LAYER PRODUCTION IN GHANA: A COST FUNCTION APPROACH BY YAW OSEI-OFORI A THESIS SUBMITTED TO THE DEPARTMENT OF AGRICULTURAL ECONOMICS AND AGRIBUSINESS, UNIVERSITY OF GHANA, LEGON, IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF PHILOSOPHY IN AGRICULTURAL ECONOMICS. DEPARTMENT OF AGRICULTURAL ECONOMICS AND AGRIBUSINESS FACULTY OF AGRICULTURE UNIVERSITY OF GHANA LEGON JUNE, 2001 University of Ghana http://ugspace.ug.edu.gh 368176 $$ tl£2- 6rS Oc-X University of Ghana http://ugspace.ug.edu.gh DECLARATION I Yaw Osei-Ofori, the author of this thesis do hereby declare that the work presented in this thesis titled 'Layer Production in Ghana: A Cost Function Approach' was done entirely by me in the Department of Agricultural Economics and Agribusiness, University of Ghana, Legon from September 1999 to June 2001. This work has never been presented either in whole or in part for any degree in this University or elsewhere. Yaw Osei-Ofori (Student) This thesis has been presented for examination with our approval as supervisors. (Major Supervisor) Rev. (Dr) S. Asuming-Brempong (Co-Supervisor) University of Ghana http://ugspace.ug.edu.gh This piece is dedicated to my darling mum who is my role model, my lovely wife whose priceless contributions have brought this work to a successful end and finally to my two wonderful sons. DEDICATION ii University of Ghana http://ugspace.ug.edu.gh Glory, honor and thanks, first and foremost go to God Almighty who gave me the strength, intellect to bring this work to a successful end. Secondly, I wish to thank Dr. E. K. Andah, my major supervisor for having painstakingly guided me, giving useful suggestion throughout the study period. I am also grateful to Rev. (Dr.) S. Asuming_Brempong, my co-supervisor who also gave useful suggestions and in addition encouraged me to finish hard. I am indebted to Mr. K. Y. Fosu who although not one of my supervisors took interest in the work and willingly shared some ideas with me to enrich the work. I wish to acknowledge also, Dr. D. B. Bruce-Sarpong who helped me during the estimation of the model. Mr. Akwasi Mensah-Bonsu need not be forgotten for the instrumental role he played. Likewise, my gratitude goes to Messers E. T. Adika and R. Darkoh od the Department Of Agricultural Economics and Agribusiness for their priceless assistance. Special mention needs to be made of my lovely beloved wife for her unflinching support and finally Mr. Jorge Odoi who helped me a great deal in the collection of date. From the depths of my heart I say, well done and may Lord richly bless you. ACKNOWLEDGEMENT iii University of Ghana http://ugspace.ug.edu.gh ABSTRACT This study tries to find out why the Ghanaian Poultry Industry is unable to produce enough poultry chicken to meet the local market demand which has led to the large importation of frozen chicken for the period 1988-1999. It determines how responsiveness major poultry inputs such as vaccines, feed, labor and institutional credit are to price change and the economies of scale of layer production in the poultry industry. The study therefore estimates parameters of the input variables from the cost function and cost share equations, Allen Partial Elasticities of Substitution between inputs. These estimations are used in computing own price elasticities of demand for the poultry inputs, cross price elasticities of factor demand and scale elasticities in layer production over the period 1988-1999. The study also sought to determine what production function that best describes layer production in the Ghanaian Poultry Industry. The study's empirical econometric results indicate that a production function, which is characterized by non-homotheticity, non-homogeneity, non-unitary University of Ghana http://ugspace.ug.edu.gh elasticities of substitutions, and non Cobb-Douglas model is required to adequately represent the production of layers by the Ghanaian Poultry Industry implying no restrictions on the production function. It is therefore a Constant Elasticity of Substitution production function. Inputs are found to be highly elastic which means that when their price rise the quantity demanded drastically falls. The relatively high price elasticities of the inputs indicate non-optimum production by poultry firms hence inability of meeting the market's demand. Layer production in the Poultry Industry exhibited both economies and diseconomies of scale over the study period 1988-1999. There was eight years of positive economies of scale with only four years of diseconomies of scales. University of Ghana http://ugspace.ug.edu.gh TABLE OF CONTENT DECLARATION i DEDICATION ii AKNOWLEDGEMENT iii ABSTRACT iv LIST OF TABLES ix LIST OF APPENDICES x CHAPTER 1. INTRODUCTION Background and problem Statement 1 The Objectives 7 Method of Analysis 8 Relevance of study 8 Scope and Limitation of Study 9 Organization 10 2 . LITERATURE REVIEW 12 Introduction 12 Theoretical Literature 12 Price and Cost Function 15 Empirical Application of P a g e vi University of Ghana http://ugspace.ug.edu.gh Duality Formulation CHAPTER Advantages of Duality 3. THE GHANAIAN POULTRY INDUSTRY Introduction History of the Poultry Industry Performance of the Poultry Sub-Sector Overtime The Structure of the Poultry Industry Nature of Demand Marketing of Poultry Products 4. METHODOLOGY Introduction Theoretical Concepts and Framework of Analysis of Multivariate Regression The Theoretical Model Economies of Scale Method of Estimation Multivariate Regression System Model Selection Statistical Test vii PAGE 24 27 28 32 34 35 38 40 40 44 49 5 0 52 54 55 University of Ghana http://ugspace.ug.edu.gh P a g e CHAPTER Statement of Hypothesis 56 Expected Results 57 Method of data collection 57 Description of Variables and Sources of Data 58 5.0 RESULTS AND DISCUSSION OF ANALYTICAL MODEL Empirical Econometric Results 62 6.0 SUMMARY, CONCLUSION AND RECOMMENDATION Summary 71 Policy recommendation 72 BIBLIOGRAPHY 81 viii University of Ghana http://ugspace.ug.edu.gh LIST OF TABLES 1.1 Poultry Population in Ghana 1970-1998 4 5.1 A Summary of Test Statistics for Model Selection (1988-1999) 63 5.2 Results of Estimates of Allen Partial Elasticity of Factor Substitution 64 5.3 Results of Price Elasticities of Input Demand 66 5.4 Results of Scale Elasticities 67 TABLE P a g e ix University of Ghana http://ugspace.ug.edu.gh APPENDIX 1: Results of Unconstrained Model with Symmetry 74 2: Results for Testing Homotheticity 75 3: Results for Testing Homogeneity 76 4: Results for Testing Unitary Elasticity 77 5: White Heteroskedasticity Test for testing Homoskedasticity 78 6: Breusch-Godfrey Serial Correlation LM Test 79 7: Total Cost, Cost Shares and Prices Inputs 8 0 LIST OF APPENDICES P a g e x University of Ghana http://ugspace.ug.edu.gh CHAPTER ONE INTRODUCTION Background and Problem Statement The term 'poultry' is used to designate those species of birds which render man an economic service and reproduce freely under his care. It includes chicken, turkeys, ducks, geese, swans, guineas, pigeons, peafowls, pheasants, and ostriches and refers to them whether dressed or alive.1 Poultry products are used extensively in industries. For instance, eggs are used in the preparation of culture media for the growth of some species of bacteria and fertile eggs used in the preparation of vaccines. Chickens are being used extensively in biological research work because they are inexpensive and readily available, reproduce freely, have a sensitive metabolism and are good laboratory research materials.2 The exact ancestry of the chicken is obscured by the antiquity of its origin. For more than five thousand years the domesticated fowl has been one of man's benefactors. Authorities agree quite generally that the red jungle fowl, Gallus bankiva, was one of the ancestors. More recent investigations suggest that at least four species of the 1 Winter, A. R. and Funk, E. M., Poultry Science and Practice, ed. R. W. Gregory. Published by J. B. . Lippincot Company, New York, 1956 p.3. 2 Ibid. p.7. 1 University of Ghana http://ugspace.ug.edu.gh jungle fowl may have contributed to the development of the domestic fowl.3 Chicken and turkeys dominate the world poultry industry with broiler (young or fryer) chicken and turkeys providing most of the world's production and consumption of poultry meat.4 Broilers and layers are specialized types of chicken developed through the application of genetics with the former being efficient in meat production and the latter efficient in the production of larger number of eggs5; but in Ghana layers produce both eggs and about 60% of the poultry meat.6 Poultry have high turnover and if produced under efficient conditions, three batches of broilers can be raised in a year with the same facilities. Nevertheless, poultry being monogastric physiologically as man is tend to compete directly with man for the same basic food commodities especially maize and fish. The competition is particularly severe in a developing country like Ghana, where per capita food production is low and the major staple food is maize. 