Optimal Size in the Californian Wine Industry: A Survivor Technique Analysis of 1984 2009 Don Cyr 1 and Joseph Kushner 2 1 Associate Professor of Finance Dept of Finance, Operations and Information Systems Faculty of Business Brock University, Ontario, Canada 2 Professor of Economics Department of Economics Brock University, Ontario, Canada December 2009 Paper for the pre-aares conference workshop on The World s Wine Markets by 2030: Terroir, Climate Change, R&D and Globalization, Adelaide Convention Centre, Adelaide, South Australia, 7-9 February 2010.
Optimal Size in the Californian Wine Industry: A Survivor Technique Analysis of 1984 2009 Don Cyr 1 and Joseph Kushner 2 1 Associate Professor of Finance Dept of Finance, Operations and Information Systems Faculty of Business Brock University, Ontario, Canada 2 Professor of Economics Department of Economics Brock University, Ontario, Canada Keywords: wine producer, survivor technique, Stigler, firm size. Contact author: Professor Don Cyr Department of Finance, Operations and Information Systems Faculty of Business, Brock University St. Catharines, Ontario L2S 3A1 Telephone: 905-688-5550, ext. 3136 E-mail: dcyr@brocku.ca We would like to thank Kate Biggs and Tingting Liu for their helpful assistance. All remaining errors are solely the responsibility of the authors.
Optimal Size in the Californian Wine Industry: A Survivor Technique Analysis of 1984 2009 Abstract The optimal size for a wine producer is driven by market factors. In recent years, there appears to be substantial growth in the number of smaller wine producers in the US market. In this paper we apply the Stigler survivor technique to examine the North Coast region of the Californian wine industry over the period of 1984 through 2009 in an attempt to determine the optimal size for a wine producer. We find a statistically significant trend in terms of smaller producers becoming an increasing proportion of the total number of firms and of market share. Introduction Determining optimal firm size in an industry has long been an area of interest in industrial organization because of its effect on market structure. Other factors such as monopoly power, labour relations and governmental regulations also play an important role in the market structure. The wine industry not only has a variety of firm sizes but is also vertically integrated which makes it difficult to determine the cost functions for the various components. A major element in the recent growth of the US wine industry has been the development of boutique or artisan winemaking with almost half the wineries in North America producing less than 15,000 cases per year (Caputo, 2007). Although many US wine consumers enjoy the consistency of big brand wines, it appears that an increasingly sophisticated and growing component of US consumers has focused on limited production wines. This trend in market demand has even resulted in some larger Californian wineries creating smaller wineries within their larger context. Although a number of techniques for determining the optimal size of a firm exist, the advantage of Stigler s (1958) survivor technique is that it incorporates the cumulative effects of all relevant variables. Although not without fault, a number of recent studies provide credibility for the
survivor technique as an empirical method of determining economies of scale (Giordana, 2003 and 2008; Sengupta, 2004). The purpose of this paper is to examine the structure of the California industry over the period of 1984 to 2009. Using data from the Wines & Vines Annual Directory, individual California wine producers are categorized into size classes as measured by storage capacity and also output. The market share of the various size categories from 1984 to 2009 is examined to determine whether an optimal size exists. In doing so, we would have some insight into the future size distribution of the industry. We begin with a discussion of the survivor technique followed by a description of the data used. The analysis and results are then presented along with conclusions. Survivor Analysis Survivor analysis is a long standing methodology first developed by George Stigler (1958). The primary purpose of survivor analysis is to determine the minimum efficient size of a firm which is the size of a firm where all economies have been exploited. This information which is indicative of the long run average cost, is of value to potential entrants and also to policy makers and industry regulators. According to Stigler, over time efficient sized firms will tend to survive and remain in business whereas inefficient sized firms will decline and cease to exist. Firms are classified according to size and if the output of the size class falls over time, then that size class is deemed to be inefficient, whereas if the output of the size classification increases over time, then that size class is deemed to be efficient. The methodology indicates efficiency in light of all the factors that businesses in an industry encounter, while avoiding the need to explicitly and perhaps artificially model these factors. The methodology was the subject of significant criticism since its inception. Bain (1969) contended that the continued presence of apparent suboptimal firm size might be due to smaller firms supplying a product that is significantly differentiated from that of larger producers. 2
