Application of a Multi-Generation Diffusion Model to Milk Container ...

NORTH- HOLLAND

Application of a Multi-Generation Diffusion Model to Milk Container Technology MARK

W. SPEECE

and DOUGLAS

L. MACLACHLAN

ABSTRACT

A recently introduced multi-generation model 1181, developed for high-technology industries and tested on a high-tech product class, is applied to a very different situation. It is tested by fitting and forecasting use of three generations of packaging technology in the fluid milk market, glass, paperboard cartons, and plastic, across two submarkets: gallons and half gallons. Results in the gallon market show that the model can be successfully applied to industries not usually associated with high technology, and to specific submarkets, rather than across a whole product class. It is less successful in the half-gallon market, which violates some of the assumptions underlying the model. Extension of the model with the addition of pricing and growth terms allows slightly improved forecasts over the basic model without these terms.

Introduction Much research on forecasting new product adoption has focused on modeling the innovation diffusion process, because many new products are essentially technological innovations. In general, when cumulative sales (or cumulative percentage of adoptions out of the total potential market) are graphed over time, a characteristic S-shaped curve results. Such patterns can be modeled by various forms of the logistic curve and related functions, which are quite familiar by now in marketing [ll, 12, 15, 16, 171. Recently, one of the most widely used models in marketing (i.e., the Bass [l] mixed influence model) has been extended to the multi-generation situation [ 181, although multigeneration research has been around longer in the field of technological forecasting [lo, 22, 23, 251. So far, the Norton and Bass multi-generation model has been tested mostly on high-tech and/or durable products where it has been applied to product categories [18, 191. In these kinds of situations, it seems to work quite well. But it has not been tested in other sorts of industries or markets. Here we use milk-container data to show that the model may have applications in industries not usually associated with advanced technology, and in fitting individual

MARK W. SPEECE is Professor of Marketing at the School of Management, Asian Institute of Technology, Bangkok, Thailand. DOUGLAS L. MACLACHLAN is Professor of Marketing at the Department of Marketing and International Business, University of Washington, Seattle, WA. Address reprint requests to Professor Mark W. Speece, School of Management, Asian Institute of Technology, G.P.O. Box 2754, Bangkok, 10501, Thailand. Technological Forecasting and Social Change 49, 281-295 0 1995 Elsevier Science Inc. 655 Avenue of the Americas, New York, NY 10010

(1995) 0040-1625/95/$9.50 SSDI 0040-l 625(95)OOOO6-V

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submarkets (i.e., gallon or half gallon milk containers), rather than whole-product categories (beverage containers). Furthermore, the nature of milk containers is fundamentally different from products for which the model was originally developed. The milk container data also demonstrates the importance of one key assumption behind the Norton and Bass multi-generation model. New generations eventually completely replace old ones in the model, as for gallon milk containers, which the model can account for quite well. But this is not happening in half-gallon containers, and therefore, the model should not work well in this market. This study also extends the multi-generation model by adding pricing and market growth. There has been some work on bringing pricing into single generation models [2, 3, 6, 8, 20, 3 11. Only Silvennoinen and Valnanen [24] have used prices to help capture competition across generations, however. Neither their model nor their method of incorporating prices follow current innovation diffusion research, though. Pricing has not yet been used to extend the multi-generation Norton and Bass [18] model, although recently Mahajan et al. [12] have called for exactly this kind of extension.

