) 3 ECONOMIC EFFECTS OF INCREASED VERTICAL CONTROL IN AGRICULTURE: Bulletin 592 4 April 1988 Alabama Agricultural Experiment Station Auburn University Auburn University, Alabama Lowell T Frobish, Director CONTENTS Page INTRODUCTION ................................................ 3 The Egg Industry and Vertical Control ................... 3 Causes of Vertical Control............................ 7 Hypothesized Effects of Vertical Control .................... 11 METHODOLOGY, DATA, AND STATISTICAL ANALYSIS .............. 12 The Analytical Framework ............................ Specification of the Margin Equation ........................ Data ..................................................... Econometric Results............. ................. RESULTS ...................................................... 12 14 17 19 21 Tests of Coordination and Concentration Hypothesis ......... 21 Impacts of Increased Vertical Control on Marketing Costs, Retail Prices, and Farm Prices ................... 22 CONCLUSION ...................... ............................ LITERATURE CITED ............................................ 26 28 APPENDIX A.................................... APPENDIX B ........................................ FIRST PRINTING 3M, APRIL 1988 .............. 30 34 Information contained herein is available to all persons without regard to race, color, sex, or national origin. Economic Effects of Increased Vertical Control in Agriculture: THE CASE OF THE U.S. EGG INDUSTRY ALEX BRAND, HENRY KINNUCAN, and MARC WARMAN2 INTRODUCTION CONTROL is the linking of firms in the vertical food system either through common ownership of business entities or by contracts between them. This is the prominent structural characteristic of several agricultural industries important to the Southeast and Alabama. Broilers, sugar cane, citrus fruits, fluid milk, and some tree nuts have production/marketing structures where vertical control is virtually complete (29). Eggs and turkeys are rapidly approaching that status. The purposes of this bulletin are to elucidate the economic causes of vertical control and quantify the economic impacts of vertical control on consumers, producers, and middlemen. The U.S. egg industry serves as the focus of analysis because of its importance to the agricultural economy of the Southeast and because its industry structure has moved toward one dominated by vertical control (from 12 percent of volume in 1960 to 81 percent in 1977). The Egg Industry and Vertical Control Since the early 1970's, the U.S. egg industry has been buffeted by a series of shocks, largely beyond its control, that has caused severe 'This research was funded in part by Cooperative Agreement No. 12-25-A-3122, Agricultural Marketing Service, U. S. Department of Agriculture. 2Research Associate and Assistant Professor of Agricultural Economics and Rural Sociology, Auburn University, and Economist, Agricultural Marketing Service, USDA, respectively. Appreciation is expressed to Robert Brewer for assistance in the conduct of this research and to John Adrian, Patricia Duffy, and Lee Schrader for reviewing an earlier version of the manuscript. VERTICAL 4 ALABAMA AGRICULTURAL EXPERIMENT STATION economic hardships for many of the industry's participants. Concerns over cholesterol, less breakfast eating, aggressive marketing of fast breakfasts, and diets containing fewer cakes, pies, and other foods using eggs have contributed to a 17.6 percent decline in per capita egg consumption between 1970 and 1985 (3, p. 22). Yet over the same period, improvements in production technology, nutrition, breeding, and management techniques have led to a 13.3 percent increase in layer output (3, p. 11). Increases in egg supply, against an inelastic and declining demand for eggs, have placed severe downward pressures on price and industry revenue. Exacerbating the effects of the downward price pressure were random supply shocks caused by the cyclical nature of egg production and disease epidemics. Of particular importance was the outbreak of avian influenza in the fall of 1983. Anticipation of a supply shortage caused retail egg prices to soar to $1.33 per dozen in February 1984 only to collapse 5 months later to 8 8 ¢ per dozen (3, p. 7). Such extreme price volatility makes reliance on price signals as a guide to production levels and resource allocation in the industry risky at best. Industry response to the problems of price volatility and declining prices appears to have taken two forms. First, the industry sought government assistance by spearheading a movement that resulted in an amendment passed by the U.S. Congress in 1983 which brought eggs under the Agricultural Marketing Agreement Act of 1937. Since then, the industry has used the authority of the Act to propose a national egg marketing order. The purpose of the proposed marketing order, which was eventually defeated in a June 1987 producer referendum, was to provide for a mandatory national checkoff of 0.5¢ per dozen eggs marketed to be used to finance industry-sponsored advertising and promotion programs and other market development activities (20). The referendum, if passed, would have resulted in annual checkoff monies of about $25 million. The second industry response to downward price pressure and price volatility, and the one that serves as the central focus of this study, is a restructuring of organizational relationships within the industry. According to one estimate, between 1980 and 1984, the number of commercial egg operations in the United States declined from 6,600 to 3,800 (16). In addition to a declining number of firms, the egg industry has evolved into a highly specialized sequence of production and marketing activities, figure 1. For example, eggs at the farm level are produced in three distinct stages-hatching, growout, and layer services each usually being performed by a separate economic entity. Value-added activities include assembly, grading, pack- EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 5 Production activities I I I I I I Value-added \ activities Note: The solid arrows indicate the direction of product or service flow; the dashed arrows indicate the direction of vertical control via ownership or contracting. FIG. 1. Retail egg production stages and vertical control. aging, wholesaling, and retailing and some of these, too, are performed by separate business firms. Because the different stages are interlinked, a pivotal factor governing the performance of the total egg production and marketing system is the level and smoothness of interstage coordination and communication. There are essentially two ways in which the various stages can be linked: through market exchange or by vertical control. Under the market exchange option, vertical flow of product or services is accomplished via market transactions. For example, an egg layer operation buys replacement hens on the open market at a market-determined price.This firm generally has no voice in the affairs of the growing services firm other than the price that is to be paid for a specified number of pullets. Under the vertical control alternative, vertical flows are accomplished via internal organization. That is, rather than relying on the market to provide inputs (outputs), the firm gains control over quantity, quality, and price through purchase of the upstream or down- 6 ALABAMA AGRICULTURAL EXPERIMENT STATION stream firms (vertical integration) or via contracting. Thus, the firm or industry chooses to substitute managerial and organizational skills for market transactions to achieve interstage coordination under the vertical control alternative. In the egg industry, vertical control is both the forward and backward types. An egg packer often contracts with a layer services firm for the eggs. Or, if the egg packer owns a feed mill, a growout operation may be purchased to assure a market for feed. The packer also may forward integrate into wholesaling to assure a steady market for the packaged product. The variety of other options for achieving vertical control is illustrated in figure 1. In the U.S. egg industry, market exchange as a coordinating mechanism has been virtually replaced by vertical control since 1970. Between 1970 and 1977, the quantity of eggs (on a dollar volume basis) produced under vertical control arrangements increased from 40 to 81 percent, table 1. Most of the increase has occurred in contracting (44 percent of the dollar volume of eggs in 1977), but integration also increased greatly (to 37 percent of dollar volume in 1977). TABLE 1. VERTICAL CONTROL IN THE U.S. EGG INDUSTRY, SELECTED YEARS, 1960-77 Year 1960 ......................... 1970 ......................... 1977 ......................... Percent of eggs (dollar volume basis) sold under Production or Vertical marketing contract integration Both 7.0 20.0 44.0 5.5 20.0 37.0 12.5 40.0 81.0 Source: Rodgers, George. 