Price elasticities for softwood plywood and structural particleboard in the United States 1

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1 528 Price elasticities for softwood plywood and structural particleboard in the United States 1 HENRY SPELTER ForestProductsLaboratory, 2 United States Department ofagriculture Forest Service. Madison, WI, U.S.A Received October 28, Accepted March 1, 1984 SPELTER. H Price elasticities for softwood plywood and structural particleboard in the United States. Can. J. For. Res. 14: A multiequation model analyzing the price elasticities for construction panels (softwood plywood and structural particleboard) was developed. The response of softwood plywood demand to price was found to have declined substantially over the 30-year span of analysis, dropping from an estimated 0.83 in 1950 to 0.10 in This decline indicates the maturing of softwood plywood markets and the limitedgrowth opportunities for the product. The price elasticityofstructural particleboard, by contrast, was estimated at substantially higher levels in the late 1970's. These particleboards compete for some ofthe same markets as softwood plywood and are priced at substantial discounts in most markets. The model results indicate the demand for structural particleboards is highly sensitive to price. and pricing will be a key variable determining its growth. SPELTER. H Price elasticities for softwood plywood and structural particleboard in the United States. Can. J. For. Res. 14: On a développé un modèle d'analyse a equations multiples dans le but d'étudier les élasticités des prix des panneaux destinés a la construction (contreplaqués de résineux et panneaux de particules structuraux). La réponse de la demande du contreplaqué de résineux au prix a montré un déclin substantiel durant la période de 30 ans qui a fait l'objet de l'analyse, baissant d'une valeur de 0.80 en 1950 à 0.10 en Ce déclin indique une maturation des marchés du contreplaqué de résineux et la limitation des possibilités de croissance du produit. L'élasticité des prix des panneaux de particules structuraux, par contre, a été estimée à des niveaux substantiellement plus élevés à la fin des années 70. Ces panneaux entrent en compétition avec certains secteurs du marché des contreplaqués de résineux et leurs prix sont établis à des niveaux substantiellement inférieurs sur la plupart des marchés. Les résultats obtenus du modèle indiquent que la demande pour les panneaux de particules structuraux est hautement sensible aux prix et que l'établissement des prix contribue la clefde route determinant sa croissance. [Traduit par le journal] Introduction Elasticities ofdemand are numerical indexes measuring the percent change in demand for a product caused by a percent change in any of its determinants. Determinants include the price ofthe product, prices ofsubstitutes, and market activities in areas where the product is used. Among the set ofelasticities used by economists, price elasticity is probably the most importantbecause it is one ofthe few determinants of demand that is directly influenced by the producing industry. The forest products industry is particularly interestedinestimatingpriceelasticitybecauseofitsusefulness in long-range planning. For example, knowing the price elasticity for softwood plywood could help predict whether, when the cost of plywood increases by a given percentage, the demand will decrease proportionally or by a greater or lesser percentage. This tells whether total industry revenues will remain unchanged, increase, or decrease. Unfortunately, a problem exists in the way price elasticities have been estimated over the years. Economists have not fully accounted for external changes in markets caused by technological advances and innovation, economic shocks and dislocations, negative publicity, and equally important, the maturation of a product in its market. These changes constitute an important, but little recognized, phenomenon we call "structuralchange."the price elasticity model developed in 1This article was written and prepared by United States Government employees on official time, and it is therefore in the public domain (i.e.. it cannot be: copyrighted). 2Maintained at Madison, WI, in cooperation with the University of Wisconsin. 'Revised manuscript received February 17, this paper incorporates the effects of structural changes on the elasticities of demand for construction panels (softwood plywood and structural particleboard). Structural changes Briefly, a structural change is any development that alters the market relationship between demand and its determinants. Technological advances Technological advances can boost an industry by opening new opportunities, or cripple it by creating new competition. For example, softwood plywood was a minor industry and its product confined to interior uses (such as paneling and furniture) until the developmentofacommercially feasible waterproof glue in the 1930's allowed its use for exterior sheathing. Later on, particleboard panels (developed in the 1950's) and flakeboard or waferboard sheathing (developed in the 1970's) cut into the sales of softwood plywood. Economic shocks Disruptions caused by sudden changes in one part of the economy, like the energy price increases of the 1970's, can also alter market relationships. In the case of panels, recent increases in energy costs have focused attention on the need to improve insulation in homes. This led to increased use of foam-based panels in wall sheathing at the expense of woodbased panels. even though the latter are less expensive. Bad publicity Negative publicity about some aspect of a product's performance is another cause of structural change. The discovery in the late 1970's that particleboards bonded with ureaformaldehyde resins give off potentially harmful formaldehyde fumes hurt sales of such products and helped sales of other wood-based panels.

