a l S u r v e y D a t a . Low Response Reg ion H igh Response Region Regres s ion Number R 15 R l 6 R 1 7 R18 R19 R 25 R26 R 2 7 R 2 8 R 2 .933 921 925 .820 . .818 .841 830 .846 .836 2 Independent V a r i a b l e Xj Land (Acres ) .202 (.122) ( 459* 093) ( 132 126) .264* (.109) .276* (.089) ( .326** . 162) ( 383* 096) .174 (.086) . 103* (.049) X 2 Labour (Man-days) .411* (.094) ( 460* 099) .450* (.094) .492* (.093) .502* (.094) ( .429* .115) ,( 416* 108) .445* (.095) .500* (.108) Xj F e r t i 1 i z e r (Rs.) .191* (.053) ( 178* 056) ( 172* 052) .145* (.051) .166* (.050) .283* (.064) .287* (.068) .258* (.059) .156* (.060) Machinery s e r v i c e s (Rs.) -.027 (.016) ( 028 017) - -( .027 .024) ( 031 022) - -X,. Animal s e r v i c e s (Rs.) .019 (.018) ( 012 017) - -( .029** .013) ( 087 062) -X^ A g r o - c h e m i c a l s (Rs.) .016 (.019) .062 (.046) -( .092** .040) ( 089 050) .114 ( . 0 7 0 -Seed m a t e r i a l (Rs.) .299 (.130) ( .222 .115) - -( .054 .126) - -Xg D r a f t s e r v i c e s (Rs.) -( .076 .092) .156** (.074) . 174-(.063) .299* (.093) • 313* (.107) Constant 70 .328* * 52 (2.03*0 (2 091* .017) * 16 (1 102** .306) 23.196** (1 .537) 23.289* (0.815) 51 (1 . 008* .069) 62 (1 364* .519) 18.065* (0.521) 15.059* (0.597) Sum o f E l a s t i c i t i es 1.111 1 .057 1 .052 1.119 1.118 .998 1 .113 1.290 1.072 ' C o r r e l a t i o n M a t r i c e s are p re sen ted in Append ix , Tab les 7 and 8. These r e f e r to logar i thmic va1ues o f v a r i a b l e s and may be expected to be s i m i l a r to those f o r untransformed d a t a . 2 V a r i a b l e s are d e f i n e d in Chapter IV. Parentheses i n d i c a t e s tandard e r r o r s ( those f o r cons tant term r e f e r to l o g - l i n e a r e q u a t i o n ) . * S t a t i s t i c a l l y s i g n i f i c a n t a t .01 L.O.S. * * S t a t i s t i c a 1 l y s i g n i f i c a n t a t .05 L.O.S. 100 when these two v a r i a b l e s are inc luded in the f unc t i on as a composite v a r i a b l e , namely, the d r a f t s e r v i ce s v a r i a b l e , the l a t t e r shows s t a t i s t i c a l l y s i g n i f i c a n t c o e f f i c i e n t . Th is i s seen in R^g and R^-The h ighest R f o r low and high response areas are g iven by equat ions Rj£. and R^^, r e s p e c t i v e l y . Un fo r tunate l y a number o f c o e f f i c i e n t s in these func t i on s are n o n - s i g n i f i c a n t . Equations and R 2 g rep re sen t -ing each region have s t a t i s t i c a l l y s i g n i f i c a n t c o e f f i c i e n t s and a l s o 2 show high R va lue s . These f unc t i on s are judged s t a t i s t i c a l l y the most s a t i s f a c t o r y . They a re : f o r the low response reg ion , .2761 .5023 .1660 .1744 Y L = 23.289 X ] X 2 X Xg [5.14] and f o r the high response reg ion , .1030 .5002 .1561 .3131 Y R = 15.059 Xj X 2 X 3 Xg [5.15] where the v a r i a b l e s X., X„, X,, and X Q represent l and , l abour , f e r t i l i z e r I z i o and d r a f t s e r v i c e inputs r e s p e c t i v e l y . Tests on the c o e f f i c i e n t est imates of the low response reg ion equat ion show that the corresponding popu la t ion parameters cou ld a l l take values as est imated by equat ion R^  f o r the t o t a l farm sample. Hence, n u l l hypotheses were not r e j ec ted at .01 L.O.S. When s i m i l a r t e s t s were performed f o r the high response regiion equa t i on , n u l l hypotheses were not r e j e c t ed a t .01 L.O.S. in a l l cases except f o r the land c o e f f i c i e n t . It i s po s s i b l e to t e s t c o e f f i c i e n t s in the R^  equat ion to see whether in r e l a t i o n to the standard e r r o r s , the corresponding popu la -t i o n parameters could take values est imated f o r the reg iona l f u n c t i o n s . 101 To p lace s t r e s s on such te s t s would put the onus of showing d i f f e r e n c e s the wrong way around. Even i f i t were done the e a r l i e r observat ions f o r n u l l hypotheses a t the .01 L.O.S. would on ly change w i t h regard to the a lpha constant term f o r the low response region equat ion and the land and d r a f t s e r v i ce s regres s ion c o e f f i c i e n t s in the high response reg ion equat i on . Then in the case of the f i r s t , the n u l l hypothes is that the popu la t i on a lpha constant could equal the e s t imate g iven by the low response region equat ion was r e j e c t e d . In the case o f the land and d r a f t s e r v i ce s regress ion c o e f f i c i e n t es t imates in the high response reg ion equat i on , the former was judged to be a va lue that the corresponding popu la t ion parameter could take in the t o t a l sample equat i on . The oppos i te was t rue f o r the d r a f t s e r v i ce s c o e f f i c i e n t . In conc lu s i on one cannot but note that these f i nd i n g s along w i t h 2 the f a c t that reg iona l funct io r i R values were lower than that shown by equat ion Rg, do not show that the reg iona l f unc t i on s are much improvement over the R^  f u n c t i o n . In f a c t the high response region f unc t i on leads to c e r t a i n d i f f i c u l t i e s in a p p l i c a t i o n as w i l l be shown l a t e r . Neverthe-l e s s , the in format ion prov ided by the reg iona l f unc t i on s i s such that i t serves as a new bas i s f o r s tudy ing resource p r o d u c t i v i t i e s , thereby, pe r -m i t t i n g a usefu l comparison w i th prev ious r e s u l t s . k. Assessment of Resource P r o d u c t i v i t i e s a t the Regiona1 Level Resu l t s from the a n a l y s i s o f resource u t i l i z a t i o n at the reg iona l l e ve l are reported in t h i s s e c t i o n . The s p e c i f i c aspects that w i l l be d e a l t wi th a re : (a) marginal va lue p r o d u c t i v i t i e s of i nput s ; 102 (b) e f f e c t s of changing input l e v e l s on t o t a l paddy output, (c) i n t e n s i t i e s of resource use in low and high response reg ions , (a) MVP's of Inputs in Low and High Response Regions Determinat ion o f MVP est imates f o r inputs was based on product ion f unc t i on equat ions [5.14] and [5.15] (p. 100). The der i ved marginal value p r o d u c t i v i t i e s f o r the corresponding geometric mean l e v e l s of i n -puts a re reported in Table 5.17., columns (3) and (5) . Table 5.17. Marginal Value P r o d u c t i v i t i e s and Corresponding Geometric Mean Levels o f Inputs per Farm in Low and High Response Regions. Low Response Region High Response Reg ion Geometric Mean MVP Geometric Mean MVP V a r i a b l e Level of input (Rs.) . Level of Input (Rs.) (1) (2) (3) (4) (5) x l Land (Acres) 1.115 233.58 3.55 136.72 X 2 Labour (Man-days) 62.40 7.59 195.00 12.09 X 3 F e r t i l i z e r (Rs.) 40.80 3.83 • 201.00 3.65 h Draf t s e r v i ce s (Rs.) 274.82 0.59 460.00 3.20 Study of MVP values f o r reg iona l p roduct ion inputs i n d i c a t e s a con s ide rab le degree of maladjustment of resource use. Th is i s n o t i c eab l e p a r t i c u l a r l y in the case of f e r t i l i z e r and d r a f t s e r v i c e s . F e r t i l i z e r shows high MVP's amounting to Rs.3.83 and Rs.3.65 in the low and high response regions at geometric mean l e v e l s of a p p l i c a t i o n . Th is i n d i c a t e s an u n d e r - u t i 1 i z a t i o n of f e r t i l i z e r on the t y p i c a l farm in both reg ions . 103 On the other hand the d r a f t s e r v i c e s input i nd i ca ted over-use in the low response region and s u b s t a n t i a l under use in the high response r eg i on . The MVP o f d r a f t s e r v i c e s in the high response region suggests that i t i s almost as important as that f o r f e r t i l i z e r in the same region in i n d i c a t i n g u n d e i — u t i l i z a t i o n . This obse rva t ion is probably exp la ined by the shortage o f bu f f a l oe s and t r a c t o r s dur ing peak per iods of farming. In c o n t r a s t , the extremely low MVP o f d r a f t s e r v i c e s - i n the low response reg ion is not e a s i l y e x p l a i n e d , a lthough i t may be exp la i ned by an ade-quate supply of bu f f a l oe s f o r farm operat ions in the reg i on . At geometric mean l e ve l the MVP o f labour in the low response region amounts to Rs.7.59 which i s almost equal to the p r e v a i l i n g wage r a t e . In the high response r eg i on , labour shows an MVP o f Rs.12.09 which i s very much g rea te r than the farm wage r a t e . Th is aga in suggests a product ion s i t u a t i o n s u f f e r i n g from r e s t r i c t e d labour. It i s ev ident from Table 5.17 (p. 102) that the marginal va lue p r o d u c t i v i t y o f land in the high response area i s s u b s t a n t i a l l y lower than that f o r the low r e s -ponse a rea . The important f a c t to note i s that too much land i s used on a t y p i c a l farm in high response regions in r e l a t i o n to other l e v e l s of resources. The p r i c e o f land s e r v i c e s was approx imate ly 228 rupees. There-f o r e , the MVP of land in the