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Measuring the tangible benefits of environmental improvement : an economic appraisal of regional crop… Spash, Clive Laurence 1987

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MEASURING THE TANGIBLE BENEFITS OF ENVIRONMENTAL IMPROVEMENT: AN ECONOMIC APPRAISAL OF REGIONAL CROP DAMAGES DUE TO OZONE by CLIVE LAURENCE SPASH B.A. Hons. (Econ.), University of Stirling, Scotland, 1984 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES (Department of Resource Management Science) We accept this thesis as conforming to the required standard UNIVERSITY OF BRITISH COLUMBIA June, 1987 © Clive Laurence Spash, 1987 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of Rssourna Managfimfint SrHfinnfl The University of British Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date June. 1987 ABSTRACT The main purpose of this thesis is to empirically calculate the welfare changes which might be expected to result from potato yield reductions caused by ambient ozone loadings in the Lower Mainland of British Columbia. The objectives of the research are: (1) to review the scientific literature pertaining to the effects of ozone loadings on agricultural crops; (2) to review the methodologies employed in previous regional economic assessments of ozone damages; and (3) to apply an economically defensible technique to the analysis of welfare losses due to ozone. Ozone in the Lower Mainland may be pictured as being restricted laterally by the mountain ranges surrounding Vancouver, and vertically by stagnant high pressure systems. Land/sea breezes aid in transporting ozone and its precursors from Vancouver up the Fraser Valley towards important crop growing regions. The highest levels of ozone occur during spring and summer coinciding with the most active season for many crops. Seasonal ambient ozone dose, measured as hours-ppm>0.1Oppm was found to be high in rural areas, especially Abbotsford, during the late 1970's and early 1980's, dropping to low levels in more recent years. Potatoes are one of the economically important crops in the Lower Mainland known to be sensitive to i i ozone. Potato tuber weight reductions are estimated to have reached 16.5 percent in the Abbotsford region in 1981 at seasonal ambient ozone loadings. An aggregate supply/demand model is set up for potato production in B.C. based upon prior estimates of supply and demand e l a s t i c i t i e s . This model assumes the price in the B.C. market is set exogeneously by U.S. imports. Thus, a l l policy relevent welfare changes affect producers' quasi-rent alone. Sensitivity of the model to import price, and the price elasticity of supply is tested. A range of welfare estimates is reported for a variety of ambient ozone loadings. The total damages to potato producers, assuming a l l regions of B.C. are affected by the same seasonal dose as Abbotsford, are calculated to be around one million dollars at ambient ozone loadings in four out of eight years. A peak occurred in 1981 at 2.4-2.9 million dollars total damages. Damages may be overestimated because 20-30 percent of potato production takes place outside the Lower Mainland, Abbotsford often appears to receive higher ambient ozone loadings than other regions, and not a l l potato cultivars grown in the Lower Mainland are as sensitive to ozone as that employed here. However, there are also reasons to be cautious over discounting these estimates as too large. Potato response to ozone is restricted to tuber weight reductions while other important effects may include increased plant stress and damage to crop quality. In addition, missing air quality information for some years and stations, suggests that actual ozone dose could be higher than calculated. TABLE OF CONTENTS ABSTRACT i i TABLE OF CONTENTS iv LIST OF TABLES v i i i LIST OF APPENDIX TABLES ix LIST OF FIGURES x LIST OF APPENDIX FIGURES , xi AKNOWLEDGEMENTS x i i CHAPTER I INTRODUCTION 1 1.1 Background Information 1 1.1.1 Agriculture in the Lower Mainland 1 1.1.2 Crop Selection 4 1 . 2 Objectives 8 1.3 Research Procedure..... 9 1 .3 Outline 11 II SCIENTIFIC ASPECTS OF OZONE DAMAGE TO AGRICULTURAL CROPS 14 2.1 Introduction.. 14 2.2 Sources of Ozone 16 2.2.1 Natural Ozone 16 2.2.2 Anthropogenic Ozone 17 2.3 Ozone Formation and Transportation 19 2.3.1 Ozone Formation 19 2.3.2 Seasonal and Diurnal Cycles of Urban Ozone. 21 2.3.3 Ozone Transportation, Dispersion and Removal 23 2.4 Ozone in the Lower Mainland 28 2.4.1 Atmospheric Conditions 28 2.4.2 Ambient Ozone Concentration and Potato Damage 32 2.5 B i o l o g i c a l Response of A g r i c u l t u r a l Crops 40 2.5.1 Factors Affecting Plant Response to Air Poll u t i o n 40 iv 2.5.2 Methodologies for Deriving Dose-Response Functions 46 2.5.3 The Research Programme of the NCLAN 50 2.5.4 Characteristics of Response Functions Applied in Economic Crop Loss Assessments 52 2.5.5 Economically Important Response Characteristics 55 2.6 Conclusion 57 Footnotes 58 III METHODOLOGIES AND APPLICATIONS IN THE REGIONAL ECONOMIC ASSESSMENT OF OZONE EFFECTS ON AGRICULTURAL CROPS 65 3.1 Introduction 65 3.2 Methodologies for the Valuation of Agricultural Crop Yield Changes: With Reference to Air Pollution 69 3.2.1 The Traditional Model 69 3.2.2 Optimization Models 71 3.2.3 Econometric Models 72 3.3 Microtheoretic Approaches to Modelling Agricultural Production Decisions 75 3.3.1 Duality Models and Environmental Changes... 75 3.3.2 Duality Models Applied to Agricultural Crop Production 76 3.4 A Review of Recent Regional Economic Assessements of Ozone Effects on Agricultural Crops 81 3.4.1 A Traditional Study 81 3.4.2 Quadratic Programming Approaches 86 3.4.3 Econometric Approaches 90 3.4.4 A Duality Study.. 95 3.5 Issues in Economic Models of Ozone Induced Crop Loss 97 3.5.1 Modelling the Impact of Airborne Pollutants on Agricultural Inputs 97 3.5.2 Cross-Crop Substitution 99 3.5.3 The Distribution of Benefits 103 3.6 Conclusion 112 Footnotes 113 v IV BENEFITS FROM OZONE REDUCTION IN THE LOWER MAINLAND.. 119 4 . 1 Introduction 119 4.2 The Economic Model 121 4.2.1 Spatial Equilibrium Theory 121 4.2.2 The Potato Market in B.C 123 4.2.3 Potato Supply and Demand in B.C 126 4.2.4 The Market Equilibrium for Potatoes.. 130 4.3 Economic Assessment of Potato Damage Due to Ozone in the Lower Mainland 131 4.3.1 Net Welfare Areas 131 4.3.2 Approach to Economic Assessment 133 4.3.3 Base Model Welfare Estimation 134 4.3.4 Sensitivity Analysis 137 4.3.5 Summary and Discussion of Results 142 Footnotes 146 V SUMMARY AND CONCLUSIONS 147 BIBLIOGRAPHY 152 APPENDIX I CONSUMER WELFARE THEORY 166 Historical Note 166 Dupuit Surplus 166 Consumer Surplus - 170 Compensating Measures of Consumer Welfare 175 II PRODUCER WELFARE THEORY 186 vi III AN ECONOMETRIC MODEL OF THE AGRICULTURAL SECTOR IN BRITISH COLUMBIA 196 Introduction 196 The Theoretical Model 198 Cost Function 198 Behavioural Assumptions 199 The Econometric Model 201 The Multiple-Output Multiple-Input Translog Cost Function 201 Variable Definitions and Data Description 203 Empirical Results 205 Cost Function for B.C. Agriculture.. 205 Scale Economies 206 Ela s t i c i t i e s of Substitution 210 Marginal Cost 218 Conclusion 219 Footnotes 220 IV COST FUNCTION INPUT AND REVENUE SHARE EQUATION ESTIMATES 223 v i i LIST OF TABLES 1. Percentage of Provincal Cash Receipts from Agriculture in the Districts Closest to Vancouver, in 1981 3 2. Crops Generating Over One Million Dollars Per Annum in the Lower Mainland 5 3. Susceptibility to Ozone of Crops Grown in the Lower Mainland 7 4. Oxidant Precursor Emissions in the Lower Mainland for 1978 1 8 5. Air Quality Monitoring Stations of the Lower Mainland. 34 6. Ambient Ozone Concentrations at Rural Monitoring Stations in the Lower Mainland 38 7. Predicted Percentage Tuber Weight Reduction in the Lower Mainland 39 8. Factors Affecting Plant Sensitivity to Air Pollutants. 42 9. Details of Ozone Exposure in 23 Studies of Effects on Crop Productivity 44 10. Measures of Ozone Occurrence Used in Studies of Effects on Crop Productivity 45 11. Main Source(s) of Response Functions Used in 15 Recent Economic Studies of Ozone Effects on Agriculture.... 53 12. Processes and Characteristics of Crop Plants that may be Affected by Ozone 56 13. Methodologies for the Economic Evaluation of Crop Loss 75 14. Applications of the Profit Function in Agricultural Economics 78 15. Applications of the Cost Function in Agricultural Economics 81 16. Summary of Recent Regional Studies of the Economic Losses Due to Ozone Pollution 83 17. Crops Included in Regional Assessments 84 18. Price E l a s t i c i t i e s of Demand Reported for Potatoes.... 129 19. Potato Producer Loss Due to Ozone: Scenario Analysis.. 142 20. Total Damages to Potatoes Based Upon Ozone Dose at Abbotsford Monitoring Station 149 v i i i LIST OF APPENDIX TABLES A3.1 Parameter Estimates for Translog Cost Function of Agriculture in B.C 207 A3.2 Product-Specific and Ray Economies of Scale for Agriculture in B.C 209 A3.3 Product-Specific and Overall Scale Economies Reported by Ray 210 A3.4 Translog Cost Function Estimates of Partial E l a s t i c i t i e s of Substitution 212 A3.. 5 Sample Mean El a s t i c i t i e s of Substitution in Agricultural Cost Function Studies 213 A3.6 Translog Cost Function Estimates of Own Price E l a s t i c i t i e s for B.C. Agriculture 215 A3.7 Own Price E l a s t i c i t i e s in Agricultural Cost Function Studies 216 A3.8 Expected and Estimated Input Parameters 217 ix LIST OF FIGURES 1. P h o t o l y t i c C y c l e and Ozone Prod u c t i o n 20 2. Seasonal and D i u r n a l C y c l e s of Urban Ozone 22 3. I n v e r s i o n s 26 4. Schematic Diagram of Land/Sea Breeze Over Vancouver... 29 5. Box Model of a Stagnant High Pressure System Over Vancouver 31 6. The A i r Q u a l i t y M o n i t o r i n g Nertwork i n the Lower Mainland 33 7. D i u r n a l Ozone Cyc l e i n Vancouver 35 8. Conceptual Model of F a c t o r s Involved i n A i r P o l l u t i o n E f f e c t s on V e g e t a t i o n 41 9. Repres e n t a t i o n of A g r i c u l t u r a l Crop Producing A c t i v i t i e s 67 1 0 . The T r a d i t i o n a l Model 86 11. Supply S h i f t Due to Ozone Decrease 102 12. Supply I n t e r c e p t Assumptions 107 13. P a r a l l e l Versus R o t a t i o n Supply S h i f t 110 14. S p a t i a l E q u i l i b r i u m 122 15. Consumption of Potatoes i n B.C. 1964-1 984 124 16. Net Potato Imports i n t o B.C. 1964-1984 125 17. Lower Mainland and B.C. Potato Production 1964-1984... 127 1 8 . Consumer and Producer Welfare Areas 132 19. Base Scenario T o t a l Damage Fu n c t i o n f o r Potatoes 136 20. Supply Scenario T o t a l Damage Fu n c t i o n f o r Potatoes.... 139 21. Import Scenario T o t a l Damage Fu n c t i o n f o r Potatoes.... 141 x LIST OF APPENDIX FIGURES A1.1 Dupuit Consumer Surplus 168 A1.2 M a r s h a l l i a n Consumer Surplus 171 A1.3 Compensating and E q u i v a l e n t V a r i a t i o n s 178 A1.4 R e l a t i o n s h i p Between Ordinary and Compensated Demand Curves 179 A1.5 W i l l i g Approximation 184 A2.1 Producer Surplus 190 A2.2 Quasi-Rent 1 90 A2.3 Producer Surplus and N o n - e l a s t i c F a c t o r Supply 192 x i ACKNOWLEDGEMENTS Foremost amongst those who have aided the completion of this thesis are my parents, who have provide moral and financial support throughout. I also feel indebted to A l i s t a i r Dow, Professor of Economics at Sti r l i n g University in Scotland, who gave me early encouragement to pursue my chosen fate. In the actual execution of this study I wish to thank Gordon Brown for discussion and advice on the sci e n t i f i c , especially biotic, aspects of ozone pollution, and helping in the analysis of air quality data. I am indebted to Vinay Kanetkar for advice and help throughout the many runs of the duality model. Finally, I would like to thank Angus Bell for providing the entertainment. The blame for errors, if they dare occur, is to be placed at my door and mine alone. x i i CHAPTER I INTRODUCTION Several types of air pollution result from f o s s i l fuel combustion causing many types of damages. This thesis describes the effects of one such pollutant, ozone, upon agricultural crops. Methodologies and applications in the regional assessment of economic crop loss due to ozone are reviewed. An attempt was made to set up a model of B.C. agriculture to assess the aggregate impacts of ozone in the Lower Mainland. Serious problems were encountered and an alternative approach was chosen; namely, to concentrate upon damages to potatoes. Producer quasi-rents were used to measure the effect of ambient ozone loadings on potato farmers. This study is restricted to only one aspect of the potential damages from ambient ozone loadings and therefore does not reflect the f u l l tangible benefits of control. 1.1 Background Information 1.1.1 Agriculture in the Lower Mainland Approximately one third of the provincial cash income from crops orginates from the Lower Fraser Valley, which produces the majority of the provincial small f r u i t , vegetable, potato and horticultural crops. 1 The high capability arable lands of the 1 Mainland Agricultural Reporting Region are the most suitable lands in the Province in terms of yield potentials and crop diversity. The region has the highest yield estimates for many vegetables, berry, grain and root crops; the only group of crops 2 not suitable for the region is tree fr u i t s . In December 1972 the importance of this area was confirmed when the government set up an Agricultural Land Reserve to prevent highly productive land being removed from agricultural 3 . . . use. Land was selected on the basis of either being taxed as farmland, zoned for agriculture, or rated in the top four land 4 classification classes of the British Columbia Land Inventory. The Agricultural Land Reserve showed that the best agricultural land of Mainland British Columbia was concentrated in the areas closest to Vancouver. In Chapter 2 ozone episodes are shown to occur under anticylonic inversions, which combined with the surrounding mountain ranges restricts the dispersion of air pollutants within an almost closed area of the Lower Fraser Valley i.e., a "box model" is hypothesised. On this basis the areas of prime susceptibility to high ozone concentrations are to the south and east of Vancouver. Three agricultural d i s t r i c t s surround Vancouver, namely Abbotsford, Chilliwack and Cloverdale. A large area of Cloverdale d i s t r i c t which extends beyond the North Shore 5 mountains can therefore be assumed to be unaffected. However, only a relatively small amount of agricultural crop production takes place outside the Greater Vancouver region of the Cloverdale d i s t r i c t , e.g., the GVRD accounts for 99 percent of 2 the area under berry cultivation and 93 percent of potato product ion.^ In 1981 the three districts received cash receipts of approximately 30 million dollars from the production of each of the following: (1) small fruits (mainly berrys), (2) f i e l d vegetables, and (3) floriculture/nursery products. Field crops were relatively unimportant contributing only 0.6 million dollars., Table 1 shows the relative contribution of the three agricultural d i s t r i c t s to total provincal cash receipts from each of these production ac t i v i t i e s . The three regions are responsible for 74, 79 and 67 percent of provincal cash receipts from small fruit s , f i e l d vegetables and floriculture/nursery, respectively. Table 1. Percentage of Provincal Cash Receipts from Agriculture in the Districts Closest to Vancouver, in 1981 Products Cloverdale Abbotsford Chilliwack Small Fruits 25.59 44.45 1 7 7 4 Field Vegetables 30.86 23.43 24.82 Floriculture/Nursery 14.67 31.56 20.75 Source: B.C., Ministry of Agriculture, Agricultural Profile  Cloverdale, Abbotsford and Chilliwack (1984) p25 Table 20. Floriculture/nursery may be impacted by ozone, but was not analyzed because: (a) the plants are largely grown indoors (in greenhouses) and therefore ambient ozone levels may not reflect the actual dose, (b) variations in the greenhouse environment could be important in determining the response of plants, and (c) an i n t i a l literature survey showed no dose-response functions available for such crops. 3 1.1.2 Crop Selection The c r i t e r i a for crop selection were the economic importance of the crop and the sensitivity of the crop to ozone. (a) Economic Significance Numerous varieties of vegetable and berry crops are grown in the Lower Mainland with production ranging from potatoes to Chinese vegetables. Intial selection was restricted to those crops which generated an average annual revenue over one million dollars during the ten-year period from 1975-1984, in constant 1981 dollars. Table 2 shows the fifteen crops which qualified, together with the annual cash receipts from each for the ten-year period. These fifteen crops account for approximately 83 percent of Lower Mainland and 70 percent of provincal farmgate revenue from vegetable and berry crops. The revenue from these crops has averaged approximately 72 million dollars, with a peak in 1982 of 95 million (1981 dollars). Mushrooms have become increasingly important relative to other crops as production and revenue quadrupled in the ten year period. Potatoes have for a long time been an important contributor to farm revenue, but in the last five years revenue declined some four million dollars. Besides these two vegetables the most important source of revenue in the Lower Mainland has been small fruit production, mainly raspberries, strawberries, cranberries and blueberries. Production of a l l four berry crops has increased. In particular, raspberry production has doubled since 1975, and revenue from this crop in recent years has only been exceeded by mushrooms. These two vegetable and four berry 4 Table 2. Crops Generating over One Ml 11 ion (thousands of i Dol1ars dol1ars per Annum in 1981=100) the Lower Ma 1nland CROP 1975 1976 1977 1978 . YEAR 1979 1980 1981 1982 1983 1984 ANNUAL AVERAGE mushroom 7269 8880 10957 12146 12755 14918 22380 18910 26478 29021 16371 raspberry 4996 6340 1 1518 16716 16499 7758 12380 19308 12302 15661 12348 potato 10407 10899 9457 8624 1 1478 12279 7701 9462 8751 7965 9702 strawberry 5014 4525 5584 6074 6352 8161 7274 8736 8841 5358 6592 cranberry 2504 3354 4580 4531 4693 4793 8115 7704 9815 6529 5662 blueberry 2555 4384 7921 7150 5254 5204 3791 9227 6552 4082 5612 pea 3522 2361 3635 2471 2595 2176 2103 3698 2734 3701 2900 1ettuce 1574 2701 1629 2260 2810 1850 2001 2045 2528 2630 2203 sweet corn 2024 1867 1425 1887 2270 1570 1342 3586 1966 1947 2000 brusse1s 1672 1 101 1466 1961 1622 •1995- 1216 2745 1551 894 1622 br o c c o l i 801 652 1245 1449 1668 1850 2221 2681 1590 1926 1608 caul 1 flower 795 680 735 1484 2010 2064 1329 3031 1485 1723 1534 cabbage 1337 1 195 969 1384 1477 1732 1 176 1374 2283 1767 1469 onion 1757 818 1361 1566 1529 1455 1084 1388 1395 733 1309 green bean 1223 593 1081 1237 1227 900 1029 1 106 859 1334 1059 TOTAL 47450 50350 63563 70941 74240 68708 75141 95001 89132 85270 71980 TRLM 57200 58552 74197 83609 87427 81093 87122 107040 97754 92840 82683 TRBC 79099 75300 91921 105733 106926 102773 107735 128585 125040 1 12834 103595 TRLM Is the total revenue for a l l vegetable and berry crops grown 1n the Lower Mainland. TRBC Is the total revenue for a l l vegetable and berry crops grown in B r i t i s h Columbia. Source: Ministry of Agriculture and Food. Production of Berry Crops, Grapes and F i l b e r t s Together with an Estimate of Farm Value ( V i c t o r i a : Ministry of Agriculture, various annual issues); Ministry of Agri c u l t u r e and Food. Production of Vegetable Crops Together with an Estimate of Farm Value ( V i c t o r i a Ministry of Agriculture, various annual issues). crops have consistently been the largest revenue earners in the Lower Mainland since 1975. Peas have maintained a relative position above the remaining crops, followed by lettuce and corn. The other six crops have rarely contributed more than two million dollars each in any one year. In Table 2 the crops are ranked in order of the average annual cash receipts from each between 1975-1984. While this picture of relative importance may alter considerably from year to year, a definite division exists between the revenue contribution of the f i r s t six crops and that of the other nine. A weaker division can be drawn between peas, lettuce and corn and the remaining six crops. (b) Crop Sensitivity to Ozone The literature on plant response to ozone was reviewed in order to discover the relative susceptibility of each of the fifteen crops in Table 2. No information could be found on the response of blueberries, cranberries, raspberries, mushrooms or brussel sprouts. The remaining ten crops may be characterised as either susceptible, intermediate or tolerant to ozone, as shown in Table 3. This categorization is helpful in as far as showing the general results of previous research. However, the rankings may be misleading due to the wide variety of responses possible across cultivars. While the evidence is that strawberries are almost certainly tolerant, with seven cultivars commonly grown in California 7 found to be tolerant, a general ranking is not always easy with different cultivars showing different susceptibilities to ozone. 6 Table 3. Susceptibility to Ozone of Crops in the Lower Mainland Suscept i b i l i ty to Ozone Crop Source Sensitive Potatoes 1,2, Lettuce 1, 2, Sweet Corn 2, 3 Onions 1, 3 Green Beans 2, 6 Intermediate Peas 3 Cabbages 3 Tolerant Strawberries 1, 3 Broccoli 4 Cauli flower 4 Unknown Blueberries Cranberries Raspberries Mushrooms Brussel Sprouts Key:1. California Department of Food and Agriculture (1986) 2. Stern et a l . (1973) 3. Bialobok (1984) 4. Adams et a l . (1982) 5. Heck, Taylor, et a l . (1982) 6. Heggestad and Bennett (1984) 7 Indeed a crop may be ranked differently by different sources. For example lettuce is shown as sensitive in Table 3 based upon the 8 9 response of head lettuce and leaf lettuce, but lettuce has also been stated to be resistant. 1^ The rankings as shown in Table 3 give a higher ranking where a discrepancy was found so as to emphasise the possibility of damage. For example, green beans are categorised as sensitive but, in a four-year study at Beltsville, Maryland investigations showed two of four cultivars were tolerant. 1 1 Obviously, the actual cultivars grown in a region and their relative importance need to be assessed to fully account for crop susceptibility. On the basis of the above analysis, potatoes were chosen as the crop to be analysed. In the Lower Mainland the six common potato cultivars are Gem Russet, Warba, Norland, Norgold Russet, 1 2 Keenebec and Norchip. These have been given ozone susceptibility rankings by U.S. studies as follows: Norland and Norchip sensitive, Keenebec intermediate, Norgold Russet and Gem 1 3 Russet tolerant, and Warba unknown. 1 . 2 Objectives The main objective of this thesis is to calculate the welfare changes which might be expected to result from potato yield increases caused by the reduction of ambient ozone loadings in the Lower Mainland of British Columbia. The main sub-objectives are: 1 . Review of the scientific literature pertaining to the effects of ambient ozone loadings on agricultural crops. 2 . Review of the economic literature on the methodologies 8 employed when regional air pollution assessments are to be made. 3. The estimation of a cost function for B.C. for the assessment of changes in economic welfare due to aggregate crop damage from ambient ozone loadings. 4. Calculation of potato producer welfare losses at ambient ozone loadings in the Lower Mainland. 5. The use of scenario analysis to evaluate the sensitivity of consumer and producer welfare to changes in important model parameters. 6. To draw policy conclusions, and identify areas for future research and possible improvements in regional economic crop damage estimates. 1.3 Research Procedure Two major tasks were undertaken in this thesis. F i r s t l y , the calculation of potential physical damage to regionally important crops due to ambient ozone loadings in the Lower Mainland of B.C. Secondly, to employ the findings of the f i r s t area of research to perform an economic estimation of ozone induced crop damage. More emphasis was placed upon the second area in order to achieve subobjectives 2 to 5. This envolved surveying the literature on ozone formation and transportation in recent journal articles and books. Reports by government agencies in Canada and the United States of relevence to ambient ozone loadings, and related issues were sought. Reports specific to the Vancouver region were of particular interest. The surveys of work carried out by the National Crop 9 Loss Assessment Network of the United States were collected. Dose-response information and relationships were obtained from the California Department of Agriculture and Food. The engineering division of the Greater Vancouver Regional District was contacted for information on ambient ozone loadings and the operations of their air quality monitoring network. The second sub-objective also involved a literature survey. This survey f e l l into two parts; namely reviewing economic methodologies for crop loss assessment, and studying applications of such methodologies in relation to ozone pollution. Environmental and agricultural economics, and pollution related journals were searched for articles attempting or discussing economic crop loss assessment. The bibliographies of a l l such reports were checked for further references. This literature was used to identify a methodology which could be employed in the assessment of crop loss due to ozone in the Lower Mainland, and to identify issues important to conducting such an assessment. This identified the dual approach as a theoretically well founded method of modelling agricultural production which had been applied to regional ozone crop loss assessment. A multiple-output, multiple-input cost function model of the B.C. agricultural sector was developed using the translog functional form. Data on the B.C. agricultural sector were collected from Statistics Canada. Econometric estimation of the model was achieved using the Statistical Analysis System (SAS) available on the main U.B.C. computing network. In particular, the SAS's systems regression procedure was used with three-stage least 10 squares. This method was required because the cost function, input share and revenue share equations were estimated together. This approach increases the efficiency of parameter estimation compared to estimation of the cost function alone. Due to the limited time-series information available, increased efficiency in the estimation procedure was important. Failure to achieve sub-objective 3 required the selection of another methodology by which to perform an economic assessment of ozone damages to crops. A crop-specific analysis of damages was performed. Information on specific crops produced in B.C. and the Lower Mainland had already been obtained from provincal government publications and the B.C. Department of Agriculture and Food. Studies related to potato production and consumption were sought. On the basis of a previous econometric study of the B.C. potato industry, supply and demand functions were calculated. A model was set up to include the percentage reduction in yield predicted by a dose-response function, and using SAS a total damage function was derived and marginal damages calculated. The results were then compared to total and marginal damages calculated under various scenarios. 1.3 Outline Chapter Two describes the sources of ozone, its formation and transportation. Ambient ozone loadings in the Lower Mainland and their potential physical damage to potato production are outlined. The second part of the chapter reviews the factors affecting the response of plants to air pollution and the methodologies for deriving dose-response functions. The chapter 11 finishes with a look at certain requirements of response function proposed for use in ecomomic assessments. Chapter Three opens by describing the methodologies available for the valuation of agricultural crop yield changes induced by air pollution. This is followed by a review of recent applied work in the regional economic assessment of the effects of ozone upon agricultural crops. The chapter concludes with an analysis of specific issues relevent to the economic assessment of air pollution which were raised by the literature review. Chapter Four concerns the attempt at estimating a multiple-output, multiple-input translog cost function model of B.C. agriculture. The data are described and the parameter estimates presented. The results for ray and product-specific economies of scale are given, along with the estimates of input substitution. The problems encountered with regard to parameter estimates are summarised. Chapter Five develops an alternative to the aggregate analysis attempted in Chapter Four. A model of the potato market in British Columbia is presented. Supply and demand functions are specified and the spatial equilibrium of the market described. Several scenarios are then employed to analyse the effects of changes in ambient ozone concentrations on potato production in the Lower Mainland. The sensitivity of the model to changes in import prices, and supply and demand e l a s t i c i t i e s , is analysed. Finally, the results are discussed in Chapter Six. 12 Footnotes 1 British Columbia, Legislative Assembly, Select Standing Committee on Agriculture. Land Productivity in British  Columbia (1978) p.91. 2 Ibid, p.93. 3 See, Canada, Environment Canada, Lands Directoriate, Edward W. Manning and Sandra S. Eddy. The Agricultural Land Reserve  of British Columbia; An Impact Analysis Land Use in Canada Series No. 13 (1978). 4 Land in the f i r s t three classes is defined as capable of sustained production of common cultivated crops, and those in the fourth are marginal for sustainable agriculture. In order for land to be rated in the top classes i t must meet certain climatic and so i l quality c r i t e r i a . See, B.C., Legislative Assembly, SSCA. Land Productivity in B.C.. 5 This concers with work done in California where mountain ranges have been assumed to provide protection for crop areas. See, S. K. Leung, W. Reed and S. Geng "Estimation of Ozone Damage to Selected Crops Grown in Southern California" Journal of Air Pollution Control Association Vol.32 No.2 (February, 1982) p.160-164. 6 Canada, Statistics Canada. Census of Agriculture, British  Columbia (1981). 7 California, Department of Food and Agriculture. Air Pollution  Manual (1986). 8 W.W. Heck et a l . , "Assessment of Crop Loss from Ozone" Journal of Pollution Control Association 32:4 (April, 1982) p. 353. 9 California, Department of Food and Agriculture. Air Pollution  Manual. 10 S. Bialobok, "Controlling Atmospheric Pollution" in M. Treshow (ed.) Air Pollution and Plant Life (Chichester: John Wiley and Sons, 1984). 11 H.E. Heggestad and J.H. Bennett, "Impact of Atmospheric Pollution on Agriculture" in M. Treshow (ed.) Air Pollution  and Plant Life (Chichester: John Wiley and Sons") 1984). 12 British Columbia, Ministry of Agriculture an-d Food. Vegetable  Marketing Guide (1982). 13 H.E. Heggestad and J.H. Bennett, "Impact of Atmospheric Pollution on Agriculture"; and California, Department of Food and Agriculture. Air Pollution Manual. 13 CHAPTER II SCIENTIFIC ASPECTS OF OZONE DAMAGE TO AGRICULTURAL CROPS 2.1 Introduction Photochemical oxidants is the term used to describe ozone and other compounds consisting of oxidised organics such as ketones, aldehydes, peroxyacetyl nitrates (PAN) and peroxy compounds.1 They are capable of causing plant damage, affecting human health, disrupting ecosystem structure and stability, and reacting with a number of nonbiological materials (e.g., rubber), as well as forming a visibility-reducing blue haze. Oxidant air pollution mixtures consist of three phytotoxic (i.e. toxic to plants) compounds: ozone, oxides of nitrogen, and PAN. The PAN are the most phytotoxic, but occur in relatively small 2 concentrations. Nitrogen oxides are of concern for three reasons, namely: (a) phytotoxicity, (b) as precursors to ozone, and (c) as precursors to acid precipitation. Ozone is the most prevalent photochemical oxidant, has been 3 studied most extensively, and is used as the basis for photochemical oxidant air quality standards in both the United States and Canada. Injury to plants from photochemical smog was f i r s t noted in the mid-1940's, when stippling and glazing or 14 bronzing of the leaves of vegetables were discovered in the Los Angeles basin, California. 4 Tropospheric (the lowest 10-15 kilometers of the atmosphere) ozone concentrations alone or in combination with sulphur dioxide and nitrogen dioxide have since been identified as the major source of crop losses caused by air pollution in the United States.^ ^ In this chapter the pathway of tropospheric ozone through the environment, from sources to receptors, is described and characterized. The f i r s t two sections discuss the factors which determine the amount of ozone at a site; namely the nature of 7 relevant emissions and the state of the atmosphere. The final section covers some of the main issues concerning the biological response of agricultural crops to ozone. The effect of various ozone concentrations has been summarised in biological dose-response functions for certain crops and most economic D assessments of crop losses are dependent upon this information. An understanding of the limitations of the dose-response information base is therefore important. 15 2.2 Sources of Ozone Ozone in the lower atmosphere has two sources, namely anthropogenic and natural. Ozone is not released directly into the atmosphere but is formed from precursor emissions. The most important precursor emissions for natural and man-made tropospheric oxidant formation have been identified as 9 hydrocarbons and oxides of nitrogen. A l l hydrocarbons present in the atmosphere are not significant oxidant precursors, but only non-methane hydrocarbons.1*^ Of the eight oxides of nitrogen found in the atmosphere, the main contributors to oxidant formation are nitrogen dioxide and nitri c oxide. 1 1 2.2.1 Natural Ozone The concentration of natural ozone in the troposphere is the result of stratospheric (upper atmospheric layer begining approximately six miles above earth's surface) transfers and photochemical reactions involving naturally occurring precursors. The major source of atmospheric hydrocarbons is the natural . . . 12 decomposition of organic material. Sources of natural oxides of nitrogen include decomposition in the so i l and oceans, 1 3 stratospheric photochemistry, and lightning. The photochemical production of ozone from natural hydrocarbons and nitrogen oxides has been estimated to make only a minor contribution to natural ozone levels in the troposphere, which can thus be largely 1 4 attributed to stratospheric transfer. The meteorological and climatological conditions for this transfer will therefore determine the levels of naturally occurring ozone. Background ozone concentrations in the troposphere are 16 1 5 generally about 0.02 or 0.03 ppm (parts per million). Monitoring has shown natural ozone to have a seasonal pattern, being at its highest in spring, then winter. 1^ Also natural ozone concentrations increase with latitude in the northern 1 7 hemisphere. In southern Canada, springtime high background ozone levels are estimated at 0.04 to 0.05 ppm, decreasing to a 1 8 low of 0.02 ppm in late summer and f a l l . Despite these latitudinal and seasonal variations, a constant natural ozone level of 0.025 ppm has been assumed in experiments to determine 1 9 the response of plants to ozone in the United States. 