Ambiguity of measured WTP for quality improvements when quantity is unconstrained: a note

1. Introduction

The use of contingent valuation (CV) to measure willingness-to-pay (WTP) for public goods has increased greatly in the last three decades. CV techniques are therefore a tempting methodological option when evaluating consumers' attitudes towards new goods, especially when they incorporate some quality change or an environmental improvement, as in the case of an organic product. Nevertheless, we argue that when the CV technique is used to evaluate a new consumer good, more attention should be paid to differences between the theoretical and empirical background of this case and the context in which the technique is used for valuing environmental goods.

In one of the most usual settings where CV is applied to environmental goods, respondents are presented with a choice between a lump sum payment and a given change in the quantity or quality of the environmental good. CV is an appropriate approach for assessing the benefits from a particular scheme, or from any proposed change either in quality for a given quantity, or in the available quantity of the environmental good, since in these cases the trade-off is determined. However, the setting is different when it concerns market goods whose quantity can be freely chosen by consumers. In this latter case, consumers' WTP cannot be assessed if respondents are asked the maximum price they are willing to pay without further qualification. The question ‘How many euros per kilogram (or how many euros per kilogram more, relative to the standard product) would you pay for this organic product?’ seems at first sight a sensible way to assess consumers' WTP for an organic product. But it should be immediately followed by the question ‘For how many kilograms?’. It makes a difference to the price one is prepared to pay if organic products will be bought every day or once a month.

In the literature, this issue seems to be almost totally ignored. A number of papers have dealt with consumer attitudes towards organic products and safe food in a broader sense (Thompson (1998) provides a detailed review of US studies on consumer demand for organic produce). A first stream of literature (e.g. Huang, 1996; Thompson and Kidwell, 1998) simply analysed consumer preferences for organic produce in connection with their willingness to accept sensory defects, but did not quantify their WTP. A second group of papers assessed consumers' willingness to pay a premium (in terms of an absolute or percentage increase in price) for organic or safer products, without computing WTP measures (e.g. Ott, 1990; Weaver et al., 1992; Underhill and Figueroa, 1996; Govindasamy and Italia, 1999; Wessells et al., 1999). Some studies make more explicit reference to the environmental CV literature and estimate WTP measures based on a common framework: consumers are given a reference price for the baseline good and are asked to state their willingness to pay a premium, using open-ended or single- or double-bounded elicitation formats (Mullen and Wohlgenant, 1991; Henson, 1996; Fu et al., 1999; Boland et al., 1999; Loureiro and Hine, 2002; Gil et al., 2000). The common feature of this literature is that it is silent as to the quantity involved, and simply asks the price, or the premium relative to the regular quality, that consumers are willing to pay (an exception is Henson, 1996, whose interview specified that the reference quantity was the usual yearly consumption of the base quality). In these papers, nevertheless, respondents were given the choice between two qualities at different prices, so the quantity is implicitly defined; moreover, they were only given a constrained, take-or-leave-it choice,¹ and the possibility of consumers consuming both the standard and the improved quality, or buying only the improved one, but in a different quantity, was ignored.²

The problem in general terms is that asking the price the consumer is willing to pay for a good for which he can decide the quantity purchased means asking his marginal WTP, which is contingent on the quantity purchased, and not the overall WTP for a given change in quantity (or for a change in quality, for a given quantity) of the good. When consumers are free to choose the quantity of the old and of the new product, asking the price they are willing to pay for the new quality is at best ambiguous, since the relevant quantity is undefined. This applies to all new products that do not completely substitute for the previously available good, and that can be consumed along with it, or when the change concerns the quality of a good, but the individual is free to adjust the purchased quantity. This is the case when an environmental quality improvement is embodied in a market good such as an organic product, and more generally to all goods whose quantity can be freely chosen.

The main goal of this paper is to discuss theoretically the issue of the exact meaning of WTP for a quality change when measured with reference to the price of a market good whose quantity can be freely adjusted. This is done in Section 2. The estimation issues involved in such situations are discussed in Section 3, Section 4 presents some conclusions.

2. Theoretical issues

The main argument made in this paper is that the price consumers are willing to pay for a characteristic embodied in a good that is purchased in unconstrained quantities is not a fixed value, but depends on the purchased quantity. The discussion will therefore for simplicity focus on a single characteristic of a good, which is the object of interest of most of the above literature. First, divisible goods will be examined.

It is convenient to begin by recalling why WTP expressed in terms of price depends on quantity. Consider the standard problem of a consumer maximising his utility, u = u (X), subject to M = PX, where X is a vector of divisible market goods, P is the relevant price vector and M is income. The solution of the dual to this problem yields the expenditure function e = e(P, u(X)) = M, showing the expenditure on the optimal bundle corresponding to each price configuration. The marginal WTP for x_i, an element of X, (MWTP(x_i)), indicates how much the consumer is willing to pay for a marginal increase in the quantity of the good. MWTP(x_i) is obtained by differentiating e(·) with respect to x_i. Thus, MWTP(x_i) = ∂e/∂x_i = ∂M/∂x_i = p_i. Since for normal goods ∂p_i/∂x_i < 0, also ∂MWTP(x_i) /∂x_i < 0.