1979. Poultry and Eggs. Another Revolution in U.S. Farming? USDA Economics, Statistics, and Cooperatives Service Report No. 441: 168. Industry concentration has increased in concert with the trend towards vertical control, although occurring at a less rapid rate. The 20-firm concentration ratio, which measures the percentage of industry sales or volume conducted by the largest 20 firms, increased from 20.6 percent in 1978 (the earliest available figure) to 32.0 percent in 1986, table 2. Four-firm and eight-firm concentration ratios show a similar trend toward increased concentration, especially in recent years. The heightened industry concentration reflects a move toward industry consolidation in response to the economic pressures enumerated previously. The research objectives of this study were to investigate the economic impacts of the foregoing structural changes. Impacts of increased vertical control and industry concentration were to be analyzed at the consumer, middleman, and producer levels, with EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY TABLE 2. CONCENTRATION IN THE U.S. EGG LAYER INDUSTRY, 1978-86 7 Year Percent of layers owned by the largest 4 8 20 firms 1978 1979 1980 19811 1982 1983 1984 1985 1986 .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. .................................. 8.5 8.5 9.1 9.3 9.4 10.8 12.3 12.4 firms 12.9 12.9 13.9 - firms 20.6 21.6 24.0 25.5 25.8 28.7 31.7 32.0 14.3 14.5 17.0 19.0 19.5 'Not available. Source: Poultry Tribune, various issues, 1978-86. emphasis on describing and quantifying the price effects of these structural changes. The analysis to be used proceeds as follows. First, the general economic causes of vertical control are reviewed. Next, hypotheses to explain the economic effects of increased vertical control specific to the egg industry are developed. An analytical framework for testing these hypotheses is presented. Econometric models are estimated which serve to test the hypotheses and to quantify the effects of increased vertical control on marketing margins for eggs. The analysis would then conclude with a discussion of the effects of vertical control on retail- and farm-level egg prices and likely future impacts. Causes of Vertical Control A review of the economics literature indicates five broad reasons for vertical control: market failure, uncertainty, declining industry, market power, and coordination economies. Market Failure The market failure argument contends that firms opt for vertical control when transaction costs associated with obtaining supplies (selling goods) via market exchange become prohibitively high (37). Transaction costs rise as markets become less "perfect" in their ability to efficiently allocate resources. Market imperfections occur when (1) competition among buyers and sellers is inadequate to insure price-taking behavior, (2) information gaps exist about relevant features of market exchange, (3) commodities traded are not homogeneous but differ in quality or other relevant aspects, and (4) there is uncertainty about such factors as availability of supplies, level of prices, and costs. Under these conditions, price signals are distorted, 8 ALABAMA AGRICULTURAL EXPERIMENT STATION forcing firms to rely on auxiliary sources of information in determining value and costs. Depending on the relative cost of verifying the veracity of price signals, the firm substitutes internal organization for market exchange, especially if the firm possesses superior internal coordinating ability. Because transaction costs are zero in "perfect" markets (i.e., those characterized by perfect competition, perfect information, readily identified products, and lack of risk), vertical control is seen as a strategy for coping with market imperfections. That is, under the market failure argument, vertical control is an outgrowth of market imperfections which, in turn, impose information-acquisition and other transaction-related costs. Because of these costs, the firm finds it less expensive to obtain supplies through internal organization than from market exchange. Uncertainty Firms also may integrate as a risk-reduction strategy If supplies of an important input, such as eggs, are uncertain to a downstream firm (the assembler-packer), an incentive may exist to purchase the upstream firm to obtain a better estimate of the price of the uncertain input (2). Vertical control through ownership enables the integrator to achieve costs savings via improved decisions about quantities of inputs that are used in conjunction with the uncertain input. Because there is always an incentive for the downstream firm to buy more upstream firms to improve price forecasts, supply uncertainty implies a tendency toward imperfect competition, even when the industry initially is perfectly competitive. Declining Industry To understand the declining industry argument, it helps to view industries in a life cycle sense. Firms making new products have a limited market and, moreover, may have difficulty finding the technical expertise and requisite new inputs in the general economy and thus must fabricate their own. As the firm or industry grows, markets expand sufficiently to make specialization cost-effective. Other firms begin to supply raw materials; undertake marketing tasks, utilize byproducts, and even train skilled workers. Governing this process of specialization is economies of scale made possible by expanding markets. As the industry matures and competing products emerge, the market for the original product begins to contract. With declining demand and the associated price pressures, volume eventually becomes insufficient to support independent firms performing special- EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 9 ized functions. These specialized functions are reappropriated by the surviving firms via integration, perhaps employing new cost-cutting technologies (17,27). Based on this argument, Stigler (36) argues that "vertical disintegration is the typical development in growing industries, vertical integration in declining industries." Market Power Anticompetitive incentives for vertical control are three: (1) to practice price discrimination, (2) to circumvent monopoly, and (3) to erect barriers to entry (36, pp. 237-238). A firm having monopoly power in an intermediate market, such as the production of aluminum, will have an incentive to integrate forward into the customer market to practice price discrimination. If a cartel sets monopoly prices for a raw material, a buyer can avoid these prices by integrating backward into the raw materials market. The barriers-to-entry incentive is based on the notion that integration impedes entry by (1) discouraging nonintegrated entry (such firms may be subject to price squeezes and supply cutoffs), and (2) by raising the cost of entry (because capital markets would charge higher interest rates for the larger borrowings necessitated by an integrated vis-a-vis nonintegrated entry (19, p. 746). Also, integration may "foreclose" part of the market, thereby reducing the size of the "open" part of the market and raising the economies-of-scale barrier to entry (21). CoordinationEconomies Processors in the food marketing system often face variable supplies of the farm-based input due to seasonality, random factors connected with weather, pests, and other biological hazards, and inadequate information about market needs. Hence, over shorter periods of time, e.g. weekly or daily, food processing plants may experience spot shortages. Moreover, the available supplies might not meet the required quality standards. Because processors operate most efficiently when production occurs at a continuous rate, an incentive exists to seek ways to stabilize the flow and quality of raw materials via vertical control (24, pp. 26-28). The potential gains from interstage coordination depend on cost conditions of the processing plant, the degree and duration of variability in raw material flows, and the cost of market transactions. If the average costs of a typical processing plant are as depicted in figure 2, minimum cost (AC °) occurs at a daily processing rate of Q° units of output. If reduced availability of raw materials causes the firm to temporarily reduce output to Q', the daily average cost of production 10AAAA 10 ALABAMA AGRICULTURAL GIUTRA EXPERIMENT XEIEN STATION TTO Dollars/unit ATC AC' AC*------AC o Q' Q* QO Quantity FIG. 2. Potential cost savings through vertical control. over this time period increases to AC'. Average annual production costs will increase by some amount between AC ° and AC', depending on the number of days the firm is forced to operate at reduced capacity Q'. For example, if the firm operates at reduced capacity onehalf of the