2.2.2 Anthropogenic Ozone Anthropogenic precursor emissions are dominant in and around urban centres where the most severe oxidant problems occur, e.g., 20 in Canada, Vancouver, Quebec City, Montreal and Toronto. Anthropogenic production of hydrocarbons is small compared to natural releases, but the compounds are highly reactive and 21 important in the formation of ozone. Hydrocarbons are produced during f o s s i l fuel combustion and the evaporation of gasoline, and hydrocarbon emissions are closely related to t r a f f i c density. The principal anthropogenic sources of oxides of nitrogen are vehicles, coal and natural gas burning, and f e r t i l i z e r and 22 explosives factories. The transportation sector has been identified as the primary source of anthropogenic ozone precursor emissions in the United 23 States. Since the transportation sector is a population-dependent activity, most areas with a high population density are areas with high hydrocarbon and oxides of nitrogen emission 17 rates. Precursor emissions due to residential heating, fuel wood combustion and solid waste incineration are also population 25 dependent, which explains the urban nature of severe oxidant problems. A breakdown of anthropogenic hydrocarbon and oxides of nitrogen emissions for the Lower Mainland is given in Table 4. The total oxides of nitrogen emitted in the Lower Mainland in 1978 was 68,800 tonnes while the total for British Columbia was 2 6 176,500 tonnes. Total emissions of hydrocarbons (i.e., including non-methane hydrocarbons) in the Lower Mainland were estimated to be 95,700 tonnes in 1978. Gasoline'powered vehicles are the predominant source of ozone precursor emissions, contributing 49 percent to total hydrocarbons and 44 percent to total oxides of nitrogen in the Lower Mainland. Table 4. Oxidant Precursor Emissions in the Lower Mainland for 1978 (Tonnes) Precursor Source Hydrocarbons Nitrogen Oxides (95,700 tonnes) (68,800 tonnes) % of Total % of Total Gasoline Powered Vehicles: Light-Duty Vehicles 37. .6 34. ,0 Heavy-Duty Trucks 6. .2 5. ,0 Medium-Duty Trucks 4, .7 6. .3 Stationary Fuel Combustion 0, .5 16. ,7 Off-Highway Mobile Sources 2. .0 9. .5 Petroleum Refining 12. .3 3. ,3 Gasoline Marketing 13. .8 Diesel Powered Engines 1 , .9 22. . 1 Applications of Surface Coatings 7. .6 Other 13. .4 3. . 1 Source: R.G. Wilson, J.B. Mills, and E.P. Wituschek, A Report on  the Assessment of Photochemical Oxidants in the Lower Mainland (Victoria, B.C: Ministry of Environment, 1984), Table 2 p.14. 18 2.3 Ozone Formation and Transportation 2.3.1 Ozone Formation The formation of photochemical smog in the troposphere is a complex process involving the reactions of hundreds of primary precursors in the presence of ultraviolet sunlight to generate 27 ozone. Figure 1 shows the basic processes involved. Oxygen atoms (0) are derived principally from the dissociation of 2 8 nitrogen dioxide (N02) by solar radiation. N02 + Ultra-Violet Sunlight > NO + 0 This atomic oxygen reacts rapidly with molecular oxygen (0 2) to form ozone (0^). o + o 2 — - > o 3 Ozone in turn reacts with nitrogen oxide (NO) to form nitrogen dioxide again. NO + 0 3 > N02 + 0 2 These three equations make up the naturally occurring nitrogen dioxide photolytic cycle. In the absence of reactive hydrocarbons there is no significant ozone production, because ozone and nitrogen oxide are formed and destroyed constantly with no net production. Reactive hydrocarbons released by vehicle exhausts unbalance the cycle by converting nitrogen oxide to nitrogen 29 dioxide without consuming an equivalent amount of ozone. A complex series of chemical reactions follow which create a wide range of secondary pollutants of which ozone is quantitatively 30 the most important. Photochemical smogs are characterised by a 31 distinctive odour, and a yellow-brown haze (due to N0 9). 19 Figure 1 Photolytic Cycle and Ozone Production Ultra-Violet Light Source: Adapted from A.C. Stern et al. Fundamentals of Air Pollution (1984) Figure 11-4 p.169 2.3.2 Seasonal and Diurnal Cycles of Urban Ozone The necessity for high intensity short-wave radiation to initiate the phytolytic cycle gives variations in photochemical smogs distinct diurnal and annual cycles. Figure 2(a) shows the annual patterns of ozone concentrations in Los Angeles and Denver, using a monthly average of the mean daily maximum one hour average concentration. Sunlight is a limiting factor in Denver creating a mid-summer peak, while in Los Angeles the peak is in late summer and autumn when cloud cover is least and winds 32 are weak. The seasonal peak for ozone will vary depending upon local conditions, but outside the tropics the occurrence of photochemical smogs tends to be restricted to summer. Three factors create the diurnal ozone cycle: (a) the temporal variation of precursor emissions, (b) atmospheric 33 dispersion capacity, and (c) the intensity of solar radiation. The diurnal cycle for ozone is characterized in Figure 2(b), which shows one days variation of nitrogen oxide and dioxide, and ozone for Los Angeles. Peak precursor emissions occur in the early morning, with rush hour t r a f f i c , when dispersion and solar intensity are weak. Exhaust products such as nitrogen oxide and hydrocarbons rapidly accumulate, leading to the production of nitrogen dioxide. Increasing solar radiation intensity and nitrogen dioxide levels cause a rapid increase in ozone, which reaches a peak at midday. Meanwhile, precursor emissions drop, atmospheric instability increases aiding dilution, and other reactions alter the nature of essential smog chemicals. In the afternoon, ozone concentrations decrease with radiation 21 Figure 2 Seasonal and Diurnal Cycles of Urban Ozone (a) Annual Ozone Variations in Denver and Los Angeles - i — i — i — r 0.20 M 0.16 Z o r -< r -Z U J o z o u 0.12 0.08 0.04 Los Angeles 1964-65 J I I I I I I I I TIME (mth) (b) Classic Diurnal Ozone Cycle in Los Angeles 0.16 E OL Q . I -< I* r -z Ul U z o o 0.12 h 0.08 0.04 h i—i—r j i 00 04 J I I I L 24 TIME (h) Source: T.R. Oke, Boundary Layer Climates (1978) Figure 9.14 p.296 22 intensity, dilution continues and ozone is removed by reaction with atmospheric constituents (nitrogen oxides and hydrocarbons) 34 and surface receptors such as plants. This general pattern may be modified as a parcel of air moves across a region accumulating more pollutants. For example, in the Los Angeles Basin oxidant pollution is highest in downwind communities, and in the late afternoon. Diurnal peaks occur at midday in West Los Angeles, 1300 hours in downtown, and 1400 hours in Azusa where ozone concentrations are higher than the 35 upwind locations despite lower local precursor emissions. The multiple input of pollutants in this manner (i.e., due to the random alignment of sources) is called cumulative loading. The cumulative loading of reactive chemicals can cause downwind (e.g., rural) areas to receive high ozone, or other secondary pollutant, concentrations not apparent at upwind (e.g., urban) 3 6 monitoring stations. 2.3.3 Ozone Transportation, Dispersion and Removal (a) The Role of Wind Wind diffuses (dilutes) pollution in the along-wind direction, and by turbulent diffusion in the across-wind and 37 vertical directions. Turbulent diffusion is the dilution of material in the atmosphere as a result of random or irregular fluctuations in the wind. Wind fluctuations may cover an arc of 30-40 degrees centered upon the mean wind direction. The mean direction determines the path followed by pollutants. Wind speed is responsible for forward stretching and the distance pollutants are transported. Weak winds curtail both horizontal transport and 23 turbulent diffusion, and allow local circulation systems to develop. Local circulation systems are not good pollution diffusers because of low wind speeds, closed circulation and diurnal reversal in the direction of flow. (b) Dispersion and Inversion Dispersion of pollutants is achieved when turbulence causes them to mix with clean a i r. Turbulence is the result of mechanical overturning of near-surface layers by frictional contact with rough surfaces, and thermal instability produced by vertical temperature structure. Mechanical instability is relatively unimportant above 100 meters or with weak air flow. Thus, the vertical temperature structure is of prime concern when 39 considering regional air quality. The stability of a parcel of air is determined by the variation of temperature with height. In general, i f the parcel of air has a higher temperature than the air above, i t will be able to rise and is "unstable". A "stable" parcel of air has a lower temperature than the air above and may sink. Days with good surface heating are characteristic of instability (the depth affected by this heating is called the "mixing layer") which enhances dispersion. 4^ Inversions are particularly important to dispersion and exist when warm air overlies cooler a i r . 4 1 Inversions may be due to (a) cooling from below, such as on nights with l i t t l e or no cloud cover when the ground cools; (b) warming from above, most importantly due to subsidence inversion; or (c) advection of warmer or cooler a i r , due to weather fronts or sea breeze. 24 Advection due to weather fronts occurs when cold air is wedged under warm air by a cold front or warm air over-rides colder air in a warm front, as shown in Figure 3(a). Frontal inversions are normally short-lived and not important to air pollution. However, exceptions may occur with slow moving warm fronts, and when pockets of cold air are trapped in valley bottoms by warm air behind a front. Advection may also occur due to the sea breeze (see below), when land cools at night and warmer air flows inland 42 from the sea. Large scale subsidence in an anticyclone is of particular concern for the concentration of ozone because i t combines an inversion with clear skies which allow high levels of solar radiation at ground level. As an anticyclone (high pressure area) moves into an area of low pressure the air flow is "divergent", as shown in Figure 3(b). The diverging air is replaced by air from above as i t subsides. The subsiding air is warmed as i t becomes compressed owing to increasing pressure, as the mass of air above the air parcel increases. This warming may cause the air some distance above the surface to be warmer than near-surface air, not participating in the subsidence, creating a temperature inversion. 4"^ In general, the most unfavourable dispersion conditions occur with weak air flow and a shallow mixing layer, conditions characteristic of anticyclonic weather. As air becomes stagnant pollutant concentrations may increase with time. Thermal breezes circulate the air around inside an almost closed box. Additional topographical confinement of the source area can restrict lateral 25 Figure 3 Inversions (a) Frontal Inversions Cold Front Warm Front (b) Subsidence Inversion WARM > Top f / Base COLD Divergence Surface Source: After T.R. Oke, Boundary Layer Climates (1978) Figure 9.3 (a) and (b); Figure 9.2 (a) p.275. 26 44 spreading, and further enhance pollutant concentration, (c) Removal Over one or several hours, chemical reactions involving precursors can generate significant amounts of ozone which, if not quickly destroyed, can be transported over great distances before removal from the atmosphere. Long range transportation of ozone and i t s precursors can cause high ozone concentrations to occur in rural areas hundreds of kilometres from precursor 45 sources. Ozone may persist overnight in rural areas where there are fewer reactive compounds (such as NO), or in parts of the 46 atmosphere where there are few removal mechanisms. Primary processes removing pollutants from the atmosphere are chemical transformation, gravitational settling (dry deposition), adsorption (impaction) and precipitation scavenging. 4 7 Precipitation scavenging is not considered a major sink for ozone because ozone is relatively insoluable in water, and forms under 48 warm, dry, stagnant conditions. However, nitrogen dioxide may be removed by this process, affecting the potential for smog production. Adsorption by so i l and vegetation surfaces represents a major sink for pollutants introduced into terrestrial 49 ecosystems, and especially for ozone. Pollutant transfer from the atmosphere to a sink is expressed as a flux (pollutant uptake) rate, and is defined as the weight of pollutant removed by a given surface area per unit of time. Factors determining flux rates include atmospheric conditions (wind, turbulence, temperature, and humidity), pollutant nature and concentration, 50 sink surface geometry and moisture, and other parameters. 27 2.4 Ozone in the Lower Mainland 2.4.1 Atmospheric Conditions Vancouver experiences its worst air quality in summer under anticyclonic conditions. Local features which contribute to the formation and accumulation of ozone in the Lower Mainland are 51 similar to those found in the Los Angeles Basin . They are: 1. Anticyclonic conditions found in summer, providing high solar radiation, and a lack of precipitation. 2. Subsidence inversion associated with anticyclonic conditions, preventing vertical mixing. 3. Surrounding mountains restricting inland escape of pollutants. 4. Land/sea breezes, which develop in light winds, and are associated with anticyclonic conditions. Land/sea breeze circulations are essentially closed and completely reverse their flow from day to night, thus minimizing the net transportation out of a region. This system may be augmented by others (e.g. mountain/valley winds). Figure 4 characterizes the circulation of the land sea breeze in Vancouver. At night the breeze can take pollutants off-shore. The vertical exchange rate over the Pacific is very weak, so that ozone and its precursors are not rapidly destroyed or absorbed by 52 the sea surface. These pollutants can then be returned to the city the next day as the circulation reverses. 53 Hay and Oke have characterised the occurrence of a summer stagnant high pressure system over Vancouver in terms of a "box" model. The Fraser Valley is enclosed by mountain walls on either side and a l i d , provided by a subsidence inversion, below the top of the valley sides. When the airflow system is of the 28 Figure 4 Schematic Diagram of Land/Sea Breeze Over Vancouver Source: J.E. Hay and T.R. Oke, The Climate of Vancouver Figure 17 (a) p.37. 29 closed circulation type the ends of the box may be considered closed, as shown for Vancouver in Figure 5. The box is restricted to a small volume. At night in Vancouver the base of the inversion layer is about 100 meters above the surface, due to heat from the city and the warm waters of the Burrard Inlet. In the rural areas of the valley the base is essentially zero. On a good heating day the mixing layer may reach 300 to 500 meters, but this is s t i l l below the height of the valley walls (i.e., approximately one kilometer).^ 4 When pollutant removal is weak, the continual emissions from the floor of the box w i l l cause the concentration of pollutants to build up. Such periods of anticyclonic weather often last two to four 55 weeks in the late summer and f a l l . The Lower Mainland area is susceptible to transboundary pollutants due to its proximity to the United States. Determining the transboundary nature of oxidant problems in Vancouver was the prime objective of a study carried out for the Environmental Protection Service by Concorde Scientific Corporation.^ The study concluded that there was no indication that the long range transport of ozone or its precursors is a factor that contributes to ozone episodes in Greater Vancouver or the Lower Fraser Valley. In summary, ozone and its precursors travel up the Fraser Valley from the Burrard Inlet, towards major agricultural crop growing areas. During the day, sea breezes transport precursor emissions from the high density commercial and t r a f f i c areas of Vancouver eastwards. These winds, combined with the restricted 30 Figure 5 Box Model of a Stagnant High Pressure System Over Vancouver Source: J.E. Hay and T.R. Oke, The Climate of Vancouver (1973) Figure 19 p.45. atmospheric dispersion within the topographic setting of the Burrard Inlet, create conditions virtually ideal for the concentration of air pollution at areas east towards the Fraser 57 Valley. ' 2.4.2 Ambient Ozone Concentration and Potato Damage Several air quality monitoring stations have been operating in the Lower Mainland, providing ambient ozone concentration and meteorological data since 1977. The location of the stations is shown in Figure 6 and their GVRD codes and descriptions are given in Table 5. Rural sites now exist at Surrey East, Pitt Meadows, Chilliwack and Abbotsford, and a new station was set up in 1986 at Richmond South. A l l other stations are in urban areas of the GVRD (Greater Vancouver Regional D i s t r i c t ) . The National Air Quality Objectives for ozone define Maximum Desirable, Maximum Acceptable and Maximum Tolerable one hour 59 concentrations of 0.051, 0.082 and 0.153 ppm respectively. The acceptable level is defined as providing "adequate protection" against adverse effects on s o i l , water, vegetation, materials, animals, v i s i b i l i t y , personal comfort and well-being.^ Spring (April to June) has the highest ozone levels, but the greatest number of exceedances of the acceptable level occur in summer (July and August). Diurnal patterns for ozone and its precursors are shown, for station T7, in Figure 7, and in spring and summer follow the classic pattern as outlined earlier. At T7 there is a peak in nitrogen oxide and hydrocarbon levels in the morning between 0800 and 1000 and, after a lag, nitrogen dioxide levels rise. However, a l l these species peak later in the day at T7 than 32 Table 5. Air Quality Monitoring Stations of the Lower Mainland Station Description Station Code Robson Square Robson and Hornby Vancouver T1 Rocky Point Park 2294 West 10th Avenue - Vancouver T2 Marpole 250 West 70th Avenue - Vancouver T3 Kensington Park 6400 East Hastings St.- Vancouver T4 Confederation Park - Willingdon & Penzance - Burnaby T5 Second Narrows 75 Riverside Drive N. Van. T6 Anmore Sunnyside Road Anmore T7 Lions Gate West end of Welch Road- W. Van. T8 Rocky Point Park Murray Street Port Moody T9 Eagle Ridge 475 Guilford Way Port Moody T1 0 Abbotsford Airport - - Abbotsford T1 1 Chilliwack Airport - - Chilliwack T1 2 Annacis Island Derwent Way Delta T1 3 Burnaby Mountain Ring Road, SFU Burnaby T1 4 Surrey East 1900 blk. 72nd Avenue - Surrey T1 5 Pitt Meadows Pitt Meadows Airport T1 6 Richmond South Williams and Aragon Richmond T17 SFU = Simon Fraser University Source: Personal communication with Greater Vancouver Regional D i s t r i c t , Engineering and Operations Department (March, 1987). 34 NO N0 2 Oj 50 100n Figure 7 Diurnal Ozone Cycle in Vancouver Station T7 August 1981 HC r3500 40 80 30 60H JO a a 20 40i -10 20H t-3000 H2500 2000 Source: Environmental Protection Service, Vancouver Oxidant Study: Air Quality Analysis (1982). Fig.7.3 p.172. for stations T4 and T2, with ozone peaking approximately one hour later, around 1400 hours. This suggests the transportation of precursors from upwind sites makes a significant contribution. Despite low oxides of nitrogen concentrations at station T7 relatively high ozone levels are found there, again implying precursor transportation from upwind (west) of the station.^ 1 Rural stations T11 and T12 experience peaks even later in the afternoon, between 1500 and 1700 hours, with Abbotsford reaching a peak approximately one hour after Chilliwack. The indication from other stations is clearly that precursors are transported by westerly flows, away from T1, T2, T3 and T8, which have high precursor concentrations but relatively infrequent episodes, towards T7 and points east. During the period from 1978-1981 the maximum tolerable one hour concentration was exceeded in two or more years at stations T4, T5, T7, T9, T10 and T11. Oxidant levels in the Lower Mainland were frequently in excess of the acceptable level for ozone. For example, station T7 consistently recorded the greatest number of exceedances with 134, 84, 191 and 215 exceedances of the maximum acceptable level for ozone in 1978, 1979, 1980 and 1981 62 respectively. Station T7, at the eastern end of the Burrard Inlet, has also consistently recorded the highest annual mean ozone levels. The two rural stations which were operational during this period (T11 and T12) have also recorded relatively high ozone concentrations. Abbotsford (Til) consistently recorded the second or third highest annual mean, while the annual mean for Chilliwack (T12) ranked between second and f i f t h highest. 36 In more recent years ozone concentrations have been significantly lower. Information from the rural monitoring stations was obtained from the GVRD Air Quality Monitoring 63 Network, and analysed in order to assess the potential for impacts on potato yields for the entire period from 1977 to 1985. Table 6 reports two seasonal ozone dose measures for the four rural stations, and includes one urban station T7. As Table 6 shows, the rural monitoring sites have often recorded higher ambient ozone loadings than the urban site, especially for ppm-hours>0.1Oppm. These measures were calculated for the 124 day period from May 15th to August 15th, which coincides with the busiest potato growing season. The number of valid days (ranging from 29-124) shows how much data are missing. The seasonal seven hour mean incorporates hourly readings between 9 a.m. and 4 p.m., and is included to allow comparisons with U.S. studies. The ppm-hours>0.1Oppm includes a l l readings in a 24 hour period, and is compared below with the potato dose-response function of the "Air Pollution Manual" of the California Department of Agriculture and 64 Food. Dose-response relationships and exposure statistics are discussed in section 2.5. As mentioned in Chapter I, of the six common potato cultivars grown in the Lower Mainland experimental data from the U.S. shows three to be susceptible to ozone, two tolerant and one unknown. The dose-response function from the Air Pollution Manual is for a sensitive cultivar (Centennial). The percentage reduction in potato tuber weight is given by the formulae: Percentage Reduction = 0 + (1.03 x Dose), where Dose is calculated in ppm-hours>0.1Oppm for a 120 day 37 Table 6. Ambient Ozone Concentrations at Rural Monitoring Stations In the Lower Mainland Stat ion I Year Dose S t a t i s t i c s | 1977 1978 1979 1980 1981 1982 1983 1984 1985 Anmore Dose>0.10ppm 0 0 1 .025 0 0 0.408 0 0.117 hrs>0.lOppm 0 0 5 0 0 4 0 1 7hr seasonal av, . ppm 0.045 0.027 0.036 0.030 0.021 0.035 0.024 0.037 Number of valId days 29 94 111 103 1 19 82 1 14 107 Abbotsford Dose>0.10ppm NA 8.456 3.099 5.593 16.002 6.522 0.218 0 hrs>0.10ppm NA 67 27 48 121 56 2 0 7hr seasonal av. ppm NA 0.048 0.052 0.048 0.057 0.046 0.029 0.029 Number of val1d days NA 122 88 124 115 47 77 1 1 1 Chi 11Iwack Dose>0.10ppm NA NA 0. 105 0.79 0. 745 0 NA 0. 223 hrs>0.lOppm NA NA 1 7 7 0 NA 2 7hr seasonal av. ppm NA NA 0.036 0.027 0.028 0.026 NA 0.034 Number of val 1d days NA NA 115 95 120 39 NA 106 Surrey Dose>0.lOppm NA NA NA NA NA NA NA 0.2 17 hrs>0.10ppm NA NA NA NA NA NA NA 2 7hr seasonal av. ppm NA NA NA NA NA NA NA 0.034 Number of v a l i d days NA NA NA NA NA NA NA 1 10 P1tt Meadows Dose>0.10ppm NA NA NA NA NA NA NA NA hrs>0.10ppm NA NA NA NA NA NA NA NA 7hr seasonal av. ppm NA NA NA NA NA NA NA NA Number of valId days NA NA NA NA NA NA NA NA 0. 107 1 0.037 107 0.41 4 0.035 1 10 0.615 6 0.037 95 0. 422 4 0.045 1 1 1 0. 1 14 1 0.037 1 15 NA = no data a v a i l a b l e because st a t i o n not operational period. The source document does not justify the assumption of no plant damage below 0.1Oppm, and may therefore under estimate actual reductions. In addition, i f such a threshold exists i t may be lower for other crops and cultivars. Ozone dose (from Table 6) and the corresponding percentage potato yield reduction are shown in Table 7. Extrapolating the linear response function over a wide range of ozone doses would not seem justified, as the rate of damage is hypothesised to increase and then decline. However, over the relatively small range of ozone doses of concern here the linear function is adequate. In 1985, 1984, and 1983 no substantial potato damage is predicted. Although, substantial missing data at Abbotsford, the only operational rural site in 1983, makes reductions possible for that year. The predicted yield reductions for Abbotsford in the years 1978, 1979, 1980, 1981, and 1982 are approximately 9, 3, 6, 16.5, and 7 percent respectively. The reductions for 1982 are based on 47 days data, and those for 1979 on 36 days, instead of the f u l l 124 day season, and may therefore be higher. Table 7. Predicted Percentage Reduction in Potato Tuber Weight for the Lower Mainland Ozone Dose (ppm-hrs>0.1Oppm) Potato Tuber Weight Reduction (percentage) 0.10 0.20 0.40 0.80 1 .00 3.10 5.59 6.52 8.46 16.00 0. 1 03 0.206 0.412 0.824 1 .030 3. 193 5.758 6.716 8.714 16.480 39 2.5 Biological Response of Agricultural Crops 2.5.1 Factors Affecting Plant Response to Air Pollution (a) Environmental and  Biological Factors A conceptual model of air pollution effects on vegetation is shown in Figure 8 and the biotic, climatic and edaphic factors are defined in Table 8. Inherent genetic resistance has been cited as probably the most important factor influencing plant response to air pollutants. Plant response to ozone varies among species of a given genus (e.g., potato) and varieties or cultivars (e.g., Netted Gem) within a given species.^ Ozone, as with other air pollutants, damages a plant after 6 6 entering the stomatal leaf opening. Thus, factors affecting stomatal size and opening determine pollutant uptake and the potential for damage. For example, reduced moisture or increased temperature can cause reduced stomatal apertures and higher 67 resistance to air pollution. Plants under no such stresses, growing under favourable conditions, may therefore be more susceptible to damage. In general, plants are more able to cope with exposure to ozone at night because stomata are closed, and at lower temperatures and relative humidity; and are more susceptible to ozone damage when the leaves are mature, due to the increase in c e l l gaps.^^ Farm practices may also alter plant response to air pollution. For example, attempts to improve growing conditions (e.g., irrigation) and reduce plant stress, could increase ozone susceptibility. The mixture of production inputs is a factor often ignored in the derivation of dose-response functions under 40 Figure 8 Conceptual Model of Factors Involved in Air Pollution Effects on Vegetation Pollutant Concentrat ion Number of Exposures DOSE Durat ion of Each Exposure Climatic Factors Biotic Factors Plant Receptor Edaphic Factors Botanic Factors Mechanism of Action RESPONSE Source: adapted from S.N. Linzon, W.W. Heck, and F.D.H. Macdowall "Effects of Photochemical Oxidants on Vegetation" National Research Council of Canada, Subcommittee on Air, Photochemical Air Pollution: Formation, Transportation and  Effects (Ottawa: Environmental Secretariat, 1975) Figure 4-3 p. 128. 41 Table 8. Factors Affecting Plant Sensitivity to Air Pollutants Botanic: Climatic Genetic Composition Stage of Plant Development Light Quality Light Intensity Precipitation Temperature Relative Humidity Carbon Dioxide Edaphic Soil Moisture Soil Type Soil Nutrient's (salinity, nitrogen and other nutrients' a v a i l a b i l i t y ) Biotic: Other: Insects Biological Pathogens Pollutant Mixtures Edaphic factors w i l l be subject to alteration due to irriga t i o n , f e r t i l i z a t i o n and cultural management practices. Source: adapted from R.M. Adams, M.V. Ledboer, and B.A. McCarl, The Economic Effects of Air Pollution on Agriculture: an  Interpretatve Review of the Literature (Oregon, Corvallis: Oregon State University, Agricultural Experiment Station, 1984) Special Report 702, Table 2.1 p.10. 42 experimental c o n d i t i o n s . C u l t u r a l and input v a r i a t i o n s between regions make dose-response f u n c t i o n s which have been d e r i v e d i n one area i n a p p r o p r i a t e f o r use i n another area. Even when the same inputs and c u l t i v a r s are used in two d i f f e r e n t r e g i o n s , a l l the other f a c t o r s i n Table 8 would have to concur before a dose-response f u n c t i o n d e r i v e d i n one region c o u l d be used to a c c u r a t e l y p r e d i c t the y i e l d l o s s i n the second r e g i o n . (b) Ozone Dose The ambient ozone c o n c e n t r a t i o n , the l e n g t h of time a p a r t i c u l a r c o n c e n t r a t i o n p e r s i s t s , and the frequency of occurrences combine to form a measure of the dose of an a i r p o l l u t a n t t o which a p l a n t i s exposed; the "exposure dose". Other c h a r a c t e r i s t i c s of p l a n t exposure may a l s o be important determinants of the nature and magnitude of the e f f e c t s of ozone on p l a n t s the l e n g t h of time between exposures, the time of day of exposures, t h e i r sequence and p a t t e r n , and the t o t a l f l u x of ozone to the p l a n t as i t i s a f f e c t e d by canopy c h a r a c t e r i s t i c s 70 and l e a f boundary l a y e r s . However, as Table 9 shows, ozone s t u d i e s have d e f i n e d exposure dose i n terms of c o n c e n t r a t i o n , d u r a t i o n and frequency to the e x c l u s i o n of other f a c t o r s . C e r t a i n f a c t o r s imply the c o n c e n t r a t i o n of gas surrounding a p l a n t or the dose may not a c c u r a t e l y r e f l e c t the c e l l u l a r dose to 71 which the p l a n t a c t u a l l y responds. Thus, an a l t e r n a t i v e to 7 2 exposure dose was suggested by Runeckles, and c a l l e d the " e f f e c t i v e dose". The e f f e c t i v e dose i s the amount of an a i r p o l l u t a n t t h at e n t e r s a p l a n t , as opposed to that i n the a i r surrounding the p l a n t . The use of e f f e c t i v e dose excludes 43 response variability due to pollutant uptake and thus focuses 73 upon physiological differences in plant sensitivity. A major drawback of the effective dose measure is the inability to 74 calculate i t directly from available air monitoring data. Thus exposure dose has remained the common measure used in studies of the effects of ozone on crop productivity. Table 9. Details of Ozone Exposure in 23 Recent Studies of Effects on Crop Productivity Details Provided Number of Publications Concentrat ion 23 Duration 18 Frequency 16 Time Between Exposures 13 Time of Day 6 Fluctuation of Concentrations 3 Pattern (sequence) 0 Flux 0 Source: Jay S. Jacobson, "Ozone and the Growth and Productivity of Agricultural Crops", in M.H. Unsworth, and D.P. Ormrod (eds.), Effects of Gaseous Air Pollution in Agriculture and Horticulture (London, U.K.: Butterworths, 1982) p.298 Table 14.2. Several types of exposure dose measures have been employed in ozone studies, as is shown in Table 10. An extensive project on crop damage due to ozone has been conducted by the National Crop Loss Assessment Network (NCLAN) of the United States Environmental Protection Agency (E.P.A.). NCLAN has employed a seasonal seven-hour/day mean ozone concentration exposure statis t i c in a l l i t s published dose-response functions. This mean is calculated upon the seven hours judged to be the most susceptible for plants; that i s , between 0900 and 1600 hours. The daily means for the seven-hour period are then averaged over the 44 entire growing season. Table 10. Measures of Ozone Occurrence Used in Studies of Effects on Crop Productivity Mean values for 1, 3, 6, 7, or 24 hours Maximum hourly average concentrations Diurnal variation of hourly average concentrations Number of hourly average concentrations exceeding 0.05, 0.10, 0.15 ppm Frequency distribution of hourly average concentrations Cumulative dose (ppm-h) greater than 0.10 ppm-h Source: Jay S. Jacobson, "Ozone and the Growth and Productivity of Agricultural Crops", in M.H. Unsworth, and D.P. Ormrod (eds.), Effects of Gaseous Air Pollution in Agriculture and Horticulture (London, U.K.: Butterworths, 1982) p.299 Table 14.3. The seasonal seven-hour mean statis t i c combines a large 75 number of ozone concentration observations. However, i t should be noted that: There is no consensus on an exposure statistic(s) that will best relate to the potential response of plants to varying O^  concentrations over a growing season. It is generally accepted that the degree of plant response is affected more by differences in concentration than by differences in duration of exposure. Thus a given seasonal mean concentration that includes many high 0, concentrations could cause greater effects than would the same mean that includes few high 0 3 concentrations. This hypothesis is untested for O,. Possibly no single exposure st a t i s t i c will be adequate for a l l crops under a l l environmental conditions. The implication is that high ozone concentrations may be lost in the st a t i s t i c but could be an important explanation of crop loss which should not go unobserved. Thus NCLAN has also discussed the use of alternative exposure statistics such as the peak (maximum) daily seven-hour mean ozone concentration occurring during the growing season; the seasonal mean of the daily maximum one hour mean ozone concentrations; and the peak (maximum) one hour mean 45 ozone concentration occurring during the season. The measure of dose used must be compatible with ambient air quality data to enable the development of useful predictive 7 8 models. In Canada, the annual one hour peak ozone concentration is used to set ozone standards, whose primary concern is with the 79 threshold for acute damage to human health. In order to use a different exposure statistic for a standard and a response model, the distribution of ozone in the ambient air needs to provide a 8 0 basis for using one statistic as a surrogate for another. For example, assume a seasonal average concentration is discovered at which there is no crop loss, and this seasonal average is never exceeded when a certain hourly peak ozone concentration is not exceeded. Under these circumstances i t is reasonable to assume 8 1 crops are protected when the hourly peak is not exceeded. Unfortunately, the seasonal mean can vary widely while the peak value remains constant, and is unlikely to always remain at or below a certain value. The implication for ozone standards is that they should employ concentration measures which relate to chronic, as well as acute, damage. 2.5.2 Methodologies for Deriving Dose-Response Functions Three main approaches have been employed to derive dose-response relationships for ozone foliar injury models, secondary data and experimentation. 46 (a) Foliar Injury Models Early studies assumed a threshold below which no damage was presumed to occur and related this to visible, normally f o l i a r , injury. These foliar injury models can be misleading as signs of yield loss because tubers, roots, and dry weight, among other 82 factors, can be affected without visible damage. Conversely foliar injury may overestimate damage because some plants can suffer severe leaf damage without loss of photosynthetic a b i l i t y , 8 3 and recovery from visible injury can be quick. Generally, three types of response to air pollution can be defined; visible injury 84 symptoms, growth responses, and quality changes. Foliar injury models ignore "hidden injury", which may occur with the latter two responses. Hidden injury may include: . (1) reduced photosynthetic activity, (2) accumulation of a pollutant or its byproducts within a leaf, (3) an overall unhealthy apperance without necrotic lesions, (4) reduced growth or yield, and (5) increasedggSusceptibility to disease, particularly insect invasion. Recent studies with soybeans, tomatoes, annual ryegrass, spinach, wheat, lettuce and potatoes have demonstrated that foliar-symptom production is not a reliable index of ozone effects on plant 86 growth or yield. (b) Secondary Response Data This technique has been employed in two recent studies of 8 7 regional economic crop losses from ozone. Cross sectional analysis of crop yield data is used to obtain dose-response functions via regression techniques. This requires information on the existing outdoor variations in air pollution and actual crop yields, and other environmental factors. This approach can save 47 time and money compared to the chamber study approach. Leung et a l . (1982) obtained s t a t i s t i c a l l y significant results for nine crops using this technique, but the results were not always consistent with experimental chamber studies, and 8 9 ozone levels in the study region were high. Rowe and Chestnut (1985) attempted to derive dose-response functions for ten crops 90 but could only obtain significant results for four of these. They found the success of the approach was generally dependent upon the effort made to measure and incorporate non-air pollution variables in the yield functions. Generally, their results suggested that ozone was causing yield losses but the secondary data regression approach only captured the effects for the most sensitive crops; i.e., those which experienced high rates of damages at low ozone levels such as dry beans, cotton, grapes and potatoes. Rowe and Chestnut used their results in comparison with other similar studies to define the conditions under which the secondary data regression approach might be most appropriately employed. The approach has the most chance of being successful when there are high 0- levels in the study area, for example regular exposures of T2 pphm (0.12 ppm) and higher, so that there may exist significant 0, induced damage to detect; when crops known to be "very sensitive" are being studied in moderately high 0- environments; or as a relatively inexpensive means to identify potentially sensi|jve crops to be more carefully examined with chamber studies. 