high response region i s w e l l below t h i s f i g u r e , wh i l e the MVP of land in the low response reg ion i s almost equal to the p r i c e of land s e r v i c e s . The preceeding comments are important in the context of va ry ing a s i n g l e resource and ho ld ing other resources f i x e d as s ta ted geometric mean l e v e l s . It w i l l be noted that both areas show i nc rea s i ng returns 104 to sca le f o r t h e i r p roduct ion f u n c t i o n s , which means that optimum o u t -puts cannot be recommended. Rather, resources f o r any g iven output should be combined in l i n e w i t h expansion path p ropor t i on s as exp la ined e a r l i e r in the chapter . Of course ho ld ing one or more inputs f i x e d in the equat ions w i l l a l l o w opt imal outputs and resource combinations to be determined owing to d im in i s h i n g marginal p r o d u c t i v i t y c o n d i t i o n s . Turning to the expansion path mode of a n a l y s i s , which was introduced in the prev ious s e c t i o n , i t i s u se fu l to apply i t to the reg iona l f unc t i on s R^g and ^28" From t n e i n fo rmat ion g iven in Table 5.18 i t is obvious that the geometric mean l e v e l s o f inputs in the high and low response regions are out o f l i n e w i t h recommended expansion path resource combinat ions. In the case of the low response reg ion the opt imal p r opo r t i ona l mix of inputs is one acre o f land combined w i t h approx imately 68 man-days o f labour, Rs.137 of f e r t i l i z e r and Rs. l44 of d r a f t s e r v i c e s . These p ropor t i ons show that input commitment a t geometric mean l e v e l s was i n -s u f f i c i e n t l y i n t en s i ve in f e r t i l i z e r and labour, w i t h the former being most u n d e r - u t i l i z e d . Draft s e r v i c e s , however, in r e l a t i o n to the geo-met r i c mean acreage of 1.12 acres were shown to be used o v e r - i n t e n s i v e l y . When the optimum resource mix i s c a l c u l a t e d f o r the geometric mean output per farm (Rs.1130) in the low response r eg i on , the f i n d i n g s are that the t y p i c a l farmer employed c l o se to the recommended land a rea , too many d r a f t s e r v i c e s , and i n s u f f i c i e n t labour and f e r t i l i z e r . Lack o f i n t en s i ve use o f f e r t i l i z e r is shown by the a c tua l use of approx imate ly Rs.4l worth on 1.12 acres compared w i t h the opt imal use of Rs. l47 worth on 1.07 ac re s . 105 Table 5.18. Expansion Path Resource Combinations f o r Low and High Response Regions a t Geometric Mean Levels o f Ou tpu t— Incorporat ing Tota l Survey Data EXPANSION PATH INPUT COMBINATIONS Low Response Region High Response Region Labour X 2 = 67.85 X ] (Land Acres) (Man-days) Labour X 2 = 181.12 X ] (Land Acres) (Man-days) F e r t i l i z e r X, = 136.78 X. (Rs.) 3 ' F e r t i l i z e r X_ = 344.78 X. (Rs.) 3 ' D ra f t Serv ices X Q = 143-70 X. (Rs.) 8 1 Draf t Se rv i ces X g = 691.33 X ] (Rs.) EXPANSION PATH INPUT COMBINATIONS1 For Geometric Mean Output Rs.1129.87 For Geometric Mean Output Rs.5166.85 X ] = 1.07 (Acres) Xj = 1.30 (Acres) X 2 = 72.93 (man-days) X £ = 234.87 (man-days) X 3 = 147.01 (Rs.) X 3 = 447.12 (Rs.) Xg = 154.45 (Rs.) Xg = 896.52 (Rs.) Based on R]cj and R28 p roduct ion f u n c t i o n est imates f o r Low and High Response Regions, r e s p e c t i v e l y (see Table 5.16, p. 99). In understanding these r e s u l t s i t should be r e c a l l e d that the reg iona l p roduct ion func t i on s i n d i c a t e i n c rea s i ng returns to s c a l e fo r the v a r i a b l e s i nc luded . Therefore , when a l l inputs a re assumed v a r i a b l e opt imal output l e v e l s cannot be c a l c u l a t e d . Of course when one or more v a r i a b l e s are f i x e d the func t i on s w i l l permit optimum outputs to be determined. Never-t h e l e s s , expansion path output combinations are very usefu l in gu id ing 106 resource adjustments and a l l o c a t i o n , e s p e c i a l l y in r e l a t i o n to g iven output l e v e l s . Un fo r tunate l y the der i ved expansion path equat ions f o r input combinations in the h igh response reg ion do not permit conf idence to be p laced in t h e i r a p p l i c a t i o n . The reason f o r t h i s i s that a sma l le r number of sample un i t s {kk observat ions ) has c on t r i bu ted to e s t ima t i on of the expansion path , which q u i c k l y de f ines l e v e l s of resources , other than land, to l i e ou t s i de the re l evan t ranges of sample data and fo r that matter paddy product ion data in gene ra l . Consequently, the c a l c u l a t i o n s f o r opt imal input l e v e l s at the geometric mean l e ve l of output per farm (Rs.5167), are very high—much h igher than the a c tua l geometr ic means--f o r a l l inputs o ther than land, which at 1.3 acres i s s u r p r i s i n g l y sma l l e r than the a c tua l geometric mean l e ve l of 3.55 a c re s . I f one were to ex -t r a c t any usefu l i n fo rmat ion from t h i s a n a l y s i s f o r the high response reg i on , i t would be that land i s used too e x t e n s i v e l y , and f e r t i l i z e r , labour and d r a f t s e r v i ce s should be used more i n t e n s i v e l y . But even here the p r opo s i t i o n of more i n ten s i ve use of d r a f t s e r v i c e s must be t rea ted c a u t i o u s l y , s ince i t is the f i r s t occas ion in the study that t h i s input has been shown to be u n d e r - u t i l i z e d . Coupl ing t h i s w i th the comments above regard ing the s u i t a b i l i t y of the der i ved r e l a t i o n s h i p , t h i s p a r t i c u l a r f i n d i n g c o n s t i t u t e s no more than an hypothes i s . I n t e r e s t i n g l y enough, however, the high response reg ion has been observed by some researchers to s u f f e r from d r a f t power shortages. Therefore , there may be some grounds f o r t h i n k i n g that the hypothes is may be t r u e . 107 (b) E f f e c t s of Changing Input Leve l s  on Tota l Paddy Output A c r i t e r i o n that can be usefu l in a d j u s t i n g resource inputs w i t h i n and between regions i s the product ion e l a s t i c i t y o f a s p e c i f i c i nput . Th i s e l a s t i c i t y i s de f ined as the percentage change in product ion a r i s i n g from a one per cent change in the input l e v e l , c e t e r i s pa r i bu s . In a Cobb-Douglas product ion f unc t i on these e l a s t i c i t y measures are g iven by the r e spec t i ve input c o e f f i c i e n t s . The product ion e l a s t i c i t i e s of d i f f e r e n t inputs in the low and high respons ive regions are presented in Table 5.19., and are prov ided by the Cobb-Douglas p roduct ion func t i on s R^g and R^g re spec t i v e l y . Table 5.19. Product ion E l a s t i c i t i e s o f D i f f e r e n t Inputs in Low and High Response Regions—Based on Cobb-Douglas Funct ions R^g and R^g Product ion E l a s t i c i t i e s Input V a r i a b l e Low Response Region High Response Region Xj Land (Acres) .2761 .1030 X 2 Labour (Man-days) .5023 .5002 X^ F e r t i l i z e r (Rs.) .1660 .1561 Xg Draf t Se rv i ces (Rs.) .1744 .3131 Sum of E l a s t i c i t i e s 1 1.1188 .1 .0724 N u l l hypothes is that sum of E l a s t i c i t i e s (e) , equals 1 was a c -cepted at .01 per cent L.O.S. Table 5.19 i nd i c a te s that a one per cent increase in labour ( c e t e r i S par i bus) could r e s u l t in a .5 per cent increase in output in both 108 reg ions . The f e r t i l i z e r input in low and high response regions i nd i ca te s output e l a s t i c i t i e s of .160 and .156 per cent r e s p e c t i v e l y . As regards d r a f t s e r v i c e s , i t s product ion e l a s t i c i t i e s i n d i c a t e that fo r the same p r opo r t i ona l increase of t h i s input ( c e t e r i s par ibus) in the low and high response reg ions , the r e s u l t i n g p ropo r t i ona l increase in output f o r the high response region would be more than twice that f o r the low response reg i on . (c) I n t e n s i t i e s of Resource Use in Low  and High Response Regions For the purpose o f e va l ua t i n g i n t e n s i t y of resource a p p l i c a t i o n in paddy product ion and the r e s u l t i n g outputs in the two reg ions , per acre data were compiled in va lue terms. The r e s u l t s are presented in Table 5.20 below. Table 5.20. Geometr ic Mean Levels of per Acre Inputs and Outputs on Paddy Farms in Low and High Response R e g i o n s -Incorporat ing Tota l Survey Data. Output/Inputs Low Response Region High Response Region Tota l output (Rs.) 1,013 .34 1,455 .45 Labour (Man--days) 55 .96 54 .92 T rac to r Se rv i ces (Rs.) 71 .22 113 .02 B u f f a l o Serv ices (Rs.) 156 .63 43 .07 Draf t S e r v i c e s ' (Rs.) 246 .47 1 29 .57 F e r t i 1 i z e r s (Rs.) 36 .59 56 .61 Agro-Chemicals (Rs.) 16 .50 12 . 00 . . . . Includes both b u f f a l o and t r a c t o r s e r v i c e s . 