Data on Milk Packaging Data on unit sales and market share of packaging materials for gallon and half-gallon containers in the fluid milk industry for the years 1963 to 1987 was obtained from a manufacturer of paperboard cartons (Tables Al, A2). It was corroborated by data on volume sales of milk by container type in Federal Milk Marketing areas from 1963 to 1985 [32]. These areas do not constitute the total market in the U.S., but they do cover a substantial and representative portion of it. The data showed close agreement on market shares with that obtained from the paperboard manufacturer. Although milk sales overall have been relatively flat over most of this period, gallon sizes have steadily gained share over other sizes. Gallons accounted for 13% of fluid milk sales in 1963, against 56% for half gallons. By 1987 gallons accounted for 62%, and half gallons 21%. Smaller sizes made up 3 1% and 17% of volume sales at the beginning and end of this period, respectively. Thus, the gallon submarket shows substantial growth, whereas the half-gallon segment declined over the period under investigation. The multi-generation model should be able to account for growth of the gallon market easily. It assumes that new technology will expand uses for the product and increase demand for it. In the half gallon submarket, again an assumption is violated. The new technology is causing a shift out of the segment, not an increase. The introduction of an explicit growth germ into the model may help to deal with this situation, where technology is changing, but the market segment as a whole is declining. The data also included information on total dollar value of paper milk cartons so that unit prices could be computed. Prices covering most of the period for glass and plastic were developed from price indices for glass beverage bottles and high-density polyethylene (HDPE) resin [33]. Before 1976, HDPE resin was not distinguished from other polyethylene resins, so the beginning part of the HDPE series was constructed from prices for HDPE milk bottles in Stephens 1281. The prices (Table A3) were checked for consistency against scattered references to pricing in trade publications [cf. 26 for these references]. Glass, paperboard, and plastic represent the three generations of technology on which the model was tested. Glass bottles were still present in the early part of this period, but have now nearly disappeared for gallon and half gallon sizes. Plastic jugs had captured nearly all of the gallon market by the mid-1980s, but they have displaced paperboard cartons much more slowly in the half-gallon market. To model this competition, the

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times of introduction (7,) for each generation and each size had to be determined from trade literature on the history of packaging in the milk industry. What follows is simply a brief summary; Speece and MacLachlan [26] cite detailed references on technological development and market competition of milk packaging. We have taken rl, the time of introduction for glass bottles, to be 1900. The modern glass milk bottle was developed in the 188Os, but was initially used in a very specialized market niche: boiled bottled milk for infants. Sealed glass bottles for the mass distribution of milk began appearing around 1900, the beginning of a period of several technical advances that helped accelerate development of mass markets for bottled milk. In practice, the fit to glass was not very sensitive to a range of about a decade on either side of 1900, since the introduction year is substantially before the range of our data. Paperboard cartons were first used commercially as containers in 1929 but were not immediately adopted for milk packaging. After about 1935, paperboard first penetrated smaller-sized milk containers, so 1937 was used as the time of introduction in the halfgallon market. By 1940, paper accounted for only 4.8% fluid milk containers, mostly in smaller sizes, and none at all in gallons. Paperboard cartons began to become popular for larger sizes by the early 1950s. We have used 1953 as the time of introduction r2 for gallon-size paperboard cartons. Plastic milk bottles, manufactured from HDPE resin, were introduced into milk packaging in 1964, which is used for 73. Gallon jugs weigh only a few ounces, and are much more sturdy in this size than paper cartons. But half-gallon paper cartons are more sturdy than gallon ones, so for this size plastic has little differential advantage although it costs more. In quarts and smaller sizes, plastic has made hardly any impact at all. With shortages and steep price hikes for HDPE in 1987 and 1988, adoption of plastic half gallons actually reversed, and paperboard began to regain market share.

Testing the Norton and Bass Model In the Norton and Bass [18] multi-generation of product have the form: s,(t) = m,F(t) S2(f) = s,(t)

=

[ 1 -F(l--

[mz

+ m1ml

(m3

+

model, sales of successive generations

72)1, F(f

-

T2) [ 1 -

[m2 + rnJwlF(I

-

FU c))F(t

-

t3>l, -

r3);

where S,(t) is cumulative sales of the ith generation, of successive generations of product technology. We In the original single generation model [l], the adoptions can be solved if the initial condition F’(to cumulative percentage of adoptions can be written: F(t)

(1 - e-‘P+q)l)>,t,O / = I \

P

.