2 SPELTER 529 penetration rates. Of the three, the logistic function approaches the saturation point the fastest while the reciprocal logarithmic curve has the fastest initial growth but ultimately is the slowest to approach the maximum. Which one is appropriate in a given situation depends on the receptivity of the market to innovation. The greater the percentage of innovators in a population, the faster a new product is adopted initially. The greater the proportion of nonadopters, the slower the rate of ultimate adoption (Beal and Bohlen 1962). The starting point for the model is the following identity, defining consumption at a given time (t): FIG. 1. Examples of three market diffusion curves. Market maturity The process whereby a product matures in its markets influencesmarketbehavior. Eachcommodityhasapotentialmarket niche where its performance characteristics or lower costs make it the favored product. When that niche has been filled, the product is said to have matured in terms of its life cycle. It seems reasonable to assume that a given change in price would exertdifferingpercentchanges indemandoverdifferentphases and stages of market penetration. In the traditional approach to estimating price elasticity, theseeffectsofstructural changes are not readily incorporated. For each determinant, a coefficient is estimated from a given historical data base. These coefficients represent the average effect of that factor on demand over the given period of estimation. The average effect, however, may be aweak indicator iftrends induced by structural change are systematically altering relationships. Not accounting for structural change can be particularly detrimental when these coefficients are used for predicting the future in long-range planning. The formulation of a model that accounts for such changes, and its application to the analysis of softwood plywood markets, is the research focus of this paper. Becausetheclassofproductscalledstructuralparticleboards (SPB) (i.e., waferboards, flakeboards, assorted oriented strandboards)competesalmostexclusivelywithsoftwoodplywood, this analysis of price elasticity of softwood plywood entails a corresponding analysis ofstructural particleboards. I will begin by describing the model developed for the study and the data used in the estimation. Then I will give the empirical estimates and apply the estimated model to analyze the impacts of alternative economic scenarios on a projection of demand for construction panels in the 1980 s. Theoretical basis of the model The diffusion theory of market penetration states that technologies and innovations reach market maturity in similar ways, following a fixed pattern, from the time they are introduced until they saturate the market. The pattern traced by this process when graphed against time resembles an S-shaped curve starting at zero and ending at an asymptotic upper bound (Fig. 1). Diffusion models based on these observations were first used to study the adoption of new strains of hybrid corn (Griliches 1957) and since have been found applicable in a variety of situations (e.g., Bass 1969; Buongiorno and Oliveira 1977; Heeler and Hustad 1980). Figure 1 traces the outlines of three curves yielding the basic S-shaped curve but producing significantly different market [1] where Q is the sum of consumption in i markets and the S i, F i, and the M i are the product s market shares, maximum market potentials, and market activity indicators. The latter consist of such variables as housing starts, furniture production, nonresidential construction, etc. Changes in the variables are caused by government policies and broad economic and demographic trends. Such issues are dealt with in the realm of macroeconomic analysis. For this microeconomic study of the plywood and structural particleboard industries, these variables are treated as exogenous, leaving the focus on the market shares, S i, and the maximum market potentials, F i. For each of the i sectors, use factors are defined through time as the amount of product consumed per unit of the end-use commodity. This leads to the following equation to be estimated: [2] Market shares To quantify the growth of the market share term, S i, over time, the following three functions may be used: [3a] logistic [3b] Gompertz [3c] Reciprocal logarithmic where t is time measured from the date of an innovation s market appearance (say 1950 is the introduction date, then in 1950 t = 1, 1960 t = 11, etc.) and a and b are the parameters to be estimated. The curves described above, however, are only descriptive, defining the proportion of the market an innovation captures at a given time t. It is assumed that the fundamental reason an innovation wins market acceptance is that overall it costs less than existing alternatives. To transform these curves so that they incorporate relative prices of competitive products, I have used the definition of the time-trend variable: [4] Rather than leaving K an arbitrary constant, I measure it as a function of the normalized difference between the prices of the substitute products in the given period: [5] and where P (e) is the price of the existing commodity and P (n) is the price of the innovation. This formulation incorporates a market feedback mechanism into the diffusion process that is missing from the models in [3a], [3b], and [3c]. The rate of diffusion becomes a direct