3 Ibid. p. 21 4 Food and A gricultural O rganization, 1985, Rome. s Taylor, R. E. and Bogart R ., 'The Poultry Industry' in Scientific Farm A nim al Production . (M acm illan Com pany, 1988, N ew Y ork), p.88 6 G overnm ent o f Ghana, N ational Livestock Services Project, S ta ff A ppraisal Report, Accra, 1992, pp 9-10. 2 University of Ghana http://ugspace.ug.edu.gh In order to satisfy higher demand for animal protein, notably poultry products, large-scale farms were established mainly in urban areas and between 1970 to 1980 an extensive poultry infrastructure was established in the country.7 The poultry industry in Ghana consists of a traditional sector, which supplies poultry meat and eggs for a lot of the rural people and a commercial sector that depends on imported inputs for production. The commercial poultry industry is dominated by egg production that gives a by-product (old layers), which contributes about 60% of poultry meat in Ghana.8 Achieving food security requires the use of productivity enhancing inputs in the livestock and poultry industries, and not only in the crop production sub-sector. These inputs include hybrid layer and broiler strains of day-old-chicks (DOCs), raw materials (ingredients) to formulate feed, drugs, premixes and vaccines. The Poultry Industry in Ghana has gone through a cycle of rapid growth. Annual output of birds rose from 3.lmillion (3.1M) in 1970 to a peak of 9.7 million (9.7M) in 1982 before easing to 8.8 million (8.8M) in 1989 and 7 Koney, E. B. M ., Poultry H ealth and Production. The A dventist Press, 1993, Accra, p. 1 8 Governm ent o f Ghana, N ational Livestock Services Project, opcit, pp. 9-10 3 University of Ghana http://ugspace.ug.edu.gh then rising again from 9.9 million (9.9M) in 1990 to 15.54 million (15.54M) in 1998 (Table 1.1). Table 1.1: Poultry Population in Ghana 1970 - 1998 (Million Heads) Year Number 1970 3.1 1971 4 . 0 1972 4 . 0 1973 3.3 1974 4 . 2 1975 3 . 8 1976 3 . 8 1977 4.6 1978 6.3 1979 7.3 1980 7.5 1981 N/A 1982 N/A 1983 N/A 1984 N/A 1985 N/A 1986 N/A 1987 8.2 1988 8 . 0 1989 8.7 1990 9.7 1991 10.57 1992 11.23 1993 12 .17 1994 12 .29 1995 13 . 08 1996 14.59 1997 14 . 83 1998 15.54 Source: Ministry of Food and Agriculture, Veterinary Services Department, Accra. N/A: Not Available. The poultry industry has some excellent infrastructure consisting of about twenty-three commercial feed-mills with a capacity of over two hundred thousand metric tones (200,000 Mt) of feed per month and eleven commercial University of Ghana http://ugspace.ug.edu.gh hatcheries with a potential to produce twenty-five million (25M) day-old-chicks per year in the country.9 Prior to liberalization in 1990 and deregulation, government was the sole procurer of all agricultural inputs, as they could not rely on the tender and undeveloped private sector to deliver such inputs to achieve a sustainable food security. Government realized in the mid 1980s that it could no longer sustain the financial burden associated with subsidizing agricultural inputs and the guaranteeing of product prices for the farmers. A policy reform was therefore implemented in 1990 with the aim of liberalizing trade and privatising the agricultural inputs market. The implementation of this policy saw the exit of government in the importation and marketing of day- old-chicks, drugs and poultry feed and the entry of private firms into the market. Poultry products alone contributed about £6 0 billion to Gross Domestic Product (GDP) in 1993 as against $9 billion for livestock.10 As noted by Okantey, Ghana can 9 Koney, p. 1 Opcit 10 Livestock Planning and Information Unit. Analysis of Meat and Animal Product Imports. Occasional Report, No. 1,1994, Accra. 5 University of Ghana http://ugspace.ug.edu.gh solve a national problem of protein deficiency in diets through poultry production.11 Although, the Ghanaian poultry industry has seen some growth yet Boa-Amponsem observed that from 1984 to 1986, the country produced less than 2 0 percent of its meat requirement with poultry contributing only 2.5 percent.12 This led to a large importation of poultry meat and products into the country, which is enough to indicate that local production is not responding to the market demand. Ministry of Food and Agriculture (MOFA) data indicates that only 23 percent of the estimated total meat demand of about 195,000 Mt comes from domestic sources.13 This implies that the excess demand is met through imports. In 1997, more than £88 million was expended on the importation of frozen whole chicken and this figure increased to £2.8 billion in 1998 . Given the potential high turnover of poultry production per year and the liberalization of the sale of poultry inputs, why is local production not responding to the local market demand? 11 Okantey, S. A.(1995) ‘The Poultry Industry in Ghana: Past, Present and Future’ in Osei (1995) (ed). The Poultry Industry in Ghana: Any Future? Proceedings of the First Anniversary Symposium of the Ghana National Association of Poultry Farmers (GNAPF) held at the Osu Children’s Home, Accra. 12 Boa-Amponsem, K. (1988), 'Status o f the Poultry Industry in Ghana'. First Annual General Meeting of Ghana Society o f Animal Production. Accra, p. 10. 13 Osei, S. A., ‘The Poultry Industry in Ghana - Any Future?: An Overview’ in ‘The Poultry Industry in Ghana: Any Future?, ed. S. A. Osei. ( Proceedings of the First Anniversary Symposium of the Ghana National Association of Poultry Fanners ( GNAPF) held at the Osu Children’s Home, 1995, Accra. 6 University of Ghana http://ugspace.ug.edu.gh Objectives The main objective of the study is to find out why local production of poultry meat is not responding to the local market demand. To attain this major objective some specific objectives are pursued. These include: ̂ the determination of the responsiveness of poultry inputs to price; ̂ the determination of economies of scale of layer production in the Ghanaian Poultry Industry. In pursuance of these specific objectives, the following estimations are done: 't, the estimation of parameters of the input variables from the cost function and cost share equations; % the estimation of Allen Partial Elasticities of Substitution between inputs; ̂ the estimation of own price elasticities of demand for the major poultry inputs; i; the estimation of cross price elasticities of factor demand, and 4 the estimation of scale elasticities in layer production over the period 1988-1999. 7 University of Ghana http://ugspace.ug.edu.gh Method of Analysis The structure of production is analyzed using the cost function approach. The quantification of the dual cost function is achieved by the joint estimation of the total cost function and the cost share equations as a multivariate regression system using the translog functional form. The system of equations forms a seemingly unrelated regression model and the parameters are estimated using maximum - likelihood approach. The selection of model is done by testing different hypotheses when various restrictions are imposed on the parameters of the model using the Wald's test. The dual cost function is characterized by the form, C = C ( P IC, P L, P p, P v , Q ) ( 1 . 1 ) Where PiC = the yearly price of institutional credit, P L = the yearly price of labor, P F = the yearly price of feed, Pv = the yearly price of vaccines and Q = annual total output. Relevance of study The estimation of a production function or cost function is a useful tool for overcoming the problems of University of Ghana http://ugspace.ug.edu.gh casual observation, and providing for the better understanding of the production structure of a farm by way of making relationship among variables more explicit. A cost function analysis is capable of providing quantitative insights into the response of producers to rising input prices, substitution possibilities between inputs and scale elasticities. Such information may aid poultry firms in making the best decisions concerning the use of scarce resources in production activities. Moreover, the estimated values of the cost function might be useful for future planning purposes because they provide an indication of the increase in output that could be expected with some decrease in the cost of production. In addition, an increase in the production of layers will lead to the meeting of market demand, and therefore (all things being equal) an increase in poultry meat, which will enhance the protein supplement of the individual. Scope and Limitation This study is limited to intensive large-scale poultry firms in the Greater Accra and Ashanti Regions because commercial poultry farms are concentrated in these two regions, technology for intensive commercial poultry production