48 (c) Experimentation Several experimental approaches have been developed in studies of ozone effects on crops; these include the use of greenhouses, f i e l d chambers (open-top or close-top), unenclosed fi e l d plots and the pollution gradient approach. Each approach varies in the design of the exposure system, but for use in economic assessments, the environmental and exposure conditions occurring on actual farms should be replicated, with only air 92 pollution concentration being modified. While general responses to ozone of plants grown in different environments may be similar, the quantitive relationships between dose and response 93 are clearly affected by environmental conditions. The different experimental designs may affect the environment, and so plant response to air pollutants. Plant response may vary with differences in: 1. wind conditions: speed, variability; 2. ozone flux; 3. plant density; and . . 94 4. other environmental conditions. Crops grown in the f i e l d may experience wide fluctuations in temperature, wind conditions, rain, and crowding which are not imposed on experimental plants. In particular, air flow 95 alterations can be important to pollutant uptake. Open-top f i e l d chambers have been the method preferred by NCLAN because they closely simulate actual f i e l d conditions, only 96 affecting air flow. Closed-top chambers affect air flow and 97 precipitation, and greenhouses affect the total environment. Thus, a l l these approaches suffer in varying degrees from 49 "chamber effects", with field-grown plants showing different 98 susceptibilities to pollutant injury. An alternative approach is the use of unenclosed f i e l d plots such as zonal air-pollution systems (ZAPS). ZAPS expose plants by releasing gaseous pollutants from a perforated pipe manifold supported above or within the vegetation, and thus supplementing 99 ambient ozone concentrations. Problems with this approach include adequately describing the air quality achieved and uncertainty as to the distribution and mixing of released 100 gases. The pollution gradient approach was employed by Oshima et a l . to develop a dose-response function for ozone damage to a l f a l f a in Southern C a l i f o r n i a . 1 ^ 1 An area source of ozone supplies the exposure dose with standardised f i e l d plots being set up downwind. This method also has problems, similar to the secondary data approach, particularly with regard to the effects of 1 02 uncontrolled variables upon response. 2.5.3 The Reasearch Programme of the NCLAN A major source of experimentally derived ozone dose-response information in recent years has been the United States National Crop Loss Assessment Network (NCLAN) run under the Environmental Protection Agency. The primary objectives of NCLAN are to define the relationship between yields of major agricultural crops and ozone exposure; to assess the national economic consequences resulting from the exposure of agricultural crops to ozone; and to advance the understanding of the cause and effect relationships that determine crop responses to pollutant 50 exposure. Although originally other air pollutants were to be 1 0 4 . studied, the main focus has been on ozone because alone, or in combination with sulphur dioxide and nitrogen, ozone is the main cause of crop losses in the United States due to air pollution. The NCLAN open-top chambers attempt to simulate actual farm input conditions, 1^ because farmers are more likely to set variable inputs at levels which minimize the cost of producing a given output, rather than providing plants with optimal conditions. The NCLAN has several experimental sites, namely in New York, North Carolina, Maryland, I l l i n o i s , California, and Oregon. The sites were selected on the basis of differing climatic conditions, distribution of crop species and the existence of established research groups. Maintaining sites in major U.S. crop growing regions means environmental factors w i l l be similar to those on the actual farms producing the main U.S. 1 0 7 . cash crops, which should f a c i l i t a t e the accuracy of economic crop loss assessments. NCLAN has conducted multi-year studies at the regional sites deriving dose-response functions for corn, soybean, kidney bean, peanut, lettuce, turnip, winter wheat, tomato, barley, clover/fescue, tobacco, red clover/timothy, cotton and a l f a l f a . The results of the seven year research programme provide the most comprehensive review yet of the effects of ozone on major agricultural crops. 51 2.5.4 Characteristics of Response Functions Applied in Economic Crop Loss Assessments Response functions derived from each of the methodologies reviewed above have been applied in economic assessments of air pollution damage to agricultural crops. Early work in this area depended upon trained f i e l d observers to use their judgement to 1 OR estimate crop damage from visible symptoms. These subjective estimates (often arbitrarily converted into monetary values) were replaced by foliar injury models. In turn, foliar injury models have been found deficient in several aspects and response functions derived from scientific f i e l d experimentation are now commonly applied in economic assessments. Economic assessments of ozone in the U.S. have in recent years concentrated on the use of response functions derived from f i e l d experiments. As Table 11 shows, ten out of fifteen studies since 1982 have relied upon NCLAN response data as their main source. A l l six studies recently carried out at the national level (for the United States) have used the NCLAN data. At the 1 09 regional level a mixture of data sources is often used. For example, the two studies using secondary data, discussed above, also make use of experimental data for some crops. NCLAN data is a primary source of response information but has so far been restricted to major U.S. agricultural crops. Thus the research of other scientists is employed for important regional crops. 52 Table 11. Main Source(s) of Response Functions Used in 15 Recent Economic Studies of Ozone Effects on Agriculture Source of Dose-Response Data Number of Publications Experimentation: NCLAN Other 10 3 2 Secondary Foliar Injury Field Observation 0 While the derivation of response functions used in economic assessments has improved, the application of the functions has sometimes been both technically and economically deficient (the economic issues are fully discussed in Chapter 3). Serious errors can arise from extrapolating from a limited data base. For example, the Organisation for Economic Cooperation and Development (OECD) performed a cost-benefit analysis of sulphur oxide which included the benefits expected from crop loss reductions under various scenarios. 1 1^ A dose-yield relationship was developed from information on the response to sulphur dioxide of rye grass (Lolium perenne), and applied to a l l crops throughout Europe. Major criticisms of this study included: 1. Ignoring crop and cultivar sensitivities: rye grass being one of the most sensitive crops to sulphur dioxide, resulting in overestimation of damages; 2. Ignoring differences in s o i l sulphur content: the rye grass studies used gave the plant nutritionally adequate supplies, again leading to overestimation of damage, because nutrient deficient soils actually benefit from sulphur deposition. 3. Overestimation was created by extended extrapolation beyond 53 plant threshold and background pollutant levels, thus creating the illusion of damages when they would not occur or would be irrelevant to the control of anthropogenic sources; 4. The research into rye grass used was mostly from laboratory or greenhouse experiments. This can give results widely varying from plant response to sulphur oxide under f i e l d conditions. 1 1 1 This kind of extrapolation and use of response functions ignores the limits of the data base. The application of one set of results to other crops, cultivars, regions and countries ignores variations in plant sensitivity and environmental conditions. However, this does not mean certain extrapolation is not justified. In the case of ozone, data are not available for many regionally important crops and cultivars, and so far, experimental results are largely derived for the major crop growing regions of the United States. In the absence of alternative data, "surrogate" response functions have been used for crops judged to be of similar sensitivity. For example, Howitt, Gpssard and Adams studied the economic effects of ozone 1 1 2 on thirteen crops. They used NCLAN data for seven crops and derived five "surrogate" response functions. Such use of response data relies upon the judgement of researchers, and implicitly 113 involves the subjective estimation of uncertainty. This type of probabilistic estimation requires explicit explanation of the areas of uncertainty so that the accuracy of, and possible bias in, the final results are clear. 54 2.5.5 Economically Important Response Characteristics In performing an economic assessment of crop loss the response changes of interest are those related to both the costs 1 1 4 of production and the marketability of a product. That i s , there are two routes via which pollution-induced crop damage can influence the welfare of consumers and producers. First, a reduction in crop damage, expressed as an increase in yield, which will reduce costs and therefore reduce the minimum price the producer must recieve to supply a given quantity. Secondly, altered levels of air pollution may affect the attributes of a crop, thus changing the consumers' willingness to pay and the welfare derived from the consumption of a given quantity of a crop. The change in cost implies a supply response, while the change in quality a demand response. Recent studies conducted on ozone crop damage have tended to concentrate upon yield, and therefore are only relevent to the supply response. Research upon the potential crop quality changes has apparently not been emphasised. Yet, there is evidence that such quality changes result from ozone pollution. Examples of quality changes which have been found are shrivelling in kernels of corn, reduction in the size of tomatoes, and alterations in chemical composition that affect cooking quality of potatoes and . . 1 1 5 nutritional values of a l f a l f a . Table 12 clearly shows that there is a wide range of possible crop responses to ozone. Research is required to estimate the importance of these responses. This may be a d i f f i c u l t problem to resolve where consumer tastes are concerned, requiring objective 55 characteristics to be associated with economic values in order to allow the derivation of dose-response functions appropriate for economic benefit assessments. However, without work in this area economic assessments cannot be made of the f u l l range of possible economic impacts. Table 12. Processes and Characteristics of Crop Plants that may be Affected by Ozone Growth Development Yield Quality Rate Flowering Number Appearance: size, shape, colour Pattern Branching Mass Storage l i f e Fruit set Texture and cooking quality and development Nutrient content Viabilit y of seeds Source: Jay S. Jacobson, "Ozone and the Growth and Productivity of Agricultural Crops", in M.H. Unsworth, and D.P. Ormrod (eds.), Effects of Gaseous Air Pollution in Agriculture and Horticulture (London, U.K.: Butterworths, 1982) p.296 Table 14.1. 56 2.6 Conclusion The dose which a particular target crop w i l l receive in a given growing season is a function of precursor emission levels, and meteorological, climatological and topographical factors. In the Lower Mainland high levels of precursor emissions are directed towards important agricultural areas due to restricted atmospheric dispersion within the Fraser Valley. When certain meterological conditions prevail, high ozone concentrations may result. The highest ozone levels occur during the spring and summer months coinciding with the growing season for many agricultural crops. Comparison of the ambient ozone dose at rural sites in the Lower Mainland with response information from California shows the potential for' sensitive varieties of potato to suffer tuber weight reductions of up to 16.5 percent in certain years. Crop damage is a function of the ozone dose, crop species and cultivar, and biological, climatic, edaphic, production and other factors. The interaction of these variables makes accurate crop loss assessment, especially over large areas, an error prone task. Results from f i e l d experiments, especially those of NCLAN, have increased the accuracy with which the economic consequences of plant damage caused by ozone can be estimated. Where crop or region specific information is lacking, qualified approximations to actual response can be made using surrogate functions. Finally, current economic assessments of crop loss from ozone are restricted by a lack of information as to the importance crop quality responses, and must therefore concentrate upon supply response alone. 57 Footnotes 1 R.G. Wilson, J.B. Mills, and E.P. Wituschek, A Report on the  Assessment of Photochemical Oxidants in the Lower Mainland (Victoria, B.C.: Ministry of the Environment,1984) p.7. 2 W.H. Medeiros, and Paul D. Moscowitz, "Quantifying Effects of Oxidant Air Pollutants on Agricultural Crops" Environment  International, Vol.9 p.505 (Dec, 1983). 3 Ibid. 4 Howard E. Heggestad, and Jesse H. Bennett, "Impact of Atmospheric Pollution on Agriculture" in Michael Treshow (ed.) Air Pollution and Plant Life (Chichester: John Wiley and Sons-; 1984) p.357. 5 Walter W. Heck et a l . , "Assessment of Crop Loss from Ozone" Journal of Air Pollution Control Association Vol.32 No.4 p.353 (April, 1982). 6 Another ozone problem was discovered in the late 1970's; namely, ozone depletion in the stratosphere (the upper layer of the atmosphere approximately six miles above earth's surface) which threatens to increase ultra-violet radiation to lethal proportions [6], Stratospheric ozone is not of concern here beyond the contribution i t makes to natural background ozone concentrations in the troposphere. The discovery of this problem is fully discussed in L. Dotto, and H. Schiff, The Ozone War, (New York: Doubleday & Co., 1978) 7 Timothy R. Oke, Boundary Layer Climates (London: Methuen and Co. Ltd., 1978). 8 Microtheoretic duality approaches need not depend upon dose-response functions, as will be dicussed in Chapters 3 and 4. Also see Philip Garcia et a l . , "Measuring the Benefits of Environmental Change Using a Duality Approach: The Case of Ozone and I l l i n o i s Cash Grain Farms" Journal of Environmental  Economics and Management, Vol.13 pp.69-80 (1986). 9 CM. Benkowitz, "Characteristics of Oxidant Precursor Emissions from Anthropogenic Sources in the United States", Environment International Vol.9 No.6 pp.429-446 (Dec. 1983). 10 Ibid. 11 Ibid. 12 Oke, Boundary Layer Climates p.272. 13 Benkowitz, "Characteristics of Oxidant Precursors". 58 14 Walter W. Heck et a l . , "Assessing Impacts of Ozone on Agricultural Crops: I. Overview", Journal of Air Pollution  Control Association Vol.34 No.7 p.731 (July, 1984). 15 Heggestad and Bennett, "Impact of Atmospheric Pollution on Agriculture" p.360. 16 Robert A. McCormick and George C. Holzworth, "Air Pollution Climatology" in A.C. Stern (ed.), Air Pollution: Volume 1,  Air Pollutants, Their Transformation and Trabsportation 3rd edition (New York: Academic Press, 1976) p.694-695. 17 Ibid 18 Wilson et a l . , Assessment of Oxidants in the Lower Mainland, p.7. 19 The seasonal seven hour mean and other exposure sta t i t i c s are discussed in section 2.5.1(b); also see, Heck et a l . , "Assessing Impacts of Ozone on Agricultural Crops: I" p.731. 20 Bencowitz, "Characteristics of Oxidant Precursors"; Wilson et a l . Assessment of Oxidants in the Lower Mainland. 21 Oke, Boundary Layer Climates p.272. 22 Ibid. 23 Benkowitz, "Characteristics of Oxidant Precursors". 24 Ibid. 25 Canada, Environment Canada, Environmental Protection Service. Vancouver Oxidant Study: Air Quality Analysis: Final Report (1982) p.27. 26 M.S. Kotturi et a l . , British Columbia Acid Rain Program: A  Brief Overview (Victoria, B.C.: Ministry of Environment, 1985). 27 G.Z. Whitten, "The Chemistry of Smog Formation: A Review of Current Knowledge", Environment International Vol.9 No.6 pp.447-464. 28 Ibid; see also,Wilson et a l . , Assessment of Oxidants in the  Lower Mainland, p.7 29 OECD Photochemical Oxydants and their Precursors in the  Atmosphere (Paris: OECD, 1979) p.19. 30 Oke, Boundary Layer Climates p.283. 31 Ibid. 59 32 Ibid. 33 Ibid pp.297-298. 34 Oke, Boundary Layer Climates p.298; and Whitten "The Chemistry of Smog Formation". 35 Oke, Boundary Layer Climates pp.298-300. 36 Ibid p.280. 37 Ibid pp.278-281. 38 John E. Hay and Timothy R. Oke, The Climate of Vancouver (Vancouver: Tantalus Research Ltd., 1973) p.41 . 39 Ibid. 40 For a f u l l discussion on the various types of inversion see Oke, Boundary Layer Climates pp.274-278. 41 Ibid. 42 Hay and Oke, The Climate of Vancouver p.41. 43 Oke, Boundary Layer Climates p.298. 44 Jay S. Jacobson, "Ozone and the Growth and Productivity of Agricultural Crops", in M.H. Unsworth, and D.P. Ormond (eds.), Effects of Gaseous Air Pollutants in Agriculture and  Horticulture (London, U.K.: Butterworths, 1982 ) . 45 Ibid, p.293. 46 William H. Smith, "Pollution Uptake by Plants" in Michael Treshow (ed.) Air Pollution and Plant Life (Chichester: John Wiley and Sons Ltd., 1984). 47 T.W. Tesche, "Photochemical Dispersion Modelling: A Review of Model Concepts and Application Studies", Environment  International, Vol.9 No.6 pp.465-490 (Dec, 1983). 48 Smith,"Pollutant Uptake by Plants" p.428. 49 Ibid. 50 Ibid. 51 Compare the points given for Vancouver here with those given for Los Angeles in R.E. Munn "The Oxidant Climatology of Canada" in Canada, National Research Council, Subcommittee on Air, Environmental Secretariat. Photochemical Air Pollution:  Formation, Transportation and Effects (1975). 52 Ibid p.53. 60 53 Hay and Oke, The Climate of Vancouver. 54 Ibid, pp.44-45. 55 Ibid. 56 Canada, Environmental Protection Service, Vancouver Oxidant  Study. 57 Wilson et a l . , Assessment of Oxidants in the Lower Mainland, p. 1 3. 58 The stations at Langley and Pitt Meadows were set up in 1982 and 1985 respectively. The one at Richmond was set up in 1986. 59 The National Air Quality Standards are given in micro-grams/cubic meter, and discrepancies may arise when converting to ppb. The maximum acceptable level for ozone is 160 micro-grams/cubic meter for one hour, and this is normally taken as equivalent to 80 ppb. Telephone conversation with E.P. Witushek, Manager Air Programmes, E.P.S. Pacific Region, 9th July 1986. 60 Canada, Environment Canada, National Air Pollution  Surveillance (1983). 61 Canada, Environmental Protection Service, Vancouver Oxidant  Study p.108. 62 Canada, Environmental Protection Service, Vancouver Oxidant  Study, p.1. Note maximum acceptable standard is given as 82 ppb, see footnote 62 above. 63 Information on the monitoring stations and air quality in the Lower Mainland was obtained on magnetic tape from Al, J. Percival, Monitoring Supervisor, Pollution Control, Engineering and Operations Department, GVRD. 64 California, Department of Food and Agriculture. Air  Pollutiion Manual (1986). 65 S.N. Linzon, et a l . Ozone Effects on Crops in Ontario and  Related Monetary Values (Ontario: Ministry of Environment,1984). 66 Holdgate, Environmental Pollution, p.130 67 Medeiros and Moscowitz, "Quantifying Effects of Oxidant Pollutants on Crops", p.507. 68 Ibid. 61 69 Richard M. Adams, and Thomas D. Crocker, "Economically Relevant Response Estimation and the Value of Information: Acid Deposition", in Thomas D. Crocker (ed.), Economic  Perspectives of Acid Deposition Control (London: Butterworth, 1984). See also, James Mjelde et a l . , "Using Farmers' Actions to Measure Crop Loss Due to Air Pollution", Journal of Air  Pollution Control Association, Vol.31 p.361 (1984). 70 Jacobson, "Ozone and Agricultural Crops", p.298. 71 D.T. Tingey and G.E. Taylor "Variation in Plant Response to Ozone: A Conceptual Model of Physiological Events" in M.H. Unsworth and D.P. Ormrod (eds.) Effects of Gaseous Air  Pollution in Agriculture and Horticulture (London: Butterworth Scientific, 1982) pp.113-138. 72 Victor C. Runneckles, "Dosage of Air Pollution and Damage to Vegetation", Environmental Conservation, Vol.1 No.14 (1974). 73 Walter W. Heck, Ralph I. Larsen, and Allan S. Heagle, "Measuring the Acute Dose-Response of Plants to Ozone" (Presented at E.C. Stakman Commemorative Symposium, University of Minnesota, Minneapolis, 1980), pp.32-49. 74 Ibid. 75 Heck et a l . , "Assessing Impacts of Ozone on Agricultural Crops: I", p.732. 76 Ibid. 77 Ibid. 78 Heck, "Measuring the Acute Dose-Response of Plants to Ozone". 79 Environment Canada. National Air Pollution Surveillance (Ottawa: Environment Canada, 1983). 80 Heck et a l . , "Assessing Impacts of Ozone on Agricultural Crops: I", p.734. 81 Ibid. 82 Medeiros and Moscowitz, "Quatifying Effects of Oxidant Pollutants on Crops" 83 Steve Leung et a l . , Methodologies for Valuation of  Agricultural Crop Yield Changes: A Review Corvallis, Oregon: U.S., E.P.A., 1978) EPA/600/5-78/018, NTIS/PB-288 122, p.46. 84 Ibid, p.31. 85 Medeiros and Moscowitz, "Quatifying Effects of Oxidant Pollutants on Crops", p.506. 62 86 Jacobson, "Ozone and Agricultural Crops", p.294. 87 Steve Leung, W. Reed, and S.Geng, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in Southern California" Journal of Air Pollution Control Association Vol.32 pp.160-164 (1982); and, Robert D. Rowe and Lauraine G. Chestnut, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in the San Joaquin Valley", Journal of Air Pollution Control Association Vol. 35 pp.728-734 (1985). 88 Rowe and Chestnut, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in the San Joaquin Valley" p.729. 89 Leung et a l . , "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in Southern California". 90 Rowe and Chestnut, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in the San Joaquin Valley". 91 Ibid, p.731. 92 M.H. Unsworth, "Exposure to Gaseous Pollutants and Uptake by Plants ", in M.H. Unsworth, and D.P. Ormond (eds.), Effects of Gaseous Air Pollutants in Agriculture and Horticulture (London, U.K.: Butterworths, 1982). 93 Jacobson, "Ozone and Agricultural Crops", p.295. 94 Ibid. 95 Unsworth, "Exposure to Gaseous Pollutants". 96 Heck et a l . , "Assessment of Crop Loss from Ozone". 97 Martha Smith and Deborah Brown, Crop Production Benefits From  Ozone Reduction: An Economic Analysis, (Indianna: Agricultural Experimentation Station, Purdue University, 1982) Station Bulletin No.388, p.2. 98 Gordon L. Brown and Victor C. Runneckles, "Predicting the Impact of Air Pollutants on Plants: A Review of Techniques and Sources of Uncertainty", (Presented at annual meeting of Air Pollution Control Association, Calgary, Alberta, 1985). 99 Gordon L. Brown, and Victor C. Runneckles, "Risk Assessment and Management of Ecological Effects of Ozone" (Vancouver, B.C.: Plant Science Dept., U.B.C., 1986), p8. 100 Ibid. 63 101 R.J. Oshima et a l . , "Ozone Dosage-Crop Loss Loss Function for Alf a l f a : A Standardized Method for Assessing Crop Losses from Air Pollutants", Journal of Air Pollution Control  Association, Vol.26 No.9 (Sept., 1976). 102 Brown, and Runneckles, "Risk Assessment and Management of Ecological Effects of Ozone", p.8. 103 United States, E.P.A. "Air Quality Criteria for Ozone and Other Photochemical Oxidants: Draft" (November, 1985). 104 Heck et a l . , "Assessing Impacts of Ozone on Agricultural Crops: I", p.730. 105 Heck et a l . , "Assessment of Crop Loss from Ozone", p.353. 106 Mjelde et a l . , "Using Farmers' Actions to Measure Crop Loss", p.361 . 107 Heck et a l . , "Assessment of Crop Loss from Ozone". 108 United States, Environmental Research Center, E.P.A. The  Economic Damages of Air Pollution ,(1974) EPA-600/5-74-012. 109 The regional assessment of the economic effects of ozone on agriculture is discused in Chapter 5. 110 OECD, The Costs and Benefits of Sulphur Oxide Control (Paris, France: OECD, 1981). 111 R.A Barnes, G.S. Parkinson and A.E. Smith, "The Costs and Benefits of Sulphur Oxide Control", Journal of Air Pollution  Control Association, Vol.33 pp.737-741 (1983) . 112 R.E. Howitt, T.E. Gossard and R.M. Adams, "The Economic Effects of Air Pollution on Annual Crops", Journal of Air  Pollution Control Association Vol.34 pp.1122-1127 (1984). 113 Brown, and Runneckles, "Risk Assessment and Management of Ecological Effects of Ozone", p.4. 114 Richard M. Adams, Thomas D. Crocker, and Richard W. Katz "Yield Response Data in Benefit-Cost Analyses of Pollution-Induced Vegetation Damage" in William E. Winner, Harold A. Mooney and Robert A. Goldstein Sulphur Dioxide and  Vegetation: Physiology, Ecology, and Policy Issues (Stanford, California: Stanford University Press, 1985). 115 Jacobson, "Ozone and Agricultural Crops". 64 CHAPTER III METHODOLOGIES AND APPLICATIONS IN THE REGIONAL ECONOMIC ASSESSMENT OF OZONE EFFECTS ON AGRICULTURAL CROPS 3.1 Introduction The problem of measuring and interpreting the benefits to society from air pollution reduction is given a consistent conceptual framework by applied welfare economics. Most economic assessments of policy issues now measure benefits in terms of the economic surplus accruing to consumers and producers, 1 a stance 2 which i s supported by recent literature. This literature and the theoretical issues surrounding the development of consumer and producer surpluses as measures of welfare are discussed in Appendix I and II. The correct generation and use of economic surplus information requires some understanding of the behavioural assumptions of individual decision makers, e.g., farmers and consumers. Detailed coverage of these issues can be found in the intermediate/advanced economics literature. The economists' production function is a concept somewhat analogous to the biologists' dose-response function, and has traditionally been used by agricultural and resource economists 4 to assess farm level decision problems. A change in pollution 65 levels alters the elements in, and form of, the set of alternatives which bound production choices and so affect the decisions of the firm in the pursuit of maximum profits. The assessment of the benefits resulting from such a change requires the analysis of biological processes, technical poss i b i l i t i e s , their interactions with producer decisions, and the effect of resulting production changes on consumer welfare. Biological or production response data provide a link between 5 pollutant dose and the performance parameters of a crop system. The response relationship, as discussed in Chapter 2, may be quantified directly from biological experimentation, indirectly from observed producer output and behavioural data (secondary data), or from some combination of data sources. Procedures based upon producer data, for example production or cost functions, are preferable from the viewpoint of economic analysis.^ Cost and production functions have been applied in the regional assessment 7 of crop losses from ozone, but data and s t a t i s t i c a l d i f f i c u l t i e s p have prevented their use across large geographical areas. At present, dose-response functions are commonly applied in economic 9 assessments of environmental stress to agriculture. Agricultural production is affected by inputs from the natural system outside the farmer's control and typically results in multiple outputs from a single firm. 1^ Ozone is only one element in the set of potentially important variables affecting agricultural production processes. Figure 9 illustrates the types of choices, regarding technology and output mix, facing the profit maximizing crop farmer. The quality of the so i l and the type of climate define the feas i b i l i t y constraints for crop 66 F i g u r e 9. R e p r e s e n t a t i o n of A g r i c u l t u r a l C rop P r o d u c i n g A c t i v i t i e s N a t u r e ' s I npu t s S u n l i g h t , l e n g t h o f g row ing s e a s o n , p r e c i p i t a t i o n , g round w a t e r , and o t h e r c l i m a t i c f a c t o r s ( e . g . , wind) ON F a c t o r I n p u t s and P r i c e s S e e d s , b u l b s , p l a n t s . M a c h i n e r y and e q u i p m e n t , e . g . , a u t o m o b i l e s , t r u c k s , t r a c t o r s , = c o r n p l c k e r s , b a i l e r s , comb ine s . f e r t i l i z e r , e . g . , commerc i a l f e r t 1 1 1 z e r , 11me. P e s t i c i d e s , e . g . , d e f o l i a n t s . I n s e c t i c i d e s , h e r b i c i d e s . = E n e r g y , e . g . , Kwh, g a s o l i n e , d i e s e l f u e l . L a b o u r , e . g . , f a rm l a b o u r , c o n t r a c t l a b o u r , mach ine 1 a b o u r . Wa te r . = B u i l d i n g m a t e r i a l s . Land s o i l and t o p o g r a p h i c a l c h a r a c t e r i s t i c s . I Crop P r o d u c t i o n O p e r a t i o n s U n i t O p e r a t i o n s / O t h e r P r o d u c t i o n V a r i a b l e s 1. Crop M ix , e . g . v e g e t a b l e s . 2. 3 . f i e l d c o r n , b a r l e y , Crop R o t a t i o n P a t t e r n and S c h e d u l e , e . g . , c o n t i n u o u s c o r n , c o r n - c o r n - a l f a l f a - c o r n . T i l l a g e Method, e . g . , minimum t i l l a g e , no t i l l a g e , s h a l l o w p low, ha r row, d i s k . P l o w i n g P r a c t i c e s , e . g . , c o n t o u r i n g , g r a d i n g rows, r i d g e p l a n t i n g . F e r t i l i z a t i o n P r a c t i c e s mix o f f e r t i l i z e r s ; a p p l i c a t i o n r a t e s , methods, and s c h e d u l e s . P e s t i c i d e P r a c t i c e s mix of p e s t i c i d e s ; a p p l i c a t i o n r a t e s , methods and s c h e d u l e s . I r r i g a t i o n Me thods / Sy s tems , i f any , e . g . , s p r i n k l e r s , l i n e c a n a l s . H a r v e s t i n g T e c h n o l o g y . O n - s i t e Crop P r o c e s s i n g , e . g . wash ing and p a c k a g i n g . 1 0 . O t h e r . P r o d u c t Output C r o p s H a r v e s t e d F i e l d C o r n f o r a l l p u r p o s e s e . g . , f o r g r a 1 n f o r s i1 age . Soybeans f o r a l1 p u r p o s e s e . g . , s eed g r a i n , s i l a g e . Wheat f o r g r a i n O t h e r smal1 g r a i ns Soybeans Hay P e a n u t s T o b a c c o P o t a t o e s V e g e t a b l e s O r c h a r d C rop s G reenhouse p r o d u c t s O t h e r C r o p s P r o d u c t O u t p u t s e i t h e r : 1.go d i e c t 1 y t o => consumer marke t s or t o 2 . o f f - s i t e I n t e r m e d i a t e p r o c e s s i n g & r e f i n i ng = > e . g . , c a n n i n g v e g e t a b l e . o l 1 p r o c e s s i n g & r e f i n i n g e t c . ( t h e s e o p e r a t i o n s a r e cons i d e r e d s e p e r a t e => a c t i v i t i e s & a n a l y s e d a c c o r d i n g l y ) S o u r c e : R . J . Kopp, W.T. Vaughan and M. H a z l l l a A g r i c u l t u r a l S e c t o r B e n e f i t s A n a l y s i s f o r Ozone: Methods E v a l u a t i o n and D e m o n s t r a t i o n ( N o r t h C a r o l i n a : R e s e a r c h T r i a n g l e Park U.S. E . P . A . , 1984) F 1 g u r e 2 - 2 . growing, and given these constraints, the farmer selects the input sets, crop mixes and rotation patterns that, based upon factor prices and output market values, maximize p r o f i t s . 1 1 Air pollution concentrations can be an important variable in this decision making process. The individual's decision problem is to modify his or her choices so as to maximize the gains from pollution reductions and to minimize losses from pollution increases. The complete economic concept of pollution control benefits embodies the physical and biological changes in the receptors of interest (crops, buildings, human health), as well as the adaptive responses of individuals and institutions (including markets) to these changes. In addition to the direct economic impacts of air pollution on producers and consumers, indirect impacts can also be important. Indirect impacts are those changes induced by alterations in the pollutant-affected product which occur in other markets and sectors of the economy, e.g., the disruption of livestock production as a result of ozone damage to forage crops. A comprehensive economic model would include a l l such indirect welfare changes in the assessment of benefits. 68 3.2 Methodologies for the Valuation of Agricultural  Crop Yield Changes: With Reference  to Air Pollution Various methods have been applied to the valuation of the benefits from the reduction of crop losses. Three main categories can be defined; namely, traditional type models, optimization models and econometric models. 3.2.1 The Traditional Model The "traditional" type model is a simple method of approximating a monetary value for crop yield changes. The model has various names in the literature, the historical approach, the naive model, the biologist's approach, and the ad hoc approach. Until the late 1970s the traditional model was the most 1 3 prevalent type of crop loss assessment reporting dollar losses. The model multiplies estimates of a physical crop change, based on current acreage in production, by the current price of the crop. This implies a simple response assumption that resource use and prices, and thus consumer surplus, do not change. In regional crop loss assessments, assuming the market price wi l l not be affected by yield increases may be particularly tempting because the size of the increase is assumed to be small relative to the national market. However, this can cause serious errors in benefit estimates where the crop in question is regionally concentrated in production; for example, a substantial increase in corn yield in the Corn Belt area of the United States could not r e a l i s t i c a l l y be assumed to leave prices unaltered. Unlike other methodologies, the traditional model cannot drop the constant price assumption, cannot measure changes in consumer 69 surplus and thus ignores distributional impacts. Despite this, Kopp et a l . (1984) have claimed that the approach of the traditional model "... may be justified as a f i r s t order approximation to the change in consumers' surplus arising from a policy change, and is hence not totally devoid of 14 . . . economic content." However, studies comparing the traditional model and more comprehensive techniques have found the former to 1 5 overestimate benefits by 20-100 percent. Since the traditional model can only measure quasi-rent (see Appendix II for definition), not consumer surplus, the difference is even more dramatic. When considering only producer effects, the estimates of the traditional procedure are up to four times greater than other economic techniques. 1^ As Adams et a l . (1982) state, The comparison between the traditional and the more comprehensive approach reported here suggests a substantial divergence in estimates. Further, shifts in cropping patterns within and across regions, as well as distributional effects of environmental degradation, seem likely to be of considerable interest to policy makers. The traditional analysis is incapable of capturing them. The advantage of the traditional model is that the informational requirements are relatively modest, allowing a quantitative measure of damages to be calculated quickly and 1 p inexpensively. Yet, the results from, and the procedure of, the model are largely discounted by economists as being an unrealistic abstraction that ignores well documented price effects and is incapable of addressing distributional 1 9 consequences. As Adams and McCarl (1985) have stated, "... one should resist the temptation to resort to such simple minded 20 models in future assessments for the sake of expediency". 70 3.2.2 Optimization Models There are two types of optimization model Linear Programing (L.P.) models and Quadratic Programing (Q.P.) models. They require extensive data sets and are normally established as computer programmes due to their complexity. Both L.P. and Q.P. are similar in their approach. They both require an objective function capable of being maximized, or minimized; alternative methods or processes for obtaining the objective; and resource and other constraints. They describe the world as i t should be given certain assumptions; that i s , they are normative models. The L.P. model can be set up as cost minimizing or profit maximizing. In the former case, the cost minimizing set of production activities is selected to produce specific goods given constraints on c r i t i c a l inputs (e.g., land). The basic 2 1 assumptions of the L.P. model are: 1. Linear production relationships; i.e., constant input-output coefficients. 