Furthermore, because of a fear of anti-trust actions, larger firms may set the price high enough to allow the smaller firms to survive. All of these issues have potential implications of the current application to the wine industry. The choice of specific size categories has also been the source of early criticisms (Saving, 1961; Weiss, 1963; and Shepherd, 1967) since the results may be sensitive to the size categories chosen. The solution is to create size categories that correctly locate the areas of change between increasing and decreasing market share. Where the number of firms considered is large, as in the present study, doing so is less problematic. The empirical measure of firm size is also a concern. The variables used to measure size include such diverse measures as number of employees, total assets, output, input, and plant capacity. The variables selected are often determined by the availability and nature of the data which remains the case in the present study. 1 For the most part, the survivor analysis has been applied to industries where the product tends to be homogeneous such as steel. Unlike such industries, the wine industry which is comprised of firms of vastly different size, exhibits complex product differentiation and extensive vertical integration. Thus, it could be argued that there potentially as many differentiated product as there are firms. In this sense, the criticisms of Bain (1969) are valid. Because wine tourism is dependent on highly differentiated products, it may be in the interest of the larger firms to promote the industry by promoting the survival of the smaller firms. Another reason for the survival of sub-optimal firms is the role of entrepreneurial absorption of losses. Specifically, there may be a persistent willingness for owner-entrepreneurs to accept profits that yield subnormal returns for their investments. Thus, the value of self employment and utility associated with wine production might result in lower costs of the smaller firms. 1 For succinct summaries of the debate including compelling counter arguments regarding the survivor technique, see Flanagan (1986) and Giordano (2003). 3
The wine industry was one of 50 industries considered by Stigler in his original work of 1958. Using total asset data he computed the optimal company size and range of sizes. Unfortunately he did not report on the number or change in the number of firms involved. Later, Flanagan (1986) employed survivor analysis to examine the Californian wine industry over the period of 1948 to 1985 and predicted a potential decline in the number of smaller wine producers. Unfortunately, there have been very few studies since the work of Flanagan (1986). In this paper, we extend the work of Flanagan by examining the California wine industry from 1984 to the present. Data The data employed for the study was obtained from the annual Wines & Vines Directory of North American wine producers. Because there is approximately a 5 year period from the planting of vines to harvesting, we chose a 5 year interval for study and gathered data for the periods1984, 1989, 1994, 1999, 2004 and 2009. The data collected by Wines & Vines is based on voluntary submissions from the firms and so the relative completeness of the data on a firm level varies from year to year. Missing data was sometimes an issue, particularly in the earlier periods of 1984 and 1989. As Table 1 indicates, several capacity variables such as storage and fermentation, daily bottling and crush capacity were reported up to 2004 but subsequently were discontinued and from 2004 the only variables reported were acreage and annual case production with firms pre-classified into the following 5 categories by annual production: Category 5= 500,000 + cases Category 4= 50,000-499,99 cases Category 3= 5,000-49,999 cases Category 2= 1,000-4,999 cases Category 1 < 1,000 cases 4