exists and they supply the largest percent of 9 University of Ghana http://ugspace.ug.edu.gh poultry meat. The study is restricted to live layers instead of broilers because the former is mostly produced all year round by most farms for eggs and meat and contributes about 60% of poultry meat in Ghana whilst the latter is produced by fewer farmers mainly on festive occasions on a lower scale. The translog cost function, despite its flexibility, is not without problems. In using this model two estimation problems are envisaged. Firstly, as the number of inputs increase, the number of parameters to be estimated also increase rapidly. Secondly, the additional terms are squares and cross products of input variables, thus making multicolinearity a difficult problem. Future studies could use earnings in the agriculture Sub-sector instead of average monthly earnings as an appropriate proxy for the price of labor. Due to the small size of the dataset (1988-1999), the model selection procedure, which involves iterating on one small dataset, is prone to the data-mining problem. Organization Chapter Two is devoted to Review of Literature. The theoretical method of estimation of the parameters and model specification of the cost function falls under 10 University of Ghana http://ugspace.ug.edu.gh Chapter Three. Chapter Four gives an overview of the Ghanaian Poultry Industry. Data analysis and parameter estimations find a placement in Chapter Five. In Chapter Six, conclusions are drawn on the estimated parameters and policy recommendations presented. 11 University of Ghana http://ugspace.ug.edu.gh CHAPTER TWO LITERATURE REVIEW Introduction This Chapter is to purposely give an exposition of an econometric method for modeling producer behavior. Important innovations in specifying econometric models have arisen from the dual formulation of the theory of production. The main advantage of dual formulation is the specification of demand and supply functions as explicit functions of relative prices. By using duality in production theory, these functions can be specified without imposing arbitrary restrictions on patterns of production. Theoretical Literature The economic theory of production presented in classic treatises as Hick's Value and Capital 14 and Samuelson's Foundations of Economic Analysis15 is based on the maximization of profit, subject to a production function. The objective of this theory is to characterize demand and supply functions, using the restrictions on producer behavior that arise from optimization. To achieve this objective the implicit function theorem is employed as the 14 Hicks, J. R. Value and Capital. 2nd ed. (1st ed. 1939),: University Press, 1946, Oxford. 12 University of Ghana http://ugspace.ug.edu.gh main analytical tool.16 The use of this theorem is not convenient for econometric application. The traditional approach, which makes assumption that the production function is additive and homogeneous was originated by Cobb and Douglas17 and was used in empirical research by the latter and his associates for almost two decades.18 Limitations of this approach was made apparent by Arrow, Chenery, Minhas, and Solow19 (ACMS), who pointed out that the Cobb-Douglas production function imposes a priori restrictions on patterns of substitution among inputs. In particular, elasticities of substitution among all inputs must be equal to unity. The constant elasticities of substitution (CES) production function introduced by ACMS adds flexibility to the traditional approach by treating the elasticity of substitution as an unknown parameter.20 However, the CES production function retains the assumptions of additivity and homogeneity and imposes very stringent limitations on patterns of substitution. 15 Samuelson, P. A. 0 Foundation o f Economic Analysis. 2nd ed. (1st ed. 1947), Harvard University Press. 1983, Cambridge. 16 This approach to production theory was employed by Carlson (1939), Frisch (1965), and Schneider (1934). 17 Cobb, C. W. and P. H. Douglas (1928) "A Theory of Production", American Economic Review, March, 18(2), pp. 139-165. 18 These studies are summarized by Douglas (1948), (1967), (1976). 19 Arrow, K. J., H. B. Chenery, B. S. Minhas and R. M. Solow (1961) "Capital-Labor Substitution and Economic Efficiency", Review o f Economic and Statistics, august, 63(3), pp. 225-247. 13 University of Ghana http://ugspace.ug.edu.gh McFadden21 and Uzawa22 have shown, essentially, that elasticities of substitutions among all inputs must be the same. The limitations of traditional approach to econometric modeling have been overcome by the dual formulation of productin theory. This dual formulation was introduced by Hotelling23 and later revived and extended by Samuelson24 and Shepard.25 The main features of the dual formulation are the characterization of the production function by means of a dual representation such as a price or cost function and also to generate explicit demand and supply functions as derivatives of the price or cost function.26 The dual formulation of production theory embodies the same implications of optimizing behavior as the theory presented by Hicks27 and Samuelson.28 However, the dual formulation has 20 Econometric studies based on CES production function have been surveyed by Griliches (1967), Jorgenson (1974), Kennedy and Thirlwall (1972), Nadiri (1970), and Nerlove (1967). 21 McFadden, D. (1963) "Further Results on CES Production Functions", Review o f Economic Studies, June, 30(2), pp. 83, 73-83. 22 Uzawa, H. (1962) "Production Functions with Constant Elasticity of Substitution", Review o f Economic Studies, October, 29(4), pp. 81,291-299. 23 Hotelling, H. S. (1932) "Edgeworth's Taxation Paradox and the Nature o f Demand and Supply Functions", Journal o f Political Economy, October, 40(5), pp. 577-616. ^Samuelson, P. A. (1953-1954) "Prices of Factors and Goods in General Equilibrium", Review o f Economic Studies, 21(1), pp.54, 1-20. and Samuelson, P. A. (1960) "Structure of a Minimum Equilibrium System", in: R. W. Pfouts, ed., Essays in Economics and Econometrics. Chapel Hill: University o f north Carolina Press, pp. 1-33. 25 Shepard, R W. Cost and Production Functions, and Theory o f Cost and Production Function. Princeton University Press, 1953 andl970,. Princeton: 26 Surveys of duality in the theory of production are presented by Diewert (1982) and Samuelson (1983). 27 Hicks, opcit. 28 Samuelson, opcit 14 University of Ghana http://ugspace.ug.edu.gh a crucial advantage in the development of econometric methodology. Demand and supply functions can be generated as explicit functions of relative prices without imposing the arbitrary constraints on production patterns required in the traditional methodology. In addition, the implications of production theory can be incorporated more readily into an econometric model. Price and Cost Function Producer equilibrium implies the existence of a price function, giving the price of output as a function of the prices of inputs and the level of technology. The price function is dual to the production function and provides an alternative and equivalent description of technology. A cost function is so referred to when the total cost is defined as the sum of expenditures on all inputs and the minimum value of cost can be express as a function of the level of output and the prices of all inputs. Empirical Application of Duality Formulation Functional forms for cost functions have been developed by researchers over the years, which have two attractive features: they imply derived demand equations which are linear in parameters and at the same time they 15 University of Ghana http://ugspace.ug.edu.gh represent very general production structures, even though they cannot be derived from explicit production functions. Several specific flexible functional forms have been proposed. A partial list of these includes the Generalized Leontief (GL), the Translog (TL), the Generalized Cobb- Douglas (GCD), the Generalized Square Root Quadratic (GSRQ) , and the Generalized Box-Cox (GBC) .29 For many of the production and price frontiers employed in econometric studies of production the translog frontiers provide accurate global approximations.30 The translog function can exhibit non-constant marginal productivity, that is increasing, decreasing and negative marginal products, singularly, in pairs, or all three simultaneously. As a result, this form of production function is useful in describing input-output data encompassing all the three traditional stages of production with increasing positive, and declining positive and negative marginal products. It also permits variable elasticity of production and variable elasticity of substitution over the range of inputs. 29 The GL, GCD and GSRQ forms were introduced by Diewert ( 1971, 1973, 1974 ). The TL was developed by Christensen, Jorgensen and Lau ( 1971,1975 ). Bemdt and Khaled proposed the GBC 30 Christensen, L. R. et al. ( 1973 ), ‘Transcendental Logarithmic Production Frontiers’, Review of Economics and Statistics LV, 29. 