109 The geometric mean va lue of t o t a l paddy output per acre in the high response region amounts to Rs.l455- The corresponding f i g u r e f o r the low response reg ion is Rs. 1013-34. When con s i de r i ng expendi tures fo r b u f f a l o and t r a c t o r s e r v i c e s , i t i s c l e a r that p roduct ion in the high response region i s more machine-or iented than in the low response reg i on . R ice farms in the low response region used a t o t a l of 56 man days per ac re . The corresponding va lue f o r the high response area i s 55 man-days. A more i n ten s i ve use o f f e r t i l i z e r i s made by farmers in the high response reg i on . Thus the higher p r o d u c t i v i t y per acre in t h i s region can be l a r g e l y a t t r i b u t e d to the i n t en s i v e use o f n o n - t r a d i t i o n a l i nput s . 5. Resource P r o d u c t i v i t y Ana l y s i s at the D i s t r i c t Level As a l ready i n d i c a t e d , i n i t i a l s e l e c t i o n o f the farm sample in the present study was on a d i s t r i c t ba s i s . There fo re , measures of resource p r o d u c t i v i t y in each of the d i s t r i c t s would be u se fu l in gu id ing resource a l l o c a t i o n between d i s t r i c t s . Inadequacy o f obse rva t ions in each d i s t r i c t imposed a se r i ous l i m i t a t i o n on t h i s type of a n a l y s i s . Work was l i m i t e d to e s t ima t i n g o v e r a l l p r o d u c t i v i t i e s o f inputs and computing a p r o d u c t i v i t y index value fo r each o f the d i s t r i c t s . In doing t h i s , land was not i n -cluded in the input cos t assessments f o r the reason that i t remained r e l a t i v e l y f i x e d per farm w i t h i n each d i s t r i c t . A l s o f e r t i l i t y o f land was thought to show l i t t l e v a r i a b i l i t y w i t h i n each d i s t r i c t . Therefore, the p r o d u c t i v i t y index values a f f o r d d i s t r i c t comparisons w i th regard to output and the more s t r i c t l y v a r i a b l e i nput s . 110 The p r o d u c t i v i t y i nd i ce s f o r inc luded inputs ( l abour , d r a f t s e r v i c e , f e r t i l i z e r , a g ro - chemica l s ) , are reported in column ( 6 ) of Table 5 . 2 1 . Column ( 5 ) i nd i c a te s the output/ input r a t i o s ob ta ined by d i v i d i n g t o t a l va lues o f output by t o t a l va lues o f inputs (geometric mean l e v e l s ) . Using t h i s type of ou tput/ input r a t i o as a p r o d u c t i v i t y measure impl ies a rather s i m p l i f i e d l i n e a r product ion f unc t i on w i t h pe r f e c t sub-s t i t u t i o n among f a c t o r s o f p roduc t i on . The p r o d u c t i v i t y index is der i ved from the output/ input r a t i o s and represents de v i a t i o n s from the mean r a t i o f o r a l 1 d i s t r i c t s . Table 5 . 2 1 . Ove ra l l Input P r o d u c t i v i t y Measures and Corresponding Leve l s o f Input A p p l i c a t i o n on Paddy Farms Accord ing to D i s t r i c t s Geometric Geometric D i s t r i c t No. of fa rms Mean Output (Rs.) Mean Inputs ' (Rs.) Output 1 nput Ra t i o Product i v i ty 1ndex 2 ( 0 ( 2 ) ( 3 ) ( 4 ) ( 5 ) ( 6 ) 1. Polonnaruwa 30 6 , 7 2 4 . 6 2 2 , 6 7 9 . 2 0 2 . 5 1 0 . 7 9 9 2 . Hambantota 14 5 , 2 4 1 . 1 5 2 , 4 7 2 . 1 8 2 . 1 2 0 . 4 0 8 3 . Kurunegala 2 2 2 , 0 4 9 . 1 8 1 , 6 8 6 . 4 3 1 .2151 - . 4 9 7 4 . Colombo 2 0 1 , 6 4 4 . 3 0 1 , 2 6 4 . 8 8 1 .300 - . 4 1 2 5 . Kandy 21 1 ,023.22 722.61 1 . 4 1 6 - . 2 9 6 Excludes va lue of l and. Includes l abour , d r a f t s e r v i c e s , f e r t i l i z e r s and ag ro -chemica l s . A r i t h m e t i c dev i a t i on s from mean d i s t r i c t ou tput/ input r a t i o s . 111 Consequently, any p o s i t i v e index value i s i n d i c a t i v e o f an o ve r -a l l input p r o d u c t i v i t y l e v e l h igher than the average f o r a l l d i s t r i c t s . S i m i l a r l y a negat ive index value shows p r o d u c t i v i t y below the average. The r e s u l t s of t h i s a n a l y s i s reveal i n t e r e s t i n g i n f o rmat i on . The h ighest i npu t s ' p r o d u c t i v i t y is shown by Polonnaruwa d i s t r i c t wh i l e ;the lowest i s shown by Kurunegala d i s t r i c t . Kurunegala, Colombo, and Kandy d i s t r i c t s show negat ive index va lues , i n d i c a t i n g that they can be regarded as sepa ra te l y from Polonnaruwa and Hambantota. This supports e a r l i e r f i n d i n g s concerning reg ions , based on dummy v a r i a b l e and d i s c r im i nan t ana ly se s . From the output/ input r a t i o s i t i s easy to see which d i s t r i c t s show the g rea te s t output increments per rupee o f o v e r a l l Input expend i -t u r e . For example, Polonnaruwa has almost twice Colombo's output from a given input expend i tu re . CHAPTER VI SUMMARY, IMPLICATIONS AND RECOMMENDATIONS OF THE STUDY This chapter deals w i th the summary and conc lud ing remarks f o r the study. It i s d i v i ded i n t o three s e c t i o n s . Sec t i on A presents a summary account of the a n a l y s i s , s e c t i on B s t a te s the i m p l i c a t i o n s o f r e s u l t s f o r p o l i c y d e c i s i o n s , and sec t i on C o u t l i n e s p o t e n t i a l areas f o r f u tu re research a c t i v i t y . A . SUMMARY OF F IND INGS The present study deals w i th r i c e product ion in major r i c e grow-ing areas in S r i Lanka dur ing the 1972-73 Maha (wet) season. Almost a l l the farmers in the survey areas adopted f e r t i l i z e r - r e s p o n s i v e h i gh -y i e l d i n g v a r i e t i e s of r i c e , yet were very dependent on t r a d i t i o n a l f a c t o r s of p roduc t i on . Levels of f e r t i l i z e r a p p l i c a t i o n on paddy farms were gene r a l l y lower than recommended l e v e l s . No e l abo ra te machines o ther than t r a c t o r s were used, and product ion was r e l a t i v e l y more dependent on an i n ten s i ve use of labour. Although product ion techniques of farmers d id not always r e f l e c t complete modern i za t ion , they were c l e a r l y i n d i c a t i v e of the changing nature of a g r i c u l t u r e . Thus, t h i s study can be cons idered as an economic i n v e s t i g a t i o n o f a major crop under a s i t u a t i o n of chang-ing subs i s tence a g r i c u l t u r e . The a n a l y s i s was based on data from r i c e farms in the d i s t r i c t s o f Hambantota, Polonnaruwa, Kandy, Kurunegala and Colombo. The primary 112 113 o b j e c t i v e of the study was to determine resource p r o d u c t i v i t i e s on the farms and to i d e n t i f y problems o f resource a l l o c a t i o n . The a n a l y t i c a l method was based on product ion f u n c t i o n s . The important f i nd i n g s of the study can be summarized as f o l l o w s : 1. P roduct ion func t i on s were est imated us ing two techn iques , namely, the f a c t o r shares and l ea s t squares methods. The f a c t o r shares method d i d not y i e l d complete ly s a t i s f a c t o r y r e s u l t s due to i nhe ren t l y r i g i d assumptions in the method. Never the les s , i t prov ided a useful bas i s f o r comparison of r e s u l t s achieved from reg re s s i on . There fo re , the l e a s t squares e s t imat i on technique became the pr imary research t o o l . The Cobb-Douglas product ion f unc t i on was found to be the most s u i t a b l e f unc t i on form fo r the da ta . The est imated p roduct ion f unc t i on f o r t o t a l survey data i s : y = 17.2187^.2570-^.5987 ^.2030 ^.1272 [ 6 ] ] where Y is the value of t o t a l output of paddy in Rupees, i s land in a c re s , X^ i s t o t a l labour input in man-days, X^ is the value o f f e r t i l i z e r input in rupees, and Xg i s the value of d r a f t s e r v i ce s in rupees. 2. Est imates of marginal va lue p r o d u c t i v i t i e s (MVP's) o f r e -sources were computed from t h i s f u n c t i o n . A l l the MVP's were computed at geometric mean input l e v e l s per farm. The MVP of an acre of land was est imated at Rs.220.43; a man-day, Rs.8.89; a rupee of f u r t i l i z e r i npu t , Rs.3-89, and a rupee of d r a f t s e r v i c e s , Rs.0.99. 114 A comparison of the i m p l i c i t p r i c e s (MVP's) and market cost s (p r i ce s ) of input resources suggested that t y p i c a l farmers were concent ra t i ng on us ing land and d r a f t power resources a t e f f i c i e n t l e v e l s . However, f e r t i l i z e r and labour inputs were shown to be not i n t e n s i v e l y enough used. In p a r t i c u l a r , f e r t i l i z e r input showed marked u n d e r - u t i I i z a -t i o n . The a n a l y s i s a l s o i nd i ca ted that r e a l l o c a t i o n of e x i s t i n g farm resources could lead to increases in output. S h i f t i n g resources from d r a f t power to f e r t i l i z e r is a case in p o i n t . Expansion path resource combinat ional r e l a t i o n s h i p s f o r the t o t a l farm sample product ion func t i on were e s t a b l i s h e d as f o l l o w s : X 2 = 86.81 X}; X^ = 179.47 X]} X8 = 112.28 X]f where Xy X^, Xy and Xg r e f e r to acres of land, man-days o f labour, rupees of f e r t i l i z e r and rupees o f d r a f t s e r v i c e s , r e spec t i ve The a r i t h m e t i c mean l e v e l s of paddy product ion inputs per acre f o r a l l survey farms were as f o l l o w s : labour 56.25 man-days; f e r t i l i z e r , Rs.55 .51; d r a f t s e r v i c e s , R s . 