(1)

and ri is the time of introduction assume that rl = 0. differential equation representing = 0) = 0 is assumed, so that the

(2)

/

Here, F(t - ri) is just this cumulative distribution function from the Bass [l] model, or the cumulative percentage of potential adopters of generation i who have adopted by time 1. The parameters mi are the incremental market potential in any time period t of generation i over potential of the (i - l),’ generation. Thus, ml is the maximum one-period market potential of the first generation. Only a proportion F’(t) of the potential market

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M. W. SPEECE

AND D. L. MACLACHLAN

TABLE 1 Parameter Estimates and R* for Gallon Data Fit to 1963-1985 Parameter P 4 ml m2 m3

Estimate

Approx. std. error

T ratio

Approx. prob. > 1TI

.0008893 1 0.37537 323.46714 848.18425 6671.79

.00056884 0.0458122 6.55237 13.84858 264.09516

1.56 8.19 49.37 61.25 25.26

0.1322 O.oool 0.0001 0.0001 0.0001

Generation

R-square

Glass Paper Plastic

0.9683 0.9826 0.9494

would actually buy, so m#‘(t) represents (potential) sales of the first generation. But actual sales S,(t) have been reduced by some proportion of buyers who decided to buy the second generation instead [l - F(t - Q)]. Implicit in the Norton and Bass model is the assumption that technological substitution proceeds one generation at a time, that is, buyers do not immediately skip the second generation and jump to the third. Market potential in the second generation will be the sales potential of the first generation, m#‘(t), plus some increment m2 due to new uses of the product made possible by the technological advance embodied within the product. One-period market potential is thus [m2 + m,F(t)], which is then multiplied byF(t - 72) to get (potential) sales. Then similarly to S,(t), S2(t) is reduced by those who decided to buy generation three [l - F(t - TV)]. S,(t) is also modeled similarly. An increment m3 is added to the one-period market potential of the second generation [m2 + m,F(t)]flt - 24, which is multiplied by F(t - TV)to get (potential) sales. The result is not reduced here because there is no fourth generation on the market to take sales from the third, however. As in the original model, the constants p and q are interpreted as coefficients of innovation and imitation, respectively. A key assumption in building the multi-generation model is that these coefficients do not change as successive generations are introduced. They remain constant in the cumulative distribution function regardless of which generation is being modeled, because they are characteristics of the overall market, not of the individual product generations. Model parameters for the milk-carton data were estimated using the nonlinear threestage least squares procedure SYSNLIN in SAS [21]. Only the years 1963-1985 were used to fit the equation, whereas 1986 and 1987 were held out to check the accuracy of shortterm forecasts. Tables 1 and 2 show estimates and fit to gallon and half-gallon data, respectively. The coefficient of innovation p is not significant (probability = 0.13) when the model is fit to gallon data, but otherwise all parameters are significant with p < 0.01. Parameter magnitudes are reasonable. The p values are much smaller than average (0.03) for diffusion model application, but Sultan et al. [30] do report minimump values

TABLE 2 Parameter Estimates and R* for Half-Gallon Data Fit to 1964-1985 Parameter P Q ml m2 m3