16 University of Ghana http://ugspace.ug.edu.gh Wales,31 in his Monte Carlo study to investigate the ability of GL and TL forms to represent two-commodity homothetic preference exhibiting a constant elasticity of substitution, found that in some cases the GL performed better, whilst in other cases the TL performed better. Berndt, et. al,32 using Canadian expenditure data to estimate three-commodity non-homothetic GL, TL, and GCD forms, on the basis of better fit and conformity to neoclassical restrictions, concluded that the TL form was the preferred form for their data set. Christensen and Greene employed the Translog cost function,33 in their study of economies of scale in the United States (U.S.) electric power generation because the function places no 'a prior' restrictions on substitution possibilities among the factors of production. It also allows scale economies to vary with the level of output and this feature is essential to enable the unit cost curve to attain the classical U shape. Berndt and Wood,34 in their attempt to characterize more completely the structure of 31 Wales, T. J. ( 1977), ‘On the flexibility o f flexible functional forms: An empirical approach’, Journal of Econometrics 5, 183-193. 32 Bemdt, E. R. et al. ( 1977 ), Flexible functional forms and expenditure distribution: An application of Canadian consumer demand functions’, Int. Econ. Rev. 18, 651-675. 33 Christensen, L. R. and Greene, W. H. ( 1976), ‘Economies o f Scale in U. S. electric power generation’, Journal of Political Economy 84 (4), 655-676. 34 Bemdt, E. R. and Wood, D. O. ( 1975 ), ‘Technology, prices, and derived demand for energy’, Review of Economics and Statistics 57, 259-268 17 University of Ghana http://ugspace.ug.edu.gh technology in United States manufacturing, arbitrarily chose to employ the translog cost function. Bigsby 35, gave the following reasons for using the translog function in the study of production structure of the Australian saw milling industry: the estimates of the elasticity of substitution and technological change bias can be obtained even though it may not be possible to specify the exact form for the production function: the elasticity of substitution does not need to be restricted to any particular value or to be restricted to any particular value over time; the assumption of constant returns to scale is not necessary; the bias of technological change can be calculated rather than be assumed to be Hicks-neutral; and the rate of technological progress can be estimated. The translog cost function was used by Nautiyal and Singh,36 Singh and Nautiyal,37 Martinello,38 and Sherif39 in studies of the pulp, paper and 35 Bisby, H. R. ( 1994), ‘Production structure and the Australian saw-milling industry’, Australian Journal of Agricultural Economics 38(3), 271-288. 36 Nautiyal, J. B. and Singh, B. K. ( 1985 ), ‘Production structure and derived demand for factor inputs in the Canadian lumber industry’, Forest Science 31(4),871-881. (1986), ‘Long-term productivity and factor demand in the Canadian pulp and paper industry’, Canadian Journal o f Agricultural Economics 34, 21-44. 37 Singh, B. K. and Nautiyal, J. B. ( 1986), ‘A comparison o f observed and long-run productivity o f and demand for inputs in the Canadian lumber industry’, Canadian Journal o f Forest Research 16, 443-455. 38 Martinello, F. ( 1987), ‘Technology, cost structure and rates o f technical progress in the British Columbia Coast lumber industry’, Working paper, Economics Branch, Canadian Forest Service, Ottawa. 39 Sherif, F. ( 1983 ), ‘Derived demand for factors of production in the pulp and paper industry’, Forest Products Journal 33(1), 45-49. 18 University of Ghana http://ugspace.ug.edu.gh sawmilling industries in Canada and by Stier40 for the United States. Denny and May 41 disaggregated labor input into white collar and blue collar labor, capital input between equipment and structures and grouped all other inputs into a single aggregate input for Canadian total manufacturing, using a translog functional form. Field and Grebenstein42 analyzed substitution among physical capital, working capital, labor, and energy for ten two-digit U.S. manufacturing industries on the basis of translog price functions, using cross section data for individual states for 1971. Cameron and Schwartz,43 Denny, May, and Pinto,44 Fuss,45and McRae46 constructed econometric models of substitution among capital, labor, energy, and materials inputs based on translog functional forms for manufacturing 40 Stier, J. C. ( 1980 ), ‘Estimating the production technology in the U. S. forest products industries’, Forest Science 26(3), 471-482., Stier, J. C. ( 1985 ), ‘Implications o f factor substitution, economies of scale, and technological change for the cost o f production in the U. S. pulp and paper industry’, Forest Science 31(4), 803-812. 41 Denny, M. and J. D. May (1978) "Homotheticity and Real Value-Added in Canadian manufacturing", in: M. Fuss and D. McFadden, eds., 2, pp. 53-70. 42 Field, B. C. and C. Grebenstein (1980) "Substituting for Energy in U.S. Manufacturing", Review o f Economic and Statistics, May, 62(2), pp.207-212. 43 Cameron, T. A. and S. L. Schwartz (1979) "Sectoral Energy Demand in Canadian Manufacturing Industries", Energy Economics, April, 1(2), 112-118. 44 Denny, M. and J. D. May and C. Pinto (1978) "The Demand for Energy in Canadian Manufacturing: Prologue to an Energy Policy", Canadian Journal o f Economics, May, 11(2), pp.300-313. 45 Fuss, M. (1977a) "The Demand for Energy in Canadian Manufacturing: An Example of the Estimation of Production Structures with Many Inputs", Journal o f Econometrics, January, 5(1), pp. 89-116. 46 McRae, R. N. (1981) "Regional Demand For Energy By Canadian Manufacturing Industries1', International Journal o f Energy Systems, January, 1(1), pp.38-48. 19 University of Ghana http://ugspace.ug.edu.gh in Canada. Friede47 analyzed substitution among capital, labor, energy, and materials inputs for total manufacturing in the Federal Republic of Germany. He assumed that technical change is neutral and utilized a translog price function, disaggregated the results to the level of fourteen industrial groups, covering the whole of West German economy, separated materials inputs into two groups- manufacturing and transportation services as a group and other non-energy inputs as a second group. Ozatalay, Grubaugh, and Long48 modeled substitution among capital, labor, energy and materials inputs, on the basis of a translog price function using time series data for total manufacturing for the period 1963-74 in seven countries. Friedlander and Spady49 disaggregated transportation services between trucking and rail service and grouped other inputs into capital, labor and materials inputs using cross section data for ninety-six three-digit industries in the U.S. for 1972 employing translog functional form with fixed inputs. 47 Friede, G. (1979) Investigation of Production Behavior in the Federal Republic o f Germany Using the Translog Price Function. Cambridge: Oelgeschlager, Gunn and Hain. 48 Ozatalay, S., S. S. Grumbaugh and T. V. Long III, "Energy Substitution and National Energy Policy", American Economic Review, May, 69(2), pp. 369-371. 49 Friedlaender, A. F. and R. H. Spady (1980) "A Derived Demand Function for Freight Transportation", Review o f Economic Statistics, August, 62(3), pp. 432-441. 20 University of Ghana http://ugspace.ug.edu.gh Humphrey and Wolkowitz50 grouped energy and materials inputs into a single aggregate input in a study of substitution among inputs in several U.S. manufacturing industries utilizing translog price functions. Berndt and Wood51 generated an econometric model, by expressing the price of aggregate inputs as a function of the prices of capital, labor, energy, and materials inputs of the total manufacturing sector of the U.S. economy and found that capital and energy inputs are complements, while all other pairs of inputs are substitutes. Employing the Fourier functional model for price function, Elbadawi, Gallant, and Souza52 estimated price elasticities of demand for inputs. In using the translog parametric form, Woodland53 tested separability and modeled substitution among two types of capital input and two types of labor inputs for the U.S. total manufacturing. Parameter estimates on the patterns of substitution among industries in a study done by Jorgenson and 50 Humphrey, D. B. and B. Wolkowitz (1976) "Substituting Intermediates for Capital and Labor wiyh Alternative Functional Forms: An Aggregate Study", Applied Economics, March, 8(1), pp. 59-68. 51 Berndt, E. R. and D. O. Wood (1975) "Technology, Prices, and the Derived Demand for Energy", Review o f Economics and Statistics, August, 57(3), 376-384. 