1 3 6 . 3 3 ; agro-chemica l s , Rs.18.77. The geometric mean l e ve l of output per acre was 56.8l bushels whereas the a r i t h m e t i c mean output per acre was 62.29 bushe l s . The es t imated a r i t h m e t i c mean per acre a p p l i c a t i o n of f e r t i l i z e r from t o t a l va lue data , was 2.1 cwts. (mixed compos i t i on ) . The p roduct ion f unc t i on f o r a l l survey data gave a t o t a l p r o -duct ion e l a s t i c i t y measure of 1.186 f o r inc luded v a r i a b l e s . This i nd i ca te s the ex i s t ence of approx imately constant r e -turns to sca le in paddy farming in S r i Lanka. 7- From the product ion f unc t i on f o r a l l survey data , determina-t i o n of responses of output to v a r i a t i o n in l e v e l s of input a p p l i c a t i o n revea l s that one per cent changes (ceter i s  par i bus) in land, labour, f e r t i l i z e r and d r a f t s e r v i ce s i n -puts would r e s u l t in .257, .599, .203 and .127 per cent changes in paddy output , r e p e c t i v e l y . 8. A l l o c a t i o n of t o t a l va lue product to each of the f a c t o r inputs showed that labour input accounted f o r h a l f the t o t a l output, 50.6 per cent ; wh i l e l and, f e r t i l i z e r and d r a f t s e r v i c e s accounted f o r 21.6, 17.0 and 10.8 per cent respec-t i v e l y . 9. Average apport ioned p r o d u c t i v i t i e s of inputs were a l s o de-termined. These values were Rs.l85.5O per acre of land; Rs.7.49 per man-day; Rs.3.28 per rupee of f e r t i l i z e r i npu t ; and Rs.O.83 per rupee o f d r a f t s e r v i ce s input . 10. Attempts were a l s o made to i d e n t i f y p r o d u c t i v i t y reg ions w i t h i n the area p rov i d i ng t o t a l farm sample data . Two regions i n d i c a t i n g d i f f e r e n t resource p r o d u c t i v i t i e s were i d e n t i f i e d . They were termed low response and high response reg ions . The former inc luded Polonnaruwa and Hambantota d i s t r i c t s , wh i l e the l a t t e r inc luded Kurunegala, Colombo and Kandy d i s t r i c t s . The product ion f u n c t i o n es t imates f o r the two regions were: 116 ( i ) Low response reg ion , Y, = 23.289 X - 2 7 6 1 X - 5 ° 2 3 X , J 6 6 0 X • 1 7 / 1 / 1 ' [6.2] L 1 2 3 o ( i i ) High response reg ion , Y H = 15.059 X 1 - 1 0 3 0 X 2 - 5 0 0 2 X 3 - 1 5 6 1 X g " 3 1 3 1 [6.3] where, the v a r i a b l e s have the same d e f i n i t i o n s as given f o r p roduct ion f unc t i on [6 .1 ] . 11. MVP est imates fo r Inputs a t geometric mean l e v e l s in the two regions showed notab le d i f f e r e n c e s in the case of d r a f t power. The re levant value f o r the low response region was Rs.0.59 per rupee of i npu t , wh i l e in the high response region the comparable value was Rs.3-20. T y p i c a l l y t h i s suggests an over use in the low response reg ion and an under use in the high response reg ion . The MVP's of labour and f e r t i l -i z e r inputs in the high response region were s u b s t a n t i a l l y higher than those in the low response r e g i on . The MVP o f land was g reater in the low response region than in the high response reg ion . 12. Expansion path equat ions were der i ved from each reg iona l p ro -duct ion f u n c t i o n . While they prov ide i n t e r e s t i n g comparisons w i t h the p r e v i ou s l y est imated expansion path equat ion f o r the t o t a l farm sample f u n c t i o n , the comments in the t e x t regard ing the use o f a l l these r e l a t i o n s h i p s should be duly noted. 13. Comparison of i n t e n s i t i e s o f resource use per acre in the two 117 regions i nd i ca ted that h igher l e ve l s of t r a c t o r s e r v i c e s and f e r t i l i z e r s have been used by farmers in the high response reg i on . On the other hand, higher l e v e l s of labour , bu f fa l oe s and chemicals have been used on farms in the low respons ive reg ion . 14. Increas ing returns to s ca l e were i n d i c a t e d by the inc luded v a r i a b l e s f o r both low and high response reg ions : 1.1188 and 1.0724 r e s p e c t i v e l y . S ince these values do not s t a t i s -t i c a l l y d i f f e r from 1, near constant returns to s ca le may be sa id to app ly . 15. Compari sons;,of o v e r a l l resource use (except land) in d i f f e r e n t d i s t r i c t s was undertaken us ing a p r o d u c t i v i t y index approach. The r e s u l t s showed that the h ighest p r o d u c t i v i t y of inputs was in Polonnaruwa, w h i l s t the lowest was in Kurunegala. The p r o d u c t i v i t y ind ices of farm inputs in Colombo and Kandy d i s t r i c t s were not s u b s t a n t i a l l y d i f f e r e n t from that o f Kurunegala. In Hambantota d i s t r i c t , the resource p r o d u c t i v i t y index was c l o se to that of Polonnaruwa. B. IMPLICATIONS AND POLICY RECOMMENDATIONS OF THE STUDY 1. Need f o r P r o d u c t i v i t y Increases in the Paddy Sector The need to increase p r o d u c t i v i t y o f resource input investment in S r i Lanka 's paddy sec to r requ i re s immediate a t t e n t i o n in any development p o l i c y f o r i nc reas ing the domestic output o f r i c e . Support f o r t h i s a rgu -ment i s a l s o given by the f o l l o w i n g d i s c u s s i o n . 118 Despite many attempts to increase p roduc t i on , t o t a l domestic output o f r i c e s t i l l accounts on ly f o r about 60 per cent o f t o t a l con -sumption. Never the les s , there has been a s i g n i f i c a n t increase in domestic paddy output over the past three decades. Tota l home product ion rose from 31-3 m i l l i o n bushels in 1956-57 to 48.1 m i l l i o n bushels in 1961-62, represent ing an increase of 70 per cent over a pe r i od of s i x years . Two major reasons fo r these output increases can be g i ven . F i r s t l y , expansion of land under c u l t i v a t i o n has occurred and secondly, per acre y i e l d increases have been a c h i e v e d . ' Before 1965, land expansion played a major r o l e in the na t i ona l increase in r i c e ou tput . For i n s t ance , from 1957-65 the increase in net area harvested was 29 per cen t , wh i l e y i e l d s increased by on l y 14 per cent in the same p e r i o d . Now that expan-s ion of land under c u l t i v a t i o n has slowed up y i e l d increases become a c r u c i a l f a c t o r in i nc rea s ing domestic r i c e p roduc t i on . The magnitude of the de s i r ed output inc rease in the paddy sec to r 2 has been est imated by K a r u n a t i l a k a . On the assumption of a net annual popu la t ion increase o f 2.5 per cent per annum, w i t h no changes in e x i s t -ing per c a p i t a consumption, he est imated that r i c e requirements to meet t h i s ra te o f inc rease can be produced on the e x i s t i n g acreage on l y i f 1.5 e x t r a bushels per acre are forthcoming every yea r . However, dur ing P.C. B a n s i l , " Impact o f Food P o l i c y on A g r i c u l t u r a l Development in C e y l o n , " Indian Jour . A g r i c . Econ.: 21, 1966, No. 1, p. 240. 2 H.N.S. K a r u n a t i l a k a , Economic Development in Ceylon, New York, Praeger P u b l i s h e r s , Inc., 1971, p. 312. 119 the pe r iod 1955-65 the r e a l i z e d increase in na t i ona l per acre y i e l d was on ly about .9 bushels per annum. The argument f o r r a i s i n g output through land p r o d u c t i v i t y i n -creases r a the r than t r a d i t i o n a l acreage inc reases , i s again supported by a con s i de ra t i on o f the large investments made on c e r t a i n major i r r i g a t i o n p r o j e c t s . It seems l o g i c a l to say that the pay -o f f from such expensive land expansion p o l i c i e s w i l l be low so long as the les s i n t en s i ve t r a d i -t i o n a l p roduct ion techniques are used. Therefore, i t f o l l ows that the fundamental o b j e c t i v e of p o l i c y in the fu tu re should be to inc rease r i c e product ion more through i n t e n s i f i e d use of resources and less through land expans i on . 