Estimate

Approx. std. error

T ratio

Approx. prob. > ITI

.00250047 0.20448 8322.52 - 2394.9 -4649.5

.00077473 0.0164825 642.02177 762.38132 229.13379

3.23 12.41 12.96 -3.14 - 20.29

0.0041 0.0001 0.0001 0.0049 0.0001

Generation

R-square

Glass Paper Plastic

0.9670 0.7474 0.7047

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of only 0.00002 in their survey of 213 diffusion model applications. This indicates substantially less innovativeness in the milk container industry than in most others. The q value for gallons (0.375) is very close to the average value of q (0.38) reported by Sultan et al. [30]. For half gallons, q is smaller, indicating that people are much less likely to imitate in this market. The mi for gallons are positive and monotonically increasing. This is indeed expected if each generation “can do everything the previous generation could do, and possibly more,” and the market does follow “the substitution of actual and potential sales from earlier to later generations” [ 18, p. 10751. For half gallons, though, m2 and ml are negative. Norton and Bass [ 191 noted in discussion that the last mi sometimes comes out negative, but they offered only the statement that they do not trust this last mi very much. If the model is valid, however, the mi should all be interpretable within the context of the situation. Because the mi are interpreted as incremental potentials, we suggest that a negative m, indicates that the total potential for a generation is actually less than the total potential of the previous generations it is supposedly replacing. This could certainly be possible if the new technology is more specialized than the older one; then total potential over the period of use of the new technology could be smaller. But negative mi could also result if buyers do not like the new technology very well. Then potential could be smaller than that of the older generation, and it may never replace the previous generation. This is certainly the case for half-gallon plastic milk containers: consumers perceive plastic to have less utility than paper in half-gallon sizes [26], so that m3 is negative. But here m2 is also negative, even though paper was clearly considered vastly superior to glass containers in half-gallon sizes. It is likely that these mi also account for the fact that the total half-gallon market has lost market share to gallons, that is, they are the only parameters in the current form of the model that can (imperfectly) represent the impact of declining total sales. Both consumer perceptions of the technologies and a term to account for growth (or decline) were added in the modified version. Examination of (pseudo) R2 values and visual inspection of Figures 1 and 2 indicate very good fit for gallon data, and poor fit for paper and plastic half gallons. But short-term forecasts are mostly poor in either market. These mixed results show promise, but also indicate the need for improvement. The Norton and Bass [18] model was modified to account more explicitly for one thing consumers see in judging new products: value (i.e., prices and utility) of different generations. A growth term was also added to account for the fact that one market is growing, whereas the other is declining. Model Extension Two forms of pricing function were investigated, representing the two main trends in single generation research. One [2, 3, 81 assumes a pricing function of the form G(P) = p(t)“: G (I’,) =

($d$i’

(3)

The second form assumes G(P) = em’) [following .

6, 20, 311: (4)

When prices of generation i are above market price, sales should be discouraged, whereas prices of generation i below market price should encourage sales. Therefore,

M. W. SPEECE AND D. L. MACLACHLAN

286

Model fit to Gallon (Fit

I .5

to

Data

1963-1985) 7

1.4

PlOZtK 1.3 V

1.2

(l0t.W

yem

plosbc

cmtted)

I

1

1.1

0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 65

70

75

80

a5

YCIX 0

Glassdoto

h

Paper

Model

V

data

fit

to Plastic (Fit

to

Plaftlc

Gallon

doto

Data

1963-1985)

14 13 12 II IO

V V

9

a V

7 V

6

/

5

V

4 3 2

0 70

65

75 Yl%X

V

Plastic

data

Fig. 1. Model fit to gallon data.

80

85

A MULTI-GENERATION

DIFFUSION

MODEL

Model

281

Fit to Half Gallon (Fit

ta

1963-t

Data

985)

6

2

0 65

70

75

60

a5

Year 0

Glassdata

A

PaDer datn

V

Plastic

data

Fig. 2. Model fit to half-gallon data.

one would expect n to be negative. We assume, just as for p and q, that n, a measure of price sensitivity, is a characteristic of the market, not of an individual product generation. It remains constant across generations. Pricing can affect share of the (potential) market that a product will achieve, that is, F(t) is multiplied by G(P). With a multiplicative, exogenous pricing function [3], this is consistent with much single-generation research including the price mentioned above. One could also assume that price affects not (potential) market share, but the ceiling on potential sales [7,9, 13, 141, that is, the mi are multiplied by the G(Pi). With either pricing function and for each way of including price, this extension reduces to the Norton and Bass 1181 model when there is no price sensitivity, that is, when q = 0.0. Pi(t) here is the (utility-adjusted) price of the ith generation, and P(t) is the market price of the product category, that is, the sales-weighted average of prices from all three generations [27]. The use of a ratio of the price of product i to the market price is consistent with other uses in forecasting market share among competing products (e.g., Wittink [34], who models competition across brands, not generations). Prices in our model have been adjusted for utility, which consumers see in various generations. (The methodology for determining milk container utilities and adjusting prices is detailed in [26] .) Once consumer utilities are determined, they can be normalized to get an index for generations, and divided into the price of each generation. The resulting utility-adjusted price will then be more like (the inverse of) a measure for value. The use of relative utilities to model competition across generations has occasionally been proposed in technological forecasting [25, 291, though only Stern et al. [27] used these utilities to adjust pricing in the models.