time, average annual output is the simple average of Q° and O'-Q* in figure 2. The corresponding average cost is AC*. The difference between AC' and AC* is the annual cost savings that could be achieved through vertical control that stabilizes raw material supplies so that the plant could operate continuously at its optimum capacity Q°. Of course, whether cost savings from vertical control are sufficient to encourage its adoption depends on the cost of internal organization. Firms with superior coordinating talents might find the difference between AC' and AC* adequate inducement to adopt vertical control; others who experience greater frictions in internal organization may still find market exchange the more cost-effective means of obtaining raw material supplies. An important element of the coordination economies argument is EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 11 the sharing of cost savings between the respective stages of economic activity (24, p. 27). If markets continue to be competitive after vertical control is adopted, cost savings experienced by the marketing firm eventually will be shared with the producer. For example, if the processor depicted in figure 2 integrates backward into the supply market, the cost savings AC'-AC*, net of added internal organization costs, is shared with the input supplier. Thus, unless supply schedules of input suppliers are perfectly elastic, there is an incentive for both parties to adopt vertical control. Hypothesized Effects of Vertical Control As is evident from a review of its causes, vertical control has different economic impacts depending on the motivations of firms involved. Two basic motivations can be identified: production efficiency and market power enhancement. A firm that integrates backward in an attempt to stabilize the supply or quality of raw materials or to obtain better information about its price is motivated by efficiency concerns. This type of vertical control, assuming that the cost of internal organization to the firm does not rise appreciably, will result in net cost savings. On the other hand, a firm may integrate forward or backward in an effort to block new entrants into the industry by making financing costs higher, introducing supply risks, and reducing the size of potential markets for would-be rivals. In this case, the result may be higher costs, especially if there are correlated increases in industry concentration. Moreover, a common feature of imperfectly competitive markets is higher selling costs due to increased advertising, promotion, and other attempts by large firms to differentiate products from the competition (22). Because neither motive for vertical control in the U.S. egg industry can be rejected a priori, two hypotheses are entertained: the coordination hypothesis and the concentration hypothesis. The coordination hypothesis posits that increased vertical control results in reduced marketing costs because of economies achieved through improved coordination of economic activity between vertical exchange points. The concentration hypothesis posits that increased vertical control results in higher marketing costs because of excess plant capacity, higher selling costs, higher profit margins, and other factors associated with enhanced market power. The next section presents an analytical framework for testing the economic implications of each hypothesis. 12 ALABAMA AGRICULTURAL EXPERIMENT STATION METHODOLOGY, DATA, AND STATISTICAL ANALYSIS The Analytical Framework Because vertical control relates to organizational arrangements in the vertical food delivery system and these arrangements affect marketing efficiency, a suitable analytical framework is the marketing margin model developed by Gardner (9) and extended by Fisher (8). The model consists of six equations describing a food processing sector which combines a farm based-input (factor F) with a second input called "marketing services" (factor M) to produce a retail food commodity (output R). Market equilibrium conditions are established from six equations describing retail demand, input supplies, the farm-retail production process, and marginal conditions for profit maximization. Assuming long-run competitive equilibrium, profit maximizing behavior on the part of industry participants, and a farmto-retail production function characterized by constant returns to scale and fixed proportions production technology, the solution of the model on vertical control is indicated in figure 3 (8,9). In the upper diagram, the intersection of the farm level supply curve (SF)with the farm level demand curve (not shown for illustrative convenience) establishes the initial equilibrium farm price of fo. In the same diagram, the initial equilibrium retail price (ro) is determined by the intersection of retail demand (DR) and the retail supply (not shown) curves. The lower diagrams'indicate equilibrium in the marketing services market. SM and DM are defined as the supply and demand curves, respectively, for marketing services. The intersection of these curves determines the initial equilibrium price for marketing services, m°. If markets are perfectly competitive and the farm-based input and retail product are measured in equivalent units (so that, for example f and r refer to farm and retail price, respectively, for one dozen eggs), then equilibrium prices in the upper and lower diagrams of figure 3 are linked as follows: (1) o mo= r-f _ . Equation (1) says that the margin of retail price over farm price determines the price of marketing services. Thus, m is interpreted as the farm-retail marketing margin for eggs. A second point to note about figure 3 is the direct linkage between quantities in the two diagrams. The assumption of fixed proportions EFFECTS EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 13 13 mentioned earlier means that retail output (R) is linked in a proportional manner to inputs (F and M). Hence, a change in the quantity of marketing services utilized by the industry results in a proportional change in output. The effects of vertical control on market equilibrium as implied by the coordination hypothesis are indicated in panel (a) of figure 3. Increased vertical control, by lowering the cost of existing marketing services (e. g., processing plant labor, transportation, energy), shifts the supply schedule for marketing services to the right. The price of marketing services (the marketing margin) decreases from m° to m', causing utilization of marketing services to increase from M° to M'. Under fixed proportions, the quantity demanded of the farm-based input (eggs) and quantity supplied at retail increase proportionally, causing the farm price to rise to f' and the retail price to fall to r'. Hence, under the coordination hypothesis, increased vertical control results in a shrinkage of the marketing margin, financed by a lower retail price and a higher farm price. The economic implications of the concentration hypothesis can be described in an analogous manner by reference to panel (b) of figure 3. Here, increased vertical control causes a leftward shift in the supply schedule for marketing services. A leftward shift in the supply schedule is hypothesized because the cost of providing existing marketing services rises as the now imperfectly competitive industry begins to spend more on advertising, promotion, packaging, delivery, and service systems in an effort to differentiate products and to attract and retain new customers. In addition to higher selling costs, the added market power associated with increased vertical control may cause excess processing capacity, excess profits, and unusually large compensation for executives (31, p. 135). Thus, increased industry concentration leads to larger marketing margins, ceteris paribus, implying a reduction in farm prices and an increase in retail prices as depicted in figure 3, panel (b), upper diagram. While the coordination and concentration hypotheses are analytically treated separately, in reality both may have validity for explaining observed changes in egg marketing margins. For example, the industry concentration effect may become relevant only in the end stages of conversion to vertical control because of the requirement for industry concentration to achieve a certain minimum level before monopoly power can be effectively exercised. Parker and Connor (23) suggest an industry must achieve a four-firm concentration ratio exceeding 40 percent before monopoly power can be exercised. If this scenario is valid, forces described by both hypotheses may have rel- 14 14 ALABAMA ALABAMA AGRICULTRLEPIMNSAIO AGRICULTURAL EXPERIMENT STATION Panel (a) Coordinations hypothesis r,f Sr r,f Panel (b) Concentration hypothesis SF r 0o__ 1 -j---- iSp ---[--Ir1 fl °I--II f°---z----D I--f1 DR IR,F R,F S SS I SI 0 .e, M M 