2. Output Expansion Through Appropr ia te Product P r i c i n g The marginal value p r o d u c t i v i t y of an input i s dependent on the output p r i c e , and thus, by s u i t a b l e man ipu la t ion of output p r i c e , the l e ve l of input a p p l i c a t i o n by farmers can be changed. S ince the paddy p r i c e in S r i Lanka i s s o l e l y determined by c e n t r a l a u t h o r i t y - - t h e paddy marketing board--the p r i c e can e a s i l y be used as a powerful too l f o r m o t i -v a t i n g farmers to increase t h e i r output through employment of more r e -sources . Furthermore, a number of major economic s tud ie s have shown e m p i r i -ca l evidence fo r i n d i c a t i n g that economic i n cen t i ve i s a s t rong mot i va t ing 3 f a c t o r re spons ib le fo r spreading new innovat ions in a g r i c u l t u r e . It has Zvi G r i l i c h e s , "Hyb r i d Corn: An E x p l o r a t i o n in the Economics of Techno log ica l Change," in Readings in the Economics o f A g r i c u l t u r e , I l l i n o i s , R ichard D. I rw in, Inc. , 1969, pp. 221-243. 120 a l s o been proved that farmers, even in a subs i s tence economy, behave as "economic-men" and are q u i t e respons ive to economic i n cen t i ve s such as 4 5 p r i c e s . ' The re fo re , i t would appear that there e x i s t s a s t rong case f o r re-examining the e f f i c i e n c y of the guaranteed p r i c e mechanism f o r i n c rea s i ng na t i ona l paddy output . 3. Increased Suppl ies of F e r t i l i z e r F e r t i l i z e r input i s one of the " e s s e n t i a l s " in a package of non-t r a d i t i o n a l inputs that play a c r u c i a l r o l e in r a i s i n g paddy output . This i s ev ident from the a n a l y s i s undertaken and i t is i n d i c a t ed by the marginal and average p r o d u c t i v i t y est imates and e l a s t i c i t y c o e f f i c i e n t s . The f e r -t i l i z e r MVP est imate at the geometric mean input l e v e l f o r t o t a l survey da ta , showed that f o r an a d d i t i o n a l rupee of f e r t i l i z e r the output was increased by Rs.3-98. This i nd i c a te s a gross u n d e r - u t i 1 i z a t i o n of f e r -t i l i z e r , f a r below the economic optimum. The a n a l y s i s a l s o shows t ha t , even i f the e x i s t i n g 50 per cent subs idy on f e r t i l i z e r i s removed, i t i s s t i l l economica l l y advantageous f o r many farmers to apply more f e r t i l i z e r . This f i n d i n g in the l i g h t of heavy p u b l i c expendi ture on s ub s i d -i z i n g the i nput , l o g i c a l l y r a i s e s the problem whether such a subsidy i s , in f a c t , a n e c e s s i t y . If the subsidy i s done away w i t h , i t would lead to a higher input p r i c e . Such a p r i c e increase would have two important Welsch E. Delane, "Responses to Economic Incent ives by Aba k a l i k i Rice Farmers in Eastern N i g e r i a , " Jou r . Farm Econ., 47, 1965, pp. 900-914. ^ Jere R. Behrman, " P r i c e E l a s t i c i t y of the Marketed Surplus of a Subs i stence Crop, " Jou r . Farm Econ. , 48, 1966, pp. 875-892. 121 consequences f o r f e r t i l i z e r use. F i r s t l y , i t would reduce the optimum l e v e l of a p p l i c a t i o n which would no doubt r e s t r i c t ou tput . Secondly, i t would a l s o reduce farmers ' " a c c e s s i b i l i t y " to the i npu t . The l a t t e r has p a r t i c u l a r s i g n i f i c a n c e in a peasant farming system where ready cash i s g ene r a l l y s ca r ce . There fo re , even i f removal o f the f e r t i l i z e r sub-s idy s t i l l leaves the input p r o f i t a b l e to use a t the e x i s t i n g l e ve l of a p p l i c a t i o n , i t cou ld s t i l l a f f e c t the l e v e l o f f e r t i l i z e r a p p l i c a t i o n pu re l y through the " i n a c c e s s i b i l i t y " to cash f a c t o r . There fo re , whatever p r i c e changes are made f o r f e r t i l i z e r , i t i s necessary that the p o l i c y makers be aware of the twin problems. k. Expansion of Farm C r e d i t F a c i l i t i e s The r e s u l t s of the study po i n t to d i s e q u i 1 i b r i a in resource a p p l i c a t i o n . This i s ev ident w i t h respect to both t o t a l data and d i s -aggregated data. Ach iev ing the c o r r e c t a l l o c a t i o n of a p p l i c a t i o n o f resources depends on c a p i t a l a v a i l a b i l i t y . Therefore , the observed resource imbalances seem to be suggest ive o f a c a p i t a l r a t i o n i n g s i t u a -t i on in paddy farming. Although the need fo r c a p i t a l to increase output has been recognized and remedial measures taken over a f a i r l y long t ime, the r e s u l t s of t h i s study would i n d i c a t e that the problem i s s t i l l s e r i ou s . The modern izat ion o f paddy farming requ i res increased adopt ion of a number of non - t rad i t i ona1 i n t e n s i v e l y used i nput s , which impl ies increased cap-i t a l i z a t i o n of farms. Although a f u l l d i s cu s s i on of farm c r e d i t expansion w i l l not be entered i n t o , a major aspect of the subject that seems to have been l a r g e l y 122 over looked and requ i res c a r e f u l a t t e n t i o n concerns the r i s k s ide of paddy fa rming. The argument can be summarized b r i e f l y as f o l l o w s : development nece s s i t a te s new techniques and input s ; these inputs a re viewed by farmers as r i s k y from the s tandpo int of r e s u l t s ; farmers a re r i s k aver se . Therefore, i f inputs are to be obta ined through c r e d i t , r i s k percept ion is an important impediment to expanding farmer use of c r e d i t schemes. Hence, expansion of such schemes need to be complemented by other programmes such as crop insurance and adequate i r r i g a t i o n f a c i 1 i t i e s . 5. Investments in Farmer Educat ion Though not e x p l i c i t l y a r i s i n g from the cu r ren t study, evidence suggests that farmer educat ion is one of the high pay -o f f inputs in farm p roduc t i on . ^ S ince the product ion s i t u a t i o n in the study was c h a r a c t e r i s t i c of a changing a g r i c u l t u r e , the ex i s t ence of resource-use d i s - e q u i 1 i b r i a m may be a t t r i b u t e d , a t l ea s t in p a r t , to lack of i n f o r -mat ion. This would p a r t i c u l a r l y apply to the use of modern inputs such as new r i c e v a r i e t i e s and new types of f e r t i l i z e r , which need con s i de r -ab le managerial a b i l i t y f o r d e r i v i n g opt imal r e s u l t s . The ev idence f o r a r e l a t i o n s h i p between increased a g r i c u l t u r a l product ion and farmer educat ion has been d i r e c t l y shown by a number of Nimal Sanderatna, "Us ing Insurance to Reduce Risk in Peasant A g r i c u l t u r e : Gu ide l i ne s from S r i Lanka Expe r i ence , " Teachi ng Forum, ADC P u b l i c a t i o n No. hi, June, 1974. 7 An i n t e r e s t i n g d i s c u s s i o n of t h i s sub jec t is g iven by T.W. S c h u l t z , The Economic Value of Educat ion, New York, Columbia U n i v e r s i t y Press , 19'bX 123 s t u d i e s . The i r es t imates u s u a l l y i n d i c a t e educat i ona l b e n e f i t s that are high by most s tandards. Such returns to educat ion a r i s e b a s i c a l l y from the i nc rea s ing q u a l i t y of labour in farm p roduc t i on . In the l i g h t of t h i s ev idence i t i s reasonable to suggest that an important means of i nc reas ing p r o d u c t i v i t y in S r i Lanka 's paddy fa rming, i s to make i n -g creased investments in educat ing r u r a l farmers in the modern techniques of r i c e p roduc t i on . To conclude t h i s s e c t i on i t can be s ta ted that i t is not s u f f i -c i e n t j u s t to add more t r a d i t i o n a l input f a c t o r s to increase domestic paddy output . What i s needed a l s o is be t te r seed v a r i e t i e s along w i th adequate supp l i e s o f f e r t i l i z e r and a d d i t i o n a l i r r i g a t i o n , complemented by a p r i c e and cost s e t t i n g and an educat iona l environment would make these worth w h i l e . C. AREAS OF FURTHER RESEARCH In general the issues that have been cons idered in the above sec t i on s seem to serve as a broad framework fo r a f u t u r e research agenda, aimed at i nc reas ing p r o d u c t i v i t y in the r i c e s e c t o r . In a d d i t i o n , c e r -t a i n s p e c i f i c areas r e q u i r i n g research a t t e n t i o n are o u t l i n e d below. 