2. Linear relationships are inequalities; a productive activity can use less than or equal to, but not more than the amounts of resources available. 3. Linear objective function. 4. Specification of process relationships; as opposed to estimation in an econometric model. 5. Additivity. 6. Perfect d i v i s i b i l i t y of inputs and outputs. 7. Finiteness; there is a limit to the number of alternative activities and resource restrictions that can be allowed. 8. Single-value expectations; i.e., certainty. 71 In L.P., biological dose-response functions can be used to alter the quantity of output produced for the set of inputs required for each production activity, and so can mimic the effect of varying air pollution (e.g., ozone) concentrations. Both L.P. and Q.P. assume an inf i n i t e l y elastic supply curve for variable inputs and constant returns to scale. The quantity demanded is exogeneously fixed when cost minimization is the objective of L.P., and price is exogeneously fixed when profit maximization is the objective. In Q.P. price and quantities are endogeneously determined. This forms the main difference between the two models. Optimization models can give details on benefit distribution and model the complex interrelationships of an economy, allowing indirect effects to be considered. However, i f discrepencies arise between the model solutions and reality, i t is never certain i f they are a result of incorrect or inaccurate modelling of production ac t i v i t i e s , improper constraints, or just the fact that the real world operates suboptimally due to market 22 . . interference or distortions. Optimization models are generally poor predictive tools, but can be improved in this respect by 23 recursive programming. 3.2.3 Econometric Models In contrast, to the normative optimization models, econometric models, by the very nature of the data base used to develop them, reflect historical reality over space and time. This is not to deny that ideological bias creeps into the very selection of questions investigated, or the inferences drawn from 72 f a c t u a l evidence. These matters do not prevent a p p l i e d work from being normative in the sense that the r e s u l t s can be r i g o r o u s l y 24 examined u s i n g accepted s c i e n t i f i c and s t a t i s t i c a l methods. Econometric models cannot capture the e f f e c t s of new t e c h n o l o g i e s developed o u t s i d e of the time (or space) span of the data; nor can they estimate the e f f e c t on p r o d u c t i o n of i n s t i t u t i o n a l rearrangements which are not t r a n s l a t e d i n t o 25 changes i n market p r i c e s . The i n s t i t u t i o n a l s e t t i n g i s taken as g i v e n . Three c a t e g o r i e s of econometric model f o r a s s e s s i n g crop l o s s from a i r p o l l u t i o n can be d e f i n e d , namely, Aggregate supply/demand models, M i c r o t h e o r e t i c supply/demand models, and N e o c l a s s i c a l econometric p r o d u c t i o n , c o s t , or p r o f i t f u n c t i o n models. Aggregate supply/demand models r e q u i r e l i t t l e i n the way of theory, except f o r some general s p e c i f i c a t i o n of the v a r i a b l e s a f f e c t i n g p r i c e and a c o n c e p t u a l i z a t i o n of the aggregate system 2 6 as e i t h e r simultaneous or r e c u r s i v e i n the e s t i m a t i o n s t e p . The model may be r e c u r s i v e i n that each equation of the system can be s o l v e d i n turn because they have an o r d e r i n g i n time and the s o l v e d value can enter the next equation as a predetermined v a r i a b l e . For example, a farmer may use c u r r e n t p r o d u c t i o n methods and crop mixes to help determine next year's p r o d u c t i o n ; that i s , p r o d u c t i o n i s determined f i r s t and then p r i c e s are 27 determined; the model i s not simultaneous. M i c r o t h e o r e t i c supply/demand models s p e c i f y an o b j e c t i v e f u n c t i o n f o r the f i r m , under p e r f e c t l y c o m p e t i t i v e c o n d i t i o n s , which i s then estimated e m p i r i c a l l y . T h i s N e o c l a s s i c a l t h e o r e t i c 73 basis requires that microtheoretic approaches s t r i c t l y adhere to economic theory. Microtheoretic approaches capture both the physical engineering aspects of production and the behavioural aspects of producers. The parameters of the model can be made functions of pollution concentrations so that changes in those concentrations are reflected by changes in the parameters and shifts in the supply function. The Microtheoretic approach has the a b i l i t y to incorporate biological information, or to estimate the parameters of biological functions directly from observed producer behaviour; in the latter case the approach becomes a Neoclassical econometric model. Since the economic model presented in Chapter 4 is of the general microtheoretic category, a more detailed discussion follows. Table 13 summarises the main characteristics of each of the methodologies which have been discussed. 74 T a b l e 13. M e t h o d o l o g i e s f o r the Economic E v a l u a t i o n of C r o p Lo s s N o r m a t i v e o r P o s i t i v e Model Economic Theo ry o f the F i r m B i o l o g i c a l Do se -Re sponse F u n c t i ons Output Demand Cond i t I o n s Benef i t Measure 1 T r a d i t i o n a l Model None R e q u i r e d as i n i t i a l c o n d i t i o n Exogeneous1y f i x e d p r i c e s P r o d u c e r s u r p l u s cn 2 O p t i m i z a t i o n Mode l s (A) L i n e a r N o r m a t i v e Programmi ng (B) Q u a d r a t i c N o r m a t i v e Programming E c o n o m e t r i c Mode l s (A) A g g r e g a t e P o s i t i v e Supp ly /Demand Dual 1ty Mode l s (B) M i c r o t h e o r e t i c P o s i t i v e Supp ly/Demand (C) N e o c l a s s i c a l P o s i t i v e Econometr1c ( P r o d u c t Ion, C o s t o r P r o f i t F u n c t i on ) Cos t m in . o r p r o f i t max. s u b j e c t to c o n s t r a i n t s Net s o c i a l b e n e f i t max. s u b j e c t to c o n s t r a i n t s Some r e c o g n i t i o n of s ymet ry c o n d i t i o n s on c r o s s p r i c e terms F u l l y c o n s i s t e n t w i t h o p t i m i z a t i o n t h e o r y v i a d u a l i t y theorems F u l 1 y cons 1 s t e n t w i t h o p t i m i z a t i o n t h e o r y v i a d u a l i t y theorems R e q u i r e d as i n i t i a l c o n d i t i o n R e q u i r e d as i n i t i a l c o n d i t i o n R e q u i r e d as i n i t i a l c o n d i 11 on R e q u i r e d as i n i t i a l c ond i 11 on Not r e q u i r e d r e f l e c t e d i n p r o d u c e r c h o i c e s Exogeneous1y f i x e d quant i t i e s ( c o s t m1n.) o r p r i c e s ( p r o f 11 max.) Net p r o d u c e r and consumer s u r p l u s Net p r o d u c e r and consumer Endogeneous1y d e t e r m i n e d p r i c e / q u a n t i t y s u r p l u s e q u i 1 i b r i u m Endogeneous1y d e t e r m i n e d p r i c e / q u a n t i t y e q u i 1 i b r ium Net p r o d u c e r and consumer s u r p l u s Net p r o d u c e r and consumer Endogeneous1y d e t e r m l n e d p r i c e / q u a n t i t y s u r p l u s e q u i 1 i b r i u m Net p r o d u c e r and consumer E n d o g e n e o u s l y d e t e r m i ned p r i c e / q u a n t i t y s u r p l u s e q u i 1 i b r ium S o u r c e : A d a p t e d from R . J . Kopp, W.T. Vaughan and M. H a z i l l a A g r i c u l t u r a l S e c t o r B e n e f i t s A n a l y s i s f o r Ozone: Methods E v a l u a t i o n and D e m o n s t r a t i o n ( N o r t h C a r o l i n a : R e s e a r c h T r i a n g l e Park U.S. E . P . A . , 1984) p .15 T a b l e 3 - 1 . 3.3 Microtheoretic Approaches to Modelling Production Decisions Agricultural 3.3.1 Duality Models and Environmental Changes Several methodologies exist for the estimation of production 2 8 technologies and the derivation of supply curves. In recent years the primal approach has been cr i t i c i s e d as too restrictive, requiring the prior specification of the production technology, and the dual approach has offered an alternative which avoids 29 many of the estimation problems of the former. Assume the production unit is a firm which employs n input factors to produce m outputs, given a specific technology, which specifies the physical transformation of inputs into outputs, i.e., a production function. The primal technology set (PT) is of fundamental importance since any physical effects upon production, attributable to an environmental variable (e.g., air pollution) must impact production through an alteration in the 30 technology set. The production function picks out the maximum outputs as a function of inputs while the transformation function picks out 3 1 the maximum net output vector. The transformation function (T) can serve as a measure of technical ineffeciency. Given a transformation function T which meets certain conditions, PT may 32 . be defined in terms of T. In this way a duality exists between the technology set and the transformation function. This duality insures that any impact realized upon the technology set PT due to the effect of an environmental set of variables w i l l be 33 . . mirrored in the transformation function. In addition, the production possibilities of a firm facing a multiple output 76 technology can be fully described by a transformation function. Two dual approaches to production which have been applied to agricultural crops are the profit function and the cost function. 3.3.2 Duality Models Applied to Agricultural Crop Production (a) Profit Functions The profit function of the firm gives the maximum profits as 34 a function of prices for inputs and outputs of the firm. The analysis assumes firms act according to certain decision rules, including profit maximization given the price regime for outputs 35 and variable inputs, and the quantities of fixed i.nputs. In the short run the profit function is restricted in that the quantities of some inputs are fixed. Every concave production function has a dual which is a convex profit function, and vice 3 6 versa. The firm's supply function and input demand functions can be derived without reference to the production function. Thus, the behaviour of a profit maximizing, price-taking firm can be analysed by considering the profit function alone, without any explicit specification of the corresponding production 37 function. Table 14 summarises the main features of some recent profit function studies applied to agriculture. A variety of flexible functional forms have been employed to specify the profit function in agricultural studies Cobb-Douglas, Translog and Generalized Leontief. (Any equation that gives a second-order Taylor's approximation to an arbitrary functional form is termed flexible.) The earlier studies which employed the Cobb-Douglas 77 T a b l e 14. A p p l i c a t i o n s of the P r o f i t F u n c t i o n i n A g r i c u l t u r a l Economic s A u t h o r ( s ) / Y e a r C o u n t r y / F u n c t i o n a l R e g i o n Form Input F a c t o r s V a r i a b l e F i x e d O u t p u t ( s ) D a t a R e t u r n s t o S c a l e Comments Lau Y o t o p o u l o s 1971/2 /3 I n d i a Cobb-Doug l a s Labour Land, C a p l t a l A g g r e g a t e C r o s s - C o n s t a n t S u p p o r t s p r o f i t max.; S e c t i o n a l s m a l l f a rms 20% more 1955-57 e f f i c i e n t than l a r g e . S1dhu 1974 I n d i a P u n j a b Cobb-Doug la s Labour Land , Cap 1 ta l Wheat C r o s s - C o n s t a n t P r o f i t max. u n c e r t a i n ; (Mex i can ) S e c t i o n a l ( u n c e r t a i n ) l a r g e & s m a l l f a rms 1967-71 e q u a l l y e f f i c i e n t . Y o t o p o u l o s C h i n a Cobb- L a b o u r , Lau Ta iwan Doug la s F e r t i l i z e r , L i n An imal Power, 1976 M e c h a n i c a l Power. Land , A s s e t s . A g g r e g a t e C r o s s - C o n s t a n t S u p p o r t s p r o f i t max. ( P r i c e S e c t i o n a l Labour & Land most Index) 1967-68 i m p o r t a n t i n p u t s . S i d h u Bannan te 1979 o° S i d h u Bannan te 1981 F l i n n K a l 1 r a j a n C a s t 11 l o 1982 • I n d i a P u n j a b I n d i a P u n j a b Ph i 1 1 i -p i n e s Laguna Cobb-Doug la s T r a n s l o g Cobb-Doug la s L a b o u r , F e r t 1 1 i z e r , Water L a b o u r , F e r t i 1 1 z e r , Animal Power. L a b o u r , F e r t 1 1 i z e r , Pe s t i c l d e s , An imal Power, M e c h a n i c a l Power. Land , C a p l t a l , E d u c a t i o n . Land , S o i l , Cap i t a l , E d u c a t i o n , I r r i g a t i o n , Land, Cap i t a l , I r r i g a t i o n . Wheat (Mex lean ) Wheat (Mex i c an ) R i c e C r o s s -Sec t i o n a l 1970-71 C r o s s -S e c t i o n a l 1970-71 C r o s s -S e c t i o n a l 1978-79 C o n s t a n t Sma l l & l a r g e f i r m s e q u a l ; Land most i m p o r t a n t i n p u t . S u p p o r t s p r o f i t max. C o b b - D o u g l a s f u n c t i o n a l form r e j e c t e d . D e c r e a s i n g S u p p o r t s p r o f i t max. Weaver 1983 U.S. N o r t h & S o u t h Dako ta T r an s 1og Labour , F e r t i 1 i z e r . M a t e r i a l s , P e t r o l P r o d u c t s , C a p i t a l S e r v i c e s . Land, P r e s e a s o n , P r e c i p i t a t i o n . Food G r a i n Feed G r a i n L 1 v e s t o c k . T i me-S e r l e s 1950-70 D e c r e a s i n g S u p p o r t s p r o f i t max. Shumway 1983 U.S. T e x a s T r a n s l o g & Quadra t 1c H i r e d Labour , F e r t i 1 i z e r , M a c h i n e r y . Land , F a m i l y L abou r . C o t t o n , R1ce, T i m e -Hay, C o r n , S e r i e s Wheat, Sorghum 1957-79 Wheat n o n j o i n t . Lopez 1984 Canada G e n e r a l I z e d L e o n t l e f . H i r e d Labour , O p e r a t o r L a b o u r , Cap i t a l , Land . C r o p s , Animal P r o d u c t s . C r o s s -S e c t i o n a l 1971 O u t p u t s n o n j o i n t ; H i r e d & O p e r a t o r Labour comp lement s . specification have since been c r i t i c i s e d . Chand and Kaul (1986) have outlined some of the reasons for criticism and "... suggest caution in the use of some of the results quoted by the studies 3 8 conducted by Lau and Yotopolous, Sidhu, and others." Sidhu and Bannante used the Translog formulation in their 1981 study and found it preferable to their earlier use of the 39 Cobb-Douglas. The translog may under certain conditions collapse to the Cobb-Douglas specification and can thus be used to test for the type of technology underlying the production 40 process. A major advantage of the translog is that behavioural assumptions such as profit maximization can be tested. In comparison with both the Cobb-Douglas and the Generalized Leontief formulations, the translog has been found to be the most r e l i a b l e . 4 1 The earlier profit function studies assumed only one output, and therefore implicitly assumed nonjointness. A nonjoint commodity is produced by a decision process separate from the decisions about other commodities, and the supply of the nonjoint product can be studied without regard to other product prices. As Shumway (1983) has shown, nonjointness can be tested for using 42 the translog specification. More recent studies have looked at multioutput firms and increased the number of variable inputs included, from one to five or more. Table 14 does not show a l l the input groups of a l l the studies but only the main categories, e.g., labour may be sp l i t into family and hired labour. A l l the profit function studies are restricted (i.e., short run) except for that by Lopez (1984). Common variable inputs include labour, machinery and 79 f e r t i l i z e r , and the main fixed input is land. Many of the profit function studies have been carried out using a cross-sectional data base. The studies using cross-sectional data have recently been c r i t i c i s e d , with only Flinn et a l . (1982), of the pre-1984 43 studies avoiding most of the problems. (b) Cost Functions A variant of the restricted profit function is the cost 44 function. Production is characterized as a cost minimizing process in which the firm choses the optimal quantities of variable factors given fixed output and factor prices. At the minimum cost a firm is both technically efficient (i.e., on the transformation function frontier) and allocatively efficient 4 5 (i.e., has the correct factor intensities). The transformation function T, efficient input-output combinations and primal 46 technology set PT, can be retrieved from the cost function. Differentiation of the cost function with respect to each output produces a set of interdependent marginal cost functions. Given the assumptions of perfect competition these marginal cost functions can be used to characterize the supply responses of individual production units and thus provide another means for benefit calculation. Table 15 summarises some recent studies of agriculture using the cost function. As opposed to the profit function studies the translog is the main functional form used and time series information is the data base. A l l the studies have been performed for the long run and thus input factors are not sp l i t into fixed and variable. 80 T a b l e 15. A p p l i c a t i o n s o f the Cos t F u n c t i o n In A g r i c u l t u r a l Economic s A u t h o r ( s ) / C o u n t r y / F u n c t i o n a l Input F a c t o r s Year R e g i o n Form O u t p u t ( s ) Data R e t u r n s t o Sea l e Comments B l n swanger U.S. 1974 co Kako 1978 Lopez 1980 J a p a n Canada T r a n s l o g T r a n s 1og G e n e r a l I z e d L e o n t 1 e f f L abour , M a c h i n e r y , Land , F e r t i l i z e r , O t h e r s . L abour , M a c h i n e r y , Land , F e r t l 1 i z e r , Ml s e e l l a n e o u s . L abour , Cap i t a l , S t r u c t u r e s & l a n d . I n t e r m e d i a t e i n p u t s . A g g r e g a t e R i c e A g g r e g a t e T I m e - S e r l e s & C r o s s -S e c t i o n a l 1948-1964 T i m e - S e r i e s 1953-1970 T i m e - S e r i e s 1946-1977 C o n s t a n t R e j e c t e d P r i c e f e r t i l i z e r , l a b o u r 8> m a c h i n e r y , exogeneous t o a g r l c u l t u r e ; T e c h n 1 c a l change b i a s t o m a c h i n e r y . R e j e c t CES, & C o b b -Doug l a s f u n c t i o n a l f o r m s , & L e o n t 1 e f f p r o d u c t i o n f u n c t i o n . I nput demand 1 n e l a s t 1 c . Ray 1982 U.S. T r a n s l o g H i r e d Labour , F e e d , Seed, F e r t i l i z e r , C a p i t a l , L i v e s t o c k , Mi s e e l l a n e o u s . A g g r e g a t e T i m e - S e r i e s D e c r e a s i n g C rop s & L i v e s t o c k 1939-1977 j o i n t ; 1.8% p r o d u c t i v i t y g rowth r a t e p . a . Adomowicz Canada 1986 T r a n s l o g C a p i t a l , Land , F u e l L abour , M a t e r i a l s , L i v e s t o c k . A g g r e g a t e T Ime-Ser i e s 1940-1981 Input demand i n e l a s t i c ; Input e l a s t i c i t i e s o f s u b s t i t u t i o n t e n d i n g t o z e r o . 3.4 A Review of Recent Regional Economic  Assessments of Ozone Effects  on Agricultural Crops The majority of recent economic assessments of ozone damage 47 to crops have been at the regional level, and these have employed most of the economic modelling techniques outlined 48 above. The work done in this area before circa 1982 was sci e n t i f i c a l l y orientated and concentrated upon the accuracy of physical estimates of ozone damage to crops. Where monetary values of damages were given, the traditional model was employed without regard for the overestimation this technique can cause. Recent studies have concentrated on two main regions of the United States; namely, the Corn Belt ( I l l i n o i s , Indiana, Iowa, Ohio, and Missouri) and California. These areas have a good supply of data on crop response and air quality, and are nationally important crop growing regions. Only one study could be found which gave an economic assessment of ozone crop damages in Canada, and this used the traditional method. In a l l , nine regional studies are reviewed, and the discussion is summarised in Table 16. A l i s t of the crops covered by each study is given in Table 17. 3.4.1 A Traditional Study Linzon et a l . (1984), analysed fifteen crops in two regions 49 of Ontario, Canada. Yield reductions were estimated for each crop using the experimental results of other reseachers. No damage was assumed to occur at 0.03 ppm or lower (seven hour seasonal average). The traditional model was used to calculate monetary equivalents of the approximated crop losses. Increased 82 T a b l e 16. Summary o f Recent R e g i o n a l S t u d i e s o f the Economic Lo s se s Due to Ozone P o l l u t i o n Number Type of N a t u r e o f I n c l u s i o n o f S t u d y S t u d y S tudy Economic of Dose -Response B e n e f i t s Supp ly C r o s s - C r o p Number A u t h o r s Da te Model C rops I n f o r m a t i o n E s t i m a t e d S h i f t S u b s t i t u t i o n L1nzon P e a r s o n Donnan Durham 1984 T r a d l t I o n a l 15 E x p e r i m e n t a l Data (NCLAN and o t h e r ) P r o d u c e r P a r a l l e l Not I n c l u d e d Adams C r o c k e r T h a n a v l b u l c h a l 1982 Quadra t 1c Programming 14 F o l i a r I n j u r y Models P r o d u c e r U n c e r t a i n I n c l u d e d and Consumer H o w l t t G o s s a r d Adams 1984 Quadra t 1c Programming 13 E x p e r i m e n t a l Data (NCLAN) P r o d u c e r R o t a t i o n I n c l u d e d and Consumer co Rowe C h e s t n u t Adams M c C a r l 1985 1985 Quadra t 1c Programming Quadra t 1c Programmlng 16 F i e l d and Exper imenta l Data Exper i menta 1 Data (NCLAN) P r o d u c e r R o t a t i o n I n c l u d e d and Consumer P r o d u c e r U n c e r t a i n I n c l u d e d and Consumer Benson K r u p a Teng W e i s c h 1982 A g g r e g a t e S u p p l y / Demand Exper imenta1 Data P r o d u c e r P a r a l l e l Not I n c l u d e d Leung Reed Geng 1982 A g g r e g a t e S u p p l y / Demand 9 Secondary Data P r o d u c e r R o t a t i o n Not and I n c l u d e d Consumer Page A r b o g a s t Fab i an C i e c k a 1982 A g g r e g a t e S u p p l y / Demand 3 E x p e r i m e n t a l Da ta P r o d u c e r R o t a t i o n Not I n c l u d e d M j e l d e Adams D i x o n G a r c i a 1984 N e o c l a s s i c a l Economet r1c P r o d u c t Ion F u n c t I o n 3 Secondary Data P r o d u c e r U n c e r t a i n Not I n c l u d e d Table 17. Crops Included in Regional Assessments Frequency Crop Type Regional Assessment Study (refered of Crop to by number assigned in Table 16) Occurance in Studies 1 2 3 4 5 6 7 8 9 7 Wheat * * * * * * * 6 Field Corn * * * * * * 5 Lettuce * * * * * 5 Tomatoes * ** * * * 5 Potatoes * * * * * 4 Al f a l f a * * * * 4 Soybean * * * * 3 Celery * * * 3 Cotton * * * 3 Onions * ** * 2 Barley * * 2 Beans * * 2 Carrots * * 2 Grain Sorghum * * 2 Grape * * 1 Avacado * 1 Broccoli * 1 Cantaloupe * 1 Cauliflower * 1 Cucumber * 1 Grain Hay * 1 Green Bean * 1 Lemon * 1 Lima Bean * 1 Orange ** 1 Rice * 1 Pasture * 1 Rutabage * 1 Radish * 1 Safflower * 1 Silage * 1 Strawberry * 1 Sugar Beet * 1 Sweet Corn * 1 Spinach * 1 Tobacco * 1 White Bean * Total Number of Crops in Study 15 14 13 16 3 4 9 3 3 ** Means two types of same crop studied. 84 yields, due to pollutant reduction, were multiplied by a current producer benefit estimate. The constancy of price assumption was justified by (a) the small magnitude of crop production from the region relative to total market production, and (b) by the existence of supply management and Marketing Boards. In 'Figure 10 the implicit assumptions of the traditional model are shown. A constant price level is assumed to exist at PO. The aggregate demand curve DO is perfectly elastic (i.e., horizontal), because the quantity of the crop produced, before and after ozone concentrations are altered, is assumed to s e l l at the same price. The original quantity supplied is Q1 at high ozone concentrations, and shifts to Q2 when concentrations are reduced; and the respective aggregate supply curves are SO and S1. Instead of the normal upward sloping supply curve equal to marginal cost (under perfect competition), the model assumes marginal cost is zero up to the quantity being produced and infinite thereafter; that i s , supply is perfectly elastic up to Q2 and then price inelastic. The fact that aggregate supply curves are normally positively sloped was ignored by Linzon et a l . , and so the disjointed function of the traditional model was implicitly accepted. As has been discussed the traditional model seems certain to grossly overestimate the gain to producers from ozone reductions. This study estimated the average gain to producers of reducing ozone from current levels (the highest regional category being 0.05 ppm, 7hr. seasonal mean) to 0.03 ppm as $15 million per annum, with a range of $9 to $23 million (1980 dollars). Five crops accounted for over 80 percent of the estimate due to their 85 Figure 10 The Traditional Model Price of Crop P0 SO B DO ql q2 Quantity of Crop Source: Kopp, R.J.; Vaughan, W.J.; and Hazilla, M. Agricultural  Sector Benefits Analysis for Ozone Methods Evaluation and  Demonstration (North Carolina : Research U.S. E.P.A., 1984). 86 sensitivity to ozone namely, potatoes, soybeans, tobacco, wheat and white beans. 3.4.2 Quadratic Programming Approaches Four economic regional studies of ozone crop losses published since 1982 have used the price endogeneous Q.P. approach. Three of these were based on the agricultural crop growing regions of California, and employed similar models. The fourth study generated welfare estimates via a micro-macro model, using farm models to derive the effects of regional production changes on national markets. Adams et a l . (1982) studied fourteen f i e l d crops in four 50 regions of southern California. The dose-response functions are a major weakness of the study, being calculated from foliar injury models which have been converted to reflect yield loss (see Chapter 2). This approach showed broccoli, cantaloupes, carrots, cauliflower, and lettuce to be ozone resistant, with l i t t l e or no damage occurring. Lettuce in particular seems to be incorrectly classified, with evidence existing which states i t to be an ozone sensitive crop (see Chapter 1). The optimal crop mix after ozone concentrations were reduced showed a very significant decrease in the production of these air pollution tolerant crops, due to their substantially reduced pro f i t a b i l i t y relative to crops that were more sensitive to ozone. Linear inverse demand functions were assumed for each crop, i.e., price as a function of quantities. The supply functions for a l l production inputs were assumed to be perfectly price elastic. The Willig Approximation conditions were invoked (see Appendix I) 87 so that any differences between ordinary and compensated consumers' surplus was assumed to be t r i v i a l . This invocation was justified because neither income el a s t i c i t i e s nor expenditures as a percentage of income seemed likely to be large for the crops being studied. The model (calibrated to 1976) was set up to maximize the sum of producer and consumer surpluses. Reducing ozone levels to 0.08 ppm, the state standard, would have increased 1976 producer quasi-rents by $35.1 million and consumer surplus by $10.1 million. Production changes induced by altering ozone concentrations were assumed to leave the input mix constant. Changes in ozone concentrations from 1976 levels were reflected by changes in the optimal mix of outputs. Due to the variety of demand price e l a s t i c i t i e s across crops, the distribution of benefits was a function of the mix of demand curves and resultant crop proportions in the solution. For example, the removal of cotton from the study causes the balance between consumer and producer surpluses to be reversed. Cotton has an elastic demand curve, thus the benefits from ozone reduction are largely producer quasi-rents. The exclusion of cotton reduces the producer gain to $9 million and leaves the consumer gain almost unchanged at $10 million. Although mitigation was allowed for by cross-crop substitution, the authors felt the use of fixed 1976 production coefficients and resource levels potentially constrained the possible producer mitigative adjustments on the input side. Thus, they warn that the subsequent programming results and welfare 88 effects might be overestimated, although this seems unlikely in the case of ozone as is discussed in section 3.5.1. They also suggest, among other things, that improvements could be made by allowing for non zero, cross-price e l a s t i c i t i e s , widening the scope to include effects in other regions and markets and studying a greater variety of crops. Howitt et a l . (1984) studied thirteen crops, also in the 51 state of California. They employed the NCLAN experimental results to derive dose-response functions for seven of the crops and other experimental results for one other crop. The remaining five crops were given "surrogate" response functions. The California Agriculture Resources Model (C.A.R.M.) was used to calculate consumer and producer surplus. This Q.P. model allowed for constrained cross-crop substitution, and included twenty-seven other crops which were assumed unaffected by ozone concentrations. The model was similar to that used by Adams et a l . (1982) above but was calibrated to 1978 instead of 1976. Three ozone scenarios were compared with a base case for 1978. The total welfare gain from a reduction in ambient ozone of approximately 25 percent (to 0.04 ppm, seasonal seven-hour average) was $35.8 million per annum, and the welfare loss from an increase in ozone levels by approximately 33 percent (to 0.08 52 ppm, seasonal seven hour average) was $157.3 million. Reductions in ozone concentrations cause a "downward shift" of 53 the supply function, which is shown graphically as a rotation, i.e., the price intercept does not change. Rowe and Chestnut (1985) used the CARM, as used by Howitt et a l . (1984), to study sixteen crops in the San Joaquin Valley, 89 California. Although thirty-three crops were included in the economic model only sixteen were judged to be affected by ozone, or could be supplied with dose-response functions. The study analysed the use of f i e l d data regression to derive dose-response functions, but only obtained s t a t i s t i c a l l y significant results for four crops dry beans, cotton, grapes and potatoes (see Chapter 2). As a result, NCLAN functions were used for six other crops, and a futher six were derived from other sources and by the use of "surrogate" functions. Three ozone scenarios were studied (0.12, 0.10 and 0.08 ppm seasonal hourly maximum) and results were given for both consumers and producers. Sulphur dioxide was also included in the study, but over 98 percent of the economic value of the agricultural damages was attributed to ozone. If an ozone standard at which l i t t l e or no crop damage was expected (defined as 0.08 ppm seasonal hourly maximum) had been met in 1978, the estimated gain to consumers would have been $30.3 million and the gain to producers $87.1 million. Adams and McCarl (1985), studied three crops in the Corn Belt region of the United States, with a Q.P. model calibrated to 55 1980. The dose-response functions were taken from NCLAN results for 1980-1982, and were I l l i n o i s specific. The model analysed the changes occurring throughout the agricultural sector at the national level as a result of the adjustments in Corn Belt output, ceteris paribus. This was achieved by characterising regional agricultural production using twelve representative farm models. These representative farms were then used to generate supply adjustments in the national level model. Consumer and 90 producer surpluses were calculated under two scenarios. An improvement in air quality of 25 percent (a reduction of ozone from 0.12 ppm to 0.08 ppm one hour seasonal average) gave total benefits of $688 million (1980); a loss to producers of $1,411 million and a gain to consumers of $2,079 million. The other scenario took a 50 percent degradation in air quality (an increase in ozone from 0.12 ppm to 0.16 ppm one hour seasonal average) and gave a total loss of benefits of $2,225 million; a reduction of consumer surplus by $4,986 million and an increase of producer surplus by $2,761 million. Increases in crop supply were found to favour consumers and reductions in crop supply favoured producers. These distributional consequences are a result of supply shifts in the face of a price inelastic demand curve. 3.4.3 Econometric Approaches Several econometric approaches have been applied to the assessment of crop damage due to ozone pollution, including a dual model which is reviewed in the next section. In this section we discuss two models which analyse producer surplus and one which one includes both producer and consumer surplus. Each model has distinctive features and makes different assumptions about the nature of agricultural crop supply curves and production responses. Benson et a l . (1982), studied four crops in Minnesota. Originally, six crops were to have been studied but dose-response functions could not be calculated for soybeans and oats, so they were dropped.^ Dose-response for the four remaining crops was 91 calculated using experimental data reported by other researchers. The dose-response functions allowed for espisodic (as opposed to chronic or acute) exposure by breaking the exposure into multiple time periods over the growing season. The functions were applied to Minnesota using actual or simulated county level ozone data. This was used to derive a range of yield losses under different ozone concentrations. The economic analysis, using a comprehensive econometric model of U.S. agriculture, was carried out under two separate conditions (a) crop loss was restricted to Minnesota alone and Minnesota and United States production levels were estimated; (b) the same rate of loss as occured in Minnesota was assumed to occur over the entire United States, and again Minnesota and national production levels were estimated. A range of producer welfare estimates was derived with the worst case ozone level (0.12 ppm hourly concentration with ten occurrences per week) causing a loss of $30,366,409 under assumption (a) compared to 1980 production. The worst case estimate under assumption (b) gave a gain to producers of $67,540,745 compared to 1980 production. The explanation for the gain under (b) is that price rises as output is restricted and the "price effect" dominates, whereas under (a) the "production effect" dominates. The increase in the total value of production as ozone increases is due to the price inelastic nature of demand for the commodities studied. This "gain" to producers is in fact misleading in that: (1) costs have risen due to ozone pollution, and so a loss of comparative advantage is suffered by a l l affected farmers (the gain is at 92 best a short-run phenomenon as competition from other sources would drive high cost producers out of the industry; as the authors note, scenario (a) is more likely in the long run). (2) Focusing on the "gain" to producers ignores the dynamics of consumer and producer welfare. Benson et a l . do not calculate consumer surplus, therefore the net change in societal welfare, and the distribution of welfare changes, are unknown. In addition, scenario (b) is highly dubious because of the assumption that regional dose-response/ozone estimates can be extrapolated to the national level. Although a detailed national level model was used the economic analysis is similar to that of the traditional model. A comprehensive econometric model of the United States agricultural sector (calibrated to 1980) was used to capture crop supply and demand across multiple domestic and foreign markets. The production level estimates for various ozone concentration/frequencies were used as data input to a national crop-livestock model which considers the interrelationships of the commodities and estimates a price for each production level. These prices were then multiplied by the production i^vel estimate in order to estimate the value of production. Thus, despite accounting for national level changes, the regional model remains simplistic in that quantity is being multiplied by price in order to estimte the "value" of production (namely producer quasi-rents). Also, cross-crop substitution is ignored as a mitigative strategy. Leung et a l . (1982) studied nine crops in the south coastal 58 region of California. Linear dose-response functions for each crop were calculated from secondary data. No yield reductions 93 were found for celery which was therefore excluded. Yield reductions were estimated by calculating the difference between actual yields with 1975 ozone levels and yields predicted by the dose-response functions at zero ozone levels. The use of zero ozone levels risks overestimation of benefits by including ozone from natural sources as anthropogenic. The predicted percentage yield changes predicted were used to rotate the supply curve for each crop individually allowing no cross-crop substitution. The best f i t aggregate econometric supply curves were linear, and the demand curves were power functions. Both ordinary consumer surplus and producer quasi-rents were calculated. The ordinary consumer surplus was assumed to equate approximately with true consumer surplus because the marginal u t i l i t y of income was expected to be nearly constant; this assumes the commodities in the study commanded only a small proportion of consumer income (see Appendix I). The resulting estimates were $57.3 million in lost producer surplus and $45.7 million in lost consumer surplus (1975 dollars). An input-output model was used to translate these losses into direct income effects and indirect economic effects. The direct losses within the south coastal region were $117 million, and $14.1 million for the rest of the state. Indirect effects were estimated to cause a loss of $276 million within the region and $36.6 million in the rest of California. Page et a l . (1982) studied three crops in the Ohio River Basin (which includes a l l of Kentucky, and portions of I l l i n o i s , 59 Indiana, Ohio, West Virginia and Pensylvania). Linear dose-response functions were taken from a previous study on the 94 region, which was itself based on the experimental data of other researchers. Errors may have arisen from these data because they were originally derived for areas outside the Ohio River Basin and may include cultivars not grown in the study area. In addition, the dose-response functions overestimate crop yield reductions when compared to the results from NCLAN.