1 M FIG. 3. Hypothesized effects of vertical control on egg marketing margins, retail prices, and farm prices. evance after some point of conversion to vertical control. As indicated in figure 3, the effect of vertical control on marketing margins and hence on the appropriateness of the coordination and concentration hypotheses depends critically on the magnitude and direction of the vertical control-induced shift in the marketing services supply schedule. The next section presents the econometric procedures used to estimate the direction and magnitude of this shift. Specification of the Margin Equation To empirically distinguish the coordination hypothesis from the concentration hypothesis and to estimate the effect of increased ver- EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 15 tical control on egg marketing margins, two alternative specifications of the price spread equation are utilized. First is a conventional markup equation (Heien) of the form: 5 (2) mt = o0 + xrt + ac2 c t + c iSit + i=3 6 CV t + a 7 VI t + aoD t + t where: t = 1, 2, 3, ... , 52 (first quarter 1972 through fourth quarter 1984), m t = farm-to-retail marketing margin for grade A large eggs, rt = retail price of eggs in cents per dozen, ct = an index of labor cost specific to the food marketing industry, Sit = a vector of three quarterly dummy variables to indicate seasonality in egg marketing margins with the first calen- der quarter serving as the omitted category, CV t = coefficient of variation of weekly wholesale egg prices, VIt = percentage of eggs produced or marketed under vertical control, D t = a dummy variable assigned the value of one for the period of heightened industry concentration (1980, quarter 1 1984, quarter 4) and zero otherwise, and tt = a random error term. All price variables (m, r, c) are deflated by the consumer price index for all items (1967 = 100). More precise empirical definitions of each variable are provided in the data appendix. According to the markup pricing hypothesis, isolated increases in retail price or input cost lead to increases in the marketing margin; hence, 1 and 2 are expected to have positive signs. Because of anticipatory or monopolistically competitive pricing behavior on the part of the retailers, egg margins are expected to differ seasonally (28). However, the actual pattern of seasonal differences in margins cannot be determined a priori; hence, no expectations are placed on the signs of the coefficients of the seasonal dummy variables. Following Brorsen et al. (6) and Grant et al. (12), the CV variable is specified to account for the influence of price risk on marketing margins. Because of an inelastic demand for eggs (10) and random supply shocks due to disease and other biological hazards, the egg in- 16 ALABAMA AGRICULTURAL EXPERIMENT STATION dustry is subject to significant price volatility. (Over the sample period, the coefficient of variation of wholesale egg prices averaged 6.8 percent and ranged from 1.5 to 18.1 percent.) If egg marketing firms are risk-averse and price risk is a significant factor affecting costs, o 6is expected to have a positive sign. The VI variable is specified to reflect the effect of vertical control on farm-retail egg margins. The sign of its coefficient depends on which hypothesis is exerting a stronger influence over the sample period in question. If forces described by the coordination hypothesis dominate, the sign of c 7 is expected to be negative. If, on the other hand, concentration effects are more prominent, the sign a is expected to be positive. The D t variable is specified in an attempt to separate concentration and coordination effects. Because the two effects work in opposition to one another, holding the influence of one of the factors constant via specification of an additional variable in the model should increase the estimated effect of the other factor. This reasoning, coupled with the fact that industry concentration did not increase appreciably until the 1980s, table 2, led to the inclusion of D t to represent the concentration effect, net of the coordination effect. Because Dt is defined to assume the value of one for the 1980-84 period and zero otherwise, its coefficient is expected to have a positive sign. An implicit assumption of the markup model, equation (2), is that margin changes are caused by changes in either retail demand or farm supply, but not both. If this assumption is invalid, i.e., if margins are being influenced by simultaneous shifts in retail demand and farm supply, then equation (2) may give biased parameter estimates (9,18). In the egg industry, retail demand has been declining steadily over time due in part to cholesterol concerns. At the same time, supply shocks have occurred due to random events associated with disease as well as technological change in egg production. Thus, it appears quite possible that coincident changes in supply and demand were occurring over the sample period. To investigate the extent to which potential specification error in equation (2) might affect the results, an alternative margin specification suggested by Wohlgenant and Mullen (38) was estimated. This model, called the "relative price" model, assumes the following form: (3) mt = B0 + B1 rt + B2 C B3 rt Qt + 6 i=4 BiSit + B7 CV t + B8 VI t + B9 D t + u' EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 17 where the as yet undefined variable Qt represents industry output of eggs expressed in dozens per capita. The essential difference between markup and relative price specifications is the inclusion of the interaction term, rt· Qt , in the latter. An additional technical difference is that the relative price model omits an intercept term. Because of problems associated with estimating an equation without an intercept (11), equation (3) is specified to include an intercept. Because the two models differ both conceptually and empirically, each serves as a test against the other for robustness of statistical results. Data Equations (2) and (3) were estimated using national quarterly data for the period 1972-84. Quarterly data were selected in part to avoid the necessity of modeling lag structures, since margins appear to adjust fully to cost changes in 2 months or less (28). Also the assumption of predetermined supply implicit in the specification of price spread models (6) is more appropriate for quarterly data than for annual data. Data availability was the primary determinant of the sample period. The particular data series on egg price spreads used in this study was terminated by the USDA in 1984. Prior to 1972, reliable quarterly data on labor cost in food marketing were not available. Data depicting vertical control were not continuous over the sample period and therefore had to be estimated. Under the assumption that institutional innovations like vertical control follow a time path similar to technological innovations (13), a logistic growth function was estimated as follows (t-ratios in parentheses): (4) In [VCt/(K - VCt)] = - 13.299004 + .1908997 T (16.3) R 2 = .957 N = 13 (15.6) where VCt equals percentage of eggs sold under vertical control in year T and K is the highest level of vertical control attainable by the U.S. egg industry. Following Griliches (13), a value for K was determined empirically by reestimating the growth function under alternative values of K until the explanatory power of the model (as measured by R2) was maximized. Such a procedure yielded K = .95, meaning that eventually 95 percent of all eggs marketed in the United States will move through channels involving vertical control. 