288

M. W. SPEECE AND D. L. MACLACHLAN TABLE 3 Parameter Estimates and I

Parameter P Q ml m2 ml 1 K

Estimate X0448301 0.36927 522.59848 -55.128 79.21375 -0.213771 0.14511

for Gallon Data, ml Modified with G (P,) =

Approx. std. error JO063869 0.0133317 23.57176 20.22818 15.00401 0.0435945 JO083658

Market growth was also included,

T ratio 7.02 27.70 22.17 -2.73 5.28 -4.90 173.46

Approx. prob. > ITI 0.0001 0.0001 0.0001 0.0130 O.owl 0.0001 0.0001

Generation

R-square

Glass Paper Plastic

0.9637 0.9829 0.9920

taking the form:

G(P)eKt,

(9

where K measures the growth rate of the total market. The functional form of G(P) matches the form of G(PJ above. Rather than use the ratio of an individual generation’s price to market price, however, the ratio of current market price to market prices at the beginning of the time series, to, is used. Such a growth term has also been used before in diffusion model research ([15,22,27], who briefly discuss growth terms in their review). Tables 3 and 4 and Figures 3 and 4 show results from fitting the best combination of pricing function and method of incorporating price. All parameters are highly significant. Price sensitivity q is negative, as expected. Magnitudes reflect the greater price sensitivity in the half gallon market. K is positive in the growing gallon market and negative for the shrinking half-gallon market. Now innovativeness (p) in the two markets is more similar in magnitude, which seems more reasonable than the huge difference indicated by the p values of the basic model. The mi also seem to make more sense. For gallons, m2 is negative. Paperboard, which is not particularly well suited for gallon-sized containers, did replace glass, but did not increase the market potential. The value for m3 remains positive, showing that plastic did increase market potential for gallon sizes. For half gallons, m2 is now positive and large, indicating increased potential market for paperboard cartons over glass bottles. In the basic model, decline in the market masked this increased potential. Now that growth (decline) is explicitly accounted for, the m2 coefficient shows the technology improvement. The value for m3 remains negative, reflecting the lower utility of plastic half-gallon containers relative to paper. TABLE 4 Parameter Estimates and R* for Half-Gallon Data, F(r- TJ Modified with G (PJ = exp q Pg I( Parameter P 4 ml m2 m3 rl K

Estimate .00310757 0.13420 11745.18 12153.08 - 2766.4 - 0.342668 - .0123437

Approx. std. error

T ratio

Approx. prob. > 1TI

.00090301 0.0162761 1359.55 1271.78 63 1.9965 1 0.0318921 .00185101

3.44 8.25 8.64 9.56 -4.38 - 10.74 -6.67

0.0026 0.0001 0.0001 0.0001 0.0003 0.0001 0.0001

iI

Generation

R-square

GlaSS Paper Plastic

0.9865 0.8906 0.8365

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289

Modified

Model

Fit to Gallon

Data

(Fit to 1963-1985) 1.5 1.4 1.3 (later years

1.2

plastic omitted)

1.1 I 0.9

0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 65

70

7s

a0

a5

Yeor 0

Glass

A

data

Paper

Modified

V

data

Model

Plastic data

Fit to Gallon

Data

(Fit to 1963-1985)

70

65

75 Yeor

V

Plastic dato

Fig. 3. Modified model fit to gallon data.