^ Producer surplus was estimated under three scenarios which involved different characterizations of future energy and fuel use. Under the "business as usual" scenario, the net present value of probable total cumulative crop loss, for twenty-four years (1976-2000), from sulphur dioxide and ozone, was approximately $7002 million. The losses attributable to sulphur dioxide were 0.7 percent of the total, ozone being responsible for the other 99.3 percent. Aggregate econometric supply curves (convex, with constant price e l a s t i c i t i e s over the relevant producer surplus estimate range) were derived for each crop. Price was assumed to remain constant, which may be a serious omission considering the Ohio River Basin is a major producer of the crops studied, and a substantial change in the regional yields would most certainly affect market price, and so consumer welfare (see the Q.P. study by Adams and McCarl (1985) above). The authors felt the normally negative intercept of the supply curve made the notion of producer surplus "vacuous", and therefore adjusted their empirical results to give supply curves with zero intercepts. The problem with the position of the intercept is not mentioned in any of the other studies. Some studies use negative intercepts, 95 e.g., Howitt et a l . (1984), Rowe and Chestnut (1985), and others positive intercepts, e.g., Leung et a l . (1982).^1 Page et a l . do not explain the logic underlying their decision to assume a zero intercept. The dose-response functions were used to rotate the supply curve of each crop in turn to simulate ozone damage, and thus cross-crop substitution was excluded. 3.4.4 A Duality Study Mjelde et a l . (1984) employed the Neoclassical econometric 62 model with a profit function. Duality models are not dependent upon an explicit dose-response function to estimate the welfare changes from a change in crop yield. However, experimental data are required to frame the i n i t i a l hypothesis, and to cross-check the resulting estimates. The profit function, which includes ordinary economic variables and environmental variables (as fixed inputs), shows the effects of varying ozone concentrations on farm profits. Pollution which is deleterious to the production process will exert an exogeneous force upon producer decisions. Producers may respond, even if they are not aware of the phenomenon causing the observed effects, by varying input mixes. A profit function that has air quality as an input can be used directly to determine the producer's loss in profit and how other inputs are adjusted in response to a change in air quality. A dose-response function, while useful in establishing cause and effect relationships, does not provide this latter type of information. Futhermore, the change in the supply of a crop can be computed directly and this response is the net effect in agricultural output, i.e., the response incorporates producer adjustments triggered by price and yield effects. Part of this theoretical advantage may not be of benefit in the case of ozone as producer adjustments should not include a change 96 of input mix, as wi l l be discussed in section 3.5.1. In order to compare the results of a dual study with experimental results, such as those of NCLAN, the mix of variable inputs is assumed 64 constant. However, producers may adjust their output mix, and this is not allowed for in the study. The study analysed three crops in I l l i n o i s . Detailed farm level cost and production information was made available by the I l l i n o i s Association of Farm Business Farm Management which provided a rich source of individual farmer data not available in 6 5 many other states. The study found increased ozone levels depressed output and reduced the marginal productivity of variable inputs so that less were used. Ozone resulted in an aggregate loss in profits to I l l i n o i s farmers of approximately $50 million (1980).^ The assumption of a constant price ignores consumer surplus, and may be unjustified because I l l i n o i s is a major grain producer. Also i f ozone reduction improved crop yields throughout the Corn Belt, both consumers and producers would be expected to benefit. As the study states: These loss figures should be interpreted with extreme caution. They are computed under the assumption that price remains constant. Such an assumption is not valid i f ambient ozone levels increased in other grain producing regions. If this latter case occurs then the supply curve of feed grains would shift to the l e f t . Given an inelastic demand curve (which is typical of demand in the short run), the corresponding price rise may leave producers better off than before the ozone increase. However, consumers would be worse off than before. This illustrates the importance of analyzing both producer and consumer interactions in drawing conclusions about the impact of any pervasive environmental change. 97 3.5 Issues in Economic Models of Ozone Induced Crop Loss 3.5.1 Modelling the Impact of Ozone on Agricultural Inputs Kopp et a l . (1984) have summarised the theory pertaining to the incorporation of air pollution in a agricultural production model. The primal technology set PT is altered by changes in environmental variables, such as ozone, so that, PT is a function of E, where E is a vector of environmental influences. This implies a transformation function of the form where E impacts the manner in which x is transformed into y, that i s , inputs are transformed into outputs. The link between E and the x, y transformation can be made by the use of experimental natural science information (the approach chosen in this thesis), or from observed nonexperimental data (as done by Mjelde et a l . ) . The manner in which E affects the x, y transformation determines how i t should be modelled within the T function. Given the transformation function: T(x, y, E) = 0, the imposition of functional separability gives the impact of E on T as, T(x, y, E) = G*[H (x, y) + (E)] = 0. This implies that the frontier transformation function is neutrally displaced inward and outward as the components of E change. Alternatively, the productivity of factor inputs may be biased causing a non-neutral production function sh i f t . For example, crop fungicide retention may be reduced by acid precipitation, ceterus paribus. Thus, reducing acid precipitation can cause the productivity of fungicides to increase relative to 98 other inputs. In the case of the effects of ambient ozone upon the productivity of pre-harvest agricultural production factors, 69 "neutral factor productivity enhancement" is hypothesised. That is, the optimal mix of factors of production (i.e., their ratios) is invariant with respect to ozone concentrations, and agricultural production functions are shifted in a neutral fashion. If this hypothesis holds, the underlying production function for a single output firm can be written as, Y = * ( E ) f(x1 , ..., xn), and the corresponding cost function written as, C = [C(P, Y) M E ) ] , where P is an n-vector of input prices. Given a fixed vector x, M E ) can be interpreted as a dose-response function, and experimentally derived functions can be used as proxies to the true function M E ) . If ozone were hypothesised to differentially impact factor productivity, implying a non-neutral production function shift, then experiments would need to be designed so as to systematically vary input quantities in addition to ozone. This would lead to the derivation of dose-input functions, as well as dose-yield functions. Thus, neutral factor productivity enhancement is an implicit assumption of a l l those studies employing dose-yield functions without dose-input functions. Of the studies reviewed in the previous section, only the duality model of Mjelde et a l . (1984) is free of the neutral factor productivity enhancement assumption, because experimentally derived dose-response functions are not required. Yet in order to 99 compare the results of the model with those from NCLAN, the mix of variable inputs was assumed constant. Hence a l l the regional studies of ozone damage to agricultural crops have conformed to the neutral production function shift implying a neutral cost function shift, which determines the shift in agricultural supply * 70 functions. 3.5.2 Cross-Crop Substitution The potential to change output mix has been noted as an important producer mitigative strategy in the face of ozone 7 1 damage to crops. Given the wide range of sensitivities of crops to ozone concentrations, substantial yield reductions could be expected to cause farmers to react so as to minimize their losses by adopting more resistant crop types. The potential to employ alternative, ozone resistant, crops (or cultivars) in the face of damages will be affected by climate and s o i l characteristics, technical constraints and institutional factors. This is an empirical issue and has been analysed by Smith and Brown, and 72 Kopp et a l . Smith and Brown (1982) assessed in detail the importance of acreage shifts between differentially sensitive crops in response to ozone induced yield changes. They studied corn, soybeans, and wheat in Indiana. Demand was assumed to be i n f i n i t e l y elastic, that i s , market price was assumed constant. A L.P. model was employed to calculate producer quasi-rents based upon a representative farm. Four yield improvement scenarios were compared with a base case. The conclusion was that allowing for cross-crop substitution could increase the estimated economic 100 gain to farmers from reductions in ozone concentrations by up to 73 20 percent, depending upon the region and yield loss estimates. This was due to substantial acreage shifts to the relatively more ozone sensitive crop, soybean. Figure 11 explains the reasoning behind the results of Smith and Brown. The crop shown in the figure is assumed to be relatively resistant to ozone concentrations. In part (a) acreage is assumed not to change with differences in ozone concentrations. The aggregate demand curve is D, the aggregate supply curve shifts from SO to S1 as ozone is reduced, the price drops from pO to p1, and the quantity supplied increases to q1 from qO. In part (b) farmers are allowed to alter their acreage devoted to a particular crop. As before the supply curve may i n t i a l l y shift from SO to S1, but now as ozone concentrations f a l l farmers can substitute crops which are relatively sensitive to ozone. As this happens the acreage of the more resistant crops f a l l s and the supply curve shifts to S2. In (a) the change in consumer surplus was p0,A,B,p1 and in (b) is this area minus area p2,C,B,p1. Smith and Brown state that cross-crop substitution could move the supply curve back to, or beyond, SO. Thus, the change in consumer and producer welfare can be overestimated (underestimated) when acreage is assumed to remain constant for relatively ozone resistant (sensitive) crops in the face of a f a l l in ozone concentrations. In contrast to the findings of Smith and Brown (1982), Kopp et a l . (1985) found the potential for bias from not accounting for cross-crop substitution to be small. Kopp et a l . studied 101 Price of Crop Figure 11 Supply Shift Due to Ozone Decrease (a) No Cross-Crop Substitution Quantity of Crop (b) Allowing for Cross-Crop Substitution Price q2 qi Quantity of Crop Source: Martha Smith and Deborah Brown, Crop Production Benefits from  Ozone Reduction: An Economic Analysis (Indianna: Purdue University, Agricultural Experimentation Station, 1982) p.15 Figures 3 and 4. 102 corn, soybeans and wheat in the U.S. Corn Belt, which includes 74 Indiana, using a partial equilibrium econometric model. Ozone induced welfare changes were calculated allowing for cross-crop substitution and compared to those crop mix constant. The maximum change in acreage in response to changes in ozone concentrations was equivalent to 4 percent of total corn belt acreage (1978). Assuming prices were constant, Kopp et a l . found the benefit gains from a reduction of ozone (to 0.09 ppm) were understated by 2 percent and losses from an increase in ozone (to 0.15) overstated by 4 percent compared to a fixed crop mix model. Both Kopp et a l . , and Smith and Brown showed that if output prices were to change in response to cross-crop substitution, the benefit errors from assuming a fixed crop mix were substantially reduced. In Kopp et a l . the errors became a 0.1 percent overestimate of welfare losses from the increase in ozone and a 0.2 percent underestimate of welfare gains from the decrease in ozone. Thus, the potential error from excluding cross-crop substitution as a mitigative strategy remains uncertain. Given price changes the problem may be small and, in addition, there may be transactions costs which restrict output substitution. For example, specialised machinery (with a zero opportunity cost) may be made obsolete encouraging a farmer to remain in production as long as i t is operational (assuming variable costs are covered). Certain farmers may have traditionally grown a specific crop and may not even realize the potential for substitution, or may wish to maintain consistency and avoid uncertainty. Crops and cultivars grown in a particular region are normally selected 103 because they are those best suited to the environmental and production requirements (e.g., processing or fresh markets). In addition, the adoption of ozone resistant cultivars can be at the expense of yield reductions, because the resistant strains are 75 less productive. Producers of perennial crops may follow a fixed crop mix pattern due to the added expense of changing output mix. Similarly, farmers whose crops take several years before bearing f i r s t fruit may find themselves committed to a fixed output mix. A l l the Q.P. models reviewed included cross-crop substitution, and a l l of the other models have failed to do so (see Table 16). While the potential for a 20 percent error in benefit estimates may make this a serious exclusion, this conclusion is far from clear. The f l e x i b i l i t y of farmers in switching their output mix should be assessed before including cross-crop substitution, because errors may arise from assuming farmers are more flexible than in reality. This may be a particular problem where perennial crops and those requiring a long time to f i r s t fruit are concerned. 3.5.3 The Distribution of Benefits Benefits may be distributed between groups, such as producers and consumers, across geographical areas and amongst different sectors of the economy. Where the area being analyzed is relatively large, such as the U.S. Corn Belt or the- entire United States, the geographical distribution of welfare changes may form the central focus of attention. Similarly, where important crop growing regions are being studied, the indirect effects can be 104 significant. However, only Leung et a l . , of the studies reviewed above, have included a calculation of the latter, indirect effects, and no attempt is made to do so in this thesis. The main concern here is for the distribution of welfare changes between producers and consumers. Varying assumptions concerning the position of both supply and demand functions, and the nature of the response of supply functions to changes in ozone levels will result in wide variations in welfare estimates. (a) Demand Characteristics The distribution of welfare changes between consumers and producers is dependent upon the price e l a s t i c i t i e s of supply and 7 6 demand. A numerically large value for demand price elasticity implies that the quantity demanded is proportionately very responsive to price changes. Generally, when the demand price elas t i c i t y is large the good is a luxury, and when small a necessity. Agricultural products are usually closer to the latter 77 with inelastic, short-run aggregate demand curves. A perfectly elastic demand curve was assumed by four of the studies reviewed; namely, Linzon et a l . (1984), Benson et a l . (1982), Page et a l . (1982), and Mjelde et a l . (1984). As has been mentioned, this assumption may be justified when the change in the yield of a crop is not expected to be large enough to induce a demand response, or when some institutional arrangement fixes a rigid price, preventing market forces from operating. However, this assumption has also been employed as a method of simplifying the study so as to focus attention upon other issues besides policy orientated benefit estimates. For example, in Mjelde et 105 a l . the main goal was to test the dual approach not previously applied to air pollution benefit assessments. The benefits estimated by such studies ignore the dynamics of consumer and producer surpluses, and cannot therefore be taken as measure of 78 the net societal welfare change. The benefits obtained may also be contrary to other evidence or unrealistic, such as the results of Benson et a l . (b) Supply Characteristics The price elasticity of supply is a similar concept to that for demand; that i s , a measure of the responsiveness of supply to price changes. Supply responsiveness is dependent upon the technical characteristics of production and the underlying input cost structure. Normally, the supply curve w i l l be positively sloped and between the extremes of perfectly elastic and perfectly inelastic and, excepting the two traditional type models (Linzon et a l . and Benson et a l . ) , a l l the studies reviewed concur with this. However, two main differences occur among the supply characteristics assumed by different studies; (a) the positioning of the intercept, and (b) the nature in which the supply curve is shifted. Page et a l . mention that the notion of a negative intercept as typical in agricultral supply curves makes the notion of producer surplus "vacuous". Without any further expansion upon the matter, this leads them to assume a zero intercept. In Figure 12, SO has a negative intercept, S1 has a zero intercept and S2 a positive intercept. The supply function SO implies some quantity qO w i l l be produced when the market price is zero; that i s , the 106 107 cost of producing qO is zero. S1 implies nothing w i l l be produced until the price is positive and S2 requires a price of at least p2 before production commences. While SO is counter-intuitive, Adams et a l . (1984) suggest a zero intercept may also be unrealistic. They suggest, where the supply function is locally estimated, i t may be appropriate to truncate the function rather than extrapolate to the intercept. A supply function such as SOAB might result. However, this procedure will underestimate the increase in producer surplus from a yield increase due to a reduction of ozone (unless supply actually truncates). Therefore, in the analysis of Chapter IV the function is not arbitrarily altered, but is l e f t with a negative intercept. (c) The Nature of Supply Response  to Ozone Reduction Two types of supply function "shifts" have been used in ozone crop loss studies and discussions, (a) the parallel shift, and (b) the rotation, see Table 16. Several studies have assumed that the supply curve is rotated so that the price intercept (vertical axis) remains fixed, Howitt et a l . (1984), Page et a l . (1982), Leung et al (1982), Rowe and Chestnut (1985). However, some studies and discussions have also assumed the supply curve is shifted in a parallel fashion, the analysis of cross-crop substitution by Smith and Brown (1982), and a review paper by 79 . . . Eidman and Benson, and i t is implicit in the traditional type models of Linzon et a l . (1984), and Benson et a l . (1982). Although each supply response implies different assumptions which affect the resulting producer surplus, the underlying logic of 108 each has not been explained in any of the papers above. The parallel shift of the supply function (as in Figure 11) changes the price intercept while maintaining a constant slope. That i s , for a reduction in ozone, the average cost is reduced while the marginal cost remains constant. This implies that costs are reduced by an equal amount for every unit produced. The cost of producing the f i r s t unit is reduced by A, the second by B, the third by C, and so on, where A=B=C. Alternatively, this can be stated as implying that an extra fixed quantity of the crop in question w i l l be supplied at any price equal to or above that at the original intercept. A dose-response function gives a predicted percentage change in quantity as a result of a change in the concentration of ozone. The absolute amount of the change wi l l depend upon the quantity of the crop exposed. For example, assume that a specific reduction of ozone causes a 50 percent increase in the weight of potato tubers. If 1 unit of potatoes was being produced now there will be one and a half units, i f two then now there will be three, i f three then now four and a half, and so on. The reduction in cost is greater as the quantity increases, thus in the above example A<B<C. The gain in production at a given price is dependent upon the quantity produced at that price and exposed to ozone, before a change in the concentration of ozone. Thus, assuming a fixed quantity of crop is added over a wide range of prices is contrary to the underlying biological dose-response functions, and thus the parallel shift is an inappropriate characterisation of supply response. Figure 13 shows the effects of the parallel shift and the 109 Price Figure 13 Parallel Verses Rotation Supply Shift (a) Price Elastic Demand Quantity (b) Price Responsive Demand Quantity 110 rotation upon consumer surplus. Part (a) shows the effects of a reduction in ozone upon a crop under the two response assumptions given an infin i t e l y price elastic demand function pd,D. Supply is originally SO and moves to SP under the parallel shift, and SR under the rotation. Producer surplus is given by the area above the supply curve and below the price line. The original surplus pO,pd,A is increased by pO,A,B by the rotation and by p1,pO,B by the parallel shift. Thus, the parallel shift overestimates the gain in producer surplus by p1,pO,B. When the demand function is downward sloping, DD in Part (b), the equilibrium for the parallel shift is at a lower price and greater quantity than for the rotation. The same change as in Part (a) takes place, but this time the price f a l l s from pd to pr under the rotation and to pp under the parallel shift. Area a is lost, area d remains unchanged and area e is gained under both response assumptions. The difference in producer surplus between the two cases is then dependent upon the relative size of areas b, c and f. The lower relative price under the parallel shift means a greater loss in surplus by area b and that area c is not gained, while the gain is greater by f. Producer surplus due to the parallel shift will exceed that due to a rotation when area f exceeds areas b plus c. This seems likely even when the demand curve is perfectly inelastic ,i.e., the dotted line through A in Part (a). Thus, the parallel shift is both counter factual and like l y to cause biased welfare estimates. 111 3.6 Conclusion Several methodologies are available for crop loss assessment and have been applied to the analysis of welfare changes due to alterations in ozone pollution levels. Among these the microtheoretic econometric models provide a theoretically rigorous structure and have become a common approach to studying the agricultural sector. In conceptualizing agricultural crop production changes, neutral factor productivity enhancement is unanimously accepted, while output substitution will depend upon particular circumstances. Demand functions must be estimated i f credible welfare estimates are to be obtained. Finally, the supply function characteristics used in recent studies have not been fully explained and may cause unjustified bias in benefit estimates. 1 12 Footnotes 1 Richard M. Adams, Thomas D. Crocker, and N. Thanavibulchai, "An Economic Assessment of Air Pollution Damages to Selected Annual Crops in Southern California" Journal of Environmental  Economics and Management 9 (1982) p.57. 2 R.E. Just, D.L. Hueth, and A. Schmitz, Applied Welfare  Economics and Public Policy (London, England: Prentice-Hall International Inc., 1982). Also see, R.D. Willig, "Consumer's Surplus Without Apology" The American Economic Review 66:4 (September, 1976) 589-597. 3 J.M. Henderson, and R.E. Quandt, Microeconomic Theory: A  Mathematical Approach 3rd edition (London, England: McGraw-H i l l International Book Co., 1980). See also the comprehensive work by H.R. Varian, Microeconomic Analysis 2nd edition (New York: W.W. Norton and Co., 1984). 4 Richard M. Adams, Scott A. Hamilton, and Bruce A. McCarl, The  Economic Effects of Ozone on Agriculture (Corvallis, Oregon: Environmental Research Laboratory, U.S. Environmental Protection Agency, 1984) p.7. 5 Richard M. Adams, "Issues in Assessing the Economic Benefits of Ambient Ozone Control: Some Examples from Agriculture" Environment International 9 (1983) p.540. 6 Ibid. 7 James W. Mjelde, et a l . "Using Farmers' Actions to Measure Crop Loss Due to Air Pollution" Journal of Air Pollution  Control Association. 31 (1984) 360-364. 8 Adams, "Assessing Economic Benefits Ozone Control" p.541. 9 Ibid. 10 Raymond J. Kopp, William J. Vaughan, and Michael Hazilla, Agricultural Sector Benefits Analysis for Ozone Methods  Evaluation and Demonstration (North Carolina: Research Triangle Park, U.S. Environmental Protection Agency, 1984) p. 6. 11 Ibid. 12 Adams, "Assessing Economic Benefits Ozone Control" p.540. 13 Adams et a l . , Economic Effects of Ozone on Agriculture p.7; and Adams, "Assessing Economic Benefits Ozone Control". 14 Kopp et a l . , Agricultural Sector Benefits Ozone p.52. 113 15 Adams, "Assessing Economic Benefits Ozone Control"; Adams et a l . , "Economic Assessment Air Pollution Damages to Crops" p.57; Richard M. Adams, and Bruce A. McCarl, "The Effects of Acid Deposition on Agriculture: Summary and Recommendations." (Corvallis: Departement of Agricultural and Resource Economics, Oregon State University, 1985) p.23. 16 Adams, "Assessing Economic Benefits Ozone Control". 17 Adams et a l . , "Economic Assessment Air Pollution Damages to Crops" p.57. 18 Richard M. Adams, and Thomas D. Crocker, "Analytical Issues in Economic Assessments of Vegetation Damages" in Teng, P.S., and Krupa, S.V. (eds.) Assessment of Losses which Constrain  Production and Crop Improvement in Agriculture and Forestry (Proceedings E.C. Stakman Commemorative Symposium, Misc. Publication No.7, Agricultural Experimentation Station, University of Minnesota, 1980). 19 Scott A. Hamilton, Bruce A. McCarl, and Richard M. Adams, "The Effect of Aggregate Response Assumptions on Environmental Impact Analysis" (Corvallis: Department of Agricultural and Resource Economics, Oregon State University, 1984) p.2. 20 Adams, and McCarl, "Effects Acid Deposition on Agriculture" p. 23. 21 Steve K. Leung, Walter Reed, Scott Cauchois, and Richard Howitt, Methodologies for Valuation of Agricultural Crop  Yield Changes: A Review (Sacremento, California: Eureka Laboratories, 1978) p.62. 22 B. Oury, "Supply Estimation and Predictions by Regression and Related Methods" in Heady, E.O. (ed.) Economic Models and  Quantitative Methods for Decision and Planning in  Agriculture: Proceedings of an East-West Seminar (Iowa: Iowa State University Press, 1971) 241-275. Kopp et a l . , Agricultural Sector Benefits Ozone p.14. 23 Leung et a l . Valuation of Agricultural Crop Yield Changes. 24 The dichotomy of positive and normative is not as clear cut as is often suggested, especially by economists. For an excellent discussion of these issues see Mark Blaug, The  Methodology of Economics (Cambridge, U.K.: Cambridge University Press, 1982) Chapter 5. 25 Kopp et a l . , Agricultural Sector Benefits Ozone p.14. 26 Ibid, p.16. 27 D.G. Mayes Applications of Econometrics (London, England: Prentice-Hall International, 1981). ~~ 114 28 Ramon E. Lopez, "Estimating Substitution and Expansion Effects Using a Profit Function Framework" (Department of Agricultural Economics, University of British Columbia, 1981). 29 Bruce L. Dixon, et a l . Estimation of the Cost of Ozone on  I l l i n o i s Cash Grain Farms: An Application of Duality (Urbanna: Agricultural Economcs Staff Paper No. 84 E-276, University of I l l i n o i s , 1984). 30 Kopp et a l . , Agricultural Sector Benefits Ozone pp.20-21. 31 Varian, Microeconomic Analysis pp.9-10. 32 The transformation function must be continuous, monotonic and quasi concave in every subset of input cross output. 33 Kopp et a l . , Agricultural Sector Benefits Ozone pp.22-23. 34 Varian, Microeconomic Analysis p.21. 35 Lawrence J. Lau, and Pan A. Yotopoulos, "A Test for Relative Efficiency and Applications to Indian Agriculture" American  Economic Review 61 (1971) p.107. 36 Ibid. 37 Ibid. 38 Ramesh Chand, and J.L. Kaul, "A Note on the Use of the Cobb-Douglas Profit Function" American Journal of Agricultural  Economics 68:1 p.164. 39 Surjit S. Sidhu, and Carlos A. Baanante, "Estimating Farm-Level Input Demand and Wheat Supply in the Indian Punjab Using a Translog Profit Function" American Journal of  Agricultural Economics 63 (May, 1981) p.245. • 40 Bruce L. Dixon et a l . , "Primal versus Dual Methods Measuring the Impacts of Ozone on Cash Grain Farms". American Journal  of Agricultural Economics 67:2 (May, 1985) 402-406. 41 David K. Guilkey, Knox C.A. Lovell, and Robin C. Sickles, "A Comparison of the Performance of Three Flexible Functional Forms" International Economic Review 24:3 (October, 1983) p.614. 42 Richard C. Shumway, "Supply, Demand and Technology in a Multiproduct Industry: Texas Field Crops" American Journal of  Agricultural Economics 65:4 (1983) p.752. 1 15 43 John Quiggin, and Anh Bui-Lan, "The Use of Cross-Sectional Estimates of Profit Functions for Tests of Relative Efficiency: A C r i t i c a l Review" Australlian Journal of  Agricultural Economics 28:1 (April, 1984) pp.44-55. 44 Varian, Microeconomic Analysis p.21. 45 Kopp et a l . , Agricultural Sector Benefits Ozone. 46 Ibid. 47 Adams, "Assessing Economic Benefits Ozone Control" p.543. 48 Adams et a l . , Economic Effect of Ozone on Agriculture gives a review of national level studies. 49 S.N. Linzon, et a l . Ozone Effects on Crops in Ontario and  Related Monetary Values. (Ontario: Ontario Ministry of Enviroment, 1984). 50 Adams et a l . , "Economic Assessment Air Pollution Damages to Crops". 51 Richard E. Howitt, Thomas E. Gossard, and Richard M. Adams, "Effects of Alternative Ozone Levels and Response Data on Econmic Assessments: The Case of California Crops" Journal of  Air Pollution Control Association. Vol.34 (1984) pp.1122-1 127. 52 Adams et a l . , Economic Effect of Ozone on Agriculture p.10 gives these percentage estimates. 53 Howitt et a l . , "Effects of Ozone and Response Data on Econmic Assessments". 54 Robert D. Rowe, and Lauraine G. Chestnut, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in the San Joaquin Valley" Journal of Air Pollution  Control Association. Vol.35 (1985) pp.728-734. 55 Adams, and McCarl, "Effects Acid Deposition on Agriculture". 56 E.J. Benson, S. Krupa, P.S. Teng, and P.E. Welsch, "Economic Assessment of Air Pollution Damages to Agricultural and Silvicultural Crops." (Final report to Minnesota Pollution Control Agency, 1982). 57 Ibid. 58 Steve K. Leung, Walter Reed, and S. Geng, "Estimation of Ozone Damage to Selected Crops Grown in Southern California." Journal of Air Pollution Control Association. Vol.32 (1982) pp.160-164. 116 59 W.P. Page, et a l . "Estimation of Economic Losses to the Agricultural Sector from Airborne Residuals in the Ohio River Basin Region" Journal of air Pollution Control Association Vol.32 (1982) pp.151-154. 60 United States, Environmental Protection Agency, Research Triangle Park, North Carolina. "Criteria Document for Ozone: Draft" (1985) p.7-190. 61 Howitt et a l . , "Effects of Ozone and Response Data on Econmic Assessments"; Rowe, and Chestnut, "Economic Assessment of the Effects of Air Pollution on Agricultural Crops in the San Joaquin Valley"; Leung et a l . , "Estimation of Ozone Damage to Selected Crops Grown in Southern California". Mjelde et a l . , "Using Farmers' Actions to Measure Crop Loss Due to Air Pollution". 62 Mjelde et a l . , "Using Farmers' Actions to Measure Crop Loss Due to Air Pollution" p.361. 63 Dixon et a l . , "Primal versus Dual Methods Measuring Impacts of Ozone" p.404. 64 Ibid. 65 Adams et a l . , Economic Effect of Ozone on Agriculture. 66 Mjelde et a l . , "Using Farmers' Actions to Measure Crop Loss Due to Air Pollution". 67 Ibid. 68 Kopp et a l . , Agricultural Sector Benefits Ozone. 69 Ibid. 70 Raymond J. Kopp, et a l . "Implications of Environmental Policy for U.S. Agriculture: the Case of Ambient Ozone Standards" Journal of Environmental Management 20 (1985) 321-331. 71 Adams et a l . Economic Effect of Ozone on Agriculture. 72 Martha Smith, and Deborah Brown, Crop Prodution Benefits from  Ozone Reduction: An Economic Analysis. Station Bulletin No.388 (Indianna: Purdue University, Agricultural Experimentation Station, 1982). Kopp et a l . "Implications of Environmental Policy". 73 Smith and Brown, Crop Production Benefits from Ozone  Reduction p.32. 74 Kopp et a l . "Implications of Environmental Policy". 1 17 75 H.E. Heggestad and J.H. Bennett "Impact of Atmospheric Pollution on Agriculture" in M. Treshow (ed.) Air Pollution  and Plant Life (Chichester: John Wiley and Soni"^ 1984) . 76 Demand/supply price elasticity is the proportionate rate of change of the quantityof a product demanded/supplied divided by the proportionate change of price, with the price of other goods and income held constant. 77 Adams et a l . Economic Effect of Ozone on Agriculture p.96. 78 See review of Mjelde et a l . above, especially the last quote. 79 Vernon R. Eidman and Fred J. Benson "Economic Assessment of Crop Loss: Discussion" in Si Duk Lee (ed.) Evaluation of the  Scientific Basis for Ozone/Oxidant Standards (Pittsburg: Air Pollution Control Association, 1985). 1 18 CHAPTER IV OZONE POLLUTION IN THE LOWER MAINLAND AND THE WELFARE FROM CROP YIELD CHANGES 4 .1 Introduction In this chapter a model of the potato industry in B.C. is presented and employed to analyze the potential benefits from reducing ambient ozone levels in the Lower Mainland. The sensitivity of the predicted welfare estimates of the model is tested using various scenarios. These scenarios include changes in the price of U.S. imports, and price elas t i c i t y of supply. Originally, as suggested in Chapter 3, an aggregate dual model of crop production was intended for use in an aggregate analysis of the response of producers and consumers to alterations in ambient ozone loadings. However, attempts to estimate a translog cost function model with two outputs and three inputs for the agricultural sector in B.C. were unsuccessful. The best model estimated from available data showed serious parameter errors. Appendix III presents the data base and parameter estimates of the final model. Data availability restricted the usefulness of this approach. 