52 Elbadawi, I., A. R. Gallant and G. Souza (1983) "An Elasticity Can Be Estimated Consistently Without a Prior Knowledge of Functional Forms", Econometrica, November, 51(6), pp. 1731-1752. 53 Woodland, A. D. (1975) "Substitution of Structures, Equipment, and Labor in Canadian Production", International Economic Review, February, 16(1), pp. 171-187. 21 University of Ghana http://ugspace.ug.edu.gh Fraumeni54 revealed that the elasticities of the shares of capital with respect to the price of labor are nonnegative for thirty-three of the thirty-five industries, so that the shares of capital are non-decreasing in the price of labor for these thirty-three sectors. Similarly, elasticities of the share of capital with respect to the price of energy are nonnegative for thirty-four industries and elasticities with respect to the price of materials are nonnegative for all thirty-five industries. The share elasticities of labor with respect to the prices of energy and materials are nonnegative for nineteen and for all thirty-five industries, respectively. Finally, the share elasticities of energy with respect to the price of materials are nonnegative for thirty-five industries. Jorgenson55 employed translog price functions with capital, labor, two kinds of energy, and materials inputs to model substitution and technical change for thirty-five industries of the U.S., dividing energy inputs between electricity and non-electrical energy inputs and found that technical change is electricity-using and non-electrical 54 Jorgenson, D. W. and B. M. Fraumeni (1981) "Relative Prices and Technical Change", in; E. R. Bemdt and B. C. Field, eds., 17-47; revised and reprinted in : W. Eichhom, R. Henn, K. Neumann and R. W. Shepard, eds., 241-269. 55 Jorgenson, D.W. (1984b) "The Role of Energy in Productivity Growth", in: J. W. Kendrick, ed., International Comparisons o f Productivity and Causes o f the Slowdown. Cambridge: Ballinger, 279-323. 22 University of Ghana http://ugspace.ug.edu.gh energy-using for most U.S. industries. Stevenson56 employed a translog total cost function incorporating output and time to analyze cross sections of electric utilities for 1964 and 1972. Gollop and Roberts57 used a similar approach to study annual data on eleven utilities in the U.S. for the period 1958-1975. The results were used to decompose the growth of the total cost among economies of scale, technical change, and growth in input prices. Griffin58 modelled substitution among different types of fuel in steam electricity generation four cross sections of twenty OECD countries. Halvorsen59 analyzed substitution among different fuel types, using cross section data for the U.S. in 1972. Fuss60 in his model-to-model substitution among inputs and economies of scale for seventy-nine steam generation plants for the period 1948-61 permitted the total cost function to differ ex ante, before a plant was constructed, and ex post, after the plant was in place, employing the generalized Leontief cost function with four 56 Stevenson, R> E. (1980) "Measuring Technological Bias", American Economic Review, March, 70(1), 162-173. 57 Oollop, F. M. and M. J. Roberts (1981) "The Sources of Economic Growth in the U. S. Electric Power Industry", in: T. G. Cowing and R. E. Stevenson, eds., pp.107-145. 58 Griffin, J. M. (1977b) "Interfuel Substitution Possibilities: A Translog Application to Pooled Data', International Economic Review, October, 18(3), pp. 755-770. 59 Halvorsen, R (1978) Econometrics Studies of U.S. Energy Demand. Lexington: Lexington Books. 60 Fuss, M. (1977b and 1978) "The Structure o f Technology Over Time: A Model for Testing the Putty- Clay Hypothesis", Econometrica, November, 45(8), pp.1797-1821. And "Factor Substitution in Electricity Generation: A Test of the Putty-Clay Hypothesis", in M. Fuss and D. McFadden, eds., 2, pp. 187-214. 23 University of Ghana http://ugspace.ug.edu.gh input prices structures, equipment, fuel, and labor. Atkinson and Halvorsen61 made use of the translog parametric form to test the effects of both rate of return regulation and fuel cost adjustment mechanism and for this purpose they analyzed cross section data for electric utilities in 1973. Gollop and Robertson62 studied the effectiveness of regulations on sulfur dioxide emissions in the electric utility industry. They employed the translog cost function that depended on a measure of regulatory effectiveness. This measure was based on the legally mandated reduction in emissions and on the enforcement of emission standards. Gollop and Roberts analyzed cross sections of fifth-six electric utilities for each of the years 1973-1979 and employed the results to study the impact of environmental regulation on productivity growth. Advantages of DualitY Binswanger,53 and Sankhayan,64 outlined the advantages of using the cost function instead of a production function in estimating production parameters, and stated that: 61 Atkinson, S. E. and R. Halvorsen (1980) "A Test of Relative and Absolute Price Efficiency in Regulated Utilities", Review o f Economics and Statistics, August, 63(3), pp. 225-247. 62 Gollop, F. M. and M. J. Roberts (1983) "Environmental Regulations and Productivity Growth: The case for Fossil-Fueled Electric Power Generation", Journal Political Economy, August, 91(4), pp. 654-674. 63 Binswanger, H. P. ( 1974), ‘A cost function approach to the measurement o f factor demand and elasticities o f substitution ’, American Journal o f Agricultural Economics 56, 377-386. 64 Sankhayan, p.85, opcit. 24 University of Ghana http://ugspace.ug.edu.gh 1. It is not necessary to impose homogeneity of degree one on the production process to arrive at estimation equations. Cost functions are homogeneous in prices regardless of the homogeneity properties of the production function, because a doubling of all prices will double the costs but will not affect factor ratios. 2. In general, the estimation equations have prices as independent variables rather than factor quantities, which, at the firm or industry level, are not proper exogenous variables. Entrepreneurs make decisions on factor use according to exogenous prices, which makes the factor levels endogenous decision variables. 3. If a production function procedure is used to derive estimates of elasticities of substitution of factor demand in the many - factor case, the matrix of estimates of the production function coefficients has to be inverted. This will inevitably exaggerate estimation errors. No inversion is necessary when a cost function is used. 4. In production function estimation, high multicollinearity among the input variables often causes problems. Since there is usually little 25 University of Ghana http://ugspace.ug.edu.gh multicollinearity among factor prices, this problem does not arise in cost function estimation. 5. The researcher need not worry about the specific functional form of the production function. 6. Derivation of the input demand and product supply functions from the fitted production function is often quite difficult. On the contrary, the use of Shepard lemma helps in obtaining such estimations with relative ease when the cost function approach is used. 26 University of Ghana http://ugspace.ug.edu.gh CHAPTER THREE THE GHANAIAN POULTRY INDUSTRY Introduction The Ghanaian has over the years kept poultry either by one or the combination of two or more of the species. The birds are kept in a coop or a shelter where they spend the night, then in the morning provided with a handful of maize or sorghum and, for the rest of the day, they scavenge and pick up whatever comes their way. A member of the household is given the job of cleaning the coop or shelter - each morning. The indigenous bird population kept by the Ghanaian ranges between thirty to fifty or much less and this bird population is mostly chickens. In the southeast of Ghana, precisely in the Ada-Keta areas, the bird population is predominantly ducks whereas in the north they are both chickens and guinea fowls. In addition to these, some individuals may also have a few turkeys and pigeons. The cocks and hens mate indiscriminately. Thus a hen may be observed to hatch a brood of chicks that have different color plumage. Diseases readily invade most of the birds which are poorly taken care of. However, a number of birds survive this invasion. The duck, on the other hand, is generally 27 University of Ghana http://ugspace.ug.edu.gh properly fed with a mixture of corn chaff from the corn mill, fish and beach sand. The hens lay a few fertile eggs, on the average, ten or less in a clutch and sit to hatch. About twenty to thirty of such eggs are laid in a year. History of the Poultry Industry In the late 1920' s and in 1942 the Department of Animal Health established two breeding stations at Pong, Tamale and Pokuase, respectively which were to upgrade the local fowl.65 This Department organised the first poultry exhibition in 1933 to show to the public the performance of crossbred chickens.66 By 1937, these cross-breds had scattered throughout colonial Ghana. A number of independent backyard poultry farms sprang up on the coastal plains and were operated by farmers who had received training in poultry breeding, rearing and management from Pong Tamale.67 Commercial poultry production could be said to have started in 1952 with Ghana Egg Farm in a village near 65 Gold Coast, Department of Agriculture, Annual Report 1944-45 ( Accra, 1945 ). p. 1 66 Gold Coast Farmer, ‘ The Poultry Exhibition in Accra’ ( Accra, 1934)p .l62 67 Gyasi, E. M. ‘Economic Organization of the Poultry Industry of Ghana’ Unpublished Dissertation 1970, p .14. 