Table 1: Production and Capacity Measures Reported by Wines &Vines Item 1984 1989 1994 1999 2004 2009 Acreage Yes Yes Yes Yes Yes Yes Storage capacity (including Yes Yes Yes Yes Yes No fermentation) Fermentation Capacity Yes Yes Yes Yes Yes No Bottling (Cases per day) Yes Yes Yes Yes Yes No Crush (gallons per day) Yes Yes Yes Yes Yes No Nature of Sales (retail, Yes Yes Yes Yes Yes No wholesale, export etc) Annual Case Production No Yes Yes Yes Yes Yes* * only for the 1 to 5 size categories A convenient boundary between vineyard and winery in the grape-wine industry is difficult to determine because not all wineries produce their own grapes and in some cases many vineyards produce some wine. Consistent with Flanagan (1986), a winery is defined as any firm involved in the production of wine, regardless of the type or variety of wine. Although product differentiation might also have a significant impact on firm size, most wine producers in California offer at least 3 to 4 different varietal wines often with a mix of white and red. Flanagan s (1986) study suffered because at that time the industry was difficult to determine because of the variety of wine based products such as dessert and fruit wines were a significant part of the industry unlike the past 20 years where the dominant product is table wine. Given the phenomenal increase in the number of wineries in California, particularly over the past 10 years, our study includes only the primary wine producing region of California, that of the North Coast. The North Coast is comprised of the counties north of San Francisco including Lake, Marin, Mendocino, Napa, Sonoma and Solano, and represents more than 40 American Viticultural Areas (AVAs). The North Coast forms a slightly crooked rectangle approximately 100 miles long and more than 50 miles wide from the Pacific Coast Ranges in the northwest to 5
the Blue Ridge Mountain Range in the east to the San Pablo Bay in the South, encompassing more than three million acres of land and represents nearly half the total number of wineries in California. Figure 1 provides a map of the major wine producing regions of California, indicating the North Coast Region. Figure 1: Map of 4 Major Wine Growing Regions of California Figure 2 shows the number of North Coast wine producers over the 25 year period. The numbers increased from 135 wine producers in 1984 to 1,250 in 2009 with a substantial increase of 117% between the periods of 2004 to 2009. Figure 3 shows the total production, in cases per year, for the 25 year period. Although total production increased from approximately 20 million cases in 1984 to 51 million cases in 2009, the increase in production has not matched the increase in the number of wine producers. Figure 4 which shows a general decline in the average annual production per wine producer over the 25 year period provides some preliminary evidence with respect to the change in size of wine producer. 6
Figure 2. Number of North Coast Wine Producers (1984-2009) Figure 3. Total North Coast Production (cases per Year): 1984-2009 Figure 4: Average production (cases per year) per wine producer: 1984-2009 7
Analysis of Data Storage Capacity: As Table 1 indicates, one of the measures provided in the Wines & Vines directory is that of storage capacity including fermentation (SFC). Due to a lack of output data prior to 1984, Flanagan (1986) employed this measure as a proxy for firm size. He provides a rationale for using storage capacity although output measures are generally used. For all wine producers in California, Flanagan used three size classes, small, medium and large by storage capacity: Large firms ( > 29,000,000 SFC gallons) Medium firms (3,000,000 < SFC gallons 29,000,000) Small firms ( 3,000,000 SFC gallons) As a preliminary step, we replicate this analysis. As Wines & Vines discontinued the reporting of storage capacity after 2004, Table 2 provides the results in terms of number and percentage of producers in each of the three size classes and Table 3 the results for storage capacity for the years of 1984 through 2004. For firms that did not report capacity in a given year, the variable was estimated using either the average of reported data in the previous and post five year period, or a regression estimate based on other reported measures. Table 2: North Coast Wine Producer Storage Capacity (gallons): 1984-2004 Category 1984 1989 1994 1999 2004 Large Storage capacity 0 0 0 0 46,000,000 % of industry total 0.00% 0.00% 0.00% 0.00% 22.62% Medium Storage capacity 30,000,000 39,278,500 46,746,195 97,600,200 81,516,700 % of industry total 50.88% 49.99% 50.58% 82.34% 40.09% Small Storage capacity 28,966,311 39,297,009 45,682,247 53,754,117 75,838,055 % of industry total 49.12% 50.01% 49.42% 45.35% 37.29% Total estimated storage Storage capacity 58,966,311 78,575,509 92,428,442 118,539,190 203,354,755 % of industry total 100.00% 100.00% 100.00% 100.00% 100.00% 8