119 The dual approach has several advantages over the econometric supply/demand approach employed here, some of which were noted in Chapter 3. The duality model has a sound theoretical basis. The duality model allows analysis of industry structure and gives valuable insights into both input and output interdependencies. For example, the damage to crops due to ozone may affect livestock production, and the dual approach allows tests for jointness between livestock and crop outputs. Disadvantages of the dual approach include the data requirements, and the stringency of underlying assumptions. The data requirements of the dual approach exclude its use for individual crops in B.C. Aggregation is to a higher level than that required for this study. Aggregating crops in this fashion has the disadvantage that details of individual markets are lost and cannot be analysed. Also, dose-response functions become d i f f i c u l t to apply since most dose-response functions are crop (and cultivar) specific. NCLAN has done some work on aggregate functions. However, aggregation is a problem which must be tackled at some stage i f commodity-specific, policy applicable results are to be obtained. Thus, the analysis of potatoes which follows, while indicative of the ozone damages in the Lower Mainland, may be less than a more complete study which covers a broader range of crops. 120 4.2 The Economic Model 4.2.1 Spatial Equilibrium Theory The market for potatoes in B.C. can be characterised as a situation in which two regions trade, and supply and demand functions for these two regions determine a price,i.e., a spatial equilibrium model is appropriate. Two regions, i.e., the U.S. and B.C., produce and consume a homogeneous product, and are separated but not isolated by transfer costs. The problem is to determine the equilibrium levels of production, consumption and prices in each region and the equilibrium trade flows. A geometric exposition of this problem, is presented in Figure 14.1 The f i r s t and third graphs show the known supply and demand curves of region 1 (U.S.) and region 2 (B.C.) respectively. If no trade were allowed the equilibriums would be q1,p1 in region 1 and p2,q2 in region 2. Allowing trade means that the low cost producers of region 1 can s e l l some output at a higher price than p1, and consumers in region 2 will be able to buy output at a price below p2. The amount producers in region 1 offer at prices above p1 is called the excess supply function (ES), and the quantity the consumers of region 2 demand at prices below p2 is the excess demand function (ED). The intersection of these two functions gives the equilibrium level of trade. If there are no transfer costs the equilibrium price under trade will be pT the same in both regions. However, if transfer costs do exist the excess supply function is shifted to the l e f t . The price in region 2 will now be higher than pT, at pT2. While the price in region 1 is lower than before, at pT1, with a greater quantity being supplied to the home market. The price in 121 Figure 14. Spatial Equilibrium Quantity region 2, set exogeneously, w i l l reflect both transportation costs and any t a r i f f which might be enforced. 4.2.2 The Potato Market in B.C. Data for potato production at the farm level were collected from annual reports of the B.C. Ministry of Agriculture and 2 Fisheries. The information includes data on potatoes sold to the processing industry, at the roadside and to the fresh market. Data on the quantity and value of fresh potato imports was obtained from the External Trade Reports of the B.C. Ministry of 3 Industry. A l l values and prices were deflated, 1981=100. The per capita consumption of fresh potatoes at the farm level in B.C. was calculated as the sum of net imports plus B.C. production (for processing, fresh and roadside markets) divided by the population. This per capita demand shows a distinct decline in the last ten years, see Figure 15. A downward trend in the demand for fresh potatoes is characteristic across Canada and is hypothesised to be income related, i.e., fresh potatoes are an 4 inferior product. In B.C. the mean quantity of potatoes demanded per capita was approximately 99 pounds for the 21 year period 1964-1984, but the minimum level was reached in 1984 at 72 pounds. B.C. production of potatoes has declined, while the quantity of imports has shown a slight increase. Figure 16 shows the increasing importance of imported potatoes relative to B.C. production. Competition is almost entirely from the United 5 States, and in particular Washington, California and Idaho. Imports averaged 30 percent of the total quantity sold in B.C. 123 Figure 15. Consumption of Potatoes in B.C. 1964-1984 I Total Quant 1ty (lbs per capita) 130 120 1 10 80 70 + 60 + 50 + I + + + + + + + + + + + + + + + + + + + + 6 4 6 5 6 6 6 7 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 YEAR Quant 1ty ( l b s p e r c a p i t a ) 100 + F i g u r e 16. Net P o t a t o Imports Into B.C. 1964-1984 90 + B.C. P r o d u c t i o n YEAR over the period 1964-1984, but in 1981 reached a peak of 51 percent. In the ten years from 1975-1984 imports have supplied 36 percent of the market. The other main production trend has been the increased relative importance of Lower Mainland production. Under 40 percent of the quantity produced in B.C. was from the Lower Mainland in 1965, but by 1980 this had reached 83 percent. The production of the Lower Mainland is compared to that of B.C. as a whole in Figure 17. Since the early 1970's the influence of the Lower Mainland on total output trends has been strong, and has grown stronger as the production from other areas has diminished. 4.2.3 Potato Supply and Demand in B.C. Estimates of the price elasticity of demand for potatoes in British Columbia were calculated in an econometric study by Stodola and McNeill. 6 They estimated the price elasticity of demand for fresh potatoes generated from annual data as -0.14. The demand equation used for this estimate took the form: Qd = f(wholesale prices, price of substitutes, income), where Qd is per capita potato demand. Although this is a wholesale level demand estimate i t is taken as representative of farm level demand. This is equivalent to treating the wholesale and farm levels as one, and can be justified because of the role 7 played by the vegetable marketing boards. Nuckton 1 1 has reviewed past vegetable demand studies and provides a summary of several studies which include potato demand estimates. The estimated price e l a s t i c i t i e s of demand reported by Nuckton for potatoes are shown in Table 18. The demand price 126 F i g u r e 17. Lower M a i n l a n d and B.C. P o t a t o P r o d u c t i o n 1964-1984 Quant i t y Pro d u c e d (1bs p e r c a p i t a ) YEAR elasticity derived by Stodola and McNeill appears very inelastic when f i r s t compared with these estimates. However, estimates of wholesale and farm level demand are expected to be more inelastic than at the r e t a i l level, due to the greater possibilities for substitution at the latter. Stodola and McNeill's estimate compares to that of George and King for U.S. farm level demand. The estimate of Canadian price elasticity of demand at the reta i l level of -0.85 found by Hassan is also consistent with a lower farm level elasticity e.g., -0.14. Hee found several considerably more elastic price elasticity estimates at the farm level but this can be attributed to the disaggregation of potatoes by growing season, thus allowing for greater substitution. Combining Stodola and McNeill's demand price elasticity estimate with the price and quantity data described above gives a demand function for the base model. The mean quantity demanded per capita over the period 1964-1984 was 99.34 pounds (lbs.), and the mean price was 8.67 cents (constant 1981=100). This gives the demand function for B.C. at the mean of the data as: Qd = 113.25 - 160.48Pd. (4.1) The short run supply price elasticity estimate given by Stodola and McNeill for fresh potatoes generated from yearly data is 0.343. This estimate is combined with mean values for B.C. quantity supplied and price, to derive the supply function for the base model. The mean quantity supplied by B.C. from 1964-1984 was 70.22 lbs per capita, and the mean price per lb was 8.67 cents. This gives the B.C. potato supply function as: Qs = 46.13 + 277.92PS (4.2) 128 Table 18. Price E l a s t i c i t i e s of Demand Reported for Potatoes Author/Date Period Potatoe Type Market El a s t i c i t y Blaich 1963 Hee 1967 Siebert 1967 George and King 1971 Martha and Schrimper 1974 Clevenger and Geithman 1977 Hassan 1978 1957-1961 1957-1960 1947-1960 1956-1966 Estimate to 1980 1949-1972 1 957-1974 Frozen Canned Various* Fresh Fresh Fresh Fresh Fresh U.S. Farm -0.20 to -2.00 -0.20 to -2.50 -0.21 to -2.63 California -1.20 U.S. Farm U.S. Farm U.S. Farm U.S. Retail U.S. Retail U.S. Canada Retail -0.15 -0.31 -0.50 -0.83 -0.85 *Hee c l a s s i f i e d potato types by growing season and obtained seven e l a s t i c i t i e s for fresh and stored farm level potatoes for food -0.21, -2.63, -0.59, -1.88, -0.67, -0.52, -0.48. Source: C F . Nuckton Demand Relationships for Vegetables: A  Review of Past Studies (Davis, Califonia: Giannini Foundation, 1978). 129 The data on price and quantity given by Stodola and McNeill were not used because i t only covered the period from 1961-1976. The analysis conducted in the following sections is based upon ozone doses for the period 1978-1985. Thus, an updated data base is important for the analysis of recent changes. 4.2.4 The Market Equilibrium for Potatoes Combining demand and supply functions 4.1 and 4.2 allows the market equilibrium to be calculated. In absence of imports the equilibrium quantity would be approximately 88.68 lbs per capita at a price of 15.31 cents per lb. However, as explained U.S. imports are assumed to set the price on the B.C. market. The U.S. import price is therefore assumed to equal the mean Lower Mainland farm price (1964-1984) of 8.67 cents per lb. At this price the quantity of potatoes imported is 29 lbs per capita. That i s , instead of the quantity demanded equalling that supplied by B.C. producers i t exceeds local supply by the amount of imports. The quantity supplied by B.C. producers is 70.22 lbs. and the quantity consumed 99.34 lbs per capita. In the following sections the effects of a range of ozone doses upon producer welfare is analysed. F i r s t l y , the areas of consumer and producer surplus, and the changes in producer surplus under the assumption of a constant price are described. Next the annual total and marginal damages from a reduction in potato yield due to various seasonal ozone doses are calculated. These damages are recalculated under two scenarios; (a) involving an alternative, more inelastic, supply elasticity, and (b) a higher import price. Finally, the results are discussed. 130 4.3 Economic Assessment of Potato Damage Due to  Ozone in the Lower Mainland 4.3.1 Net Welfare Areas In order to calculate the welfare changes which will occur under various ambient ozone loadings the areas shown in Figure 18 (a) and (b) must be calculated. In part (a) net consumer surplus is the shaded area between the price lines pO and p1, and bounded by the demand function DD. If the original price was pO then an increase in ozone levels which shifts the supply curve, ceteris paribus, would increase price to p1. The price change impacts consumer welfare. (This assumes the demand function does not shift i.e., that ozone does not affect the quality of potatoes.) In the case of B.C. the price of potatoes is set by the much larger U.S. market and therefore no change in the consumer surplus area is expected to occur when ambient ozone loadings in the Lower Mainland change since there is no price change in the B.C. market for this local damage. Part (b) illustrates the net producer welfare for an increase in ozone which reduces yield and shifts the supply function, but assuming the price does change. The quasi-rent (or producer surplus, see Appendix II) is the area bounded by the price line and the supply function. The original supply function SO is rotated, about i t s intercept with the price axis, to S1. When the price is impacted by this supply shift there is a price increase from pO to p1. The area C is lost by consumers and gained by producers, while area B is lost to producers. Area A is common to both situations. Thus, the net change in producer welfare is given by area C minus area B. The overall effect upon producers' 131 Figure 18. Consumer and Producer Welfare Areas (a) Net Consumer Surplus Quantity of Potatoes (b) Net Producer Quasi-Rent P r i c e Change Quantity of Potatoes (c) Net Producer Quasi-Rent Constant P r i c e P r i c e Per l b . Quantity of Potatoes 132 welfare will depend upon the price e l a s t i c i t i e s of supply and demand. Assuming the price is fixed, and set in the U.S. market, as is the case for potatoes in B.C., means area C disappears. The situation is now as shown in part (c) of Figure 18. The original area of producers surplus is given by area A plus area B. When the supply curve shifts to S1 area B is lost by potato producers, and the new surplus is area A alone. The prime determinant of the loss to producers from a given reduction in potato yield is the price elasticity of supply. Under a fixed market price, potato producers will always lose from increases (and gain from reductions) in ambient ozone loadings which cause yield reductions. 4.3.2 Approach to Economic Assessment The equilibrium situation of the base model can be regarded as the production level under which no ozone damage occurs. This is justified by the nature of ambient ozone loadings in the Lower Mainland. As shown in Table 6, the ozone dose in rural areas is not constant but varies widely between seasons from levels expected to cause no damages to levels causing 16.5 percent yield reductions. Thus, characterising ozone in the Lower Mainland as having to be reduced from a high dose to a low dose would be unrepresentative of actual ambient ozone loadings. The problem is more accurately seen as the potential for yield reductions in any given year compared to the production that would occur in the absence of damage. The alternative approach, of regarding the problem as starting from a high ozone dose, implies ozone 133 reductions and supply shifts to the right. The approach adopted here implies ozone increases, causing a shift of the supply function to the l e f t . g Mendelsohn has noted the failure of economic air pollution damage assessments to derive marginal damage functions. A l l the ozone studies reviewed in Chapter 3 (except for Page et al.) have assessed the total damages occurring at ambient ozone levels in a specific year and compared this with total damages expected at one or two other levels and/or background levels. Typically this approach is adopted to allow the assessment of damages at proposed government standards. However, economic theory suggests that the optimal level of pollution is where the marginal damages g equal the marginal costs of controlling the pollutant. Thus, economic assessments should be concerned with estimating marginal damages, i.e., the price of the pollutant. The analysis here does not therefore follow previous studies, but rather presents total damage functions and marginal damage estimates. 4.3.3 Base Model Welfare Estimation Starting from the equilibrium obtained above the supply function is rotated according to the predicted percentage changes in the quantity produced at different ozone doses. This involves introducing a yield reduction term into 4.2 so that i t becomes: Qs = (46.13 + 277.92PS).(1-R/100), (4.3) where R is the percentage reduction in quantity derived from the seasonal ozone dose. R is calculated from the dose-response function presented in Chapter 2, and taken from the "Air Pollution Manual" of the California Department of Food and 134 Agriculture. When (1-R/100) is greater than one, yield is increased (R is negative), since this implies that ozone dose is decreased. When (1-R/100) is less than one, yield is reduced. When (1-R/100) is equal to one, the quantity is constant and the equation 4.3 is the same as 4.2. Thus, for example, if R=-0.5 then (1-R/100)=1.5 and the quantity has increased by 50 percent; conversly i f R=0.5, then (1-R/100)=0.5 and the yield has decreased by 50 percent. In order to calculate the quantity of potatoes which will be supplied when yield changes occur, the supply equation 4.3 replaces 4.2. The ozone dose can then be adjusted and equilibrium price and quantity calculated. Starting with the seasonal ozone dose at zero (R=0) the quantity demanded is 99.34 lbs per capita, and the quantity supplied by B.C. is 70.22 lbs per capita. The ozone dose is then adjusted to a higher level, R increases, B.C. supply shifts and information on the price and the quantity of potatoes supplied by B.C. producers is used to calculate quasi-rents. Net producer welfare is calculated by subtracting the quasi-rent at zero hours-ppm>0.1Oppm ozone from that at the new seasonal ozone dose. Repeating this process gives a range of the total seasonal damages expected at various ambient ozone dose levels. Figure 19 shows the results of this process. Net producer welfare from potatoes is shown as dependent upon the level of the seasonal ozone dose (hours-ppm>0.1Oppm). The vertical axis measures the loss incurred by producers in thousands of constant 1981 dollars. The producer welfare loss was calculated on a per capita basis, with 1984 being the base year, and then multiplied 135 Producer Welfare Loss (Thousands of dol1ars) Figure 19. Base Scenario Total Damage Function f o r Potatoes CM 3300 + 3000 + 2700 + 2400 + 2100 + 1800 + 1500 + 1200 + 900 + 600 + 300 + Ozone Dose (hours-ppm>0.lOppm) by the population of B.C. The range of ozone doses was chosen to represent the range of actual ambient seasonal ozone dose in the Lower Mainland. For example, i f the seasonal ozone dose was 16 hours-ppm>0.1Oppm (Abbotsford, 1981) in a l l potato growing areas, producers are estimated to lose 2.4 million dollars; approximately 19 percent of farm cash receipts in 1981. The total damage function of Figure 19 gives the marginal damage function when differentiated once with respect to dose. The linear nature of the total damage function means that the marginal damage function is constant. If ozone is measured in units of dose hours-ppm>0.1Oppm, the marginal damage is 0.15 million dollars per unit of ozone. The marginal damage in this model is also equal to the average total damage. For example, 10 units of ozone causes 1.5 million dollars damage. 4.3.4 Sensitivity Analysis In order to judge the accuracy of the above annual ozone damage estimates, their sensitivity to changes in the underlying model is tested. Two scenarios are chosen; (a) a more inelastic supply price el a s t i c i t y , and (b) a higher import price. The demand elasti c i t y estimate was not varied as was the supply el a s t i c i t y . Changes in the demand elasticity would not affect the producer welfare losses because of the constant price assumption. The more inelastic supply scenario was chosen because this was presented as an alternative estimate by Stodola and McNeill, and no alternative supply elasticity estimates were found, preventing a more comprehensive comparison as conducted for the demand elasticity above. The import price is an import determinant of 1 37 the monetary value of the final damage estimates. This price has increased in real terms in the 1980's compared to the twenty-year mean. Thus, the import scenario takes a price reflecting this later period. (a) Welfare Sensitivity to Supply  Elastic ity A search of the literature revealed no studies for comparison of supply price e l a s t i c i t i e s for potatoes. However, the short run supply price elasticity of 0.343 reported by Stodola and McNeill, is one of two estimates they calculated. The other estimate was from a different formulation of the supply, equation and gave the price elasticity of supply as 0.263. In order to test the sensitivity of the base case welfare estimates to this more inelastc estimate, a new supply function was estimated at the mean. The supply function derived from the price elasticity of 0.263 i s : Qs = 51.75 - 213.lOPs (4.4) where Qs is quantity supplied per capita and Ps is price per lb. The total damage function, as shown in Figure 20, is shifted to the l e f t . At a dose of 16 (hours-ppm>0.1Oppm) the inelastic supply model predicts a loss to producers of 2.51 million dollars while the base model predicted 2.40 dollars. The more inelastic the supply curve the larger the loss to producers, and vice versa. Marginal damages are also larger at 0.16 million dollars. (b) Welfare Sensitivity to Imports In recent years the import price in the B.C. market has been considerably higher than the mean for 1964-1984. This implies 138 Producer Welfare Figure 20. Supply Scenario Total Damage Function for Potatoes Loss (Thousands of d o l l a r s ) 3300 + - + 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Ozone Dose (hours-ppm>0. lOppm) some change may have occurred in the U.S. market, and/or perhaps transportation costs have increased. This change to a higher price level has caused a loss in consumer surplus and an increase in producers' surplus relative to that of the twenty year base period. This producer surplus area is then subject to the changes due to varying ambient ozone loadings. Reworking the equilibrium equation to allow for an import price of 10 cents per lb, instead of 8.67 cents per lb., gives the quantity of imports as 23.27 lbs per capita (as opposed to 29 lbs previously). At this higher exogenous price, quantity demanded f a l l s to 97.2 lbs per capita and quantity supplied by B.C. producers increases to 73.93 lbs per capita. The net result is a rise in the estimated welfare loss to producers from increases in the seasonal ozone dose, as shown in Figure 21. This is as expected due to the higher quantity produced by B.C. under the import scenario as compared to the base scenario. The total damage function is shifted to the right at the new import price. At a seasonal dose of 16 (hours-ppm>0.10ppm) the loss to producers is now approximatly half a million dollars more at 2.85 million dollars. Marginal damages have also increased, to 0.18 million dollars per unit of ozone dose. 140 Producer Welfare Loss (Thousands of D o l l a r s ) Figure 21. Import Scenario Total Damage Function f o r Potatoes -+ 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Ozone Dose(hours-ppm>0.lOppm) 4.3.5 Summary and Discussion of Results Table 19 summarises the results of increases in ambient ozone loadings on potato yield and the effects on producer welfare under each of the scenarios described above. The ozone dose is measured as hours-ppm>0.1Oppm, which causes a percentage reduction in potato tuber weight R. The seasonal ozone dose reported in Table 19 extrapolates beyond the highest dose calculated in the Lower Mainland of 16 hours-ppm>0.1Oppm. The base scenario with inelastic demand and supply gives the lowest damage estimates. The marginal damages range from 149,768 to 178,322 dollars. Table 19. Potato Producer Welfare Loss Due to Ozone: Scenario Analysis Total Damages Under Scenarios: Ozone Dose Potato Tuber Weight More Inelastic Supply Higher Import Price Reduction Base (hrs-ppm>0.1ppm) (thousands $ deflated 1981 ) 20.00 19.00 18.00 17.00 16.00 15.00 14.00 13.00 12.00 1 1 .00 10.00 9.00 8.46 6.52 5.59 3.10 1 .00 0.80 0.40 0.10 0.00 20.6000 19.5700 18.5400 17.5100 16.4800 15.4500 14.4200 13.3900 12.3600 11.3300 10.3000 9.2700 8.7138 6.7156 5.7577 3.1930 1.0300 0.8240 0.4120 0.1030 0.0000 2995.35 2845.59 2695.82 2546.05 2396.28 2246.51 2096.75 1946.98 1797.21 1647.44 1497.68 1347.91 1267.03 976.49 837.20 464.-28 149.77 1 19.81 59.91 14.98 0.00 3139.97 3566.44 2982.97 3388.12 2825.97 3209.80 2668.97 3031.48 2511.98 2853.16 2354.98 2674.83 2197.98 2496.51 2040.98 2318.19 1883.98 2139.87 1726.98 1961.54 1569.98 1783.22 1412.99 1604.90 1328.21 1508.61 1023.63 1162.66 877.62 996.82 486.70 552.80 157.00 178.32 125.60 142.66 62.80 71.33 15.70 17.83 0.00 0.00 142 The information presented in Table 19 can be expanded upon, as included in Table 20 presented in Chapter 5, to give a perspective on actual ambient ozone doses in the Lower Mainland. For example, in 1981 the seasonal ozone dose at Abbotsford was 16.00 hours-ppm>0.1Oppm causing a 16.5 percent reduction in potato tuber weight. This potato loss casued a loss to potato producers between 2.4 and 2.9 million dollars which was 19 to 23 percent of the farm cash receipts from potatoes for 1981. In other years the seasonal ozone dose has been has been very low, and in 1984 was zero. The lowest non-zero seasonal ozone dose was in 1983 at 0.22 hours-ppm>0.1Oppm. This caused a 0.2 percent potato tuber weight reduction, and between 0.03 and 0.04 million dollars total damage or a 0.3 percent reduction in farm cash receipts from potatoes in 1983. The import scenario has the largest effect upon estimated damages. The import price imposed in the base model is likely to be lower than in recent years. Thus the import scenario may be a more accurate reflection of the expected losses incurred by farmers in the Lower Mainland from ambient ozone loadings. In this case the estimates of the base scenario would be under-estimates of actual damages. The position of the base model below the other damage estimates implies under-estimation. However, there are underlying assumptions to the above analysis which suggest that the damages reported may in fact be overestimated. Underlying the above analysis are three assumptions which can result in biased estimation of damages. Fi r s t l y , the entire B.C. crop is assumed to be affected while damages have only been 143 substantiated for the Lower Mainland. However, as was shown in Figure 17, Lower Mainland production has been steadily increasing as a percentage of total production accounting for between 70 to 80 percent of the total crop in recent years. The problem here is that aerometric data are currently only available within the confines of the Lower Fraser Valley, as shown in Figure 6. The dose received by the other major potato growing regions is unknown. If the remainder of the B.C. crop were unaffected by ambient ozone doses, then the damages reported above would be overestimated. A related problem is that a l l areas are assumed to be affected by the same ozone dose. Table 6 showed that the rural areas of the Lower Mainland do not recieve similar ozone doses but that measurements may differ substantially. If a specific dose is assumed to occur across a l l regions, the resulting bias will depend upon the distribution of actual doses around that level. The doses measured at Abbotsford have often been higher than at other stations, and therefore when the dose there is 16 (hours-ppm>1Oppm) i t would be expected to be lower elsewhere. If this were the case, overestimation of damages would result because the highest reading is taken as uniform. However, if a lower reading is taken as more representative, underestimation of damages may result. This problem may be resolved by the increased number of monitoring stations now existing in rural areas of the Lower Mainland, and by employing aerometric modelling techniques. Other studies have also assumed a uniform dose across regions e.g., Adams and McCarl (1985) assumed the same ozone dose across the entire Corn Belt. 144 Finally, a l l cultivars are assumed to be equally sensitive to ozone. In Chapter 1 the main varieties of potato grown in the Lower Mainland were identified and given susceptibility rankings, i.e. sensitive, intermediate, tolerant and unknown. The dose-response function employed here is for a sensitive cultivar, and thus the resulting damage estimates will be biased upward because not a l l potato cultivars in the Lower Mainland are sensitive. One cultivar has been used to represent the response of a l l those grown in a region in several of the regional economic studies of ozone reviewed in Chapter 3. e.g., Benson et a l . (1982), Rowe et a l . (1984), Howitt et a l . (1984), This simplifying assumption is required due to the limited information available on cultivar response. 145 Footnotes 1 The discussion here is based upon that by Larry J. Martin "Quadratic Single and Multi-Commodity Models of Spatial Equilibrium: A Simplified Exposition" 29:1 Canadian Journal  of Agricultural Economics (1981) 21-48. 2 British Columbia, Ministry of Agriculture and Food. Production of Vegetable Crops Together with an Estimate of  Farm Value (various annual); and British Columbia, Ministry of Agriculture and Food. Production of Berry Crops Together  with an Estimate of Farm Value (various annual). 3 British Columbia, Ministry of Industry and Small Business Development. External Trade Report (various annual). 4 Canada, Agriculture Canada, B.J. Stodola and R.C. McNeill. An  Econometric Study of the B.C. Potato Industry (1978); and Canada, Food Prices Review Board. Table Potatoes (1975) p.7. 5 British Columbia, Ministry of Agriculture and Food. Vegetable  Marketing Guide. 6 B.J. Stodola and R.C. McNeill. An Econometric Study of the  B.C. Potato Industry. 7 The vegetable marketing boards handle washing, packaging and transportation of farm produce to r e t a i l outlets. They replace the role played by a wholesale merchant. They operate so as to promote the products under their jurisdiction on behalf of the farmer. 8 Robert Mendelsohn "Economic Evaluation of Air Pollution Damage and Control: Discussion" 68:2 American Journal of  Agricultural Economics (May, 1982) 482-484. 9 For a more detailed discussion of the importance of marginal damage functions in environmental economics see: Anthony J. Fisher Resource and Environmental Economics (Cambridge, England: Cambridge University Press, 1981); or David W. Pearce Environmental Economics (London: Longman Group Ltd., 1978). 10 California, Department of Food and Agriculture. Air Pollution  Manual (1986). 11 C.F. Nuckton, Demand Relationships for Vegetables: A Review  of Past Studies (Davis, California: Giannini Foundation, 1978). 146 CHAPTER V SUMMARY AND CONCLUSIONS There is a growing body of evidence that ozone affects crop yields at ambient ozone loadings resulting in millions of dollars of damage. The formation of ozone via the interaction of several chemicals in the atmosphere in the presence of ultra-violet light is a complex process. Precursor emissions, of nitrogen oxides and hydrocarbons, alone are not sufficient to insure ozone formation. The dose of ozone received by agricultural crops during a growing season also depends upon atmospheric and topographic factors. Ozone forming in the Lower Mainland of B.C. is restricted laterally by the surrounding mountain ranges and vertically by stagnant high pressure systems. Land/sea breezes aid in transporting ozone and its precursors from Vancouver up the Fraser Valley towards important crop growing regions. The highest levels of ozone occur during spring and summer coinciding with the most active agricultural season for many crops. Seasonal ozone dose, measured as hours-ppm>0.1Oppm, was found to be high at rural monitoring stations during the late 1970's and early 1980's, especially at Abbotsford, but much lower in 147 more recent years. As there is no reason to believe that precursor emissions have fallen during this period, the lower ozone levels may be attributed to climatic variations. This seasonal variability of ozone concentrations means year-specific damage estimation must be interpreted with extreme caution. Studies conducting year-specific economic assessments need to cla r i f y exactly how representative their results are of a typical growing season. Table 20 illustrates the range of total damages predicted by the scenario analysis of Chapter IV, assuming a l l regions are affected by the same seasonal dose as Abbotsford. The damages shown are around one million dollars annually for four out of eight years. The last column shows the estimated total damages as a percentage of B.C. potato farm cash receipts for each year. The damage in 1981 stands out, causing a loss equivalent to 19-22.5 percent of total revenue. These total damages may overestimate actual damage even i f dose were the same across the Lower Mainland. This is because not a l l potato cultivars are as sensitive as that used in the estimation of damages, and because 20-30 percent of potato production takes place outside the Lower Mainland. In addition, Abbotsford has shown the highest readings in several years, suggesting less damage may occur in other regions of the Lower Mainland. Despite these qualifications there are reasons to be cautious over discounting these damages as too large. F i r s t l y , ozone may increase plant stress making crops more susceptible to damage from other factors, such as insect attack and biological 148 pathogens. Secondly, current research has been limited to yield loss, leaving much uncertainty as to the effects of ozone on crop quality. If crop quality is affected then, in addition to the supply shift analysed here, the demand function w i l l be shifted. Thirdly the information on air quality at rural sites has been extremely limited until recent years, and even when stations are operational, data may be missing for a large part of the growing season, as apparent in Table 20. Even with the latest additions to the Lower Mainland Air Quality Monitoring Network, no information exists as to the levels of pollutants beyond Chi 11iwack. Table 20. Total Damages to Potatoes Based Upon Ozone Doses at Abbotsford Monitoring Station Year Seasonal Ozone Dose Valid Days* R tTotal Damages to Potato Producers Proportion of Total Potato Revenue B.C. (hrs-ppm>0.1Oppm) (No.) (%) (000' s of $) (%) 1 978 8.46 122 8.7 1 ,267 - 1,507 10.05 - 1 1 .95 1 979 3. 10 88 3.2 464 553 3.12- 3.71 1980 5.59 124 5.8 837 997 5.38 - 6.41 1 981 16.00 115 16.5 2,396 - 2,853 18.92 - 22.52 1 982 6.52 47 6.7 976 - 1,163 7.52 - 8.96 1 983 0.22 77 0.2 33 39 0.26 - 0.30 1 984 0.00 1 1 1 0.0 0 0 0.00 - 0.00 1985 0.40 110 0.4 60 71 N.A • •Maximum number of valid days 124, seasonal dose calculated from 15th May to 15th August. R is the percentage reduction in potato tuber weight calculated from the dose response function presented in Chapter 2. 149 Reducing ozone levels measured as hours-ppirt>0.10ppm to a dose of zero is equivalent to a one hour annual standard of 0.10 ppm. Meeting this standard would have saved potato producers the losses in Table 20. However, the desirability of obtaining this standard from the economic point of view is not at a l l clear. Rather than focusing upon total damages, economic efficiency requires the comparison of marginal pollution damages with marginal control costs. Thus the marginal damages were presented for each sensitivity scenario in Chapter IV. The marginal damages ranged from 149,768 to 178,322 dollars per hour-ppm>0.1Oppm. The marginal damage function derived from a linear total damage function is constant, and thus a l l the estimates here are constant. These marginal damage estimates are of l i t t l e practical use because no information currently exists on the marginal costs of controlling ozone. Lave1 has argued that not only are the costs of different control options d i f f i c u l t to estimate, but also that the state of current knowledge makes calculating the resulting decrease in ozone virtually impossible. Yet he concludes that in order to develop a sensible policy for ozone control, the marginal cost of an efficient abatement programme needs to be calculated and compared with the marginal benefits. Estimating control costs is an obvious area for future research. Interpretation of the marginal damages for potatoes is futher restricted because other crops are susceptible to damage and ozone may affect human health, v i s i b i l i t y and materials. Vegetables in the Lower Mainland susceptible to ozone damage include lettuce, sweet corn, onions, green beans, peas and 150 cabbages. In addition, research is required to determine the sensitivity of important economic crops such as blueberries, cranberries, raspberries, and mushrooms. Small fruits are of particular concern because (a) blueberries, cranberries and raspberries accounted for approximately 26 million dollars (28 percent) of farm cash receipts in the Lower Mainland in 1984, (b) Abbotsford accounts for nearly half the provincial cash receipts from small fruits, (c) small fruit bushes such as cranberries require several years to reach maturity, preventing cross-crop substitution, and (d) Lower Mainland production has been steadily increasing. Regional economic assessment of ozone effects upon agriculture requires the combination of information on air quality, plant response and economic systems. This interdisciplinary approach has been employed to present evidence of damages to potato farmers in the Lower Mainland. Ozone pollution appears to be a potentially serious problem for the agricultural sector in the Lower Mainland and one which requires a comprehensive assessment of both damages and control costs. Footnotes 1 L.B. 