On the consumer Value of Complementarity

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On the consumer Value of Complementarity
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   On the Consumer Value of Complementarity  byMichele BaggioandJean-Paul Chavas *    Abstract  : The paper develops a conceptual model of the consumer value of complementarityand illustrates its usefulness in an application to fisheries. The value of complementarity arises when the willingness to pay for a set of goods is “greater thanthe sum of its parts”. We propose a measurement of the value of complementarity based on the benefit function. Our econometric analysis of fish consumption in Italyexamines these issues, with special attention given to dynamics. The investigationillustrates the importance of dynamics. Our results show that, while short-run fishdemand is characterized by substitution relationships, complementarity does developin the intermediate run and in the long run. *   Respectively, Research Assistant, Department of Agricultural and Resource Economics, Universityof Maryland, and Department of Economics, University of Verona, Verona, Italy; and Professor of Agricultural and Applied Economics, University of Wisconsin-Madison. We thank Ted McConnelland Federico Perali for the valuable comments on an earlier draft of this paper. Michele Baggio alsothanks Shinsuke “Yagi” Uchida and his classmates for the helpful discussions.  1 On the Consumer Value of Complementarity1.   Introduction The concept of complementarity has been a standard part of economic analysis (e.g., Hicks;Samuelson, 1950, 1974). Intuitively, two activities are complementary if increasing one has a positive effect of the value of the other. Hicks was first to provide a systematic treatment of complementarity in the context of consumer theory. He evaluated complementarity in termsof quantity effects (called q-complementarity) as well as price effects (called p-complementarity). 1 Our analysis focuses on q-complementarity, where two commodities aresaid to be complements (substitutes) when increasing the quantity of one tends to increase(decrease) the marginal value of the other. While there has been interest in the economics of complementarity (e.g., Samuelson, 1950, 1974), the linkages with consumer valuation andwelfare analysis remain somewhat unexplored.The issue of complementarity has also been mentioned in the valuation of  biodiversity and the services provided by an ecological system (e.g., Faith et al.; Justus andSarkar; Loreau). The role of complementarity in ecosystem functioning stems from the ideathat the economic value of an ecosystem is adversely affected by a decline in diversity (e.g.,Brock and Xepapadeas). This raises two questions. First, are the Hicksian characterizationsof complementarity related to the value of complementarity in ecosystem valuation? Second,how should we proceed to measure the value of complementarity? Answering these questionsrequires investigating the role of complementarity in welfare analysis as well as in ecosystemvaluation.  2The objective of this article is to develop a conceptual model of the consumer valueof complementarity and to illustrate its usefulness in an application to fisheries. Measuringthe value of resources based on consumers’ willingness to pay is standard in economic andwelfare analysis. What is not clear is how to apply such measurements to the valuation of complementarity. This article develops a methodology for such a measurement. Intuitively,the value of complementarity arises when the willingness to pay for a set of goods is “greater than the sum of its parts”. This means that the value of complementarity goes beyond thevaluation of each good. In this article, we develop a general approach to the consumer valuation of complementarity. And we illustrate the approach in an application to theconsumer value of complementarity with respect to fish.As a starting point, the methodology we propose is based on a standard welfareinvestigation of marginal willingness to pay. The main challenge to value complementarity isthat we need to know more than just the value of particular goods. Indeed, to evaluatecomplementarity relationships, we need to know how the marginal value of a good isinfluenced by other goods. Obtaining this information requires a joint evaluation of willingness to pay across goods. This creates three specific challenges. First, the scope of analysis requires a system approach to consumer valuation. Second, evaluating possiblecomplementarity across goods in a system requires assessing the value of the “sum of the parts”. This suggests relying on welfare measures that can be easily aggregated. Third, theapproach must be empirical tractable.This article addresses these three challenges to the consumer value of complementarity. The methodology we propose infers the economic value of complementarity through fish market price. The value of complementarity is endogenously  3determined. This approach follows Gorman’s statement, reinforced later in Barten andBettendorf, that price of fish depends on the shadow price of fish characteristics. This is thecase when prices adjust to the quantity of the good on the market. This is certainly true if thegood considered in the analysis is fresh fish, and none of it is processed or storable for somearbitrary time. If that is the case, given the perishable nature of the commodity, in the shortrun supply is inelastic, prices are adjusted to clear the market, and producers are typically price takers (Barten and Bettendorf). This suggests a system of inverse demands as a naturalway to model the nature of this particular commodity. Note that using a system approach tovalue marginal willingness to pay has been in the literature for decades. It can be based in thedistance function first proposed by Shephard and analyzed by Deaton in the context of evaluating consumer welfare. The distance function also provides a convenient framework toconduct empirical analysis. Following the early work of Barten and Bettendorf, it has beenapplied by Eales and Unnevehr, Holt and Bishop, Beach and Holt, Moro and Sckokai, andmore recently Wong and McLaren. This provides a framework to analyze empiricallyconsumer’s marginal willingness to pay for particular commodities in a way that is consistentwith consumer theory. However, Shephard distance function is based on a proportionalrescaling of quantities consumed. While it is convenient to evaluate index numbers (seeDeaton), the Shephard distance function does not have “nice” aggregation properties (e.g., itis not meaningful to add proportions across scenarios when the evaluation point changes).Yet, the evaluation of complementarity of a system requires the evaluation of the “sum of its parts.” This suggests that the Shephard distance function is not well suited to this task. Whatis needed is a welfare measure that has “nice” aggregation properties so that it can provide adirect evaluation of the “sum of the parts”. A welfare measure with this property is  4Luenberger’s benefit function (Luenberger, 1992). On that basis, we develop our analysis of the consumer value of complementarity using Luenberger’s benefit function. The benefitfunction has the convenient feature of providing a measure of willingness to pay for goods,holding utility constant. Furthermore, the benefit function approach appears superior over thedistance function because it aggregates easily across consumers and across scenarios. Thismakes it particularly attractive in the analysis of consumption activities for heterogeneousconsumers, since the distance function approach is only applicable to a single representativeconsumer (Deaton; Barten and Bettendorf). In this context, we show that the benefit function provides a conceptual framework to conduct a welfare analysis of the value of complementarity in a system framework. The empirically tractability of the approach and itsusefulness are illustrated in an econometric application to fish consumption.The article is organized as follows. Section 2 presents a brief introduction of the benefit function, and its linkages with welfare analysis in a system framework. Section 3discusses the evaluation of complementarity based on Luenberger’s benefit function. Section4 proposes a flexible specification of the benefit function that provides a basis for our empirical analysis. Section 5 presents an econometric application to the Italian fisheries, withspecial attention given to dynamics. The investigation illustrates the importance of dynamics.Our results show that, while short-run fish demand is characterized by substitutionrelationships, complementarity does develop in the intermediate run and in the long run.   Finally, section 6 presents concluding remarks.
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