1. Labour Use in Paddy C u l t i v a t i o n About one -ha l f of the r u r a l popu la t ion in S r i Lanka is d i r e c t l y dependent on paddy c u l t i v a t i o n . Under a present increase of popu la t ion F. Welsch, " Educat ion in P r o d u c t i o n , " Jou r . Pol . Econ. 78, 1970, pp. 35-59. ]2k of 2.1 per cent per annum, a mounting pressure on a r ab l e land in r u r a l areas is exerted which leads to r u r a l unemployment. Thus, s tud ie s on d i f f e r e n t aspects of labour use in r i c e farming are most important, not on ly in the context of paddy p roduc t i on , but a l s o on the general problem of unemployment in peasant a g r i c u l t u r e . An important area of research along the l i n e s suggested concerns the labour-use c y c l e dur ing the crop year . Information here would help assess the seasonal demands f o r f am i l y and h i r ed labour in paddy c u l t i -v a t i o n . This knowledge i s important in view of the w ide l y va ry ing labour requirements a t p a r t i c u l a r stages of the r i c e crop and the involvement of farm f a m i l i e s in o f f - f a r m employment. Stud ies on seasonal demand fo r labour use in product ion can a l s o y i e l d usefu l i n fo rmat ion r e l a t i n g to mechanizat ion of paddy c u l t i v a t i o n . Another usefu l area f o r study would concern the concepts of r u r a l g unemployment and d i s gu i sed unemployment. Furthermore, a not ion is o f t en held by economists concerned w i th subs i s tence a g r i c u l t u r e , that zero marginal p r o d u c t i v i t y of a g r i c u l t u r a l labour occurs in t h i s s e c t o r , e . g . , " . . . commonly ca tego r i zed f ea tu re of the dual economy [ in S r i Lanka] is the zero marginal p r o d u c t i v i t y o f labour . . . t h i s perhaps i s the bas ic economic c r i t e r i o n on which d i s t i n c t i o n s can be made between t r a -d i t i o n a l and modern s e c t o r s . " 1 ^ If t rue t h i s statement means that some a g r i c u l t u r a l workers could be t r an s f e r r ed to other tasks w i thout d im inut i on B. M. Mahajan, " Popu l a t i on Problem Recons i d e r e d , " Econ. A f f a i r s , 10, January, 1965, pp. 73-82. ^ K a r u n a t i l a k a , o p J _ c i t . , p. 23. 125 of a g r i c u l t u r a l output and new ent rant s to a g r i c u l t u r e would make no p roduc t i ve c o n t r i b u t i o n . But e m p i r i c a l r e s u l t s from the present study provided s u b s t a n t i a l ev idence to show that the marginal p r o d u c t i v i t y of r u r a l labour i s p o s i t i v e ( i n f a c t qu i t e h i gh ) . In a d d i t i o n the r e s u l t s d i d not i n d i c a t e the presence of d i s gu i s ed unemployment in the paddy s e c t o r . Further evidence fo r the absence of d i s gu i sed unemployment in c e r t a i n areas i s the seasonal immigrat ion of farm labour , e . g . , to Hambantota and Polonnaruwa d i s t r i c t s from other a reas . Many of the d i s -agreements concerning problems of d i s gu i sed unemployment stem from confus ion between seasonal unemployment and d i s gu i sed unemployment. A count of i d l e work-days per year t e l l s us nothing about the s u p e r f l u i t y of workers on a year-round b a s i s . 2. Imp l i ca t i on s of R ice P o l i c y on the Domestic Paddy Sector The fundamental o b j e c t i v e s of the S r i Lanka government 's r i c e p o l i c y may be summarized as f o l l o w s : (1) to keep farm paddy p r i c e h igh , (2) to mainta in low consumer p r i c e s , and (3) to reduce imports . Although no hard e m p i r i c a l ev idence i s a v a i l a b l e , examinat ion of some of the p o l i c y measures suggests that they may sometimes hinder the achievement of goa l s . Such problems.need to be s tud ied to determine a l t e r n a t i v e remedial measures. In broader terms, s tud ie s should eva lua te s p e c i f i c p o l i c y o b j e c t i v e s w i t h respect to past achievements, i n t e r - r e l a t i o n s h i p s , and i n t e r a c t i o n s between d i f f e r e n t goals and t h e i r r e l a t i o n s h i p to d e c i s i o n v a r i a b l e s . Re su l t i n g in format ion would be very usefu l f o r recommending and ach iev ing s u i t a b l e p o l i c y measures. 126 A broad group of economic problems a r i s e s from S r i Lanka 's t r a d i t i o n a l "cheap food" p o l i c y . The producer and consumer subs id ie s on r i c e dur ing 1964 amounted to Rs.446.9 mi 11 i on , approx imately 25 per cent of t o t a l annual government r e v e n u e . ' 1 As ide from d i r e c t e f f e c t s a r t i f i c a l l y lowering the p r i c e of r i c e to consumers, the s u b s i d i e s ' impact on l o c a l p roduct ion would a l s o have been s u b s t a n t i a l . S tud ies are needed to e l u c i d a t e such e f f e c t s . Another important area f o r research i s the e f f i c i e n c y of the government guaranteed p r i c e system (GPS), i n t r o -duced f o r i nc rea s ing domestic r i c e p roduc t i on . With regard to the con -1 2 t r i b u t i o n of GPS to paddy output , Ka runa t i l a ka comments that " . . . i t has not provided a very s i g n i f i c a n t spur to a c ce l e r a ted p r o d u c t i o n . " 1 3 B a n s i l , in a d e t a i l e d study on the same aspect concludes that " . . . perhaps we would not be f a r too wrong to conclude that GPS has m i se rab ly f a i l e d to ach ieve i t s o b j e c t i v e of i nc reas ing paddy p roduc t i on . If a t a l l i t might have served as a d i s i n c e n t i v e . . . . The GPS would then appear to have not on l y harmed the i n t e r e s t of paddy, but p r a c t i c a l l y 14 the whole o f the peasant a g r i c u l t u r a l s e c t o r . " Th is evidence seems to i nd i c a t e the p o t e n t i a l nature of the problem. The impact of food g ra i n imports, i n c l ud i ng food a i d , on the p r i c e s and domestic supply of paddy a l s o needs con s ide rab le a t t e n t i o n . 1 1 B a n s i l , op. c i t . , p. 240. 1 2 Karuna t i l a k a , op. c i t . , p. 313 13 Bans i 1 , op. c i t . ] k I b i d . , p. 245. 127 S c h u l t z ' ^ in d i s cu s s i n g Indian a g r i c u l t u r e , po inted out that the e f f e c t s of PL 480 imports upon the a g r i c u l t u r e of a r e c i p i e n t country were l i k e l y to be adverse because of a f a l l in the p r i ce s of domestic a g r i c u l t u r a l p roduct s , thus reducing the i n c e n t i v e to ma inta in or expand the a g r i c u l -t u r a l s e c t o r . The dependence on ce rea l imports in S r i Lanka i s sub-s t a n t i a l l y large and i t is necessary to t e s t the above hypothes is using sys temat ic research methods. 3. Studies on Economic Responses from the Farmer A number of recent economic s tud ies have shown evidence of economic i n f l uences r e c e i v i n g measurable responses from subs i s tence farmers. Gene ra l l y , however, there seems to be a tendency among p o l i c y makers to th ink of the subs i s tence farmer as being lazy and unresponsive to p r i c e r e l a t i o n s h i p s . Farmers are o f t en thought to be i r r a t i o n a l in t h e i r r e j e c t i o n of innovat ions ; f r equen t l y they are blamed f o r being a hinderance to modern i za t i on . Therefore , research e f f o r t s are necessary to e s t a b l i s h the v a l i d -i t y o f these a t t i t u d e s towards peasant farmers in S r i Lanka. Information from such s tud ie s would be h e l p f u l in p e r f e c t i n g the i n cen t i v e framework and improving the e f f i c i e n c y of the p r i c e mechanism f o r r a i s i n g farm ou t -put . Under usual c i rcumstances, product p r i c e can act as an i n d i c a t o r of p r o f i t in farming. But in a subs i s tence economy the measure of " p r o f i t -a b i l i t y " may not depend so much on product p r i c e . There fo re , research 5 T. W. S c h u l t z , "Va lue of U.S. Farm Surpluses to Under-developed C o u n t r i e s , " Jou r . Farm Econ., 42, I960, pp. 1019-30. 128 should be conducted to determine the mer i t s of economic i n cen t i ve s and the causes of m o t i v a t i o n . Economic aspects of innovat ion among paddy farmers have so f a r been a neg lected area of s tudy. R isk and unce r t a i n t y i n f l uences on farmers seem to have an important bear ing on the acceptance of new innovat ions . I d e n t i f i c a t i o n of the r e l a t i o n s h i p of r i s k and unce r t a i n t y to i nnovat i ve and adopt ion behaviour of farmers i s important in the d i f -f u s i on o f new techno l og i e s . Other f a c t o r s such as i n s t i t u t i o n a l and s o c i o - c u l t u r a I fo rces a l s o seem to have s i g n i f i c a n t i n f l uences on modern izat ion o f the paddy farming s e c t o r . The i n s t i t u t i o n a 1 - c u 1 t u r a 1 ma t r i x , w i t h i n which farmers opera te , has a con s ide rab le e f f e c t on t h e i r economic dec i s i on s and hence i t needs understanding. The land tenure system is a good example of an economic set of arrangements in an i n s t i t u t i o n a l and s o c i a l framework. Much can be l ea rn t about the e f f i c i e n c y of such p r a c t i c e by we 11-designed s t u d i e s . And so the recommended l i s t of research s tud ie s grows. Enough, however, has been sa id to draw the d i s cu s s i on to a c l o s e . The study f i nd i n g s appear pe r t i n en t to S r i Lanka 's problems in r i c e p roduc t i on . On the other hand they on ly serve to r a i s e many more que s t i on s . SELECTED BIBLIOGRAPHY Ag ra r i an Research and T r a i n i n g I n s t i t u t e , S r i Lanka. 1975. The Ag ra r i an S i t u a t i on Rel a.t.i ng to Paddy Cu 11 i vat ion i n F i ve Sel ected  D i s t r i c t s of S r i Lanka. A l l e n , R. G. D. 1938. Mathematical Ana l y s i s f o r Economists. London: McMi1lan and Co., L td . Anderson, J . R. and John L. D i l l o n . 