80

a5

M. W. SPEECE AND D. L. MACLACHLAN

290

Modified 6

Model

fit

to Half

[Fit to 1963-i

,

70

65

Gallon

Data

985)

75

80

a5

YCMr 0

Gloss

data

A

Paoer

datu

V

Plastic

data

Fig. 4. Modified model fit to half-gallon data.

In the gallon market, the fit to glass and paper is essentially equal to that with the basic model. For plastic, the improvement is dramatic. Paper and plastic are also substantially improved (Table 5). For half gallons, the modified model and plastic much better, although the fits obtained are still not nearly as good gallon market. Figure 4 shows that the model tracks the data better. Forecasts better for paperboard, although worse for plastic.

obtained forecasts fits paper as in the are much

Concluding Remarks These results seem encouraging. The basic model can work for submarkets, not only whole-product categories. For gallons, the basic Norton and Bass model fit well in an industry and purchase situation very different from the one for which it was developed. Gallon milk containers, though, match basic assumptions underlying the Norton and Bass model much more closely than do half gallons. With gallons, newer generations actually offer customers more utility, so that the substitution driving the model actually takes place and the process is eventually completed. The new technology (plastic) expands the submarket, which has strong growth. The half-gallon market violates some basic assumptions. The newest generation of technology in half gallons (plastic) is not perceived to be an improvement over the old (paperboard), so the substitution process is unlikely to be completed. Furthermore, the submarket is declining, not growing as technological advances increase demand. For these reasons, the basic model did not fit half gallons well. The model cannot be applied carelessly to any submarket without close examination of whether underlying assumptions apply.

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TABLE 5 Results from Forecasting 1986-1987 Glass

Paper

Plastic

1986

1987

1986

1987

1986

1987

0 0 2

0 0 2

141 80 118

140 56 94

9930 7303 9973

13860 7464 11484

Gallons: data and model values Data Basic model Modified model

Sum of sauared

Basic model Modified model

error 1986-1987

Glass

Paoer

Plastic

0.002 0.090

106.470 26.228

478084 56487

Glass

Paper

Plastic

1986

1987

1986

1987

1986

53 22 59

39 18 62

3555 2464 3107

3438 2172 3067

792 736 665

1987

Half gallons: data and model values Data Basic model Modified model

816 801 672

Sum of squared error 1986-1987

Basic model Modified model Note: SSE is divided by 100 for reporting

Glass

Paoer

9.40 6.36

27991.8 3701.1

Plastic 36.22 400.78

purposes.

Fits and short-term forecasts were generally improved by inclusion of utility-adjusted prices and a growth factor. These explicitly account for price competition among generations, perceived utility by consumers, and the fact that growth rates in markets may include components not specifically related to the change in technology. But for half gallons, even substantial improvement did not result in particularly outstanding performance. Modifying the model can help, but it cannot completely overcome the problem that the half gallon market may not really represent a technological substitution process at all. One segment buys plastic because its features fit their needs. Overall, though, consumers do not view it as an improved technology that will ever substitute for paper outside that segment. Future research to extend applications of these multi-generation models must more explicitly recognize that some substitution processes may never be completed. In such cases, the old technology will never die out, because there is an upper limit on the proportion of potential market the new technology may capture. This has occasionally been suggested [4,5], but has not been used much in diffusion research in marketing. Marketing has, though, more thoroughly investigated brand choice, which should be easy to adapt to this uncompleted substitution situation. It should prove fruitful to incorporate brand choice modeling into multi-generation diffusion research. Future research must also examine more closely the basic assumptions behind the multi-generation models. This will help provide more explicit guidance to users of the models about when reasonable forecasts can be expected and when not. Further research

292

into adding pricing (and other marketing clearly when these are needed to improve The multi-generation diffusion model plied, it can provide very good forecasts processes. It can be improved to widen the the basic model is not now suitable.