Table 3: Number of North Coast Wine Producers by Storage Capacity: 1984-2004 Category 1984 1989 1994 1999 2004 Large Number of firms 0 0 0 0 1 % of total 0.00% 0.00% 0.00% 0.00% 0.17% Medium Number of firms 4 6 10 14 13 % of total 2.96% 2.88% 4.03% 4.26% 2.26% Number of firms 131 202 238 315 561 Small % of total 97.04% 97.12% 95.97% 95.74% 97.57% Total Number Number of firms 135 208 248 329 575 % of total 100.00% 100.00% 100.00% 100.00% 100.00% Based on storage capacity, it would appear that Flanagan s (1986) predicted decline in smaller firms may have had some validity in terms of storage capacity as the proportion represented by smaller firms declined from 49.12% to 37.29% over the 25 year period. However the proportion of industry population represented by smaller producers has remained constant if not slightly increased.at the same time, by 2004 the proportion of industry population and storage capacity represented by larger firms, had increased. These results are somewhat questionable, however, given that Flanagan (1986) based his categories upon the total population of Californian wine producers, which included some exceptionally large producers that were not part of the North Coast. As a result, his broad three class categorization may not fully capture the distributional changes in the population and capacity of North Coast wine producers. Given the availability of annual output data reported by Wines & Vines after 1984, we are able to carry out a more refined study based upon production output which is the more acceptable. Production Output: Although the number of size classes can be a critical issue in survivor analysis, the lack of detailed information on annual output after 2004 limits our analysis to the five sizes used by Wines & Vines in 2009. Although not a greatly detailed categorization compared to some studies which use to 10 or 11 different classes, it is much larger than that used 9
in the Flanagan (1986) study. In cases where a wine producer s annual output was not reported, we employed the average of reported output from consecutive periods or used a regression estimate based on other variables. In the case of the 1984 period, regression models were used to estimate annual output for all producers as the data was not collected by Wines &Vines for that year. Table 4 reports the number and percentage of total of North Coast wine producers in each of the five size classes for 1984 though 2009 and Figure 5 provides a graph of the proportion of total North Coast wine producers in each size class. The results appear to be a steady decline in the proportion of the total number of wine producers in the three largest size classses while the proportion of wine producers in the two smaller classes increased. In particular, between 2004 and 2009, the number of small wine producers, producing less than 1000 cases per year increased dramatically in terms of their proportion of the producer population. Table 4: Number and percentage of total number of North Coast wine producers by annual production category. Category (measured in cases of wine) 1984 1989 1994 1999 2004 2009 500,000 + No. of firms 10 12 11 14 17 22 % of firms 7.41% 5.77% 4.44% 4.26% 2.96% 1.76% 50,000-499,999 No. of firms 24 46 50 66 88 85 % of firms 17.78% 22.12% 20.16% 20.06% 15.30% 6.80% 5,000-49,999 No. of firms 79 103 122 145 215 331 % of firms 58.52% 49.52% 49.19% 44.07% 37.39% 26.48% 1,000-4,999 No. of firms 16 42 61 94 206 445 % of firms 11.85% 20.19% 24.60% 28.57% 35.83% 35.60% < 1,000 No. of firms 6 5 4 10 49 367 % of firms 4.44% 2.40% 1.61% 3.04% 8.52% 29.36% Total No. of firms 135 208 248 329 575 1250 % of firms 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% χ 2 (period to period) *19.99 4.23 8.04 *82.04 *741.89 χ 2 (1984 base) 19.99* *45.90 96.17* *361.57 *2698.59 With degrees of freedom of 4 (5 category classes 1), Pr (14.86 < χ 2 ) =.005 *Significant at the 5% level. 10
Figure 5: Percent of total number of North Coast wine producers by annual production size: 1984-2009. Table 5 provides the estimated annual production output and percentage of total output for the 5 classes. In terms of annual output, the largest firm category has experienced a declining share of total production over the 25 year period whereas the second and third largest classes have experienced some increase. Wine producers in the two smaller class sizes have experienced an increase in the shareof total production although their total share still remains relatively small at less than 3% of total North Coast production. Figure 6 provides a graph of the percent of total output for each category class for the 25 year period. 11
Table 5: Annual production output and percentage of total annual production by annual production size category: 1984-2009 Category (measured in cases of wine) 1984 1989 1994 1999 2004 2009 500,000 + Output 14,473,228 17,394,006 12,460,500 18,267,500 32,487,500 31,879,966 % of Total 72.84% 67.25% 54.98% 60.62% 69.38% 62.43% 50,000 - Output 4,058,664 6,585,931 7,797,240 9,121,375 10,647,000 12,366,131 499,999 % of Total 20.43% 25.46% 34.40% 30.27% 22.74% 24.22% 5,000-49,999 1,000-4,999 Output 1,304,710 1,778,968 2,264,397 2,506,163 3,172,725 5,586,501 % of Total 6.57% 6.88% 9.99% 8.32% 6.78% 10.94% Output 29,387 104,336 139,931 237,450 490,275 1,025,356 % of Total 0.15% 0.40% 0.62% 0.79% 1.05% 2.01% < 1,000 Output 4,703 2,821 2,321 3,963 25,700 209,123 % of Total 0.02% 0.01% 0.01% 0.01% 0.05% 0.41% Total Output 19,870,691 25,866,063 22,664,389 30,136,450 46,823,200 51,067,078 % of Total 100.00% 100.00% 100.00% 100.00% 100.00% 100.00% χ 