1971. "On E s t imat ing A l l o c a t i v e E f f i c i e n c y in C ro s s - Sec t i ona l Ana l y s i s of P r o d u c t i o n . " Aus t ra1 ian J_. Agr. Econ. 15 (December) : 146-50. A r a j i , A. A. and R. M. F i n l e y . 1971. "Manager ia l Socio-Economic Char-a c t e r i s t i c and S i ze of Operat ion in Beef C a t t l e Feeding—An A p p l i -c a t i o n of D i s c r im inant A n a l y s i s . " Am. J_. Agr. Econ. 53 (November): 647-50. Arrow, K. J . , H. B. Chenery, B. S. Minhas, and R. M. Solow. 1961. "Gap i ta1-Labour S u b s t i t u t i o n and Economic E f f i c i e n c y . " Rev. Econ. S t a t . 43, No.3 (August):225-49-Bauer, Peter T. and B a s i l Yamey. 1971. The Economics of Under-developed Count r i e s . Chicago: U n i v e r s i t y of Chicago Pres s . B a n s i l , P . 'C . 1966. "Impact of Food P o l i c y on A g r i c u l t u r a l Development of Cey l on . " Indian J . Agr. Econ. 21, No.1:238-45. Bhat tachar jee , J y o t i P. 1955. "Resource Use and Product ion in World A g r i c u l t u r e . " J . Farm,Econ. 37:57 - 72. Cent ra l Bank of Ceylon. 1969- Survey on Cost of P roduct ion of Paddy. Dept. of Economic Research, Colombo. Chennareddy, Venkareddy. 1967- " P r oduc t i on E f f i c i e n c y in South Indian A g r i c u l t u r e . " J[. Farm Econ. 49:816-20. Chiang, A. C. 1967- Fundamental Methods of Mathematical Economics. London: McGraw-Hi l l Book Co. Cobb, Char les W. and Paul H. Douglas. 1928. "A Theory of P r o d u c t i o n . " Am. Econ. Rev. 18:139-56. Coutsoumaris, George. 1954. "Resource P r o d u c t i v i t y and Developmental P o l i c y f o r Greek A g r i c u l t u r e — A n I l l u s t r a t i v e Study. " J_. Farm Econ. 36:296-303. Dan ie l son, R. 1974. "Three Stud ies in Canadian A g r i c u l t u r e . " Van-couver: U n i v e r s i t y of B r i t i s h Columbia, unpubl ished M.A. t h e s i s . 129 130 Dhrymes, Phoebus J . 1962. "On Dev i s ing Unbiased Est imator f o r the Parameters of the Cobb-Douglas Product ion F u n c t i o n . " Econometrica 30 (Ap r i l ) : 297 -303 -Diewart, W. E. 1973. A n . A p p l i c a t i o n of Duali ty Theory. U n i v e r s i t y of B r i t i s h Columbia, Department of Economics, D i scus s ion Paper No. 89. D i l l o n , J . L. and J . R. Anderson. 1971. " A l l o c a t i v e E f f i c i e n c y , T r a -d i t i o n a l A g r i c u l t u r e and R i s k . " Am. J_. Agr. Econ. 53 (February) : 26-32. Duloy, J . H. 1959. "Resource A l l o c a t i o n and a F i t t e d Product ion Func-t i o n . " AjJSt£aJNan_ J_. Agr. Econ. 3 (December) :75~85. Ferguson, C. E. 1972. Microeconomi.c Theory. Homewood, I l l i n o i s : R ichard D. I rw in , Inc. Fox, Kar l A. and Gale D. Johnson (eds . ) . 1969. A.E.A. Readings in the  Economics of A g r i c u l t u r e . Homewood, 111 ino i s : R ichard D. I rwin, I nc. Friedman, M i l t o n . 1953- ' 'The Methodology of P o s i t i v e Economics." In M. Friedman . (ed.) Essays on Economics. Chicago: U n i v e r s i t y of Chicago Pres s , p. 23. G r i l i c h e s , Z v i . 1957- " S p e c i f i c a t i o n Bias in E s t imat i on of P roduct ion F u n c t i o n . " J . Farm Econ. 39:1"14. . 1963. " E s t imates of the Aggregate A g r i c u l t u r e Product ion Funct ion from C ro s s - Sec t i ona l Da ta . " J_. Farm Econ. 45:419-28. Heady, Ear l 0. 1946. " P r oduc t i on Funct ions From a Random Sample of Farms. 1 1 J_. Farm Econ. 28:989-1004. . . 1948. "E lementary Models in Farm Product ion Economics Re-s ea r ch . " J_. Farm Econ. 30:201-26. .. 1952. Economics of A g r i c u l t u r a l P roduct ion and Resource Use. New York: P r e n t i c e - H a l l , Inc. . 1967. A Pr imer on Food A g r i c u l t u r e and P u b l i c P o l i c y . New York: Random House. and J . L. D i l l o n . 1961. A g r i c u l t u r a l P roduct ion Funct ions . Ames, Iowa:.Iowa S ta te U n i v e r s i t y P res s . Hoch, I r v i n g . 1958. "S imultaneous Equat ion Bias in the Context of the Cobb-Douglas P roduct ion F u n c t i o n . " Econometrica 26. (October ) : 566-79. 131 Hoch, I r v i n g . 1962. " E s t i m a t i o n of P roduct ion Funct ion Parameters Combining T ime- se r ie s Data and Cross Sec t i on Da ta . " Econometrica 30 (January):34-53-Hopper, W. D. 1965- " A l l o c a t i o n E f f i c i e n c y in a T r a d i t i o n a l Indian A g r i c u l t u r e . " J . Farm Econ. 47 (August ) :6 l1-24. Izumi, K. and A. S. Ranatunga. .1973- Cost of P roduct ion of Paddy, Ya la 1972. Ag ra r i an Research and T r a i n i n g I n s t i t u t e , S r i Lanka, Research P u b l i c a t i o n No.l ( J u l y ) . Janvry , De A l a i n . 1972. "The Genera 1ized Power P roduct ion F u n c t i o n . " Am. J_. Agr., Econ. 54:234-37. K a r u n a t i l a k a , H. N. S. 1971- Economic Development in Cey lon. New York: Praeger P u b l i s h e r s , Inc. K i s l e v , Yoav. 1965- " E s t i m a t i n g a Product ion Funct ion from 1959 U.S. Census of A g r i c u l t u r e Data . " Chicago: U n i v e r s i t y of Chicago, unpubl ished Ph.D. t h e s i s . K l e i n , L. R. 1953. A Text Book of Econometr ics. Evanston: Row Peter son. K o n j i n , H. S. 1959- " E s t i m a t i o n of an Average Product ion Funct ion from Surveys . " .Economic Record 35:118-25. L i p t o n , M i chae l . -1968. "The Theory of Opt imi s ing Peasant . " Jour . dev. Stud ies (Ap r i l ) : 327 -51• Mahajan, B. M. 19&5- " P o p u l a t i o n . Problem Recons idered. " Econ. A f f a i rs 10 (January) :73"82. Marschack, J . and W. H. Andrews, J r . 1944. "Random Simultaneous Equa-t i on s and the Theory of P r o d u c t i o n . " . Econometrica 12 ( Ju l y -Oc tobe r ) : 143-205. Masse l , B. F. 1967- "Farm Management in Peasant A g r i c u l t u r e : An Emp i r i ca l S tudy. " Food Res. Inst. Studies 7:205-15-M e l l e r , John W. 1970. "The Subs i s tance. Farmer.'i n T r a d i t i o n a l Economics." In Wharton R. C 1 i f t o n , J r . (ed.) Subs i s tance A g r i c u l t u r e and  Economic Development. Chicago: A l d i n e Pub l i s h i n g Co. Mundlak, Y a i r . 1961. " E m p i r i c a l P roduct ion Funct ion Free o f Management B i a s . " JL Farm Econ. 43:44-56. • . 1963. " E s t i m a t i o n of P roduct ion and Behaviour Funct ions from a Combination of C ro s s - Sec t ion and Time Se r ie s Da ta . " In Car l F. 132 C h r i s t et a l . , Measurements in Economics. S tan fo rd , C a l i f o r n i a : S tanford U n i v e r s i t y Press . Mundlak, Y a i r and I. Hoch.. 1965- "Consequences of A l t e r n a t i v e S p e c i -f i c a t i o n s in Cobb-Douglas P roduct ion Func t i on s . " Econometrica 33 (October) :8l4-28.. Mynt, H. 1965- "Economic Theory and Underdeveloped C o u n t r i e s . " Jou r . P o l . Econ. 73 (October):477-91• Myrda l , G. 1967. Economic Theory, and Underdeveloped Regions. London: Duckworth. Ner love , M. 1965- E s t imat i on and I d e n t i f i c a t i o n o f Cobb-Douglas P ro -duct ion Funct ion. Chicago: Rand Mcna l ly and Co. Rao, P. and P. L. M i l l e r . 1971. App l i ed Econometr ics. Belmont, C a l i -f o r n i a : Wadsworth P u b l i s h i n g Co., Inc. R ichards , P. and E. S t o u t j e s d i j k . 1970. A g r i c u l t u r e in Ceylon u n t i l  1975. Development Centre S tud i e s , OECD, P a r i s . Rulon, P h i l i p J . 1951. " D i s t i n c t i o n Between D i s c r im inant and Regres-s ion Ana l y s i s and a Geometric I n t e r p r e t a t i o n of the D i s c r im inant F u n c t i o n . " Harvard Educat iona l Review 21, No.2 ( Sp r i ng ) . Sahota, Gian S. I968. " E f f i c i e n c y of Resource A l l o c a t i o n in Indian A g r i c u l t u r e . " Am. J_. Agr. Econ. 50 (August) : 584-605-S a l k i n , J . S. "On the S p e c i f i c a t i o n and E s t imat i on of A l t e r n a t i v e Func-t i o n a l Forms in the Theory of P roduc t i on : The Case of R ice Produc-t i o n in South V ietnam." Northwestern U n i v e r s i t y , unpubl ished Ph.D. t h e s i s . Seers, D. 1963- "The L i m i t a t i o n s of the Spec ia l Case. " Bui 1. Oxford  Inst. Econ. and S t a t i s t i c s 25 (May):77~98. Sethuraman, V. 1972. "Demand f o r Draf t Animals in Indian A g r i c u l t u r e . " Chicago: U n i v e r s i t y o f Chicago, unpubl ished Ph.D. t h e s i s . S c h u l t z , T. W. 1963. The Economic Va lue.o f Educat ion. New York: Columbia U n i v e r s i t y Press . . 1964. Transforming T r a d i t i o n a l A g r i c u l t u r e . New Haven: Ya le U n i v e r s i t y Press . S u i t s , Daniel B. 1957- "Use of Dummy Va r i ab l e s in Regress ion Equa t i on s . " Amer. S t a t . Assoc. 52 (December):548-51. 133 T i n t n e r , G. 1944. "A Note on the De r i v a t i on of Product ion Funct ions From Farm Records. " Econometrica 12:26-34. Tomek, W i l l i a m G. 1963- "Us ing Zero-One V a r i a b l e w i t h Time Se r i e s Data in Regress ion Equa t i on s . " vJ_. Farm Econ. 45 (November) : 8] 4-22. Wa l te r s , A. A. 1963. " P r oduc t i on and Cost Funct ions : An Economic Survey. " Econometrica 31 ( January -Apr i1 ) :1 -66 . W e l l i s z , S t an i s l aw, Bernard Munk, T. Peter Mayhew, and Car l Hemmer. 