28 University of Ghana http://ugspace.ug.edu.gh Accra68 although by 1952, poultry husbandry was seriously being undertaken at Pokuase Agricultural Station.69 Prior to this time, the country depended largely on the surrounding French colonies for poultry. The Department of Agriculture in 1952 successfully implemented a poultry extension scheme, which served as an impetus to the rapid transformation from traditional way of rearing to large-scale commercial poultry farming. This was done through the importation and distribution of day-old- chicks to the farmers and a follow up with extension work. The first consignment of chicks was received from Denmark in that year but owing to delays in the transportation only a few survived. However, by the end of the same year about 5,600 chicks were delivered without delay therefore none died.70 The Pokuase Station supplemented the chick imports by making available to farmers improved cross-bred or pure breeds and hatching eggs through its breeding programmes. The highest number of chicks imported in 1953 was 11,446 as officially recorded.71 In 1948, about 66,000 table birds were imported from Togo, Cote D'voire, United Kingdom, Netherlands and Israel. 68 William, G.E.S., ‘Rural Poultry Development and Production System in Ghana’.in: Rural Poultry in Africa, edited by E. B Soniaya ( Theila House Limited, Ile-Ife, 1990 ). p .155. 69 La-Anyane, S., ‘Poultry Marketing in Ghana’, The Ghana Farmer 1969. Vol. XIII. No.2, p.50 70 Gyasi, p. 15, opcit. 71 Gyasi, p. 16, opcit. 29 University of Ghana http://ugspace.ug.edu.gh However, by 1958 table bird imports had been reduced to half the 1948 figure.72 By 1959, expansion of the local industry begun with the direct involvement of private farmers in the importation of chicks as there was by then no foreign exchange control.73 During that year more than 100, 000 of the 121,000 total imports of day-old-chicks were made directly by farmers.74 Chick imports in that year were four times those of 1958 which reached a peak of 458,300 in 1965, signifying an expansion over the years.75 By 1967, there were four hatcheries in operation in Ghana with 973,000 chlck output.75 In 1964, Ghanachix Farm was established by an individual to breed strains of chickens to produce day-old-chicks for the Ghanaian market.77 Around the same period, the Ghana State Farms Corporation started the Odorkor State Farms which produced about 25,000 day- old-chicks a week78 and another at Kwadaso.79 The Animal Husbandry Department of the Ministry of Agriculture also put up a hatchery to produce about 72 La-Anyane, p. 48, 50, opcit. 73 Gyasi, p. 17, opcit. 74 Ghana, Central Bureau of Statistics Economic Survey 1959. 75 Gyasi, p. 17, opcit. 76Gyasi, p. 18, opcit. 77 Williams, p. 157, opcit. 78 Annang, p. 16, opcit 79 Gyasi, p. 18 opcit 30 University of Ghana http://ugspace.ug.edu.gh 12,000,000 day-old-chicks a year at Pomadze near Winneba but the target was never achieved. This hatchery was in 1971 converted into a limited liability company known as Pomadze Poultry Enterprises Limited. In addition to producing day-old-chicks, the company produces and sells poultry feed. At present only 10 percent of its installed capacity for day-old-chicks is produced because of liquidity problems. The poultry industry in the late 1950's encountered a number of problems that threatened its development. The problems included unavailability of high quality feed prepared from local ingredients, inadequate control of diseases, limited marketing outlets, and non-existing institutional credit facilities to farmers.80 The problems of feed and feeding in extensive poultry systems, account for 70% of the total poultry production in Africa. In general, the poultry industry in Africa is plagued with high feed cost resulting from inadequate knowledge of the proper mix of local feed ingredients for the various classes of poultry.81 80 Gyasi, pp. 18,19,opcit. 81 Ologhobo, A. D. ‘Feed and Feeding in Extensive Poultry Systems’, Entwicklung-und-Landlicher-raum 1990,24(4), pp.15-17. 31 University of Ghana http://ugspace.ug.edu.gh High demand deriving from the higher incomes of the increasingly urban population and the need to supplement one's income in later years due to economic depression gave a boost to intensive poultry rearing in Ghana.82 Several large-scale commercial farms emerged in different parts of the country between 1952 and 1960 with the growth of the industry greatest around Accra. By 1959, there were 406 certified poultry-keepers in the country, who were mainly involved in egg production with poultry meat production being a sideline enterprise.83 Poultry production increased sharply during the decade 1962-72 registering an average annual increase of 3 00 percent over the other livestock.84 In 1969, there were nearly 669,730 layer day-old-chicks and 1,337,580 broiler chicks.85 Because the Ghanaian cherishes a large and tough bird, and the way the chicken is cooked in the home, the broiler was not a very popular product. It tended to disintegrate in the soup during cooking. The commercial poultry meat producer had to 82 Annang, J. Q., ‘ Poultry Production and Products’ in Animal Science Symposium. University o f Ghana, Legon 1969 83 Gyasi, p. 18, opcit. 84 ‘Domestic Livestock Population in Ghana’, The Economic Survey 1969, Published by Central Bureau of Statistics, p.65. 85 Pomadze Poultry Enterprises, Ghana Economic Review, edited by Moses Danquah. Published by Editorial and Publishing Services, 1971/72, p.34 Performance of the Poultry Sub-sector Overtime 32 University of Ghana http://ugspace.ug.edu.gh keep his birds for 16 weeks to attain the size that the customer appreciated.86 The poultry sub-sector of the livestock industry is ranked fourth in terms of the growth rates, and contributed only 5 percent of the nation's agricultural output. However it also had the highest degree of modification of commercial activities. As at 1993, there were 15 commercial hatcheries in Ghana, producing their own hatching eggs for subsequent day old chick production. Other private hatcheries do exist at the University of Ghana, Kwame Nkrumah University of Science and Technology (KNUST), University of Cape Coast, Pong Tamale Veterinary College, Presbyterian Secondary School, Ghanachix and Mount Pleasant. Their combined estimated total annual capacity is 1.8 million. At present in 2000, there are only two major commercial hatcheries namely Afariwaa and Darko farms.87 The harsh economic conditions have resulted in most of these hatcheries producing on small-scale and resorting to the importation of day-old- chicks and/ or hatching eggs. Unfortunately some are folding up; for instance, Cebas Farms Ltd., which used to be a hatchery, is presently importing and distributing day- old-chicks . 86 Williams, p. 157, opcit. 33 University of Ghana http://ugspace.ug.edu.gh Darko,88 made an assertion that commercial poultry production is based on imported exotic breeds and is dominated by small-scale operators with holding capacities ranging from 100 to about 1000 birds. Birds reared under modern intensive commercial production system are sheltered properly, vaccinated regularly and fed on commercial or home made balanced rations containing maize, fish meal, oilcakes minerals and vitamins. There is little broiler production in the commercial sector. Most birds are reared primarily for egg production with spent layers supplying poultry meat. Mensah,89 made observations of labor input in the industry varying from farm to farm, even on farms of same size and with the same system of management; most small- scale farmers sell live instead of dressed birds because of the low demand of the latter. The commercial system is concentrated around heavily populated urban centers in the Ashanti and Greater Accra 87 Natural Resources Institute (2000). Discussion Paper on Feed Production and Feed Ingredients in Ghana 88 Darko, F. K ^T h e Effect o f Importation of Frozen Chicken on the Demand for Chicken in Ghana/ Unpublished Dissertation, University of Ghana, Legon, Faculty of Agricultural Economy and Farm Management, 1994, p. 11. 89 Mensah, I. Q. 