2 (period to period) χ 2 (1984 *551,958 *1,564,084 *423,140 *1,706,008 *3,331,782 base) *551,958 *3,904,806 *3,023,721 *2,781,671 *17,764,540 *With degrees of freedom of 4 (5 category classes 1), Pr (14.86 < χ 2 ) =.005 *Significant at the 5% level. To test the significance of these changes, we begin with a chi-squared (χ 2 ) test to determine whether the changes in output market share for the size classes exceed those that would be due simply to random fluctuation. This allows us to determine whether the observed year-to-year shifts in the output distribution are statistically significant. The primary assumption in survivor analysis would be that after a few years of shifting, the distribution would stabilize with a longrun equilibrium. If significant shifts continue to occur, any conclusions with regards to efficient size would at best be tentative. 12
Figure 6: Percentage of total annual North Coast Production by annual production size category: 1984-2009 The calculation of the χ 2 statistics is given by: (1) where O it is the current year (t) category class output for i = 1..5. and E it is the expected or theoretical output for asset class i given by the share of total output of the category class in the previous years, S it-1 multiplied by the current year total output Q t : 13
(2) The results of the test are provided in Table 5. In all years, the χ 2 test is significant, indicating that there are significant shifts in the distribution of total output between the years examined across the five classes. The test is also carried out with respect to the base year of 1984. In equation (1) and (2) above, S it-1 is replaced with S i,1984 and the results presented in the last row of Table 5. Again the output distribution experienced significant statistical shifts compared to the base year of 1984. We also apply similar test in terms of the number of producer firms in each size class. The same logic in terms of survival of firms of a given size can be applied to producer population as it does to output (Giordano, 2008). The analogous χ 2 statistics are provided again in Table 4. The results indicate that although there was a significant shift in firm population distribution from 1984 to 1989 the shift in distribution is not significant from 1989 to 1994 and from 1994 to 1999. There were, however, statistically significant shifts in the population distribution from 1999 onwards. In terms of the base year of 1984, the last row of Table 4 indicates that overall shifts in subsequent years were statistically significant. Although there are statistically significant overall shifts in the output distributions each period and shifts in the population distributions from 1999 to 2009, this does not guarantee that each individual category class has experienced significant changes. Consequently we test whether within the overall shifts in the distribution, each individual category class, considered separately, experienced a significant change in market share. Again a χ 2 test is employed, computed as: (3) where O i is the observed output of category class i =1 to.5, in the current year t. E i is the expected output in the current year given the category class market share in the previous year (or 14
1984 as the base year), measured as percent, multiplied by the total output in the current year. O j is the sum of the observed outputs of all other classes in the current year. E j is the sum of their expected outputs in the current year measured as the sum of their previous period (or 1984 as the base year) market shares, measured as percent multiplied by the total output in the current year. Table 6 provides the results of the χ 2 test for each of the five size classes in terms of period-toperiod changes as well as with 1984 as the base year. The results indicate that statistically significant changes occurred mainly in the latter period of 2004 and 2009. Using 1984 as the base year, significant changes occurred throughout the years for every class, by 2009. The three smallest size classes experienced the most occurrences of statistically significant change in their share of total population. By 2009 all categories had experienced statistically significant changes in their share of the total population as compared to 1984. Table 6: Chi-squared test of changes in proportion of producer population by individual category class, period versus period and with 1984 as a base year. Category Period (t) to Period (t-1) (measured in cases) 1989 1994 1999 2004 2009 500,000 + 0.81 0.81 0.03 2.38 6.24 50,000 to 499,999 2.68 0.55 0.00 *8.11 *69.75 5,000 to 49,999 6.94 0.01 3.45 *10.41 *63.57 1,000 to 4,999 *13.85 2.99 2.80 *14.83 0.03 < 1,000 2.04 0.66 4.22 *58.64 *696.28 1984 as Base Year 1989 1994 1999 2004 2009 500,000 + 0.81 3.19 *4.77 *16.61 *58.13 50,000 to 499,999 2.68 0.96 1.17 2.41 *103.06 5,000 to 49,999 6.94 *8.88 *28.28 *105.73 *528.58 1,000 to 4,999 *13.85 *38.56 *88.03 *316.34 *674.79 < 1,000 2.04 4.68 1.53 *22.51 *1,827.16 15