3 530 CAN. J. FOR. RES. VOL. 14, 1984 TABLE 1. United States softwood plywood use factors Sector function of prices, but the continuity assimilated from [4] means that their influence varies through the product s life cycle. Equations 3a, 3b, and 3c cover only the maturation phase of a product s life cycle. To account for the decline caused by succeeding innovations, a separate term(s) needs to be added. For the Gompertz model, for example. the equation changes from [6] to [7] where C and d are two new diffusion parameters, t** is the price term representing prices in the new diffusion process, and k is a parameter representing the portion of the market at risk to the new innovation (if the two can be substituted in all applications, k = 1, and k is less than one if the innovation is applicable in only a subset of end uses). Equation 5 formulates market interactions in terms of relative prices only and ignores absolute price (income) effects. Investigations by Winer (1979) showed that absolute price effects for goods that make up a relatively minor portion of overall spending and have ready substitutes are negligible. Plywood costs are a small part of total construction costs and the product has well-defined substitutes; thus any absolute price effect is apt to be small and overwhelmed by substitution effects. Market potentials of plywood The maximum physical market potential is defined as the amount of product that would be needed (per unit of end use) if that commodity alone were used for a given application. For example. if all new residential homes had 1/2-in.-thick plywood subflooring (1 in. = 2.54 cm) (the most common thickness used), then the maximum physical market potential would be 1.33 square feet (3/8-in. basis) per square foot of floor (1 ft 2 = cm 2 ), plus an amount for normal waste. The maximum physical market potentials were estimated for each market segment from the American Plywood Association (APA) market research surveys and are shown in Table 2. In some instances, however, the maximum physical market potential is misleading because it is unlikely to be attained. TABLE 2. Estimated physical maximum and feasible maximum market use factors for softwood plywood a (3/8-in. basis) Physical Feasible Sector maximum maximum Based on American Plywood Association surveys (Anderson 1973: Carney 1977). In sheathing of roofs in humid climates, some spaced lumber boards will always be used for improved ventilation. In sheathingofwalls. plywood istypically relegatedtothe comers for bracing while better insulating panels are used on the bulk ofthe wall. Likewise, wood siding, because of its higher maintenance costs, is unlikely ever to attain the potential physical limit. To reflect these considerations. more realistic estimates ofmaximum feasible levels were used forthe sectors (Table 2). Note that although these maximum potentials are treated as constants, they are variable to some extent. This stems from the way many are defined (i.e., per square foot of floor area). Changes in house characteristics. (i.e., roof pitch. or number and size of doors and windows) can affect the relationships of roof and wall surfaces to floor area. Long-term changes in building practices toward the use ofdifferent panel thicknesses could also have an effect.

4 SPELTER 53 I TABLE 3. Estimated plywood use-factor equations for new residential construction, End-use data Softwood plywood is used in many distinct markets. To analyze its demand in the framework of the diffusion theory, it is necessary to break out its consumption into relatively homogeneous end-use sectors. Data on plywood consumption by sector have been gathered periodically by the Forest Service and the APA, but at widely scattered intervals (Anderson 1973; Burdick 1969; Carney 1977: Dickerhoof 1978; Gill 1965; Gill and Phelps 1969; Merrick 1948; Phelps 1970; Reid 1976; among others). To develop consistent time-series data from these point estimates, I have used the following procedures: (i) converted the available end-use data to use factors by dividing the reported consumption for a given year by total activity in that sector during the year; (ii) derived end-use factor data for those years when no survey was done by interpolation from, and extrapolation of, the survey data: (iii) estimated the consumption within each sector by multiplying the derived end-use factors by their respective activity indicators. These were summed and compared with total apparent consumption (production plus net imports) to verify the accuracy of the end-use factor estimates; and (iv) when a discrepancy in excess of 15% existed. adjusted selected use factors based on available additional information, such as journal articles or APA field reports, which indicated a change. Altogether. estimates of use factors for nine market segments were made over the period of and are summarized in Table 1. The model The general form of the estimated use-factor demand function is as follows: [8] where the U i are use factors for softwood plywood (defined in [2]), t* L is the diffusion variable based on the prices of boards relative to plywood ([5]), t* j are the diffusion variables based on prices of plywood relative to other substitutes (SPB, particleboard, styrofoam), F i are maximum feasible market potentials of plywood. and k j are subjective estimates of the fractions of the plywood markets vulnerable to substitution by other products. Deviations from this format are explained below. Prices used are basedon wholesale mill prices obtained from either an industry price reporting service called