18 ALABAMA AGRICULTURAL EXPERIMENT STATION The trend variable T was specified to assume the values of 60 through 70, 75, and 77, indicating the years in which actual observations on vertical control were available. The observations on vertical control for the years 1960 through 1970, 1975, and 1977 were obtained from Rogers (25,26). The high R2 (.957) and significant coefficients of equation (4) suggest that the logistic growth function adequately mimics the time path of vertical control for the egg industry. To estimate actual values of vertical control to be used in later econometric analysis the following transformation of equation (4) was employed: (5) C 1 + e K -(a + bT) where VCt equals the predicted value of vertical control, K equals .95, a equals 13.299004, b equals .1908997, and T equals the year in question (1972, 1973, ... , 1984). Evaluation of the prediction performance of the logistic growth function suggests that early values may overstate and later values may understate somewhat the actual level of vertical control in the industry as suggested by the following comparison of actual and predicted values: Year 1970 1975 1977 Actual 40.0 percent 69.0 percent 81.0 percent Predicted 49.0 percent 69.8 percent 76.2 percent However, the terminal (1984) estimate of 89.2 percent seems reasonable. Further, replacing the growth function estimates with estimates of vertical control based on linear interpolation and extrapolation from historical values had little effect on estimated regression coefficients to be discussed later. Thus, the reasonableness of the growth function estimate coupled with the robustness of regression results with respect to measurement of the vertical control variable allays concerns about the appropriateness of the technique. Finally, based on the observation by Kilmer (17) that vertical control changes in a smooth manner over time, linear interpolation from estimated annual values was used to obtain quarterly figures, Appendix B. The risk variable is measured as the coefficient of variation of weekly wholesale egg prices. Other variables are measured by con- EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 19 ventional means. The actual data, along with a more precise empirical definition of each variable and a listing of sources, are provided in the data appendix. Econometric Results Econometric results relative to the markup and relative price models are presented in table 3. Initial analysis indicated the presence of first-order serial correlation; hence, the Cochrane-Orcutt procedure was used to obtain generalized least squares estimates of the parameters. Each model was estimated twice: once using the entire data set (conventional model), and again using all data except the 1983, quarter 4, observation (outlier model). Results based on the entire data set are discussed first. Then the rationale for the second set of estimates and associated regression results are presented. The overall summary statistics suggest that both models are wellspecified. Based on the F-statistic, each regression is significant at the .01 level. The R2's show 92 percent or more of the observed varTABLE 3. GENERALIZED LEAST SQUARES ESTIMATES OF ALTERNATIVE SPECIFICATIONS OF THE FARM-RETAIL EGG MARKETING MARGIN EQUATION, UNITED STATES, 1972-84 QUARTERLY DATA Variable Constant ................ Conventional models Markup Relative price 19.097 (2.84) -.035 (- .35) .058 (.92) .018 (1.05) Outlier models Markup Relative price 17.354 (3.93) .075 (4.77) .094 (2.21) - 21.0331 (3.19) r ....................... .067 (2.87) c ............ ......... .067 (1.04) r.Q .................... S2 ..................... -.281 (-.82) S3 ................... -.648 (-1.89) S4 ..................... -.541 (-1.65) CV................... -.016 (-.45) VI .............. ....... -.203 (-5.86) D ..................... -.196 (-.32) P ....................... .037 2 R .................... .917 DW .................... 1.99 62.1 F-statistic ............... N ...................... 51 'Numbers in parentheses are t-values. 16.517 (3.68) .022 (.33) .088 (2.07) .009 (.79) -.239 (- .69) -.571 (- 1.63) -.630 (-1.85) -.014 (- .39) -.171 (-3.82) -.355 (- .57) -.009 .917 1.99 56.1 51 -.195 (-.73) -.544 -.173 (- .63) -.507 ( 1.98) -.267 (-2.16) -2.18 (-.82) .005 (.19) -.205 (-9.08) .132 (.31) - .119 .949 2.01 101.58 50 (-.97) .006 (.23) -.188 (-6.16) .030 (.07) - .147 .948 2.01 90.5 50 20 ALABAMA AGRICULTURAL EXPERIMENT STATION iation in egg marketing margins being "explained" by the specified variables. The Durbin-Watson statistic indicates lack of serial correlation in the generalized least squares residuals. Moreover, the relatively small estimated values for the first-order autoregressive coefficient (-) suggest only mild serial correlation prior to adjustment. Thus, both models appear to be well specified. The estimated coefficients of the markup model agree in sign with a prioriexpectations and are, in general, significant. Retail price and labor cost have positive net relationships with the egg marketing margin. Margins are smaller in the third and fourth quarters compared to the first quarter, and price risk has no discernible effect on egg margins. The vertical control variable has a negative coefficient and is significant at the .01 level, providing results consistent with the coordination hypothesis. The coefficient of the dummy variable to indicate the concentration effect is not significant. Turning to the relative price model, results are generally consistent with the markup model, suggesting that specification error of the type mentioned previously is not adversely affecting results. The interaction term is positive as expected, but not significant at usual probability levels. The estimated vertical control effect is highly significant and is consistent with the markup model estimate in sign but is of smaller magnitude (- .171 versus -. 203). As in the markup model, the concentration dummy is not significant. Because regression results can be adversely affected by "influential" observations (4), several diagnostic tests to determine the presence of outliers were undertaken. An analysis of residuals indicated an "extreme" observation in the post-1979 period. In particular, the regression residual for 1983, quarter 4, assumed a large negative value, placing it well outside the 95 percent confidence band in the TSP-generated residual plot. Further analysis revealed an unusually small marketing margin in this quarter (9.50 per dozen compared to 11. 5 ¢ in the immediately preceding quarter and 13.3¢ in the succeeding quarter). Apparently, the avian influenza which affected the industry in late 1983 had the effect of severely squeezing the egg marketing margin. The sharp change in the marketing margin in 1983, quarter 4, was of concern because of its potential effect on the estimated coefficient for the concentration dummy variable. Recalling that this dummy variable was specified to indicate the effect of heightened industry concentration in the post-1979 period, the occurrence of an extraordinarily large negative residual in this period may vitiate attempts to estimate the concentration effect. In particular, the dummy variable EFFECTS EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUTY2 OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 21 may be measuring the effect of the avian influenza and not the desired concentration effect. To examine this hypothesis and to further assess the robustness of regression results, the markup and relative price models were reestimated with the 1983, quarter 4, observation deleted, (table 3, outlier models). Qualitatively the outlier models are identical to the conventional models: the concentration effect remains insignificant, the coordination effect is still highly significant, and corresponding coefficients change only slightly. However, significance of several of the coefficients in both markups and relative price models improves with deletion of the "outlier." The stability of coefficients across estimation procedures and model specifications increases confidence in the accuracy of the estimated concentration and coordination effects. RESULTS With econometric estimates of the margin equations in hand, it is now possible to discriminate empirically between the coordination and concentration hypotheses. In addition, the econometric results can be used to quantify the effects of vertical control on egg marketing margins, retail prices, and farm prices. Tests of Coordination and Concentration Hypotheses The coordination hypothesis posits a net negative relationship between increases in vertical control and marketing margins. To test this hypothesis, 99 percent confidence intervals for the estimated coefficients of the vertical control variable were constructed. Results show an estimated coordination effect that is clearly negative in sign, table 4. Thus, evidential support is provided in favor of the coordination hypothesis. Apparently the increased vertical control observed in the egg industry over the 1972-84 period has led to imTABLE 4. TESTS OF COORDINATION AND CONCENTRATION HYPOTHESES Hypothesis Coordination................ Concentration............... Parameter value Hypothesized Estimated sign value Negative Positive 114 -. 286 to -. 056 -1.78 to 1.38 -1.96 to 1.25 -. 292 to Result Accept Reject -. 'Ninety-nine percent confidence intervals. Upper numbers were estimated from the markup model; lower numbers from the relative price model. 