M. W. SPEECE

AND D. L. MACLACHLAN

variables) and growth terms can show more forecasts. is a fairly simple model. When carefully apof many difficult technological substitution scope of application in many situations where

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MODEL

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25. Silverman, B. G., Market Penetration Model: Multimarket, Multitechnology, Multiattribute Technological Forecasting, Technological Forecasting and Social Change 20(3), 215-233 (1981). 26. Speece, M., and MacLachlan, D. L., Measurement of Milk Container Preferences, Journal of International Food & Agribusiness Marketing 3(l), 43-64 (1991). 27. Stern, M. O., Ayres, R. U., and Shapanka, A., A Model for Forecasting the Substitution of One Technology for Another, Technological Forecasting and Social Change 7, 57-19 (1975). 28. Stephens, K. L., Technological Substitution: A Model for Market Forecasting. Unpublished MBA Thesis, University of Washington, 1977. 29. Stover, J. G., Use of Decision Modeling for Substitution Analysis: Application to Acceptance of New Electricity-Generating Technologies, Technological Forecasting and Social Change 12(4), 337-351 (1978). 30. Sultan, F., Farley, J. U., and Lehmann, D. R., A Meta-Analysis of Applications of Diffusion Models, Journal of Marketing Research 27(February), 70-77 (1990). 31. Thompson, G., and Teng, J. T., Optimal Pricing and Advertising Policies for New Product Oligopoly Models, Marketing Science 3(Spring), 148-168 (1984). 32. U.S. Department of Agriculture, Dairy Division, Agricultural Marketing Service, Packaged FluidMilk Sales in Federal Milk Order Markets. (Report 14, June 1987). U.S. Government Printing Office, Washington, DC, 1987. 33. U.S. Department of Labor, Bureau of Labor Statistics, Producer Prices and Price Indexes. (Prior to March 1978: Wholesale Prices and Price Indexes.) U.S. Government Printing Office, Washington, DC, various dates, 1974-1988. 34. Wittink, D. R., Causal Market Share Models in Marketing, International Journal of Forecasting 3(3/4), 445-448 (1987). Received 23 June 1994; revised 27 December 1994

Appendix Tables Al, A2, and A3

Container

Year

1964 1965

1968 1969 1970 1971 1972 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984

TABLE Al Type in the Gallon Milk Market

Market share

Units

Total units

Glass

Paner

Plastic

Glass

Paper

342.47 473.03 55 1.45 621.84 750.94 864.58 1029.57 1220.27 1439.18 1739.94 1951.53 2244.02 2417.33 2712.82 3052.30 3347.40 3695.35 4271.08 4871.06 5349.34 6215.38 7470.56 9358.97 10071.43 14000.00

62.04 61.48 49.27 36.13 28.39 20.51 13.76 8.66 5.13 3.43 2.59 1.59 0.81 0.45 0.30 0.17 0.09 0.06 0.05 0.04 0.03 0.02 0.00 0.00 0.00

37.96 31.63 44.61 55.32 58.46 62.92 65.95 66.21 63.30 55.40 47.04 43.32 39.92 33.10 25 62 19.42 14.18 10.09 6.98 4.77 3.25 2.28 1.56 1.40 1.00

0.00 0.89 6.12

212.47 290.82 271.70 224.67 213.19 177.29 141.67 105.70 73.83 59.75 50.54 35.62 19.58 12.31 9.16 5.64 3.33 2.49 2.44 2.13 1.86 1.18 0.00 0.00 0.00

130.00 178.08 246.00 344.00 439.00 544.00 679.00 808.00 911.00 964.00 918.00 972.00 965 .OO 898.00 782.00 650.00 524.00 431.00 340.00 255.00 202.00 170.00 146.00 141.00 140.00

8.55 13.15 16.57 20.29 25.12 31.57 41.16 50.36 55.09 59.27 66.44 74.08 80.41 85.73 89.85 92.91 95.19 96.72 97.71 98.44 98.60 99.00

Plastic 0.00

4.21 33.75 53.17 98.75 143.29 208.90 306.57 454.35 716.10 982.79 1236.27 1432.75 1802.53 2261.15 2691.76 3168.02 3837.59 4528.62 5092.21 6011.52 7299.38 9212.98 9930.43 13860.08