Random Lengths (Anonymous 1981)orthe UnitedStates Departmentof Labor (Anonymous 1982a)and,whereappropriate.fromadditional costs to the user involved in employing the product such as freight rates and worker wages. Plywood-boardsubstitution was modeled over the entire sample period of Particleboard-plywoodsubstitutionwas modeledbeginning with 1956, Styrofoam-plywood with 1973, and SPB-plywood with In addition. plywood-particleboardsubstitution caused by formaldehyde fume emission problems was incorporated with To estimate the parameters of the diffusion equations, nonlinear least squares using the Gauss-Newtonalgorithm were used. The Gompertz version ofthe diffusion model was generally found eo fit the data best and was selected for most sectors. The results are contained in Tables 3 and 4 along with descriptive statistics ofthe estimated parameters: column 1 describes the market whose use factor is defined; column 2 describes the function type (logistics, Gompertz, etc.); and column 3 contains the period over which the parameters were estimated. Column 4 describes the commodity against whose price the price of plywood is compared in the diffusion variable, or otherwise describes the coded variable in column 2. Columns 5 and 6 give the estimated values for the parameters, while columns 7 and 8 give the ratios of the parameters to their standard errors. Column 9 contains the adjusted coefficient of determination (R 2 ). Overall, 14 end-use markets were modeled in the diffusion framework with a total of 26 diffusion terms. Twenty-two of these were estimated using the Gompertz model. The logistic curve was used on three occasions and the logarithmic reciprocal once. In the case of the multifamily sector, the use factor was regressed directly against the one-family factor (and a second variable representing the proportion ofhigh-rise apartments in total multifamily starts) because theconsumption patterns in the two sectors are generally similar. For the farm-use factor, a dummy variable was used after 1975 to adjust for a discontinuity in the use factor caused by a break in the market indicator from one series to another. Finally, to simulate the substitution ofplywood for particleboard in mobile homes as a

5 532 CAN. J. FOR. RES. VOL. 14, 1984 TABLE 4. Estimated plywood use-factor equations for other markets, result of the formaldehyde problem. a dummy variable was introduced in This activates a penalty factor which increases the particleboard price by an arbitrary amount in a relative price term with plywood. The higher cost of particleboard induces plywood to retake part of the flooring market in a separate diffusion process. Multicollinearity, which frequently hampers standard demand function estimations, was generally not a problem. The one exception was the wall-sheathing formula, where two of the three price variables (SPB and styrofoam) were highly correlated. To facilitate the equation estimation, the diffusion parameters for the SPB term were constrained to values similar to those obtained for roof and floor sheathing, and then the parameters for the styrofoam variable were estimated. Most parameter estimates fell within the bounds required to model diffusion. An exception was the residential alteration and repair factor where the estimated value of the b parameter in the Gompertz diffusion term for SPB was greater than one. This is incompatible with the diffusion theory, and the equation was reestimated with this coefficient constrained to 0.7. a value near the upper end of the range estimated for the b parameters in the unconstrained Gompertz equations. Problems also occurred in estimating appropriate diffusion variables for SPB in the nonresidential building sector. But attempts at reestimating the equation with imposed values caused the parameters for the plywood-boardterm to be unrealistic. In this case, the SPB term was deleted. To incorporate short-run cyclical fluctuations in the model not reflected in the trended use factors, the use-factor derived estimates of consumption were subtracted from apparent consumption (production plus net imports). The difference accounts for inventory changes in the marketing system and any errors or omissions in the use factors. The category s fraction of total consumption was best modeled by a nonlinear time trend and the current and lagged real price of plywood. FIG. 2. Actual and model-estimated United States softwood plywood consumption, In general, the estimated diffusion equations fit the usefactor data well. The overall fit of softwood plywood consumption, obtained by solving [1] with the model-derived estimates of the use factors replacing the S it* F i terms. is close to the actual historical values. Figure 2 shows the two series whose common correlation exceeds A second test of a model s capability is how well it tracks consumption outside of the historical estimation interval. The model was simulated for the 2 years (1982 and 1983) since the analysis. For 1982 and 1983, the model predicted total structural panel consumption (both plywood and particleboard) at 15.6 and 18.5 billion square feet. The estimated actual consumption figures, derived from APA production data less exports, were 16.2 and 20.7 billion square feet for the 2 years. The model therefore underestimated consumption by 4% in 1982 and 11% in It should be noted, however, that these figures are based on preliminary and incomplete data, especially for 1983, hence the comparisons are tentative.