With 1 degree of freedom: Pr(7.89 χ 2 ) = 0.005. *significant at 5% level Thus, there has been a significant increase in the proportion of the total North Coast producer population producing fewer than 5000 cases per year with a corresponding significant decrease in the proportion of the total number of firms producing at the level of greater than 5000 cases per year. Much of this change, however, has, taken place over the past 10 years. Similarly we consider the changes in the individual size classes in terms of their proportion of annual output. Table 7 provides the period to period χ 2 tests for significant changes as well as changes using 1984 as the base year. In all cases, the changes in share of total output was significant, period versus period, and also using 1984 as the base year. Table 7: Chi-squared test of changes in proportion of total production output by individual size class, period versus period and with 1984 as a base year. Period (t) to Period (t-1) 1989 1994 1999 2004 2009 500,000 + cases *408,622 *1,548,718 *386,968 *1,507,624 *1,163,084 50,000-499,999 cases *403,652 *954,742 *228,454 *1,257,290 *63,390 5,000-49,999 cases *4,094 *343,017 *94,015 *145,660 *1,401,435 1,000-4,999 cases *114,324 *25,845 *14,280 *40,230 *454,972 < 1,000 cases *1,780 *9 *249 *62,047 *1,170,669 1984 as Base Year 1989 1994 1999 2004 2009 500,000 + cases *408,622 *3,653,563 *2,275,010 *282,297 *2,796,828 50,000-499,999 cases *403,652 *2,724,386 *1,795,865 *154,170 *451,331 5,000-49,999 cases *4,094 *433,367 *150,448 *3,365 *1,592,207 1,000-4,999 cases *114,324 *338,332 *835,967 *2,563,674 *11,963,409 < 1,000 cases *1,780 *1,726 *1,409 *19,289 *3,213,076 With 1 degree of freedom: Pr(7.89 χ 2 ) = 0.005. 16
* significant at the 5% level. Conclusions Based on our application of the survivor technique, we conclude that in the North Coast wine industry of California, an optimal firm size has not been established in which case a long run average cost curve cannot be estimated. However, we did find a statistically significant trend in terms of smaller producers becoming an increasing proportion of the total number of firms and of market share. These results are contrary to the predictions of Flanagan (1986) of a decrease in smaller firms after 1984. One may argue that our results, which show an increase in the importance of smaller firms, may not indicate efficiency but simply the impact of new entrants into the industry that may subsequently change as the industry matures. Smaller producers may simply grow or be bought up by larger wine operations. However, within the 25 year period, this phenomenon did not take place and therefore it would be difficult to conclude that such events will occur in later years. Two possible hypotheses may explain the growing importance of the smaller firms. The first could be economic where the smaller firms, because of the entrepreneurial nature of their owners and the acceptance of subnormal returns, have lower costs. Once firm size reaches a certain threshold, more costly management is required in which case costs increase until they reach a second threshold where costs begin to decline due to economies of scale. Thus the average cost curve appears to be sine curve shaped. The increasing importance of wine tourism may also contribute to the survival of smaller wineries. Also as noted by Bain (1969), their existence might be encouraged by larger firms in order to contribute to an increase in the overall market for Californian wine. Given the plausibility of these explanations, one could very well expect the trend to continue in which case the distribution of firms becomes bi-modal. References 17
Bain, J.S. 1969. Survival-ability as a test of efficiency, American Economic Review, 59, 99-104 Caputo, T. 2007. Wineries within wineries, larger producers think small to boost quality of reserve-level wines, Wines & Vines 88, 24-7 Flanagan, A.B. 1986. A Survivor Analysis of California Wine Producers, Masters Thesis in Economics, Texas Tech University. Giordano, J.N. 2008. Economies of Scale after Deregulation in LTL Trucking: A Test Case for the Survivor Technique. Managerial Decision Economics, 29, 357-370. 2003. Using the Survivor Technique to Estimate Returns to Scale and Optimum Firm Size. Topics in Economic Analysis and Policy, 3. 1-21. Saving, T.R. 1961. Estimations of optimum size of plant by the survivor technique. Quarterly Journal of Economics 55, 569-607. Sengupta, J.K. 2004. The survivor technique and the cost frontier: A nonparametric approach International Journal of Production Economics 2, 185-193 Shepherd, W.G. 1967. What does the survivor technique show about economies of scale, Southern Economic Journal, 34, 113-122. Stigler, G.J. 1958. The Economies of Scale, Journal of Law and Economics, 1: 54-71 Weiss, L.W. 1964. The survival technique and the extent of suboptimal capacity. Journal of Political Economy. 72, 246-261. 18