22 ALABAMA AGRICULTURAL EXPERIMENT STATION proved coordination in the egg production/marketing system, thereby lowering costs. The concentration hypothesis posits a net positive relationship between increases in vertical control and marketing margins. Ninetynine percent confidence intervals of the estimated coefficients of the concentration dummy variable show values that range from negative to positive, table 4. Thus, it is not possible to conclude that the increase in egg industry concentration associated with greater vertical control has had inimical economic effects. For different results with respect to the beef sector, see Hall et al. (14). However, rejection of the concentration hypothesis by these data does not mean that the concentration issue is settled. As indicated previously, a four-firm concentration ratio of 40 percent or higher may be necessary before monopoly power can be effectively exercised. In 1984 (the last year of the data period), the egg industry's four-firm concentration ratio was 11 percent, well below the requisite 40 percent. Because the industry appears inexorably headed toward increased concentration, table 2 and (1), it is quite conceivable that a follow-up study some years hence could show a significant concentration effect. Still for the 1972-84 period analyzed in this study, no significant concentration effect was isolated. Impacts of Increased Vertical Control on Marketing Costs, Retail Prices, and Farm Prices According to the coordination hypothesis, increased vertical control leads to reduced marketing costs. An estimate of the extent to which marketing margins for eggs have declined due to vertical control can be obtained from the estimated coefficients of the vertical control variable. These coefficients are -. 203 from the markup model and - .171 from the relative price model, table 3. Each coefficient tells how the marketing margin is affected by a 1 percentage point change in vertical control, assuming other factors affecting the margin remain unchanged. Thus, multiplying each coefficient by the actual change in vertical control over the sample period gives an estimate of the net effect of increased vertical control. As indicated in figure 4, egg margins declined continuously between 1973 and 1983 in real terms. The actual decline over this period was 8.2¢ per dozen in 1967 dollars (3). To calculate the percentages of the observed decrease attributable to vertical control, the previously mentioned coefficients were multiplied by the change in vertical control (26 percentage points: from 62 percent of industry EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 23 Margin, cents/doz. 20 19 18 17 16 15 14 13 12 111 I ] ] ] I I I I I I I I 1972 '73 '74 '75 '76 '77 '78 '79 '80 '81 '82 '83 '84 '85 Year FIG. 4. Real farm-retail price margin for eggs in 1967 dollars, United States, 1972-84. volume in 1973 to 88 percent in 1983). Results indicate an expected margin decline of between 4.45¢ (- .171 x 26) and 5 .2 7 ¢ (- .203 x 26). Comparing these estimates with the actual margin change (8.2¢) suggests that between 54 and 64 percent of the observed decrease may be attributable to vertical control. Stated differently, if vertical 24 ALABAMA AGRICULTURAL EXPERIMENT STATION control in the egg industry had remained constant at its 1973 level, real farm-retail egg margins over the 1973-83 period would have declined by only 3 to 4 ¢ per dozen instead of the observed 8 .2 ¢. Based on an average margin over the sample period of 15.4¢ per dozen, these results suggest increased vertical control reduced average marketing costs in the egg subsector by about 26 percent (19.4¢ without increased vertical control versus 15.4¢ with increased vertical control). Because the data reject the concentration hypothesis, competition in the egg industry should be sufficient to insure that cost savings at the middleman level are passed along to producers and consumers. To estimate the extent to which consumers and producers have benefited from cost savings achieved by the egg marketing sector through vertical control, the following expressions (derived in the appendix) were employed: (6) (7) Af Ar - - ,f ro r, and (7) (8) rI T fo rO E- am Equations (6) and (7) define price changes at producer and consumer levels, respectively, and equation (8) establishes the magnitude of the shift in the marketing services supply schedule associated with vertical control, figure 3. This shift is a function of: (1) the retail demand elasticity for eggs (-q), (2) the farm level supply elasticity for eggs (e), (3) the estimated margin change associated with increased vertical control (Am), (4) initial retail price (ro), and (5) initial farm price (fo). To apply equations (6) - (8), the following assumptions were made: 1. The retail demand elasticity (-q) for eggs is -. 330; 2. The farm supply elasticity (e) for eggs is .942; 3. The initial farm price (fo) of eggs is 39.37¢ per dozen (1967 dollars); 4. The initial retail price (ro) of eggs is 58.90¢ per dozen (1967 dollars); and 5. The estimated change in the margin due to vertical control is - 5.27¢ per dozen (1967 dollars). on rn 0 on C,) r TABLE 5. SENSITIVITY ANALYSIS OF ESTIMATED IMPACT OF VERTICAL CONTROL ON MARKETING MARGINS AND INCIDENCE OF MARGIN CHANGES, U.S. EGG INDUSTRY, 1973-83 0 Proportion of the margin change reflected hy a change in egg prices Pct. 81 83 90 68 68 90 control coefficient Retail demand elasticity (ri) 330 - .330 - .165 -. 660 -. 330 -. 330 -. Farm supply elasticity (E) Estimated effect/dozen of vertical control on' Farm Farm retail egg Retail marketing margin' egg prices egg prices (Am) (ir) (Af) Cents Cents Cents 0 r- Retail .203 .171 .203 .203 .203 .203 .942 .942 .942 .942 .471 1.884 -5.27 -5.27 -4.45 -5.27 -5.27 -5.27 -4.27 -4.09 -4.72 -3.59 -3.59 -4.72 egg prices Pct. 19 17 10 32 32 10 Farm 0 C 1.00 .36 .55 1.68 1.68 .55 m G) G) C C,) --1 'In 1967 dollars. 'The actual marketing margin declined 8.20 per dozen between 1973 and 1983. 26 ALABAMA AGRICULTURAL EXPERIMENT STATION Assumptions 1 and 2 are based on elasticity estimates obtained from a recent econometric analysis of the U.S. egg industry (7). Assumptions 3 and 4 are based on the 1973 average annual values of these two prices (3). Assumption 5 follows from the markup model estimate of the vertical control coefficient. Combining assumptions 1-5 with equations 6-8 indicates that the estimated 5.27¢ per dozen decline in egg marketing margins affected prices as follows: the retail price declined 4.27¢ per dozen and the farm price increased 1.00¢ per dozen. Thus, it appears that egg consumers are the primary beneficiaries of the vertical control-induced cost savings, although egg producers benefited as well. Because calculation of the incidence of the margin change is sensitive to assumptions about the magnitudes of relevant elasticities and the vertical control effect and there is uncertainty about the true values of these parameters, the incidence for a range of parameter values was recomputed. Results show variations in the estimated magnitude of the margin change attributable to vertical control and in the relative distribution of associated benefits to consumers and producers, table 5. In particular, the estimated portion of the observed margin change attributable to vertical control is quite sensitive to the magnitude of the vertical control coefficient. Further, the incidence of the estimated margin change appears to be most sensitive to either increases in the absolute value of the demand elasticity or decreases in the supply elasticity. Still, the basic conclusion that vertical control has substantially reduced egg marketing costs and that consumers have benefited from this cost reduction more than producers remains unchanged. CONCLUSION The purpose of this study was to investigate the economic impacts of increased vertical control in the U.S. egg industry. Results suggest a benign impact: middlemen became more efficient and, as a result, consumers paid less for eggs and producers received more. However, it is important to recognize that these results, strickly speaking, hold only for the study period (1972-84) and may not be reflective of the eventual longer run impact. A reason for citing this caveat is the continuing increase in industry concentration. The statistical results of this study showing the coordination effect dominating the concentration effect may reflect a lack of sufficient industry concentration within the sample period. If this hypothesis is correct, it will become necessary to reexamine the concentration hy- EFFECTS EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUTY2 OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 27 pothesis before a definitive statement can be made about the economic impacts of vertical control in the egg industry. Of course, to adequately restudy the concentration hypothesis with time series data, sufficient time must elapse to provide the necessary additional observations. Finally, it should be noted that the econometric results showing a 4¢ to 5¢ per dozen decline in real egg marketing costs over the 197383 period due to increased vertical control may overstate the magnitude of the vertical control effect. The vertical effect may be exaggerated because new egg processing technology was being adopted by the industry over the study period and this technology (mainly equipment that permits efficient on-farm packaging of eggs) likely led to reduced marketing costs. To the extent that the econometric model inadequately captures cost savings realized from new marketing technologies, the estimated vertical control effect may contain an upward bias. Further research to obtain more precise estimates of the vertical control effect might consider description and measurement of the relevant egg marketing technologies. In addition to improved estimation accuracy, such an approach might yield improvements in understanding about the interplay of technology adoption and vertical control. Still, while vertical control would accomplish less without the benefit of cost-cutting technology, it appears safe to conclude on the basis of this study that in the case of eggs, increased vertical control has resulted in benefits to egg producers and consumers alike. 