6 SPELTER 533 TABLE 5. Indicators of United States economic activity Sector TABLE 6. Alternative price projections of softwood plywood and structural particleboard ($/MSF, delivered Boston) FIG. 3. Softwood plywood and structural particleboard use-factor price elasticities through time. The quantitative effects of structural change on softwood plywood demand sensitivity over time, incorporated in this formulation, can now be estimated. For six periods (1950, 1955, 1960, 1970, 1978, and 1981) plywood prices were increased 1% and the effect simulated in the model. The results were compared with the corresponding values in the historical simulation, shown in Fig. 2, and the percent difference between the two computed. These l-year elasticity estimates, shown in Fig. 3, indicate a significant change over the past three decades. From a high of 0.83, the absolute price elasticity falls to 0.10 in 1970, increases to 0.11 in 1978 (reflecting the impacts of SPB and foam panels), and falls back to 0.10 in SPB elasticities, by contrast, were estimated at 0.86 in 1977 and 0.56 in These numbers reflect the market maturity of softwood plywood and the relative infancy of SPB. The average I-year elasticity over the period , derived by averaging the four figures for those years, yields a value of 0.40 which is close to the range reported in previous studies (Adams 1977: McKillop 1967; McKillop et al. 1980; Waggener et al. 1978). But the trend in the individual point estimates indicates a structure that is more elastic in the early postwar period and less elastic at more recent times. Consumption simulations Equation 1 is solvable for any set of future market activity and price assumptions to yield estimates of consumption. One such set of economic projections. based on the December 1982 Wharton long-term forecast of the U.S. economy (Anonymous 1982b). is contained in Table 5. The basic price assumptions simulated along with these economic projections are summarized in Table 6. In the base case simulation. I tested the effect of SPB prices maintaining a stable relationship to plywood equal to their 1982 ratio of about 75%. The results are shown in Table 7. Plywood demand recovers in but then levels off in a range of 19-20billion square feet annually. SPB demand, by contrast, rises steadily and reaches 3.9 billion square feet by Past experience with plywood and particleboard price behavior. however. shows a tendency for the innovation's prices to fall relative to the competition during the expansive phases. The effect of such a price scenario is tested in an alternative simulation also shown in Table 7. The price change reduces plywood consumption by 0.75 billion square feet in 1990 and increases SPB consumption by a like

7 534 CAN.J. FOR. RES. VOL. 14, 1984 TABLE 7. Projections of wood products consumption (billion feet) (3/8-in. basis) Softwood plywood Base Alternative Difference (%) Structural particleboard Base Alternative Difference (%) amount. Expenditures on waferboard in 1990, however, stay unchanged at approximately $1 billion, indicating a roughly unitary long-run price elasticity during this interval. Discussion Economic models intended for use in forecasting demand should account for the effects of structural change in markets over time. The model described here is based upon a formulation intended to accomplish that within the framework of the generally accepted law of demand, which posits an inverse relationship between demand and price. The approaches used in previous modeling and this method are similar in that both rely on price as the key determinant of substitution. Whereas previous models measured the average effects of prices over a specific historical interval, I have attempted in this model to measure these same effects at each discrete period within the study time frame. This approach recognizes that as markets change owing to new technologies, market saturation and so on, the effects of prices on substitution also change. There arethree price-relatedsubstitution processes that concern future projections. First. there is the impact ofestablished and entrenched products. Their effects are readily modeled through time in this approach because of the substantial body of data which exists from which the trajectory of market penetration as it relates to prices may be estimated. An example of such a process is the historical competition between plywood and lumber sheathing featured in this model. Such processes are important in explaining past behavior, but become less influential in forecasts as the dominant product displaces the other. A second process involves estimating