1970. "Resource A l l o c a t i o n in T r a d i t i o n a l A g r i c u l t u r e : A Study of Andhra P radesh . " J . Po_k Econ. 78, Vo l .4:655-84. Welseh, D. E. 1965. "Response to Economic Incent ive by A b a k a l i k i R ice Farmers in Eastern N i g e r i a . " J^_. Farm Econ. 47:900-14. Wise, John and P. A. Yotopoulos . 1969- "The Emp i r i c a l Content of Economic Rat i ona 1 i t y : . A Test f o r a Less Developed Economy." J_. Pol,. Econ. 77 (November-December) : 976-1004. Yotopoulos, P. A. 1968. "On the E f f i c i e n c y of Resource U t i l i z a t i o n in Subs i s tence A g r i c u l t u r e . " Food Res. Inst . Studies in A g r i . Econ. Trade and Development 8, No.2:125 - 35. and Lawrence J . Lau. 1971. "A Test f o r R e l a t i v e E f f i c i e n c y and A p p l i c a t i o n to Indian A g r i c u l t u r e . " Amer. Econ. Rev. 61, No.l (March):94-109. Z e l l n e r , A., J . Kmenta, and J . Dreze. 1966. " S p e c i f i c a t i o n and E s t i -mation of Cobb-Douglas P roduct ion Funct ion Model s . " Econometrica 34 (October):784-95-APPENDIXES 1 - 8 134a 134 b APPENDIX I PROCEDURE FOR CALCULATING MVPs MVP i s de f ined as the a d d i t i o n to t o t a l revenue by a marginal un i t o f input . In a l i n e a r p roduct ion f u n c t i o n o f the form Y = a+b^Xj+ b 2 X 2 + * " ' b n X n w n e r e » ^ ' s t n e t o t a l va lue product and b . ( i = l , 2 , . . . n ) are the reg re s s i on c o e f f i c i e n t s , the MVP o f each resource input i s g iven by i t s r eg re s s i on c o e f f i c i e n t . However, in a l o g - l i n e a r f u n c t i o n b l b 2 b n such as Y = aXj X^ •••X n » MVPs are no longer g iven by the l o g a r i t h m i c f u n c t i o n reg re s s i on c o e f f i c i e n t s . The c o e f f i c i e n t s in t h i s case r ep re -sent the e l a s t i c i t i e s o f output w i t h respect to p a r t i c u l a r i npu t s . Hence the MVP o f an input Xj can be c a l c u l a t e d w i t h regard to mean input l e v e l s . Where Y r e f e r s to the est imated mean output and X.s r e f e r to mean source i npu t s . •w b -1 b b n i . e . , MVPV = ~ = b . a X . 1 X . . . . X n [ l ] Xj 9 X ] 1 1 2 n [2] Thus, the above va lue of MVP depends on the mean values o f X ' s used. But MVPs can a l s o be c a l c u l a t e d at geometr ic mean l e v e l s o f inputs farm inputs so as to represent the t y p i c a l s i t u a t i o n . ' Geometric mean l e ve l o f an input is computed by t ak ing the a n t i l o g a r i t h m of the a r i t h m e t i c average o f the logar i thms of the i n d i -v i dua l ob se r va t i on s . Fur ther d e t a i l s regard ing the geometr ic mean are g iven in F. E. Croxton and D. J . Cowden, App l i ed general S t a t i s t i c s (New York: P r e n t i c e Hal 1 ,'• I nc. , 1955), 2nd ed. 135 APPENDIX 2 COMPUTATION OF RETURNS TO SCALE The Returns to s ca l e in Product ion are i nd i ca ted by the va lue obta ined from summation o f output e l a s t i c i t i e s of a l l i nput s . Th is va lue is a l s o r e f e r r ed to as the f unc t i on c o e f f i c i e n t (e) and i t i n d i -cates the p ropo r t i ona l change in output r e s u l t i n g from a s imultaneous 1 per cent change in a l l i n p u t s . 1 Th i s can be seen as f o l l o w s : Given the product ion f unc t i on as, Y = f ( X r X 2 , . . . X n ) [1] the output e l a s t i c i t y e. of i - t h input i s , by d e f i n i t i o n , X. e. = f , -y- ( i = l , 2 , . . . n ) [2] where, f. = [3] i Taking the t o t a l d i f f e r e n t i a l of the product ion f unc t i on [1] we have, n n dX. dY = E f . - dX . = E X . f . -T71- [k] . , i i . . i i X. 1=1 1=1 i dY n X i d X i — = E • f j - f x 1 [ 5 ] i = l i dk Let a l l inputs be increased by a constant p ropor t i on then fo r a l l i nputs X., no 1 For d e t a i l s r e f e r C. E. Ferguson, Microeconomic Theory ( l l l i ' i s : R ichard D. I rw in, Inc., 1972), pp. 161-64. 136 dX. ,. i_ _ dk X. " k i dk Then, d i v i d i n g equat ion [5] by the constant we get, dY . dk _ " X i r f i l T v X " . . f i T [ 6 ] i = l n = E e. 1 = 1 ' But by d e f i n i t i o n the l e f t hand term in equat ion [6] equals e, the f unc t i on c o e f f i c i e n t , n t he re fo re e = E e. 1-1 ' This shows that the f unc t i on c o e f f i c i e n t (E) i s s imply the sum of out-put e l a s t i c i t i e s of i n d i v i d u a l i nput s . We say when e = 1 constant returns to s c a l e e x i s t ; e > 1 i nc rea s i ng returns to s ca l e e x i s t ; and e < 1 decreas ing returns to s c a l e e x i s t . APPENDIX 3 137 METHOD OF DISTRIBUTING TOTAL PRODUCT TO INDIVIDUAL FACTORS OF PRODUCTION If a f unc t i on i s homogeneous of degree r (= f unc t i on c o e f f i -c i en t ) then by E u l e r ' s theorem i t can be shown t h a t , 1 ixrxi + i r x 2 + • • • I f X„---Y ['] 1 2 n Therefore , 1 2 n Hence, t h i s proves t h a t - t h e amoun.t con t r i bu ted to the gross va lue of product ion by an i n d i v i d u a l f a c t o r of product ion is equal to i t s mar-g i n a l product m u l t i p l i e d by the l e ve l of a p p l i c a t i o n o f the input and d i v i ded by the degree of homogeneity. For more d e t a i l s see, C. E. Ferguson, Microeconomic Theory (Homewood, I l l i n o i s : R ichard D. I rw in, Inc., 1972), pp. 411-412; and A. C. Chiang, Fundamental Methods of Mathematical Economics (London: McGraw-Hi l l Book Co., 1967), p. 376. 138 APPENDIX 4 COMPARATIVE DATA ON SRI LANKA'S MAJOR CROPS 1967; ACREAGE, OUTPUT AND EXPORTS Product Acreage ( '000 Acres) Tota l Output Volume Value of Exports (Mil 1 ion Rs.) Value o f d Tota l Output ( M i l l ion Rs.) 1. Tea 599 486.7 a 1 ,061 1,074.4 2. Rubber 475 288.8a 337 326.3 3. , Coconut 1 ,100 2,600.0b 94 260.0 4. , R ice 1,332 41 .4 C - 579-6 Tota l 3,506 - 1,492 2,240.3 a M i l l ion 1bs. b Mi 11 ion nuts. c Mi 11 ion bushe l s . c Value of exports plus Colombo market va lue of volume not exported. Source: P. Richards and E. S tout je sd i j k . , A g r i c u l t u r e in  Ceylon u n t i l 1975, Development Centre S tud ie s , 0ECD, P a r i s , 1970. 139 APPENDIX 5 COMPARATIVE DATA ON SRI LANKA'S MAJOR CROPS, 1 9 6 7 ; EMPLOYMENT AND VALUE ADDED Product Value of To ta l Output (Mi 11 ion Rs.) Val ue added (Mi 11 ion Rs.) Est imated Employment (Thousands) Value added per worker (Rs.) 1. Tea 1 , 0 7 4 . 4 8 4 6 . 6 6 5 8 1 , 2 8 6 . 6 2 . Rubber 3 2 6 . 3 2 7 3 . 5 2 2 3 1,226.5 3 . Coconut 2 6 0 . 0 2 0 6 . 5 8 8 2 , 3 4 6 . 6 4 . R i ce 5 7 9 - 6 3 7 7 . 1 6 6 6 5 6 6 . 2 Tota l 2 , 2 4 0 . 3 1 , 7 0 3 - 7 1 , 6 3 5 1 , 0 4 2 . 0 Source: P. Richards and E. S t o u t j e s d i j k , A g r i c u l t u r e in  Ceylon u n t i 1 . 1 9 7 5 , Development Centre S tud ie s , 0 E C D , P a r i s , 1 9 7 0 . 140 APPENDIX 6 DISTRIBUTION OF SAMPLE FARMS ACCORDING TO DISTRICTS D i s t r i c t No. of Farmers 1. Polonnaruwa 30 2. Hambantota 14 3. Kurunegala 22 h. Colombo 20 5. Kandy 21 Tota l 107 j APPENDIX 7 SIMPLE CORRELATION COEFFICIENTS 3 FOR LOGARITHMICALLY TRANSFORMED VARIABLES INCLUDED IN PADDY REGRESSION ANALYSIS- -TOTAL FARM DATA--LOW RESPONSE REGION ( 6 3 FARMS) Farm V a r i a b l e ' 3 Y X l X 2 X 3 X 4 X 5 X 6 X 7 X 8 Y Output (Rs.) 1 . 0 0 X l Land (Acres) • 72 1 . 0 0 X 2 Labour (man-days) . 8 8 • 71 1 . 0 0 X 3 F e r t i 1 i z e r (Rs.) . 7 6 • 6 9 .29 1 . 0 0 h Machinery Serv i ces (Rs.) • 52 • 70 • 32 .81 1 . 0 0 X 5 Animal Se rv i ce s (Rs.) . 6 8 . 4 8 . 7 6 . 7 4 - . 8 3 1 . 0 0 X 6 Agro-chemicals (Rs.) . 5 5 . 5 4 . 6 4 . 6 3 . 2 0 . 7 6 1 . 0 0 X 7 Seed Mater ia 1 (Rs.) .85 . 7 4 . 8 8 . 7 8 . 2 4 . 7 4 . 5 7 1 . 0 0 X 8 Draf t Se rv i ce s (Rs.) . 6 9 • 71 . 6 7 . 6 4 . 5 2 . 6 9 .58 . 6 4 1 . 0 0 A H q : p = 0 , r e j ec ted i f c a l c u l a t e d r > . 1 9 0 (. 0 5 L.O.S.) ; r > . 2 4 8 ( . 0 1 . L.O. .S.). b For d e f i n i t i o n of v a r i a b l e s , see Chapter IV. APPENDIX 8 SIMPLE CORRELATION COEFFICIENTS 3 FOR LOGARITHMICALLY TRANSFORMED VARIABLES INCLUDED IN PADDY REGRESSION ANALYSIS-- TOTAL FARM DATA--HIGH RESPONSE REGION ( 4 4 FARMS) Farm V a r i a b l e ' 3 Y X l X 2 V X 4 X 5 X 6 X 7 X 8 Y Output (Rs.) 1 . 0 0 X l Land (Acres) .78 1 . 0 0 X 2 Labour (man-days) .81 . 6 2 1 . 0 0 X 3 F e r t i 1 i z e r (Rs.) . 8 6 . 6 4 . 3 8 1 . 0 0 h Machinery Serv i ces (Rs.) . 3 9 . 7 8 . 4 2 . 6 9 1 . 0 0 X 5 Animal Serv ices (Rs.) . 4 2 . 4 7 . 7 3 . 6 8 - . 7 9 1 . 0 0 X 6 Agro-chemicals (Rs.) .62 . 6 8 . 7 9 • 7 * . 2 4 . 6 6 1 . 0 0 X 7 Seed Ma te r i a l (Rs.) . 7 4 . 3 4 . 6 4 . 7 9 . 2 0 . 6 4 . 6 2 1 . 0 0 X 8 Draf t Serv ices (Rs.) . 6 9 .81 . 6 7 . 6 8 .61 .72 . 6 9 . 7 8 1 . 0 0 A H q : p = 0 , r e j ec ted i f c a l c u l a t e d r > . 190 (. 0 5 L.O.S.); r > . 2 4 8 (.01 L.O. .S.). For d e f i n i t i o n of v a r i a b l e s , see Chapter IV. _c-N3 

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