M. W. SPEECE

294

AND D. L. MACLACHLAN

TABLE A2 Container Type in the Half-Gallon

Milk Market

Market share

Units

Year

Total units

Glass

Paver

Plastic

Glass

Paper

Plastic

1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987

6052.85 6364.75 6544.87 6420.33 6513.54 6603.02 6551.59 6363.23 6266.71 5818.58 5376.38 5143.79 5033.51 4767.17 4552.99 4307.01 4163.34 4009.63 3990.89 4159.28 4374.41 4410.10 4399.75 4292.13

26.57 26.46 24.90 20.54 16.33 12.46 9.76 7.79 6.30 5.28 4.75 4.33 3.52 2.75 2.43 2.26 2.05 1.85 1.63 1.45 1.37 1.34 1.20 0.90

73.42 73.53 74.99 78.89 82.34 85.37 87.44 88.87 89.76 90.40 91.16 91.80 92.14 92.34 92.55 92.57 92.28 91.38 89.40 86.89 84.26 81.54 80.80 80.10

0.01 0.01 0.11 0.57 1.34 2.17 2.79 3.34 3.94 4.31 4.08 3.86 4.34 4.91 5.02 5.17 5.66 6.76 8.96 11.66 14.36 17.12 18.00 19.00

1608.24 1684.11 1629.67 1318.74 1063.39 822.74 639.56 495.70 394.79 307.22 255.61 222.73 176.93 131.10 110.44 97.34 85.51 74.18 65.07 60.31 60.15 59.10 52.80 38.63

4444.00 4680.00 4908.00 5065.00 5363.00 5637.00 5729.00 5655.00 5625.00 5260.00 4901.00 4722.00 4638.00 4402.00 4214.00 3987.00 3842.00 3664.00 3568.00 3614.00 3686.00 3596.00 3555.00 3438.00

0.61 0.64 7.20 36.60 87.15 143.29 183.08 212.53 246.61 250.78 219.15 198.55 218.32 234.07 228.62 222.61 235.59 27 1.05 357.59 484.97 628.30 755.01 791.96 815.51

A MULTI-GENERATION

DIFFUSION

MODEL

TABLE A3 Price Data for Fluid Milk Containers

295

(cents/container)

Year

Glass half gallon

Glass gallon

Paper half gallon

Paper gallon

Plastic half gallon

Plastic gallon

1963 1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987

11.60 11.66 11.77 12.00 12.15 13.06 13.95 14.62 15.98 16.41 16.88 18.89 21.82 23.74 26.01 29.68 31.72 35.55 39.92 43.19 41.20 42.33 46.34 47.64 47.25

16.44 16.52 16.68 17.00 17.21 18.50 19.76 20.70 22.63 23.25 23.90 26.76 30.91 33.63 36.85 42.04 44.94 50.36 56.55 61.18 58.36 59.96 65.64 67.48 66.93

2.39 2.39 2.23 2.25 2.27 2.23 2.21 2.27 2.30 2.25 2.25 2.92 3.64 3.82 4.03 4.04 4.07 4.42 5.06 5.57 5.80 5.93 6.12 6.16 6.18

4.68 4.68 4.39 4.45 4.46 4.40 4.57 4.68 4.60 4.61 4.55 5.87 7.28 7.60 8.25 8.47 8.80 10.04 11.49 12.75 12.84 12.88 13.63 13.51 13.87

3.96 3.96 3.96 3.47 3.25 3.13 2.98 2.84 2.60 2.55 2.66

7.20 7.20 7.20 6.30 5.91 5.69 5.41 5.16 4.72 4.64 4.83 6.82 8.28 8.66 8.80 8.58 10.08 12.63 13.34 12.56 12.24 12.74 12.04 12.15 15.30

3.75 4.55 4.76 4.84 4.72 5.54 6.95 7.34 6.91 6.73 7.01 6.62 6.68 8.42