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United States, Congress, Office of Technology Assessment. Acid  Rain and Transported Air Pollutants: Implications for  Public Policy OTA-0-204, 1984. United States, Environmental Protection Agency, Environmental Research Center. The Economic Damages of Air Pollution , 1974. United States, Environmental Protection Agency. "Report on Photochemical Oxidants: Draft" 1985, Chapter 7. Unsworth, M.H. "Exposure to Gaseous Pollutants and Uptake by Plants." in Unsworth, M.H., and Ormrod, D.P. (eds.) Effects of Gaseous Pollutants in Agriculture and  Horticulture. London, England: Butterworths, 1982. Urone, P. "The Primary Pollutants Gaseous:Their Occurence, Sources, and Effects" in Stern, A.C. (ed.) Air  Pollution:Volume 1, Air Pollutants, Their Transformation  and Transport 3rd edition, New York: Academic Press, 1976). Varian, H.R. Microeconomic Analysis 2nd edition New York: W.W. Norton and Co., 1984. Walker, H.M. "Ten-Year Ozone Trends in California and Texas" Journal of Air Pollution Control Association 35 (1985) 903-912. Weaver, R.D. "Multiple Input, Multiple Output Production Choices and Technology in the U.S. Wheat Region" American  Journal of Agricultural Economics 65 (1983)- 45-56. Wetzstein, M.E. "Methods for Measuring the Economic Impact of Ambient Pollutants on the Agricultural Sector: Discussion" American Journal of Agricultural Economics 67:2 (May, 1985) 421-422. Willig, R.D. "Consumer's Surplus Without Apology" The American  Economic Review 66:4 (September, 1976) 589-597. Wilson, R.G.; Mills, J.B.; and Wituschek, E.P. A Report on the  Assessment of Photochemical Oxidants in the Lower  Mainland Victoria, British Columbia: Ministry of Environment, 1984. Whitten, G.Z. "The Chemistry of Smog Formation: A Review of Current Knowledge." Environment International 9:6 (1983) 447-464. 164 Yotopoulos, P.A., and Lau, L.J. "A Test for Relative Economic Efficiency Some Futher Results" American Economic Review 63:1 (March, 1973) 214-223. Yotopoulos, P.A.; Lau, L.J.; and Lin, W. "Microeconomic Output Supply and Factor Demand Functions in the Agricultre of the Province of Taiwan" American Journal of Agricultural  Economics 58 (1976) 333-340. 165 APPENDIX I CONSUMER WELFARE THEORY Historical Note The concept of a consumer being able to obtain an amount of u t i l i t y in excess of the price paid for a commodity was f i r s t expounded by Jules Dupuit, in 1844.1 Dupuit's consumer surplus was adopted by Alfred Marshall some forty years later. It was Marshall who equated the concept to the area under a demand curve. Marshall was trying to find a cardinal measure of u t i l i t y , but the conditions under which his definition of consumer surplus could act as such were restrictive and unrealistic. The connection of consumer surplus with cardinal analysis meant i t 2 was neglected as ordinal analysis came to the fore. In the 1940's John Hicks redefined the idea using ordinal 3 analysis. Hicks introduced four new measures of a consumer welfare change. Two of these became accepted as practical tools for applied welfare analysis namely, the compensating variation and the equivalent variation. However, despite the improvements these measures offered, direct measurement was not easy. Consumer surplus could be, and was, used as an approximation to the Hicksian measures but as such remained 166 controversial. Robert Willig removed the reasons for c r i t i c i s i n g this practice by providing the circumstances under which i t could • • 4 be justified. Willig showed the specific range of conditions within which consumer surplus approximated the compensating and equivalent variations, and the accuracy of that approximation when those conditions were altered. In addition, Willig showed that in most common applications consumer surplus was a close approximation to the Hicksian measures. Dupuit Surplus Dupuit described consumer surplus as being the difference between the price, actually paid when purchasing a commodity and 5 the price the consumer would have been willing to pay. This willingness to pay diminishes as more units of the commodity are consumed. Figure A1.1 shows the price a given consumer is prepared to pay for each successive unit of a commodity. The demand curve W is a marginal willingness to pay curve.^ For the f i r s t unit the consumer would be willing to pay p1, for the second p2, for the third p3, and so on. If we assume the consumer can buy a l l the units one through to qO at a constant price pO, there w i l l be a surplus of u t i l i t y on every unit consumed up to, but not including, the last, qO. (The assumption of a constant price is as would exist in a perfectly competitive market.) Thus, i f the commodity is perfectly divisible, the Dupuit surplus from buying qO at pO is given by the triangle-like area above the price and below the willingness to pay curve. The net benefits of consuming qO are given by this area, while the gross benefits are given by that area plus area pO,qO. 167 Figure Al.l Dupuit Consumer Surplus Price Pi P2 p3 p4 p5 p6 pO 0 qo Quantity 168 It should be clear that lowering (raising) the purchase price will increase (decrease) net benefits i.e., the Dupuit surplus. As Dupuit stated: Hence the saying which we shall often repeat because i t is often forgotten: the only real u t i l i t y is that which people are willing to pay for. We see that in general the relative or definitive u t i l i t y of a product is expressed by the difference between the sacrifice which the purchaser would be willing to make in order to get i t and the purchase price he has to pay in exchange. It follows that anything which raises the purchase price diminishes the u t i l i t y to the same extent, and anything which7depresses the price increases the u t i l i t y in the same manner. However, i t is important to note how the change in price is caused. The producer can reap a similar surplus to the consumer (see Appendix II) by charging more for a commodity than i t cost to produce. A price change which does not correspond to a reduction in production costs cannot increase the overall welfare of society. Such a price change merely reduces the producers welfare and increases the consumers. As Dupuit remarked: For an increase or decrease of u t i l i t y to take place, there must be, provided there is no change in quality, a decrease or increase in the cost of production. When there is merely a change in the market price the consumer gains what . the producer loses, or vice versa. In fact the changes due to a reduction in production costs are likely to cause some transfer payments as well, depending upon the relative characteristics of supply and demand. In a relativly short paper Dupuit managed to make many insightful remarks and had intended to follow these up, but never published more on the subject. When Marshall took up these ideas he was searching for a cardinal measure of u t i l i t y . The Dupuit surplus was not a measure of actual u t i l i t y changes, or the real net benefits of a commodity, but only a money measure. 169 Consumer Surplus Marshall was concered with finding the conditions under which a money measure of consumer welfare would equal the 'true' u t i l i t y surplus. It was Marshall who developed the association of consumer surplus with the curvilinear triangle under the ordinary demand curve. In Figure A1.2 an individual's Marshallian demand curve, D, is shown. The area abc is the net benefit to the consumer of purchasing quantity od of the good. The area bcdo is the gross, or total, benefit of purchasing od of the good. The difference between the two is the total cost of quantity od to the individual given by area oacd. In the remainder of this paper consumer surplus will be taken to mean this triangular area (abc). It should be noted that the equivalence of the triangle to the true surplus is not a definition; it is a theorem, true under certain restrictive assumptions, but only i f these assumptions are granted. A detailed analysis of these assumptions can be found in the literature and only the main points are summarised g here. The use of a money measure of a u t i l i t y change means i t may not always be possible to guarantee uniqueness. A money measure can vary depending upon the order in which certain changes are assumed to occur. In particular, this problem arises where the u t i l i t y change of interest involves a change in the price of more than one commodity, or an income and price change occur simultaneously. In these situations the order in which the changes are analysed can determine the size of the resulting money measure of welfare. When the path of adjustment affects the outcome in this manner there is path dependence. 170 Figure A1.2 Marshallian Consumer Surplus Price D 0 - d Quantity 171 Certain conditions when met can ensure that the money measure is unique i.e., path independent. For a simultaneous price-income change the consumer surplus is unique i f and only i f the income effect (or income elasticity) is zero. That i s , the quantity consumed remains the same when income changes. For a price-price change the consumer surplus measure is unique i f and only if a l l income el a s t i c i t i e s of demand, for the goods whose prices change, are equal. (If the prices of a l l goods are changed then the income elasticity of demand must equal unity.) This means the consumer must adjust consumption of a l l goods whose price change, proportionally e.g., a ten percent increase in income causes a five percent increase in the quantity of butter and petroleum consumed (if these are the only goods consumed, the ten percent increase in income must cause a ten percent increase in the consumption of both goods). These conditions restrict the scope of the analysis which can be performed while maintaining unique results. This would not pose a problem i f the constraints were found in consumers' preference mappings in reality. Unfortunately, i t seems unlikely that the conditions will hold in the majority of cases. It is improbable that the consumption of goods will not change as income changes. Although, there may be some goods for which the income elasticity is zero, e.g., salt, this is rarely true of most goods. Perhaps even more unlikely is the requirement that an income change cause consumption of a l l goods whose prices change to alter in proportion. "Such preference structures are contradicted by the bulk of empirical evidence." 1^ 1 72 Even when path independence is not a problem, changes in money measures of consumer surplus may not correspond to changes in u t i l i t y , and the true surplus. The problem here is that the marginal u t i l i t y of money (M.U.M.) may vary with respect to a l l prices that change as well as with respect to income, i f i t changes. Uniqueness of consumer surplus is not sufficient to guarantee any meaningful interpretation of the change in consumer surplus as a money measure of u t i l i t y changes. In order to be a meaningful money measure, the M.U.M. must be constant, which guarantees uniqueness (but not vice versa). Marshall assumed the M.U.M. was constant for two reasons: f i r s t l y , to permit the use of money as an acceptable cardinal index of u t i l i t y ; secondly, so that for movements along the ordinary demand curve, (a) the area under the the demand curve would measure the total u t i l i t y ; and (b) the consumer surplus triangle would approximate the true surplus. In order to maintain an exactly constant M.U.M., with respect to price changes, the price elasticity of demand needs to be unity, and the marginal u t i l i t i e s of other goods should be unaffected (in fact Marshall went further and, as required by cardinal analysis, assumed independent marginal u t i l i t i e s ) . In an indepth review of consumer welfare theory, Richard Just et a l . concluded that the condition of constancy for the M.U.M. is "... at least as restrictive as the implications of path independence."11 They go on to state that: 173 / ... the economic implications of these conditions on the consumer indifference map are so restrictive as to prevent use of the "money measure of u t i l i t y change" approach in an a priori sense for essentially a l l practical purposes. That i s , one would have l i t t l e basis for estimating money measures of u t i l i t y change without f i r s t carrying out considerable empirical analysis to determine for example, whether or not a l l income e l a s t i c i t i e s of demand are consistent with the implications of path independence. Even^hen, constancy of marginal u t i l i t y of income may not hold. This is a strong attack upon the practicality of using the consumer surplus measure of u t i l i t y . If this applied problem is combined with the underlying u t i l i t a r i a n background of cardinal analysis, the consumers surplus measure as proposed by Marshall becomes totally unacceptable. However, cardinal analysis was replaced by ordinal analysis and i t was in this context that John Hicks redefined consumer surplus. When Hicks argued for the rehabilitation of consumers' surplus he stated: If the marginal u t i l i t y of money is constant, i t implies that the consumer's demand schedules are unaffected by changes in his real income; a l l i t need imply for this purpose is that the demand schedule for this commodity is unaffected (or substantially unaffected) by changes in real income which arise as a result of changes from one to another of various hypothetical situations which we may want to consider. Hicks goes on to point out that the requirements for constant M.U.M. need not be unrealistic, and are equivalent to requiring that there be a small or negligible income effect. Whenever the commodity in question is one on which the consumer is likely to be spending a small proportion only of his total income, the assumption of "constant marginal u t i l i t y of money" can usually be granted; and i t can s t i l l be granted, even i f this condition is not f u l f i l l e d , provided the particular change under discussion does not involve a large net change in real incomes. Thus, the practicability of the consumer surplus measure will vary depending on the complexity of the analysis, e.g., i t might be argued that for the case of a price change in one good, which 174 is a small part of total expenditure, no problems arise. The more commodities whose prices change, the less likely is a money measure of the change in consumer surplus to match the change in the true surplus. Ordinal analysis, by concentrating on relative changes, allows money measures of consumer welfare to be developed which do not require the unrealistic preference assumptions of Marshall. Consumer surplus as a welfare measure in its own right implies unrealistic a priori assumptions and, if defined as a cardinal measure, departs from accepted indifference mappings. Compensation Measures of Consumer Welfare Hicks refined four measures of consumer welfare change 1 5 resulting from a price change. These are compensating variation, compensating surplus, equivalent variation and equivalent surplus. The compensating surplus and equivalent surplus measures require that the quantity consumed be held constant, which constrains the consumer's freedom of choice, and are inapplicable to most policy situations. These two measures were designated as Marshallian by Henderson who originally specified the four measures.1^ Mishan has contended that only equivalent variation and compensating variation are tenable in 1 7 a l l familiar circumstances. However this contention may only hold under perfectly competitive equilibrium situations, and there are circumstances where compensating and equivalent surplus 1 Q may be the more appropriate measures. Attention here is focused on the more commonly used measures which allow the consumer freedom to chose the quantities purchased after a change in the 175 economic enviroment compensating and equivalent variation. In order to illustrate the meaning of these two measures i t is assumed that only one commodity undergoes a price change. The results of this analysis can be generalised to the many goods case and more than one price change. In Figure A1.3 two goods XI and X2 are shown along with the indifference mapping of an individual. Good X2, which can be regarded as a composite good, 1 g has a price of unity and acts as a numeraire. Good X1 has an i n i t i a l price of pO. Now, assume air pollution reductions cause the cost of producing X1 to f a l l and the price changes from pO to p1. If income is held constant at mO the consumption of X2 f a l l s from X2' to X2", and the quantity of X1 consumed increases from X1 ' to X1". This is the change according to a Marshallian demand curve. The welfare gained by the consumer from this change can be defined by the variation in income. The compensating variation of the price f a l l is the sum of money that when taken away from the consumer leaves him or her just as well off with the price change as i f i t had not occurred. In Figure A1.3 this is given by the income m0-m1. That i s , the vertical distance between the new budget line and a parrallel line which is tangential to the original indifference curve. Thus, removing a sum of money m0-m1 after the price change w i l l return the consumer to the original u t i l i t y level UO. The equivalent variation of a price f a l l is the sum of money that when given to the consumer leaves him or her just as well 20 off without the price change as i f i t had occurred. In Figure 176 Figure A1.3 Compensating and Equivalent Variations A1.3 this is given by income m2-m0, or the vertical distance between the original budget line (mO, mO/pO) and a parallel line tangential to the new indifference curve. This sum of money may differ from the compensating variation, because income is being increased here whereas the compensating variation reduces income. In order to show the relationship between these two measures it is helpful to derive the Hicksian Compensated Demand Curve (H.C.D.C.). This is done by expressing the changes, just described, in the price/quantity plane for X1. The top part of Figure A1.4 shows a similar change to before. There are two price levels of X1 shown, pO and p1, and there are two u t i l i t y levels, UO and U1. Before deriving the H.C.D.C. i t is helpful to derive the ordinary or Marshallian demand curve. The Marshallian demand curve is given as: xi = xi(P, M) That is , the quantity of xi demanded is a function of its price P and money income M. This is the solution to the u t i l i t y maximization problem: Maximize U = U(X) subject to I pi.xi = M i where X is the vector of quantities (X = x1,...,xi,...,xn). The Marshallian demand curve holds income constant and gives the quantity of a good demanded at different prices, while allowing u t i l i t y to vary. In Figure A1.4 income is held constant at mO while the price of f a l l s from pO to p1. Maximizing u t i l i t y subject, to the budget constraint at the original price requires 178 Figure A1.4 Relationship Between Ordinary and Compensated Demand Curves 0 q l q4 q3 q2 Quantity of XI 179 the consumption of q1 of X1, and at the new price q2 of X1. Thus two points on the price/quantity plane can be specified p0,q1 and p1,q2. These two points l i e on a Marshallian demand curve which can be mapped by repeatedly changing the price. This curve is shown as D(mO) in the bottom part of Figure A1.4. An alternative method of approaching the u t i l i t y maximization problem involves using the expenditure function. This is the dual to the above problem: minimize E = I pi.xi i subject to U(X) = Umax That i s , minimize the expenditure on xi subject to a u t i l i t y constraint. The solution to this problem is xi' = xi' (P, U) which is the H.C.D.C. In the bottom part of Figure A1.4 two such curves are derived. The price of X1 f a l l s from pO to p1 as before. However, as i t does so, assume income is removed from the individual so as to leave him or her on the original indifference curve UO. The result is to increase the quantity consumed from q1 to q3, not q2 as before. This gives the two points p0,q1 and p1,q3 which l i e on the H.C.D.C. H(U0). The H.C.D.C. only takes account of the substitution effect, because the income effect is excluded by the reductions of income. As X1 is a normal good so the income effect is positive and the H.C.D.C. is less elastic than the Marshallian demand curve. The demand curve H(U0) is relevant to the compensating variation which was defined above, and held UO constant. The 180 equivalent variation for the price f a l l holds U1 constant. The equivalent variation is the amount of income which if given to the individual would leave him or her just as well off without the price f a l l as with i t . That i s , the amount of income which shifts the original budget constraint to the right until i t is tangential to the indifference curve which the individual would reach i f the price had fallen. In the top part of Figure A1.4 after a f a l l in price to p1, the individual would have consumed q2. If instead, the price does not change, but income is increased until U1 is reached, the quantity of X1 demanded will be q4. The two points which are plotted in the bottom part of the figure are p1,q2 and p0,q4, and l i e on the H.C.D.C. H(U1). The compensating variation associated with the price f a l l is mO-ml, in the top of the figure, and the area to the left of H(0) and between the two price lines pO and p1 in part (b). The equivalent variation for the same price change is m2-m0,in the top of the figure, and the area to the left of H(U1) and between the two price lines, in the bottom of the figure. In general, the area to the left of the H.C.D.C. cutting through the original position defines the compensating variation, whereas the area to the l e f t of the H.C.D.C. cutting through the final position 21 defines the equivalent variation. The two measures w i l l be the same if the income elasticity of demand for good X1 is zero. For a normal good the equivalent variation exceeds the compensating variation for a price decrease, and vice versa for a price increase. The higher the income elasticity of demand for X1, the larger is the difference between the compensating and equivalent variation, and between 181 each of these and the Marshallian consumers' surplus. Given that these two measures are theoretically well established, there is a problem as to which should be used in a particular situation. Myrick Freeman attempted to answer this question using four crit e r i a practicability, the implied property rights, the uniqueness of the measures and their 22 consistency. He found both measures failed the f i r s t criterion. At the same time he notes that consumer surplus is relatively easy to calculate. The second criterion does not favour either measure in preference to the other. Compensating variation takes the i n i t i a l level of u t i l i t y as the reference point. This presumes the individual has no right or claim to make purchases at the new set of prices. In contrast, equivalent variation presumes the individual has a right to the new set of prices and must be compensated i f the new price set is not attained. The choice between the two measures therefore depends upon a value judgement as to which system of property rights is more equitable. The third criterion is more decisive and "(F)or reasons that l i e in the mathematics of the measurement technique, the answers 23 are different for the two measures being considered." This criterion judges whether the measure is independent of the order of the price changes when multiple changes occur, i.e., i t is concerned with path dependence. For example, reducing ozone pollution may reduce the price of a sensitive crop by increasing output. This price change may then cause the price of substitute commodities to alter. Freeman states: 182 The CV (compensating variation) is independent of the order of evaluation. The EV (equivalent variation) will be independent of the order of the evaluation only in the special case of a homothetic u t i l i t y function, that i s , where the income el a s t i c i t i e s of the goods are unitary. Unless this condition is met ther,e is no unique EV in the case of multiple price changes. The implausibility of unitary income e l a s t i c i t i e s has already been discussed. Thus, compensating variation is the more appropriate measure in this instance. The final criterion involves the situation where more than one policy option is available. The compensating variation may not provide a ranking of alternative policies that is consistent with individual preferences. The equivalent variation does not suffer from this deficiency, and is therefore favoured under these circumstances. Thus, the choice between the two measures will depend upon the characteristics of the welfare change being analysed. For example, a price change which affects the prices of other goods but is the only policy option would favour the use of the compensating variation. However, while both measures are consistent with a theoretical definition of welfare, neither is readily observable from market data. The Marshallian consumer surplus is observable and l i e s between the two variation measures. This suggests the possibility of using consumer surplus as an approximation to the more theoretically justified variation measures. The bottom half of Figure A1.4 is redrawn in Figure A1.5. The compensating variation associated with a price f a l l is exactly equal to area x. The equivalent variation associated with a price f a l l is given by area x+z+w. The consumer surplus is given by 183 Figure A1.5 Willig Approximation 184 area x+z. Thus, for a commodity with a positive income effect, the change in consumer surplus, due to a price f a l l from pO to p 1, is bounded from below by the compensating variation and from above by the equivalent variation; and differs from the compensating variation by area z and from the equivalent • u- u 25 variation by area w. It was Robert Willig who calculated the accuracy with which 2 6 consumer surplus could approximate the variation measures. Willig showed that under certain specific conditions, area z and area w could be calculated as percentage confidence limits to the consumer surplus estimate. In this way i t could be shown that the areas z and w would be insignificant for most empirical studies. As Willig stated: ... observed consumer's surplus can be rigorously utilized to estimate unobservable compensating and equivalent variations the correct theoretical measures of welfare impact changes in prices and income on an individual. This can be achieved by deriving, ... precise upper and lower bounds on the percentage errors of approximating the compensating and equivalent variations with consumer's surplus. These bounds can be explicitly calculated from observed demand data, and i t is clear that in most applications the error of approximation wi l l be very small. In fact, the error w i l l often be overshadowed by errors involved in estimating the demand curve. 185 Footnotes 1. Jules Dupuit "On the Measurement of the U t i l i t y of Public Works", Annales des Ponts et Chausees, 2nd Series Vol.8 (1844); reprinted in English in D. Munby (ed.), Transport:  selected readings (Harmondsworth: Penguin Books Ltd.,1968). 2. Consumer surplus is reviewed in John M. Currie, John A. Murphy and Andrew Schmitz, "The Concept of Economic Surplus and Its Use in Economic Analysis", The Economic Journal Vol.81 pp.741-799 (Dec.1971). 3. John R. Hicks, A Revision of Demand Theory (London: Macmillan,1956). 4. Robert D. Willig, "Consumer's Surplus Without Apology" The  American Economic Review Vol.66 No.4 pp.587-597. 5. Dupuit, " U t i l i t y of Public Works". 6. Hicks, Demand Theory, p.86. 7. Dupuit, " U t i l i t y of Public Works", p.29. 8. Ibid, p.41. 9. See, John M. Currie, John A. Murphy, and Andrew Schmitz, "The Concept of Economic Surplus and Its Use in Economic Analysis", The Economic Journal 81 (Dec.1971), and also, Richard E. Just, Darrell L. Hueth, and Andrew Schmitz, Applied Welfare Economics and Public Policy (London: Prentice-Hall International,1982). 10. Just et a l . , Applied Welfare Economics, p.83. 11. Ibid. 12. Ibid, p.82. 13. John R. Hicks, "The Rehabilitation of Consumers' Surplus" Review of Economic Studies Vol.8 pp.108-116 (Feb.,1941). 14. Ibid. 15. Idem, Demand Theory. 16. A. Henderson, "Consumer's Surplus and the Compensating Variation" Review of Economic Studies Vol.8 pp.117-121. (Feb.,1941). 17. E.J. Mishan, "Realism and Relevance in Consumer's Surplus" Review of Economic Studies, Vol.15 pp.27-33 (1947-48). 186 18. Such as when government restricts quantities; or where goods are not perfectly divisible e.g., a given family may, under reasonable circumstances, consume only one or two automobiles, not 1.5. This essentially limits consumption quantities and may make the surplus, rather than the compensation, measures more appropriate. 19. See, A. Myrick Freeman, The Benefits of Environmental  Improvement; theory and practice (London; John Hopkins Press,1979), p.35. 20. See, Just et a l . , Applied Welfare Economics, p.87, for a willingness to pay interpretation. 21. The compensating variation equals the negative of the equivalent variation, and vice versa. That i s , the compensating variation for a price f a l l equals the equivalent variation for a price rise, and vice versa. 22. Freeman, Benefits of Environmental Improvement, pp.43-47. 23. Ibid, p.45. 24. Ibid, pp.45-46. 25. For a proof see, Just et a l . , Applied Welfare Economics, pp.89-92. 26. Willig, "Consumer's Surplus Without Apology". 27. Ibid, p.31. 187 APPENDIX II PRODUCER WELFARE THEORY Unlike consumers' welfare theory there has been relatively l i t t l e controversy surrounding producers' welfare measures. Producers' welfare can be measured directly and is observable; that i s , there need be no problems choosing the best method of approximating an unobservable concept such as u t i l i t y . Despite this, there are several methods of measuring producers' welfare. These can be placed into two categories input market measures and output market measures. The output market is where a firm sells i t s production. Two measures will be discussed in this context; namely, producer surplus and quasi-rent. 1 The input market is where factors of production (i.e., land, labour, and capital) are purchased by the firm. No measures are discussed in this context (as they do not form part of the empirical study) but some of the theoretical advantages of this approach are mentioned. Producer surplus is the traditional approach to the measurement of producers' welfare, and was developed by Marshall. It is defined as the area above the short run supply curve and below the price line. It is assumed that the firm is operating in 188 a perfectly competitve market. The supply curve for a l l variable inputs is perfectly elastic; that i s , the firm is able to purchase a l l the variable inputs i t needs at a fixed price. It is also assumed that the costs of fixed factors are sunk, during the short run. For example, a farmer pays rent for land at the begining of the season and cannot recoup that sum of money. The producer surplus of a perfectly competitive firm is shown in Figure A2.1. The firm will supply nothing below the price p1 because i t cannot cover variable costs. As long as the price stays above the average variable cost (AVC) curve the firm can make payments on fixed costs. Above the average total cost (ATC) curve profits are made", as a l l costs are covered. The short run supply curve is SS and equals the marginal cost (MC) curve. Marshall's producer surplus is given by area pO,SS,p1. The surplus accrues to the firm via the ownership of fixed factors. Only these factors can receive payments above their marginal costs, because of their limited supply in the short run. In the long run these factors become variable and the surplus to the 2 firm disappears. • This short run economic rent is a quasi-rent to the firm, and producer surplus is one method of measuring i t . In the short run, the area above a competitive firm's supply curve and below the price line provides a measure of the excess of gross receipts over prime costs i.e., quasi-rent. Prime costs are the extra costs a firm incurs in order to produce a commodity, and which i t could have avoided i f i t had not produced the commodity. Another measure of quasi-rent is total revenue (gross receipts) minus total variable costs (prime costs). 189 Figure A2.1 Producer Surplus Price P0 Pi S (=MC) ATC \ AVC Quantity-Figure A2.2 Quasi-rent Price pO TVCO s / \ X 7 / AVC qO Quantity 190 Figure A2.2 shows a similar situation to Figure A2.1. Total revenue is the quantity produced qO times the price pO, and total variable cost is the quantity qO times the average variable cost TVCO. Thus, quasi-rent is given by area x. Despite other possible measures of quasi-rent the producer surplus approach is "...the most common approach in empirical and 4 graphical theoretic work The concept can also be applied at the industry level. The industry supply curve is the sum of the firms' marginal cost curves, and the area above this aggregate curve and below the price line is the aggregate surplus accruing to the owners of the firms. However, care is required when applying the producer surplus measure. For example, relaxing the price elas t i c i t y of supply of variable inputs leads to the producer surplus measure being 5 unrelated to actual welfare. Producer surplus will overstate actual welfare changes when the price of a necessary factor input increases as industry use of the factor expands. In Figure A2.3 the industry is in equilibrium at price pO and quantity qO, and the producer surplus would be pO,B,A (if supply equalled MCO). If the price were to rise to p1, the firms, expecting marginal cost to remain at MCO, would supply q i . Working on the presumption that marginal cost (i.e., MCO) equals the supply curve the producer surplus would be measured as p1,E,A. However, as the factor demand increases, so does its price and the marginal cost curve shifts to MC1. The area of producers' welfare is pi,D,C and q2 is supplied, not q1, at price p1. The supply curve is SS and does not equal the marginal cost curve. The area above the supply curve and below the price line bears no relationship to the 191 192 economic rent accruing to producers. Certain other conditions must also be met; namely, that the income, or welfare, effect be zero and that nonpecuniary advantages be unimportant to producers. A zero income effect is required to maintain economic rent as an objective measure which can be captured by producer surplus without recourse to individual preferences. As long as the firms are explicit profit maximizers they are unaffected by welfare effects. Thus, there is no divergence between money measures and welfare changes as there is with consumer theory (where compensating or equivalent variations being different money measures of the same u t i l i t y change diverge when income effects are not zero). Similarly, nonpecuniary goals must not conflict with profit maximizing behaviour or producer surplus will not capture the f u l l extent of economic rent. The conditions for producer surplus to act as a good measure of welfare have been summarised by Mishan. He concluded that the supply curve must be: ... constructed for a period during which the output of the good in question can be increased only by adding to fixed-factors amounts of other factors that are imperfect substitutes for i t but are perfectly elastic in supply with respect to their money prices. In such cases the rent of the fixed factor is exactly equal to the area above the supply curve under the conditions mentioned zero welfare effect and complete indifference to nonpecuniary advantages. The futher we move from these conditions, especially the latter condition, the greater the divergence between the true rent (either compensating or equivalent variation) and the area in question. Mishan contended that the term producer surplus is misleading. The producer refered to is in fact the owner of the firm, while i t is only via ownership of fixed factors that any 193 surplus accrues to the firm. It is more accurate to use the term producer in reference to the input factor of concern, and therefore to the "owner" to whom the economic rent is directly 7 attributable. Currie et a l . agree with Mishan and feel, "(I)t is more satisfactory to think in terms of economic rent rent to a short-run f i x i t y of some factor of production, rent to land, rent to entrepreneurial a b i l i t y , rent to market power and so on."8 Mishan has argued in favour of input market measures. This approach is analogus to the consumer welfare measures of Hicks, and involves individual preferences. It avoids the problem just outlined by working directly with the factors of production which create the welfare. Mishan found "... that consumer's surplus and economic rent are both measures of the change in the individual's welfare when the set of prices facing him are changed or the constraints imposed upon him are- altered. Any distinction between them is one of convenience only: consumer's surpluses have 9 reference to demand prices, economic rent to supply prices." This leaves the applied welfare economist with a choice as to whether economic rent is to be measured in the input market or the output market. This choice may often be made by the availability of data. Thus, i t can be more practical to measure economic rent by the area above the supply curve and below the price line. Divergences between the theoretical assumptions and actual market conditions can cause serious errors in measuring gains and losses using producer surplus. Thus, the proximity of actual conditions to the theoretical must be assessed and 194 corrections and qualifications made where necessary. If this is done, and divergences are not serious, the producer surplus can be justified as a measure of economic rent. Footnotes 1. Diagramatic analysis of input measures follows, Richard E. Just, Darrell L. Hueth, and Andrew Schmitz, Applied Welfare Economics and Public Policy (London: Prentice-Hall International,1982) pp.52-57. 