28 ALABAMA AGRICULTURAL EXPERIMENT STATION LITERATURE CITED (1) AMEY, DAVID. 1985. Egg Industry Continues on Its Concentration Course. Poultry Tribune 81 (12):9-12. (2) ARROW, KENNETH J. 1975. Vertical Integration and Communication. Journal of Economics 61:173-183. (3) BAKER, A. AND E. ARMSTRONG. 1986. Poultry and Egg Statistics, 1960-85. USDA/ERS, Statistical Bulletin No. 747, Washington, D.C. (4) BELSLEY, D.A., E. KUH, AND R.E. WELSCH. 1980. Regression Diagnostics. (5)BREWER, 6) John Wiley and Sons, New York. R.N. 1987. Personal Interview. Auburn Univ., Ala. B.W., J.P. CHAVAS, W.R. GRANT, AND L.D. SCHNAKE. 1985. Marketing Margins and Price Uncertainty: The Case of the U.S. Wheat Market. Amer. J. Agr. Econ. 521-528. BRORSEN, (7) CHAVAS, JEAN-PAUL AND S.R. JOHNSON. 1981. An Econometric Model of the U.S. Egg Industry. Applied Economics 13:321-335. (8) FISHER, B.S. 1981. The Impact of Changing Marketing Margins on Farm Prices. Amer. J. Agr. Econ. 63:261-263. (9) GARDNER, BRUCE L. 1975. The Farm-Retail Price Spread in a Competitive Food Industry. Amer. J. Agr. Econ. 57:399-409. (10) GEORGE, PA. AND G.A. KING. 1971. Consumer Demand for Food Products in the United States with Projections for 1980. Giannini Foundation Monograph No. 26, University of Calif. (11) (12) GILLINGHAM, R.F AND D.M. HEIEN. 1971. Regression Thru the Origin. (13) (14) (15) (16) (17) (18) (19) American Statistican 25:54-55. GRANT, W.R., J.W. RICHARDSON, B.W. BRORSEN, AND M.W. RISTER. 1984. Economic Impact of Increased Price Variability: A Case Study with Rice. Agr. Econ. Research. USDA ERS 36:17-27. GRILICHES, Z. 1957. Hybrid Corn: An Exploration in the Economics of Technological Change. Econometrica 25:501-522. HALL, LANA, ANDREW SCHMITZ, AND JAMES COTHERN. 1979. Beef Wholesale Retail Marketing Margins and Concentration. Economica 46:295-300. HEIEN, DALE M. 1980. Markup Pricing in a Dynamic Model of the Food Industry. Amer. J. Agr. Econ. 62:10-18. HERNDON, KEITH. 1986. Overproduction Sends Prices Tumbling Down. Atlanta Constitution, July 3. KILMER, RICHARD L. 1986. Vertical Integration in Agriculture and Food Marketing. Amer. J. Agr. Econ. 68:1155-1160. KINNUCAN, H.W AND O.D. FORKER. 1987. Asymmetry in Farm-Retail Price Transmission for Major Dairy Products. Amer. J. Agr. Econ. 69:285-292. MARTIN, STEPHEN. 1986. Causes and Effects of Vertical Integration. Applied Economics 18:737-755. (20) MCLEOD, M.R. AND W.R. WATKINSON. 1986. Final Egg Decision Comning. In The Agricultural Law Letter. Washington, D.C., November-December, p. 5. (21) MUELLER, WILLARD E 1969. Public Policy Toward Vertical Mergers. In Weston and Peltzman (eds.), Public Policy Toward Mergers. Goodyear. (22) NATIONAL COMMISSION ON FOOD MARKETING. 1966. Food from Farmer to Consumer. Commission Report. U.S. Govt. Print. Off., Washington, D.C. EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 29 (23) PARKER, R.C. AND J.M. CONNOR. 1979. Estimates of Consumer Loss Due to Monopoly in the U.S. Food-Manufacturing Industries. Amer. J. Agr. Econ. 61:626-639. (24) PURCELL, WAYNE. 1979. Agricultural Marketing: System Coordination, Cash and Future Prices. Reston Publishing Co., Inc. Reston, Va. (25) RODGERS, GEORGE. 1979. Poultry and Eggs: Another Revolution in U.S. Farming? USDA Economics, Statistics, and Cooperatives Service Report No. 441:148-189. . 1971. Vertical and Horizontal Integration in the U.S. Egg (26) Industry 1955-69. USDA-ERS No. 477. (27) SCHRADER, LEE E 1986. Response to Forces Shaping Agricultural Marketing: Contracting. Amer. J. Agr. Econ. 68:1161-1166. (28) SMITH, DAVID K. 1983. An Econometric Analysis of California Egg Supply and Wholesale - Retail Price Adjustment. Ph.D Thesis, Univ. of Calif., Davis. (29) SPORLEDER, THOMAS L. 1983. Emerging Information Technologies and Agricultural Structure. Amer. J. Agr. Econ. 65:388-394. (30) STIGLER, G.J. 1951. The Division of Labor is Limited by the Extent of the Market. J. Pol. Econ. 59:185-193. (31) TOMEK, WILLIAM G. AND KENNETH T. ROBINSON. 1981. Agricultural Product Prices. (2nd edition). Cornell Univ. Press, Ithaca, N.Y. (32) U.S. DEPARTMENT OF AGRICULTURE, ECONOMIC RESEARCH SERVICE. 195581. Livestock and Poultry Outlook and Situation Report. Various Issues. , AGR. MARKETING SERV. 1972-85. (33) Poultry Market News Egg Report. Various Issues. (34) . 1972-85. Poultry Market Statistics. Various Issues. (35) U.S. DEPARTMENT OF COMMERCE, BUREAU OF CENSUS. 1985. Statistical Abstract of the United States, 1985. (36) U.S. DEPARTMENT OF LABOR, BUREAU OF LABOR STATISTICS. 1972-85. Consumer Price Index Detailed Reports. Various Issues. (37) WILLIAMSON, OLIVER E. 1971. The Vertical Integration of Production: Market Failure Considerations. Amer. Econ. Rev. 61:112-123. (38) WOHLGENANT, MICHAEL K. AND JOHN D. MULLEN. 1987. Modeling the Farm-Retail Price Spread for Beef. West. J. Agr. Econ. 17:119-125. 30 ALABAMA AGRICULTURAL EXPERIMENT STATION APPENDIX A Derivation of the Equations to Calculate the Incidence of Margin Changes The expressions to calculate how farm and retail prices are affected by an exogenous shift in the marketing services supply schedule can be derived with the aid of the following diagrams: Retail, farm price SF Ar ro fo Af DR quantity S Am m 0 . D AM Mo Quantity of marketing services EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 31 In initial equilibrium the retail price is r ° , the farm price is fo, the marketing margin (r ° - fo) is m °, QO units of retail product are pro- duced and sold, requiring M° units of marketing services. Now, assume that an exogenous increase in marketing cost shifts the marketing services supply schedule upward to S'. This causes the marketing margin to increase by Am, resulting in a decrease in quantity demanded of marketing services of AM. Let the magnitude of this decrease be represented by the equation (A.1) AM = XM° where X is the proportional decrease in marketing services from its initial equilibrium level when supply decreases from S to S'. Under fixed proportions production technology, it is not possible to substitute the farm-based input (eggs) for the marketing services input. Moreover, because marketing services and farm eggs are combined in fixed proportions to produce the retail product, a reduction in either input (eggs or marketing services) implies an equivalent proportional reduction in output. Hence, from the diagram: (A.2) AQ = AM = XQ° i.e., a reduction in marketing services leads to an equivalent proportional decrease in the quantity of eggs available for sale at retail. Reduced supply of eggs at retail implies a lower farm price and a higher retail price, i.e., a widening of the marketing margin. The portion of the margin change attributable to a retail price change (Ar in the diagram) can be approximated from the retail demand elasticity: (A.3) ° AQ r A Q Rewriting equation (A.3) in terms of Ar yields: (A.4) Ar _ AQ .r Substituting (A.2) into (A.4) to eliminate Q and simplifying yields: (A.5) Ar Xr I 32 ALABAMA AGRICULTURAL EXPERIMENT STATION Expression (A. 5) gives the desired change in retail price as a function of: (1) the magnitude of the shift in the marketing services supply schedule (X), (2) the initial level of retail price (ro), and (3) the magnitude of the retail demand elasticity (,q). Note that a more inelastic demand, ceteris paribus, implies a greater change in retail price. The portion of the margin change attributable to a change in the farm price (Af in the diagram) can be approximated from the farm level supply elasticity for eggs: (A. 6) Solving (A.6) for Af yields: (A.7) Af fo A Q fo E- fo AQ Qo . - Substituting equation (A.2) into equation (A.7) and simplifying yields: (A.8) Af From expression (A. 8) it is obvious that the supply elasticity is pivotal in determining how farm price is affected by a shift in the marketing services supply schedule. In general, the more inelastic the farm supply response to price, the greater the impact on farm price. Expressions (A.5) and (A.8) define the incidence of a margin change between farm and retail price, but to make them operational an expression defining the value of is needed. Such an expression was obtained as follows. First, define: X (A.9) Am = Ar- Af. Substituting expressions (A.5) and (A.8) into (A.9) and simplifying yields: (A.10) Am X(roE - f0 q) Solving expression (A.10) for (A.11) X the desired expression: yields Am roefo q EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 33 Given values for elasticities and initial price levels, expression (A.11) can be used to calculate the magnitude of the shift in the marketing services supply schedule, provided an estimate of the associated margin change (Lm) is available. In this study, the margin change associated with increased vertical control is estimated econometrically via procedures described in the text. A caveat in using expressions (A.5), (A.8), and (A.11) to calculate the incidence of a margin change is that they are only approximations. Their accuracy depends on the size of the equilibrium displacement and the type of elasticity used. If the shift in the marketing services supply is small (say 10 percent or less) and arc elasticities are used to represent -q and e, expressions (A.5), (A.8), and (A.11)will provide near exact results. 