'A Study of Pig and Poultry Production in the Accra: Agricultural District: A Linear Programming Approach.' Unpublished Dissertation, University of Ghana, Faculty of Agriculture, Department of Agricultural Economy and Farm Management 1976. The Structure of the Poultry Industry 34 University of Ghana http://ugspace.ug.edu.gh regions. Small-scale operators dominate commercial production, with holdings ranging from 100 to about 1000 birds of exotic breeds.90 Nature of Demand According to Darko,91 the price elasticity of demand for chicken was 0.532, indicating the inelastic demand for chicken. The positive sign of the own-price elasticity of demand for chicken might be due to the high demand for chicken during festivities. The cross-price elasticity of demand for live chicken with respect to frozen chicken was 5.304, which implied that frozen chicken was a close substitute for live chicken, and that high elasticity value implied that as the relative price of live chicken fell as a result of improvement in the production methods, the demand for live bird would increase to create job opportunities and also to conserve the scarce foreign exchange. Again, cross-price elasticity of live chicken with respect to beef was 2.3 94, which indicates that beef is a substitute for live bird but that of frozen chicken was closely related to live bird. This was in contrast to a 90Basta, p. 20, opcit. 91 Darko, p. 30, opcit. 35 University of Ghana http://ugspace.ug.edu.gh previous finding by Baffoe-Bonnie92 who found that chicken was not a close substitute for beef. Darko,93 therefore argued that beef and chicken are considered substitutes only on festive occasions such Christmas, Easter and Rhamadan. Cross-price elasticity for fish was -1.274 and this negative sign suggested that fish is a complement for chicken meat. The income elasticity of demand for chicken was -0.97, which was however, contrary to a priori expectations, since chicken is not an inferior commodity. The population elasticity was 112.8, which tends to suggest that as population increases the quantity demanded of chicken would increase significantly. Darko's study further revealed that high cost of production of domestic chicken was mainly due to the high cost of feed and drugs, where feed alone constituted 80% of the total cost of production of poultry. The high cost of feed was due mainly to protein carneis. Smith,94 also observed that during the last twenty years from 1970 to 1990 many countries have adopted intensive poultry production as a means of bridging the protein 'gap' and that intensively kept poultry have been seen as a way of rapidly increasing animal protein supplies 92 Baffoe-Bonnie, J. ^Statistical Analysis of the Demand for Beef in Ghana.’ Unpublished Dissertation, University of Ghana, Faculty o f Social Sciences, Department o f Economics, Legon 1976. 93 Darko, p.30, opcit. 36 University of Ghana http://ugspace.ug.edu.gh for a rapidly growing population. The elasticities of labor measured in man days, buildings, equipment, feed and initial stock, all valued in cedis were positive except that of land which was measured in hectares that showed a negative sign which was due to the fact that different management systems could be practised on the same piece of land. Nettey,95 observed in her study in 1993 that direct losses associated with Newcastle, Gumboro and Coccidiosis on a batch of 100 broilers for a period of five years and four batches per year was 2,311.13 cedis. For layers, a batch of 100 layers for a period of five years and three batches within the period of five years was 117, 968 .75 cedis. In addition, the cost of disease control per batch of 100 broilers and 100 layers on the average was 32,529. 58 cedis and 114, 032 .11 cedis, respectively. Finally the benefits of control per batch of 100 broilers and 100 layers was respectively 54, 792 .75 cedis and 269,365.48 cedis. 94 Smith, A. J., The Tropical Agricultural Poultry. Macmillan Publishers, London. 1990. p .l 1. 95 Nettey, M. N. 'The Cost of Poultry Diseases and the Benefits o f their Control: A Case Study o f three Important Diseases in the Greater Accra Region.'.Unpublished Dissertation, University o f Ghana, Faculty o f Agriculture, Department o f Agricultural Economy and Farm Management, 1993. 37 University of Ghana http://ugspace.ug.edu.gh The marketing of poultry products remains largely traditional with a small proportion marketed through restaurants and supermarkets. Marketing of spent layers and broilers is handled by wholesalers who make bulk purchase of live birds from producers and distribute through retailers at the markets. Some farmers process their broilers manually for restaurants and supermarkets. In marketing live broilers in Accra, Batsa,96 found that transportation was 49.44% of the total cost, which was the major cost item. With regards to dressed broilers, processing formed the bulkiest cost item to the producer, which represented 44.44% of the total cost. This could be due to the high cost of labor employed for dressing the birds. The marketing margin for live birds was 28.63 percent which implies that 71.37% of the retail price goes to the producer. Similarly, a large proportion of 90.37% of the price paid by the consumer goes to the producer. These results confirmed earlier study by Shepherd97 that sometimes the farmer got about half of the consumer's price and sometimes a little more than a third. He further stated 96Basta, S. T. ’Broiler Meat Marketing Margins in Accra: A Study of Some Selected Poultry Farms.' Unpublished Dissertation, University of Ghana, Faculty of Agriculture, Department o f Agricultural Economy and Farm Management 1993 97 Sheperd, G. S. Marketing Farm Products, Economic Analysis. Fourth Edition. Iowa State University Press, 1962. p.250. Marketing of Poultry Products 38 University of Ghana http://ugspace.ug.edu.gh that for poultry products over 60 percent of the retail price often goes to the producer in Ghana. Stoces,98 stressed with special reference to Ghana that the inadequacy of marketing facilities could develop a pressure towards a reduction of the volume of production. Furthermore, he said no farmer is interested in producing surpluses if he cannot find a ready market for his produce at a reasonable price. Production was geared toward egg production as the ratio of layers to broilers was found to be high for all farmers engaged in dual-purpose poultry production. Farmers also expressed that egg production was better than broiler production because they got stable income from the former than the latter. Bevan" observed that rising cost of poultry production tended to narrow the profit margin on egg production, and it would appear that producers are obliged to pay little more attention to the returns from by­ products of their egg-production enterprise. Farmers have difficulty in marketing broilers except on festive occasions such as Christmas, Easter and Rhamadan hence they plan their production activities to coincide with these occasions. 39 University of Ghana http://ugspace.ug.edu.gh CHAPTER FOUR METHODOLOGY Introduction This chapter outlines the framework within which the problems raised by the present study are analyzed. The framework involves multivariate regression analysis to examine the production structure of layers in the poultry industry over the study period 1988-1999. Theoretical Concepts and Framework of Analysis of Multivariate Regression Agricultural production can be expressed in the form of a production function which relates the level of agricultural output to the level of factor-resources used in a particular process. The production function is normally used to perform economic analysis of agricultural production. According to Chiang100 and Sankhayan101, the Cobb-Douglas production function is one of the most widely used functions in the economic analysis of the problems relating to empirical estimation in agriculture and industry but unfortunately it imposes serious and perhaps 98 Stoces, F . , ‘Agricultural Production in Ghana’, The Economic Bulletin o f Ghana 10(3). 99 Bevan, J. W. ‘ Poultry Marketing in England’, The Farm Economist 1952, Vol. VII. 100 Chiang, A. C. Fundamental Methods of Mathematical Economics. Third Edition. Me Gxaw-Hall Book Company, 1984 40 University of Ghana http://ugspace.ug.edu.gh unrealistic restrictions on the production process as indicated by Varian102. In a classic paper, Arrow et al.103 called into question the inherent restrictions of the Cobb-Douglas model that all elasticities of factor substitution are equal to one. The elasticity of substitution between each pair of factors must be identically one. That is, a constant unitary elasticity of substitution and this is a great limitation for a Cobb-Douglas technology. There seemed to be no particular reasons for the imposition of such restrictions on a prior grounds hence the development of the duality theory between the production, profit and cost function. Recent development of the duality theory has enhanced the appeal of a cost function approach. The application of duality theory to economic analysis and the concomitant development of numerous flexible functional forms that allow substitution to be unrestricted and not even constant have grown over the years104. In this 101 Sankhayan, P. Introduction to the Economics of Agricultural Production. Printice-Hall o f India Private Ltd., New Delhi, 1988. 