2. The surplus to a factor may persist under certain conditions. See, John M. Currie, John A. Murphy, and Andrew Schmitz, "The Concept fo Economic Surplus and Its Use in Economic Analysis", The Economic Journal 81 (Dec, 1971) pp.756-758. 3. Yet another measure is given in, Just et a l . , Applied Welfare  Economics, pp.55-56. 4. Ibid, p.55. 5. This example is taken from Currie et a l . , "Concept of Economic Surplus", p.755 footnote 4. 6. E.J. Mishan, "What is Producer's Surplus?" The American  Economic Review, Vol.58 p.1278 (1968). 7. Ibid, p.1279. 8. Currie et a l . , "Concept of Economic Surplus", p.758. 9. E.J. Mishan, "Rent as a Measure of Welfare", The American  Economic Review, Vol.49 p.394 (1959). 195 APPENDIX III A MULTIPLE-OUTPUT MULTIPLE-INPUT MODEL OF THE AGRICULTURAL SECTOR IN BRITISH COLUMBIA Introduction In this appendix a dual model with two outputs and three inputs is presented for the agricultural sector in B.C. This aggregate model of crop production was orginally intended for use in an aggregate analysis of the response of producers and consumers to alterations in ambient ozone levels. However, the best model estimated from available data showed serious parameter errors. This model, the data base and parameter estimates are presented. Chapter 5 applies an alternative methodology to potato production and analyses the damages from variations in ambient ozone dose. As shown in Chapter 3, duality theory has been employed by the most recent econometric studies of agricultural production. Duality approaches to microeconomic theory have been reviewed by Diewert.1 The dual approach involves specification and estimation of cost or profit functions which, unlike production functions, already embody the optimizing behaviour of producers. A cost 196 function, for example, relates the minimum costs of producing a given output to input prices and the output level. The nature of the cost function is determined by production characteristics, which can be retrieved from the parameters of the function. Advantages of the dual approach include the ease of deriving the marginal cost functions for outputs and of measuring ela s t i c i t i e s 2 of factor demand and substitution. First the theoretical cost function model is described and the assumptions necessary for a well defined function are presented. The behavioural implications of the model are then discussed in the context of agriculture. Next the empirical model is introduced and a functional form is specified, and the data base is outlined. The empirical model is then applied to the agricultural sector in B.C. Parameter estimates are used to derive ray and product-specific scale economies, and factor e l a s t i c i t i e s of substitution and demand. Finally, the inaccuracy of the parameter estimates is outlined. 197 The Theoretical Model Cost Function A fundamental paradigm in economics is that producers competitively minimize costs subject to technological constraints. Competition in this context means that factor prices are fixed, during a given time period, irrespective of an individual producers' demand. Thus, the cost function gives the minimum value of producing a given quantity of output at fixed 3 factor prices. Assume that one output y is produced using N inputs; and that the nonnegative vector of inputs x=(x1,...,x ) produces a nonnegative, maximal amount of y in a given period. Futhermore, the cost of purchasing one unit of input i is p^>0, i=1,...,N, and that the positive vector of input prices, facing the producer is p=(p1,...,p ). The cost minimization problem i s , n min C = L x ; « p ; ( i = 1.2, ,n) i = 1 subject to Y = f(x 1,x 2,...x n), and a solution to this problem can be written as, C = f(y,p 1,..,p n), which is the cost function. 4 The cost function C has the following properties: 1. Nonnegative; i.e., C(y,p)>0. 2. Linearly homogeneous in input prices for each fixed output level; i.e. C(y,hp)= hC(y,p) for y>=0 and h>=0. 3. Nondecreasing in input prices for a fixed output; i.e., C(y,P1)>= C(y,p 2) for y>=0, p1>=p2>=0. 4. Concave in prices for a fixed output. 198 5. Nondecreasing in output for fixed prices; i.e. C(y',p)>= C(y",p) for y'>=y">=0. 6. Continuous from below in output for fixed prices. Given a minimum cost function C(y,p) which satisfies these properties and is differentiable with respect to input prices then: 3C(y,p)/3Pi = x.(y,p) i( l , . . . N ) . where x^(y,p) is a cost minimizing bundle of input i needed to produce output y>0 given positive factor prices p>>0. That i s , the cost minimizing demand for the ith input is equal to the partial differential of the cost function with respect to the ith 5 input price. This result is commonly called Shephard's lemma. Behavioural Assumptions Implicit in the theoretical cost function are several behavioural assumptions. Producers are assumed to take prices as given and optimize with respect to the quantity variables they control.^ Defence of these assumptions can be made in general for agricultural production at the firm and regional levels, but may be violated by the circumstances concerning particular products. At the farm level, output prices are unlikely to be influenced by the individual farmer because agricultural products are homogeneous and supplied by a relatively large number of farms. Where fewer, larger, farms exist or regional output is concerned, price may s t i l l be assumed to be exogeneous to production because of interregional competition. Thus, in the case of crop production in B.C., the United States (especially, Washington and California) provides considerable competition for 199 the producers of many products. In the demand for factors of production the agricultural sector also seems likely to be a price taker. Labour in most industrial countries is largely employed in the manufacturing and service industries. If labour is mobile, farm wages may be set by 8 these much larger sectors. Alternatively, the price of some factors may be cost determined, e.g., petrol determining the price of f e r t i l i z e r . Evidence also exists to suggest that the price of machinery is exogeneous to the agricultural sector and is largely determined by fuel costs, and cost conditions in the machinery producing and repairing, industries. 1^ Land is a possible exception to the exogeneous factor price assumption with agriculture being a land intensive activity. However, even in this case, proximity to a major urban area may be the most important determinant of price. Thus, in general, the assumption that factor prices are exogeneous to agriculture appears acceptable. 200 Econometric Model The Multiple-Output Multiple-Input Translog Cost Function In order to generate a system of input demand (and output supply) equations a functional form for the cost function has to be postulated, and then partially differentiated with respect to each input (and each output quantity). The m-output n-input translog cost function incorporating Hicks Neutral Technical Change (HNTC) is defined as follows: m m Inq. + 1/2 Z Z d. . Inq. Inq. i=1 j=i X J 1 3 n n InW + 1/2 Z Z f InW InW r r =1 s = i r s r 5 g. Inq. InW + hT (1 ) where C is cost; q^ is the output of product i ; Wf is the price of input r; T is an annual index of time; and a^, ^ i j ' ^r> ^ r s and g^ r are parameters determined by the technology of the industry. 1^ Differentiating both sides with respect to the logarithm of the rth input price gives the input cost share, or factor demand, equation: n n s r = b r + Z f InW + Z g. lnqi (2) r r s = 1 rs s i = 1 ir where, r=(1,...,n), sr=Wr/C and x r is the quantity of the rth input. The input share equations are derived from the translog cost function and Shephard's lemma.11 In an m-output n-input model with matrices (ch j) and ^ r s ^ m + Z a • i = 1 I n + Z b r=1 r m n + Z Z i = 1 r=1 201 symetrical the number of parameters to be estimated is 1 2 (m+n)(3+m+n)/2, which is twenty parameters in this model of B.C. agriculture, not including the intercept and HNTC. In practice the data available are often not sufficient to allow estimation of the f u l l cost function, even with the restrictions imposed by homogeneity in input prices. Estimating the f u l l dual system (i.e., cost and share equations together) is a more efficient econometric approach and can compensate for informational inadequacy in the estimation of the cost function alone. 1^ 1 4 Hall has suggested that for the case of perfect competition, another m behavioural equations can be obtained by noting that marginal cost is equal to price. In the case of the translog function there would be m equations of the form: R. = 91nC/31nqi = (3C/3q. ) . (C/q. ) = p^/C, 1 5 where R^  is the share of the ith output in total revenue. These revenue share equations can be more fully specified as: m n R. = a. + L d. . lnq. + L g. InW (3) 1 1 i=i x3 1 r=1 i r r The parameters of the cost function, excluding the intercept, could be estimated indirectly from a system of input and revenue share equations alone. The estimation of cost, revenue and share equations together further increases the efficiency of parameter estimates. This approach has been applied in a cost function study of U.S. agriculture (1939-77) by Ray. 1 6 Employing the revenue share equations for B.C. data gave improved parameter estimates (evidenced by the t-statistic) and this approach was used in the final model. Following Ray, instead of using price 202 indices to obtain p^q^/C, the numerator is directly measured as market sales revenue plus government payments. Additional econometric considerations are, (a) that the cost share equations add to one and, (b) that the parameters which occur in more than one equation are unique across equations. Symetry restrictions, implied by the twice differentiable nature of the cost function, are assumed, i.e., d- .=d.. and f =f I J J I r s s r From property two for cost functions given above, the economic constraint of linear homogeneity in input prices arises, e.g., the total cost doubles when a l l factor prices double. This basic requirement implies, n n n Z a = 1, Z f = 0, and Z g. = 0 for r=(1,...,n). r=1 r=1 i=1 Under the condition that the sum of the cost shares is unity, the symetry and homogeneity constraints imply exactly the same 1 7 constraints on the parameters. Variable Definitions and Data Description Time series data were collected for the period 1961 to 1984 for two outputs and three inputs. A l l time series data were converted to index numbers with base year 1981 before estimation. Output q 1 is livestock output and q 2 is crop output. These outputs are measured by the total cash receipts from each in 1 8 B.C. The prices and cost shares of the three inputs capital K, labour L and miscellaneous M, are required in order to estimate equations 1 and 2. The cost of labour was taken as the total wage b i l l paid to 203 farm labour in B.C. The price of labour (W1) was calculated, from monthly farm wages for B.C., as an annual wage rate without board. 2 0 The cost of farm capital was calculated as the capital stock multiplied by the chartered bank prime business loan rate, 21 deflated. Capital stock was taken as the current value of livestock, land and buildings, and implements and machinery, 22 which was then deflated by a capital price index (1981=100). The interest rate used above was taken as the price of capital ( W 2 ) . Miscellaneous, or aggregate intermediate, inputs were calculated as the summation of farm operating expenses for B.C. This categorization includes expenditures on f e r t i l i z e r and seed, feeds, other animal and crop expenses, fuel and ele c t r i c i t y , debt 23 and miscellaneous expenses. The miscellaneous input price was measured by the price index of a l l commodities purchased for farm production (W^).24 The dependent variables are as follows: SHLABR =(total wages'to farm labour)/(farm operating expenses). SHCAPT =(capital cost)/(farm operating expenses), SHMISC =(miscellaneous expenses)/(farm operating expenses), SHREV1 =(livestock marketing revenue)/(farm operating expenses), SHREV2 =(crop marketing revenue + government payments)/(farm operating expenses), and COST =an index of farm operating expenses, i.e., the sum of input costs. 204 Empirical Results Cost Function for B.C. Agriculture Various models were estimated in order to obtain the best parameter estimates using the t-test s t a t i s t i c . The f u l l unrestricted model with 22 parameters was i n t i a l l y estimated. This model gave insignificant values for a l l (9^ r) terms, with the approximate probability of being greater than the t- s t a t i s t i c varying from 0.58 to 0.99. On this basis a test for separability was performed. Separability in the translog requires that: m n 3/31nW.([a. + E d . - lnq. + L q. InW ]/ 1 1 i=i ^ 3 r=i i r r m n [a k + ^ d k j l n g j + ^ g k r lnWr]) = 0 (4) That i s , the relative marginal costs of outputs are independent 25 of the input prices. Separability holds i f : 9 i r = 0 (i= 1/...,n), (r=1,...,n). The computed F-value (with 6 and 8 degrees of freedom) was 0.5801, which is insignificant. The probability greater than F was 0.7384. Consequently separability was accepted and the term m n I I g i r lnq. lnWr, i=1 r=1 was excluded from the final model. The time trend variable T was set to one in 1961 and increased annually by one. Time trend parameters were estimated for a l l three inputs and tested for significance. The F-value was 1.5772 (with 3 and 10 degrees of freedom) and insignificant with a probability greater than F of 0.2191. This result supports the use of HNTC, and provides evidence that technical change in B.C. 205 agriculture has not been biased in favor of specific inputs. The parameters of the final cost function model, assuming separability, are shown in Table A3.1, together with their standard errors and T-test s t a t i s t i c . The revenue and input share equations are reported in Appendix IV. The parameters of the cost function have l i t t l e economic meaning of their own, but are related to the el a s t i c i t i e s of input substitution and factor 2 6 demand. In order to evaluate the model, these e l a s t i c i t i e s and the ray and product-specific economies of scale were calculated. As is shown below, the scale economies appear re a l i s t i c but the input e l a s t i c i t i e s show that there are serious problems with the estimated model. Scale Economies The estimated parameters reported in Table A3.1 were used to calculate scale economies at each data point. Scale economies may be expressed as the relative change in output when costs change 27 but input prices are held constant. Christensen and Greene define scale economies (SCE) for the single output industry as: SCE = 1 - 31nC/31nY, (5) where C is costs and Y output. This results in positive numbers for increasing scale economies and negative numbers for diseconomies of scale. The concept of scale economies can be applied to the multiproduct industry by the use of two related measures: ray 28 economies of scale and product-specific economies of scale. Ray economies of scale are an extension of the concept of single-product scale economies and indicate the behaviour of costs as a 206 Table A3.1 Parameter Estimates for Translog Cost Function of Agriculture in B.C. Var iable Parameter Estimate Standard Error T Ratio Approx Prob>|T| Intercept -0.242278 0.073033 -3.3174 0.0106 T (trend) 0.073323 0.024647 2.9749 0.0177 a1 0.767015 0.033016 23.2315 0.0001 a2 0.441412 0.016373 26.9598 0.0001 d1 1 0.408438 0. 113015 3.6140 0.0068 d12 -0.630085 0.057840 -10.8935 0.0001 d22 0.522477 0.030082 17.3685 0.0001 b1 0.140495 0.004405 31.8967 0.0001 b2 0.279689 0.009316 30.0226 0.0001 b3 0.579816 0.008321 69.6799 0.0001 f 1 1 0.079989 0.039132 2.0441 0.0752 f 12 0.159833 0.063569 2.5143 0.0361 f 13 -0.239822 0.072909 -3.2893 0.0110 f 22 1.105387 0.141610 7.8058 0.0001 f 23 -1.265221 0.144578 -8.7512 0.0001 f 33 1.505042 0.188401 7.9885 0.0001 207 given bundle of outputs change proportionately. In the case of the m-output n-input translog cost function, this can be defined 29 as: m SCE = 1 - Z 91nC/31nq. (6) i = 1 1 That is 1 minus the cost elasticity along an output ray. Instead of holding the composition of output fixed while the scale varies, one output can be varied while other outputs are held constant. This gives the product-specific economies of scale which can be defined for ith output in the translog cost function as: m n SCE. = 1 -(a. + I d . , lnq. + L g. InW ) (7) 1 1 i=1 1 D 3 r=1 i r r Since the cost function for B.C. agriculture is separable the product-specific scale economies can be restated as: m SCE. = 1 -(a. + L d. . lnq. (8) 1 i=1 1 3 J On the basis of these equations the ray and product-specific economies of scale for the B.C. agricultural model were calculated. The results are shown in Table A3.2. Clearly increasing economies of scale exist across a l l data points for both livestock and crop outputs, while the ray scale economies show decreasing returns. This implies output specialisation is preferable to joint production. Table A3.2 also shows that the economies of scale in livestock production have increased, while those for crop production have remained relatively stable. The overall diseconomies have been increasing. 208 Table A3.2. Product-Specific and Ray Economies of Scale for Agriculture in B.C. Year Livestock Crop Overall SCE1 SCE2 SCE 61 0.090404 0.594598 -0.31500 62 0.099650 0.599705 -0.30064 63 0. 133001 0.562056 -0.30494 64 0.159918 0.537319 -0.30276 65 0.109351 0.593465 -0.29718 66 0.136882 0.582209 -0.28091 67 0.166325 0.554500 -0.27917 68 0.156695 0.567652 -0.27565 69 0.092905 0.618734 -0.28836 70 0.150526 0.565068 -0.28441 71 0.129103 0.584596 -0.28630 72 0.114174 0.611454 -0.27437 73 0.178829 0.586647 -0.23452 74 0.170520 0.597946 -0.23153 75 0.128471 0.628296 -0.24323 76 0.136650 0.624377 -0.23897 77 0.188641 0.572336 -0.23902 78 0.217129 0.554040 -0.22883 79 0.215936 0.563121 -0.22094 80 0.214650 0.569608 -0.21574 81 0.232985 0.558588 -0.20843 82 0.191288 0.593887 -0.21482 83 0.191676 0.577869 -0.23045 84 0.190069 0.588134 -0.22180 Mean 0.158157 0.582758 -0.25908 209 These findings are supported by Ray, who developed a cost function model for U.S. agriculture for the period 1939 to 30 1977. He reported scale economies for selected years, and those 3 1 close to the period used here are presented in Table A3.3. These estimates show the same product-specific increasing returns and overall decreasing returns as found for B.C. In addition the trends of a l l three scale economies are similar to those reported here. Although the absolute value of scale economies is different for each product between the U.S. and B.C., the overall economies are quite close. For example, the ray scale economies for B.C. in 1969 and 1977 were -0.28836 and -0.23902 respectively compared with -0.27065 and is -0.19875 in Ray's study. Table A3.3. Product-Specific and Overall Scale Economies Reported by Ray Year Livestock Crop Overall T959 0.246591 0.343703 -0.409642 1969 0.342322 0.386992 -0.270648 1977 0.413283 0.388005 -0.1987532 Source: Calculated from Subhash C. Ray, "A Translog Cost Function Analysis of U.S. Agriculture, 1939-77" American Journal of  Agricultural Economics 64:3 (1982) 490-498. Elas t i c i t i e s of Substitution The partial e l a s t i c i t i e s of substitution for the translog cost function were calculated using the formulae: e i j " 1 + ( a i j / B i - s j > { 9 ) i=K,L,M, for i not equal to j ; 210 e i i = [ a i i + si»<s.-l)]/s..s. (10) i=K,L,M; where e^j is the elasticity of substitution between inputs, and • • 32 si is the share of the ith input. The partial e l a s t i c i t i e s of substitution are related to the price elas t i c i t y of demand for 33 factors of production: E.. = s-.e... (11) These formulae are the same for single and multiple output industries. The e l a s t i c i t i e s of substitution calculated for the B.C. model are shown in Table A3.4 and are compared with the results reported by others in Table A3.5. While comparison of results is complicated by the use of different time periods, factor classifications, and areas of study, the underlying technology is not expected to vary and results are expected to conform to theoretical expectations (e.g., own price elasticity should be negative). The main differences between the B.C. model and other studies are the regional nature of the model, and that the capital category, like that of Ray (1982), includes land instead of treating i t as a separate input. The estimated substitution of labour and miscellaneous inputs is the only elasticity of substitution close to previous estimates. This estimate is almost twice that reported by Ray for a more disaggregate classification of miscellaneous. Both of Ray's other categories, aggregated as miscellaneous here, and the results of other studies show positive e l a s t i c i t i e s (i.e., labour and miscellaneous inputs are complements). Labour and capital are found to be complements as in other work but the size of the elasti c i t y this time is more than twice the closest estimate. 211 Table A3.4. Translog Cost Function Estimation of Partial E l a s t i c i t i e s of Substitution YEAR esLK esLM esKM esLL esKK esMM 61 3. 76690 -2 .4195 -6. 0804 -2. 1 1 32 5. 9038 5 .79018 62 4. 1 4373 -2 .2927 -6. 1421 -2. 0900 7. 0953 4 .94539 63 4. 23800 -2 .2684 -6. 1694 -2. 0829 7. 4088 4 .78473 64 3. 98490 -2 .3226 -6. 1 1 96 -2. 1030 6. 6304 5 .23977 65 4. 09586 -2 .2616 -6. 1697 -2. 0997 7. 0803 4 .99361 66 4. 19641 -2 .1997 -6. 2338 -2. 0985 7. 5458 4 .78773 67 3. 94041 -2 .2448 -6. 1899 -2. 1 146 6. 761 3 5 .24579 68 3. 86366 -2 .2616 -6. 1832 -2. 1 182 6. 5328 5 .41016 69 3. 94302 -2 .21 97 -6. 21 24 -2. 1 1 65 6. 8461 5 .21674 70 3. 82663 -2 .2578 -6. 1918 -2. 1204 6. 4597 5 .48172 71 3. 85692 -2 .2371 -6. 2052 -2. 1 201 6. 5898 5 .39866 72 4. 001 34 -2 . 1 661 -6. 261 0 -2. 1 172 7. 1 660 5 .06382 73 4. 92464 -1 .9486 -6. 7360 -2. 0773 1 1 . 0036 3 .85802 74 5. 1 9334 -1 .8919 -6. 9461 -2. 0681 12. 4079 3 .64547 75 4. 82004 -1 .9207 -6. 7393 -2. 0919 10. 8046 3 .92573 76 4. 5231 1 -1 .9383 -6. 6131 -2. 1093 9. 6761 4 .20491 77 4. 03716 -2 .0273 -6. 4106 -2. 1237 7. 7769 4 .88342 78 4. 56459 -1 .9213 -6. 6504 -2. 1091 9. 9101 4 .15331 79 5. 43060 -1 .8410 -7. 1578 -2. 0627 13. 7933 3 .48710 80 5. 06631 -1 .9028 -6. 8698 -2. 0761 1 1 . 8360 3 .73356 81 5. 06752 -1 .9440 -6. 8019 -2. 0653 1 1 . 5553 3 .75212 82 4. 50151 -2 .0333 -6. 4766 -2. 0969 9. 1 146 4 .28774 83 4. 12803 -2 . 1 1 66 -6. 31 59 -2. 1 138 7. 6748 4 .81921 84 4. 10364 -2 .1171 -6. 3137 -2. 1 152 7. 6074 4 .85640 Mean 4. 34243 -2 . 1 1 48 -6. 4246 -2. 1002 8. 5492 4 .66522 212 Table A3.5. Sample Mean E l a s t i c i t i e s of Substitution in Agricultural Cost Function Studies Author/ Date Labour Mi sc. Partial Labour Capital Elasticity Labour Land Estimates Mise. Capital Mise. Land Binswanger 1 974 2.22 0.851 0.204 1 .844 -0.31 Lopez 1980 0.875 1 .779 0.113 1 .555 0.99 Ray 1 982 -1.147* 0.748 1 .661* Adamowicz 1986 1 .392 0.553 -0.138 0.089 0.44 Spash 1987 -2.1171 4.10364 -6.4246 *Ray reports feed, seed and livestock costs as a seperate input giving substitution elasticites with labour of 1.527 and with capital of 0.486. Table 15 gives futher details of a l l the models. 213 Finally, miscellaneous and capital inputs are found to be complements which is clearly not supported. One explanation might be the presence of strong complementarity between land and miscellaneous, which overshadows the substitutability with capital. However, such complementarity is only reported by 34 Adamowicz whose estimate was not significant. The own elasticity of substitution has l i t t l e economic meaning and is normally used to calculate the price elasticity via equation 9. However, if the demand for inputs is to be negatively sloped, as is expected, the own substitution elas t i c i t y must be negative. As can be seen in Table A3.4, this is not the case for capital or miscellaneous inputs. The own price e l a s t i c i t i e s calculated from our share and parameter estimates are reported in Table A3.6 and compared with other studies in Table A3.7. The mean price elasticity for labour is of the correct sign, and inelastic as expected. The estimate for labour is comparable to that found by Adamowicz for Canadian agriculture. However the outstanding problem is with the capital and miscellaneous demand el a s t i c i t i e s which, as expected from the substitution estimates, are positive. The size of the error in the parameter estimates can be calculated from the predicted mean shares for given e l a s t i c i t i e s using the equations: and f i j " ( e i j - ] ) <V sj>' f i i = E i i ' s i + S i < l + * i > . These equations are calculated from 9, 10 and 11. Table A3.8 214 Table A3.6. Translog Cost Function Estimates of Own Price E l a s t i c i t i e s for B.C. Agriculture YEAR Labour Capital Mise. 61 -0.31820 2.26494 2.69698 62 -0.30217 2.49508 2.49133 63 -0.29840 2.55273 2.45066 64 -0.31013 2.40746 2.56451 65 -0.30796 2.49228 2.50344 66 -0.30719 2.57758 2.45143 67 -0.31951 2.43240 ,2.56599 68 -0.32333 2.38872 2.60611 69 -0.32140 2.44844 2.55885 70 -0.32617 2.37462 2.62342 71 -0.32572 2.39967 2.60332 72 -0.32213 2.50818 2.52098 73 -0.29562 3.14888 2.20493 74 -0.29139 3.35663 2. 14565 75 -0.30326 3.11848 2.22357 76 -0.31485 2.94089 2.29925 77 -0.33185 2.61906 2.47571 78 -0.31466 2.97845 2.28540 79 -0.28903 3.55106 2.10072 80 -0.29507 3.27342 2.17036 81 -0.29017 3.23189 2.17554 82 -0.30623 2.84899 2.32134 83 -0.31873 2.60080 2.45944 84 -0.32012 2.58869 2.46887 Mean -0.31055 2.73330 2.41532 215 Table A3.7. Own Price E l a s t i c i t i e s in Agricultural Cost Function Studies Author/ Date Own Labour Price Elasticity Capital Estimates Misc. Binswanger 1974 -0.911 -1 .089 -1.042 Lopez 1980 -0.517 -0.347 -0.410 Ray* 1982 -0.864 -0.524 -0.293 Adamowicz 1 986 -0.344 -0.168 -0.239 Spash 1987 -0.31055 2.7333 2.41532 *1977 value not mean. Table 15 gives futher details of a l l the models. 216 shows the calculated range within which the parameters of the B.C. model would have to be in order to be comparable with previous research. The f i r s t column of the range is calculated from the e l a s t i c i t i e s of previous studies, reported in Tables A3.5 and A3.7, closest to those estimated for the B.C. model. The second column is calculated from the e l a s t i c i t i e s furthest away from those found for the B.C. model. This analysis shows a l l the input parameters of the B.C. model to be outside the expected range. Table A3.8 Expected and Estimated Input Parameters Parameter Range Within Which Parameter Expected Actual Value B.C. Model f12 0.038561 to -0. 022127 0.159833 f1 3 -0.167466 to -0. 095160 -0.239822 f 32 -0.156328 to 0. 144830 -1.265221 f11 0.075900 to -0. 009150 0.079989 f 22 0. 106590 to -0. 079457 1.105387 f 33 0. 125320 to -0. 292240 1.505042 Key: 1=Labour, 2=Capital, 3=Miscellaneous. These parameter errors imply that the estimated model f a i l s to reflect the underlying technology. The errors in a l l (fjj) terms can be expected to affect the accuracy with which other model parameters are estimated. Thus, the findings of separability and HNTC are brought into suspicion, and positive conclusion are no longer possible. 217 Marginal Cost Marginal cost can be estimated for each product of the joint cost function by differentiating the fitted function with respect to that product. The marginal cost of the ith product is given by: m n 3C/9q. = (a. + Z d.. Inq. + Z g. InW ).C*/qi (12) i = 1 -1 r=1 where C* is the fitted total cost function. The term in brackets is equivalent to 1-SCE^. Assuming price equals marginal cost, 12 gives the supply curve: Ps = (1-SCEi) . C*/Y (13) This supply function is obviously dependent upon the accuracy of the parameters estimated in C*, which as shown above are in error for the B.C. model. In addition, incorrect parameters in one part of the model can be expected to have affected the estimation of other parameters, and SCE.. 218 Conclusion A 2-output 3-input translog cost function model of the agricultural sector in B.C. was estimated from data for the period 1961-1984. The parameters of the model were used to calculate input e l a s t i c i t i e s of substitution and scale economies. While the estimated scale economies appeared acceptable, serious parameter errors were discovered when the substitution e l a s t i c i t i e s were calculated. Errors in those parameters analysed can be expected to affect other parameters of the model and the marginal cost for crops. Thus an alternative approach to modelling ozone damage is utilized in the text. 219 Footnotes 1 W.E,, Diewert Duality Approaches to Microeconomic Theory Reprint No.323 (Stanford: Institute for Mathematical Studies in the Social Sciences, 1982). 2 Merits of various dual approaches are summarised in Ramon E. Lopez "Estimating Substitution and Expansion Effects Using a Profit Function Framework" (Vancouver: University of British Columbia, Dept. of Agricultural Economics, 1981). 3 W.E. Diewert "Cost Functions" Discussion Paper 86-35 (Vancouver: University of British Columbia, 1986). 4 H.R. Varian Microeconomic Analysis 2nd edition New York: W.W. Norton and Co., 1984. 5 W.E. Diewert "An Application of the Shepherd Duality Theorem: A Generalized Leontieff Production Function" Journal of  Po l i t i c a l Economy 79 (1971) 481-507. 6 See Diewert Duality Approaches to Microeconomic Theory sec 11 for a review of duality and non-competitive approaches to microeconomic theory. 7 British Columbia, Ministry of Agriculture and Food. British  Columbia Vegetable Marketing Guide (1982). 8 Hans P. Binswanger "A Cost Function Approach to the Measurement of E l a s t i c i t i e s of Factor Demand and E l a s t i c i t i e s of Substitution" American Journal of Agricultural Economics (May, 1974) 377-386; and Ramon E. Lopez "The Structure of Production and the Derived Demand for Inputs in Canadian Agriculture" American Journal of Agricultural Economics 62 (1980) 38-45. 9 Binswanger "A Cost Function Approach to the Measurement of El a s t i c i t i e s " . 10 Subhash C. Ray "A Translog Cost Function of U.S. Agriculture 1939-77" American Journal of Agricultural Economics 64:3 (1982) 491. 11 Ibid. 12 Randall S. Brown, Douglas W. Caves, and Laurits R. Christensen "Modelling the Structure of Cost and Production for Multiproduct Firms" Southern Economic Journal 46 (1979-1980) 256-273. 13 Ray "Translog Cost Function of U.S. Agriculture". 220 14 R.E. Hall "The Specification of Technologies with Several Kinds of Outputs" Journal of Po l i t i c a l Economy 81:4 (July/Aug., 1973) 878-892. 15 Brown et a l . , "Modelling the Structure of Cost and Production for Multiproduct Firms". 16 Ray "Translog Cost Function of U.S. Agriculture". 17 Toshiyuki Kako "Decomposition Analysis of Derived Demand for Factor Inputs: The Case of Rice Production in Japan" American  Journal of Agricultural Economics (November, 1978) 630. 18 Canada, Statitics Canada. Farm Cash Reciepts Catalogue 21-001 various annual, and Cansim. 19 Canada, Statitics Canada. Farm Net Income Catalogue 21-202 various annual. 20 Canada, Statitics Canada. Farm Wages in Canada Catalogue 21-002 various. 21 Canada, Bank of Canada. Review, 1985. 22 Canada, Statitics Canada. Fixed Capital Flows and Stocks Catalogue 13-211. 23 Canada, Statitics Canada. Farm Net Income Catalogue 21-202 various annual, and Cansim. 24 Canada, Statitics Canada. Farm Inputs Price Index Western  Canada Catalogue 62-004 various annual, and Cansim. 25 Brown et a l . , "Modelling the Structure of Cost and Production for Multiproduct Firms". 26 Binswanger "A Cost Function Approach to the Measurement of El a s t i c i t i e s " p.379. 27 Laurits R. Christensen and William H. Greene "Economics of Scale in U.S. Electric Power Generation" Journal of P o l i t i c a l  Economy (Aug/Dec, 1976) 655-676. 28 Elizabeth E. Bailey and Ann F. Friedlaender "Market Structure and Multiproduct Industries" Journal of Economic Literature 20 (Sept., 1982) 1024-1048. 29 Brown et a l . , "Modelling the Structure of Cost and Production for Multiproduct Firms". 30 Ray "Translog Cost Function of U.S. Agriculture". 221 31 Ray's estimates of SCE were defined as 1/(31nC/31nqi), while those reported for the B.C. model are 1 -(31nC/31nqi). Thus, Ray's estimates were converted by inversion and subtraction from one. 32 Ernst R. Berndt and David 0. Wood "Technology, Prices and the Derived Demand for Energy" Review of Economics and Statistics (August, 1975) 259-268. 33 Ibid. 34 Adamowicz, W. "Production Technology in Canadian Agriculture" Canadian Journal of Agricultural Economics 34 (March, 1986) 8 7 - 1 0 4 . 222 APPENDIX IV COST FUNCTION INPUT AND REVENUE SHARE EQUATION ESTIMATES MODEL: SHARE OF LABOUR DEP VAR: SHLABR PARAMETER VARIABLE ESTIMATE STANDARD ERROR T RATIO APPROX PROB>ITI Intercept bl b2 b3 0. 140495 0.039994 0.079917 •0.1 1 991 1 0, 002785764 0.012375 0.020102 0.023056 50.4331 3.2320 3.9755 -5.2009 0.0001 0.0042 0.0007 0.0001 MODEL: DEP VAR: VARIABLE SHARE OF CAPITAL SHCAPT PARAMETER ESTIMATE STANDARD ERROR T RATIO APPROX PROB>ITI Intercept b1 b2 b3 0.279689 0.079917 0.552694 -0.632610 0.005891932 0.020102 0.044781 0.045719 47.4699 3.9755 12.3421 •13.8368 0.0001 0.0007 0.0001 0.0001 MODEL: DEP VAR: VARIABLE LIVESTOCK REVENUE SHARE SHREVA PARAMETER STANDARD ESTIMATE ERROR T RATIO APPROX PROB>ITI Intercept a1 a2 0.767015 0.204219 0.315042 0.020378 0.034877 0.017850 37.6393 5.8554 •17.6495 0.0001 0.0001 0.0001 223 MODEL: CROP REVENUE SHARE DEP VAR: SHREVB PARAMETER STANDARD APPROX VARIABLE ESTIMATE ERROR T RATIO PROB>|T| Intercept 0.441412 0.010106 43.6799 0.0001 a2 0.261238 0.009283485 28.1401 0.0001 a l -0.315042 0.017850 -17.6495 0.0001 224 P e r m i s s i o n h a s b e e n g r a n t e d t o t h e N a t i o n a l L i b r a r y o f C a n a d a t o m i c r o f i l m t h i s t h e s i s a n d t o l e n d o r s e l l c o p i e s o f t h e f i l m . T he a u t h o r ( c o p y r i g h t o w n e r ) h a s r e s e r v e d o t h e r p u b l i c a t i o n r i g h t s , a n d n e i t h e r t h e t h e s i s n o r e x t e n s i v e e x t r a c t s f r o m i t may b e p r i n t e d o r o t h e r w i s e r e p r o d u c e d w i t h o u t h i s / h e r w r i t t e n p e r m i s s i o n . L ' a u t o r i s a t i o n a e t e a c c o r d e e a l a B i b l i o t h e q u e n a t i o n a l e d u C a n a d a d e m i c r o f i l m e r c e t t e t h e s e e t de p r e t e r o u de v e n d r e d e s e x e m p l a i r e s d u f i l m . L ' a u t e u r ( t i t u l a i r e du d r o i t d ' a u t e u r ) s e r e s e r v e l e s a u t r e s d r o i t s de p u b l i c a t i o n ? n i l a t h e s e n i d e l o n g s e x t r a i t s d e c e l l e - c i n e d o i v e n t e t r e i m p r i m e s o u a u t r e m e n t r e p r o d u i t s s a n s s o n a u t o r i s a t i o n e c r i t e . ISBN 0-315-41906-7 

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