the impacts of technologies and products that were recently introduced and are only at the beginning stage of their evolution. Because of the limited market experience, accurate estimation of their response to price is less easily made. However, their effect on future market conditions is substantial because of their potential to displace existing products. To improve upon the econometrically derived estimates of their probable effects, more research along the lines of Mansfield (1968) is needed to uncover the basic characteristics and traits that determine the adoption of new technologies. Information on such factors as the size distribution of firms in the consuming markets, the complexity and differentiation ofthe innovation relative to the existing products, and the importance of the innovation to the overall process where it will be used could be employedto help infer the probable success rate of new products. Thethirdclassofsubstitutionprocesses involvesinnovations that are not yet on the market but may become important with technological advances oreconomicupheavals. Suchpotential events are least amenable toeconometric analysis, which relies on some historical data for estimation of parameters. Within these limitations, the model presented here features two elements that should improve existing projection and simulationtechniques. First, itallows priceelasticities tovary with the extent of product penetration within markets. This reduces the danger of unbounded extrapolation of past key, but receding, trends. Second, it incorporates the impacts of existing technologieswhosecurrent influencesmaybe small, butwhose long-termpotential toalterthe markets is great. Theseelements should increase the realism and accuracy of commodity projections, particularly in intermediate-term forecasts (two or three decades) during which period technology is not apt to change radically. ADAMS, D. M Effect of national forest timber harvest on softwood stumpage, lumber. and plywood markets-aneconometric analysis. Oreg. State Univ. For. Res. Lab. Res. Bull. 15, Corvallis, OR. ANDERSON, R Softwood plywood used in new residential construction. American Plywood Association Market Research Report R-31. American Plywood Association. Tacoma. WA. ANONYMOUS Random Lengths. Random Length Publications. Inc., Eugene, OR. ANONYMOUS. 1982a. United States Department of Labor. Bureau of Labor Statistics. Producer price indexes. Washington, DC. ANONYMOUS Wharton Econometric Forecasting Associates. Long term forecast of the U.S. economy. Philadelphia, PA. BASS, F. M A new product growth model for consumer durables. Manage. Sci. 15: BEAL, G. M., and J. M. BOHLEN The diffusion process. Special Rep. No. 18. Iowa State Univ. Press, Ames, IA. BUONGIORNO. J., and R. OLIVEIRA Growth of the particleboard share of production of wood-based panels. Can. J. For. Res. 7: BURDICK, D Major end markets for softwood plywood. American Plywood Association, Tacoma, WA. CARNEY, M Softwood plywood used in new residential construction. American Plywood Association Market Research Report R-38. American Plywood Association, Tacoma. WA. DICKERHOOF, H. E Use of wood in mobile homes is increasing. USDA For. Ser. Res. Bull. FPL-4. For. Prod. Lab.. Madison, WI. GILL, T. G Wood used in manufacturing industries. USDA For. Serv. Stat. Bull. 353, Washington, DC. GILL, T. G., and R. B. PHELPS Wood used in manufacturing industries. USDA For. Serv. Stat. Bull. 440, Washington, DC. GRILICHES, Z Hybrid corn: an exploration in the economics of technological change. Econometrica, 25(4): HEELER, R. M., and T. P. HUSTAD Problems in predicting new product growth for consumer durables. Manage. Sci. 26(10): MANSFIELD, E Industrial research and technological innovation. W. W. Norton and Co., New York. MCKILLOP, W. L. M Supply and demand for forest productsan econometric study. Hilgardia. 38: MCKILLOP, W. L. M.. T. W. STUART, and P. J. GEISSLER

8 SPELTER 535 Competitionbetweenwoodproductsandsubstitutestructuralprod- residential buildings. USDA For. Serv. Stat. Bull ucts: an econometric analysis. For. Sci. 26: WAGGENER, T. R., G. F. SCHREUDER, and H. M. HOGANSON MERRICK, G. D Wood used in manufacture. USDA For. Serv. Elasticities of demand for forest products over time. Report on file Forest Res. Rep. 2. Washington. DC. at the USDA For. Serv. Pac. Northwest For. Range Exp. Stn., PHELPS, R. B Wood products used in single-family homes Portland, OR. inspected by the FHA. USDA For. Serv. Stat. Bull. 452, Wash- WINER, H Dynamics of price elasticity and brand life cycles. ington, DC. J. Mark. Res. 16(4): REID. W Wood products used in the construction of non-