102 Varian, H.R. Microeconomic Analysis. W. W. Norton and Company, New York. London, 1984. 103 Arrow, K. J. et al. (1961), ‘Capital-labor substitution and economic efficiency’. Review of Economics and Statistics. 104 Diewert, W. E. (1971), ‘Application of the Shepard duality theorem: A generalized leontief production function’, Journal o f Political Economy 79, 481-507. And Lau, L. J. (1974a), ‘Application of duality: A comment’ in Frontiers o f Quantitative Economics, edited by M. D. Intrilligator and D. A. Kendrick. (Amsterdam, North-Holland). 41 University of Ghana http://ugspace.ug.edu.gh context flexibility as defined by Caves and Christensen105 is the ability to represent production function without placing any a prior restrictions on the full set of price and elasticities of substitution and factor price elasticity of demand at a base point. Basically, the class of flexible functional forms is defined by the property that those forms can provide a second order approximation to an arbitrary twice differentiable function106. This property of flexible forms has enhanced considerably the capabilities for testing structural hypothesis with fewer maintained hypotheses than was heretofore necessary. This expanded potential for hypothesis testing has in turn reinforced the nexus between theoretical and empirical research. Despite the attractive approximation property of flexible forms, most empirical works with these functions have, for econometric convenience, maintained the hypothesis that the flexible forms being used hold exactly rather than as an approximation. 107The recent application of duality theory to problems in economics has resulted in many useful 105 Caves, D. W. and Christensen, L. R. (1980), ‘Global Properties of Flexible Forms’, American Economic Review 70(3), 422-432. 106 Lau, L. J. (1974b), Unpublished memorandum. 107 Jorgensen, D. W. and Lau, L. J. (1975a), ‘The structure of consumer preferences’, Annals o f economic and social measurement 4, 49-102 and (1975b), The integrability of consumer demand functions, discussion paper (Harvard University, Cambridge, MA). 42 University of Ghana http://ugspace.ug.edu.gh results for the study of production and cost relationships108. A fundamental result is that, given certain regularity conditions, there exist cost and production functions, which are dual to each other. The specification of a production function implies a particular cost function and vice-versa. Every cost function implies a set of derived demand equations. Direct estimation of the production function is attractive when the level of output is endogenous. Estimation of the cost function is more attractive, however, if the level of output is exogenous. A cost function corresponds to a homothetic production structure if and only if the cost function can be written as separable in output and factor prices. A homothetic production function structure is further restricted to be homogenous if and only if the elasticity of cost with respect to output is constant. The elasticity of production with respect to the ith input is not a constant but varies with the level of input j that is a linear function of its own level. This function, therefore, overcomes the limitation of constant elasticity of production of the power function. The returns to scale of the translog function which is non- 108 Diewert, W. E. (1974), ‘Application of duality’ in Frontiers of Quantitative Economics, edited by M. D. 43 University of Ghana http://ugspace.ug.edu.gh homogeneous are equal to the sum of the production elasticities and are not invariant with input levels. The Theoretical Model The study assumes that the poultry industry is characterized by a twice-differentiable production function given as Where, Q is output and IS, L, V, F are inputs of institutional credit, labor, vaccines, and feed respectively. If prices are exogenous and the firms minimize costs, then the duality principles of economic theory can be applied to derive a cost function which can reflect the production technology as indicated by Varian109. The dual cost function can be characterized by the form, where, C is the total cost of production, PIS, PL, Pv, and PF are yearly prices of institutional credit from the banks, labor, vaccines and feed respectively, and Q is output. Intrlligator and D. A. Kendrick. Amsterdam: North-Holland. 109 Varian, H.R. Microeconomic Analysis. W. W. Norton and Company, 1984. Q Q(FS, L, V, F) (3.1) C C (P fs,Pl,P v,Pf,Q ) (3.2) 44 University of Ghana http://ugspace.ug.edu.gh The translog cost function is written as a logarithmic Taylor series expansion to the second term of a twice differentiable analytic cost function around variable levels of 1, (i.e., In Q = 0, In Pi = 0, i = 1,............., n) . Rewriting equation (3.2) in natural logarithms: InC = f (InQ , In P ,, InPN) (3.3) By expanding In C in a second-order Taylor series about the point In C(.) = 0 the following is obtained: In C = a 0 + (5 InC/5 InQ )InQ + 1 ( 5 InC/3 In P, )InPi + /2IE( 92In C/d InPj InPJ)InP1InPj + I ( 9 2InC/9 InQ d InP;)InQ InP; (3.4) All the derivatives are evaluated at the expansion point. These derivatives are identified as coefficients and imposing the symmetry of cross-derivatives, the translog cost function becomes inC = aO 'ra(j,nrj T X yQ Q ,ln0j2 + ̂ t'Vnf'] + X l i I j Y ijI»PiI»Pi + I i, QiInQInPi (3.5) where yij = y-ji, C is the total cost of inputs, Q is output, and the Pi's are the prices of the factor inputs. To ensure that the underlying production function corresponds to a 45 University of Ghana http://ugspace.ug.edu.gh well-behaved production function conforming to the theory of production, certain restrictions are placed on the parameters of the cost function. Symmetry requires that yij = Yji and the cost function must be homogeneous of degree one in prices that is linear homogeneity in prices and therefore requires the following restrictions: Z -a‘= 1 > Z Z y,j = Z jYji = ZZ jYv=0 (3 -6) These restrictions imply that a proportional increase in expenditure on all factors must also cause a proportionate change in output, and that a proportionate change in all factor prices will not change the relative quantities of each factor used. Homogeneity of degree one in prices does not impose homogeneity of degree one of the production function in inputs. Also, no constraints are imposed on elasticities of substitution or of factor demand, which makes the function more general than other functional forms in use. Assuming competitive factor markets and cost minimization by firms, Shepard110 lemma is used to easily compute derived demand functions for the factors of production by partially 110 Shepard, R. W ., Cost and Production Functions. (Princeton University Press, Princeton, New Jersey 1953) 46 University of Ghana http://ugspace.ug.edu.gh differentiating the cost function with respect to the factor prices, that is, dC/d?i =X{ (3.7 This result is conveniently expressed in logarithmic form for a translog cost function as Where Si is the cost share of the ith-factor input. By differentiating the logarithm of the cost function with respect to the logarithm of each input price, the factor cost shares or input-demand equations are derived. The translog cost function yields the cost share equation The system of share equations contains all the information required to estimate the substitution and price elasticities of factor demand. Uzawa111 and Allen112 have shown that Allen partial elasticities of substitution between factors i and j can be computed from the cost function by the formula 111 Uzawa, H. (1962), ‘Production functions with constant elasticities of substitution’, Review of Economic Studies 29,291-299. ainC/9InPj=PiXi/C = Si (3.8) ̂=«i +XQlInQ + Z/-yInPj (3.9) 47 University of Ghana http://ugspace.ug.edu.gh o-y = (C)(C.j)y'(Cy.)(Ci) (3.10) where subscripts on C indicate partial differentiation of the cost function with respect to factor prices. For the translog cost function, Berndt and Wood113 and Binswanger114 have shown that, the elasticities of substitution are particularly simple to compute once the substitution parameters and cost shares are estimated. The substitution parameters are related to elasticities of substitution and of factor demand. In terms of the translog cost function, partial elasticities of substitutions become »„=r,+s,(s,-i)/s,! (3.ii) ° ii = r ij +