34 ALABAMA 34 ALABAMA AGRICULTURAL EXPERIMENT STATION AGRICULTURAL EXPERIMENT STATION APPENDIX B RAW DATA USED TO ESTIMATE THE MARGIN EQUATIONS obs 1972.1 1972.2 1972.3 1972.4 1973.1 1973.2 1973.3 1973.4 1974.1 1974.2 1974.3 1974.4 1975.1 1975.2 1975.3 1975.4 1976.1 1976.2 1976.3 1976.4 1977.1 1977.2 1977.3 1977.4 1978.1 1978.2 1978.3 1978.4 1979.1 1979.2 1979.3 1979.4 1980.1 1980.2 1980.3 1980.4 1981.1 1981.2 1981.3 1981.4 1982.1 1982.2 1982.3 1982.4 1983.1 1983.2 1983.3 1983.4 1984.1 1984.2 1984.3 1984.4 m' 19.88682 18.76504 18.04452 19.14894 19.96892 19.16350 18.75000 20.05814 19.23621 17.51373 16.72218 17.88723 18.47134 16.73981 16.14487 17.16012 17.35488 16.84397 16.46306 16.39816 16.84568 15.99336 15.54828 16.62169 14.80106 15.20165 16.27085 14.61120 15.94203 14.99299 14.78969 14.14763 15.43340 13.87755 14.10256 13.62398 14.34005 13.27137 12.61294 12.78945 13.03887 13.43543 12.50000 12.20177 12.82401 11.58639 11.48087 9.534807 13.34857 12.91572 11.59374 11.79455 r 42.03719 39.53489 42.05087 46.25690 54.93395 52.85171 64.88095 62.57267 64.07355 46.63461 47.30180 53.72651 51.97452 44.63950 45.73358 48.64048 50.50867 44.03074 49.09832 50.74798 52.51555 41.00719 43.75341 40.31300 40.79576 36.81489 39.91915 40.01981 42.94686 38.72022 37.04206 37.12654 35.13742 30.81633 34.85577 36.27871 34.84214 32.23048 32.20094 33.87959 34.34629 29.93387 28.92760 29.34560 28.92224 29.13439 30.64892 34.57605 41.44909 34.48499 28.20185 27.77426 3 V4 57. 90000 58. 95000 60.00000 61.05000 62.10000 63.10000 64.10000 65.10000 66. 10000 67. 02000 67.95000 68.87000 69. 80000 70. 65000 71.50000 72.35000 73.20000 73.95000 74. 70000 75. 45000 76.20000 76.87000 77.55000 78. 22000 78.90000 79. 50000 80.10000 80.70000 81.30000 81. 82000 82. 35000 82.87000 83.40000 83.85000 84. 30000 84.75000 85. 20000 85.60000 86. 00000 86.40000 86. 80000 87.12000 87.45000 87. 77000 88.10000 88.37000 88. 65000 88.92000 89. 20000 89. 45000 89. 70000 89. 95000 CV 5 Q 6 CP POP8 206.3000 206.3000 207.5000 207.5000 208.6000 208.6000 209.6000 209.6000 210.7000 210.7000 211.6000 211.6000 212.7000 212.7000 213.8000 213.8000 215.0000 215.0000 215.9000 215.9000 217.0000 217.0000 218.1000 218.1000 219.4000 219.4000 220.5000 220.5000 221.8000 221.8000 223.0000 223.0000 224.4000 224.4000 225.6000 225.6000 226.9000 226.9000 227.9000 227.9000 229.1000 229.1000 230.2000 230.2000 231.3000 231.3000 232.3000 232.3000 233.5000 233.5000 234.4000 234.4000 113.5812 114.1941 114.0699 115.6028 117. 4825 116.3498 114.7321 115.1889 115.4173 114.3544 113.7908 113.3506 116.4331 116.4890 115.6538 116.4350 119.0305 119.3262 119.3136 120.4258 122.3290 121. 7488 122. 0404 123.8532 126.4721 124.8707 124.1536 124.8143 125.3140 123.0266 120.6694 120.2988 119.0275 117. 5918 118.5497 118. 6843 119.3990 118.7732 117.5280 116.3520 118.6572 118.9001 117.9986 118.5753 120.1569 119. 5352 118.6689 119.6965 118. 7337 118.2112 116.5762 116.3919 5.960000 4.640000 6.810000 16.56000 6.490000 5.540000 10.83000 5.270000 8.300000 9.630000 10.54000 4.510000 4.920000 2.950000 7.770000 9.090000 8.450000 4.550000 4.960000 6.580000 8.570000 8.830000 3.720000 8.270000 6.150000 6.580000 5.070000 7.420000 5.040000 6.200000 4.790000 8.510000 6.860000 5.820000 7.910000 9.310000 3.520000 6.170000 4.530000 4.370000 6.260000 8.420000 5.810000 2.480000 4.290000 3.790000 5.570000 10.22000 9.270000 18.11000 1.520000 7.030000 7.417353 7.231701 6.954217 6.897831 6.674976 6.742569 6.471851 6.631679 6.606550 6.631704 6.379489 6.402174 6.298072 6.251528 6.252573 6.341441 6.288837 6.219069 6.182029 6.264937 6.109678 6.164516 6.112333 6.467675 6.285779 6.359161 6.277551 6.567347 6.414337 6.465284 6.437668 6.621973 6.535205 6.348485 5.905141 6.574025 6.408991 6.325695 6.332602 6.546292 6.301178 6.287647 6.240660 6.434405 6.201470 6.073930 6.025829 6.113646 5.998287 6.035118 6.093003 6.272611 123.7000 124.7000 125.8000 126.9000 128.7000 131.5000 134.4000 137.6000 141.4000 145.6000 150.1000 154.3000 157.0000 159.5000 162.9000 165.5000 167.1000 169.2000 171.9000 173.8000 176.9000 180.7000 183.3000 185.3000 188.5000 193.4000 197.9000 201.9000 207.0000 214.1000 221.1000 227.6000 236.5000 245.0000 249.6000 256.9000 262.9000 269.0000 276.7000 280.7000 283.0000 287.3000 292.8000 293.4000 293.2000 296.9000 300.5000 303.1000 306.4000 309.7000 313.1000 315.4000 See page 35 for footnotes. EFFECTS OF VERTICAL CONTROL ON U.S. EGG INDUSTRY 35 'Farm-to-consumer price spread by Grade A large eggs expressed in cents per dozen and deflated by the Consumer Price Index for all items (1967 = 100). Quarterly figures were obtained from a simple average of corresponding monthly values. Source is Baker and Armstrong (3), p. 8, table 13. This particular data series was discounted in 1984 because of declining farm prices. 2 Average retail prices for Grade A large eggs in cents per dozen deflated by the CPI (1967 = 100). Quarterly figures were computed from a simple average of corresponding monthly values. Source is Baker and Armstrong (3), p. 7, table 11. 3 An index of labor cost specific to the food marketing industry deflated by the CPI (1967 = 100). Data were made available by Dennis Dunham, USDA, ERS. 4 Percentage of eggs sold under vertical control (contracting and ownership) in the United States. Values are estimated from a logistic growth function (13) based on data provided in Rogers (25,26). See text for additional details. 5CV is the quarterly coefficient of variation of weekly nominal wholesale prices for Grade A large eggs in the United States. The coefficient of variation was obtained by computing the standard deviation of the wholesale egg prices for each quarter and dividing by the average weekly wholesale price for eggs for the quarterly and multiplying by 100. Basic data source is USDA, ARS (33). 6 U.S. production of Grade A large eggs divided by U.S. population. Basic data source is USDA, ARS (34). 7 CPI is the consumer price index (1967 = 100). Source is U.S. Department of Labor, Bureau of Labor Statistics (36). 'POP is the population of the United States in millions. Source is U.S. Department of Commerce, Bureau of Census (35). weekly Alabama's Agricultural Experiment Station System AUBURN UNIVERSITY With an agricultural research unit in every major soil area, Auburn University 3m c serves the needs of field crop, livestock, forestry, and horticultural producers in each region in Alabama. Every citi- zen of the State has a stake in this research program, since any advantage from new 14 2 ,,. and more economical ways of producing and handling farm products directly benefits the consuming public. 18 Research Unit Identification @ Main Agricultural Experiment Station, Auburn. - E. V. Smith Research Center, Shorter. Tennessee Valley Substation, Belle Mina. Sand Mountain Substation, Crossville. North Alabama Horticulture Substation, Cullman. Upper Coastal Plain Substation, Winfield. Forestry Unit, Fayette County. Chilton Area Horticulture Substation, Clanton. Forestry Unit, Coosa County. Piedmont Substation, Camp Hill. Plant Breeding Unit, Tallassee. Forestry Unit, Autauga County. Prattville Experiment Field, Prattville. Black Belt Substation, Marion Junction. The Turnipseed-Ikenberry Place, Union Springs. Lower Coastal Plain Substation, Camden. Forestry Unit, Barbour County. Monroeville Experiment Field, Monroeville. Wiregrass Substation, Headland. Brewton Experiment Field, Brewton. Solon Dixon Forestry Education Center, Covington and Escambia counties. 20. Ornamental Horticulture Substation, Spring Hill. 21. Gulf Coast Substation, Fairhope. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.