It is also convenient to analyse first the issue of WTP for an existing product, and to follow with the analysis of the introduction of a new product. To start with, in the above literature some studies ask consumers what price they are willing to pay for a given product, others ask what premium they are willing to pay for a certain quality, relative to the price of some ‘regular’ quality. These are two conceptually different questions. If WTP is asked in terms of price for the product per se, then the consideration above applies: the price consumers are willing to pay is their MWTP, which is contingent on the chosen quantity. If the WTP is asked in terms of a price premium for a particular quality embodied in a market good, the implicit assumption is that there is a price difference attached to the particular quality relative to the standard product. This is tantamount to assessing the WTP in terms of the price for that particular quality. The question is therefore whether this price difference depends on the purchased quantity of the good. To assess WTP for a particular quality b embodied in a market good, additional assumptions about the nature of the quality are needed. Assume, first, that the quality is peculiar to the market good x₁ only, and is linked to it by a linear consumption technology relationship b = αx₁, where α is fixed. Assume the utility function is u = (b, X), where X is the vector of all market goods other than x₁, which is maximised subject to M = p₁x₁ + PX, where P is now the price vector of all market goods other than x₁. The expenditure function is then e = e(p₁, P, α, u). The marginal WTP for the quality (MWTP(b)) is obtained by differentiating the expenditure function with respect to b: MWTP(b) = ∂e/∂b = ∂M/∂b = p₁/α, which states the obvious point that to obtain an additional unit of b the consumer has to buy additional units of x₁, each containing 1/α of b. Again, if the good embodying b is a normal good, ∂MWTP(b)/∂b < 0. It is apparent that if different market goods x_i embody b in different technical linear relationships α_i, and no other quality embodied in x_i enters the utility function, then only the good with the lowest p₁/α ratio will be chosen. In this case, assessing WTP for the quality is equivalent to assessing WTP for the good itself divided by α. An example might be the vitamins contained in different quantities in various pills: a perfectly informed consumer only interested in vitamins will choose the pill with the lowest price per vitamin (when excluding thresholds and dosage problems). This also applies when a consumer attaches a subjective evaluation of quality to different brands and utility is derived from both quantity and perceived quality of consumption (Chiang, 1991).

More often, different divisible goods may include a quality that cannot be described by a linear consumption technology, for example because the quality cannot be exactly measured or because it summarises many features (such as tastiness or healthiness of a food). Goods possessing the relevant quality in different, but not measurable, forms, or possessing similar qualities to different extents, can be treated as substitutes, each with a specific demand function.³ Then assessing WTP for a particular quality should be based on a comparison between the relevant quality and a baseline quality. For instance, consider a high-quality wine and an ordinary wine, and assume one wants to measure WTP for the superior quality in terms of price. It should be measured as the difference between MWTP for the high quality and MWTP for the ordinary wine. Since MWTP is contingent on the quantity, MWTP for the higher quality could be constant only if the demand curves of the two wines were parallel, and there is no compelling theoretical reason why they should be. Therefore, MWTP for a quality attribute embodied in a good is also contingent on the quantity of that particular good.

In many cases, one wants to analyse prospective consumers' reactions to the introduction of a new quality good. If a new quality is introduced, two different cases are possible: either the product embodying the new quality is introduced along with the old product, or it substitutes for the old product. Assume the new quality product is introduced but the old one remains available. If the new and the old quality do not depend on a linear consumption technology,⁴ then the new quality good can be considered as a substitute good enlarging the consumer's choice set. The demand curve of the old good shifts, and a demand curve for the new good emerges. Consumers will optimally choose the quantity of the old and of the new good, depending on prices, income and tastes. MWTP for the old and the new quality goods depends on the chosen quantities. If a researcher is interested in predicting consumers' reactions to the introduction of a new quality in a market good, asking which price the consumer would be willing to pay for the new product yields an undetermined response, unless a quantity is set. If consumers are asked to state which price they would pay for a new good without specifying the quantity and they are free to adjust the purchased quantity, there is an infinite number of responses to this question: unless consumers have a total aversion towards the new quality, for any newly chosen positive quantity of the new good there will always be a price low enough to induce them to choose it. Choosing a different quantity of the new good would lead to a different maximum price consumers are prepared to pay for it. A consumer might therefore state a price having in mind how much he would pay for the same quantity as the old good, thus revealing his MWTP for that quantity. But if he responds with the idea of buying some quantity of the new product, and not necessarily the same of the old, no information on his demand curve is gathered except his reservation price. If no quantity is specified, answers will probably reflect a mixture of both interpretations. In addition, an elicitation question asked in terms of the price premium for the new quality, taking the old quality as the baseline, is even more questionable, since the MWTP for the old good is to change following the shift in its demand curve.

The DE function is decreasing in p₁, since e₁ is increasing in p₁ and p₁ is not an argument in e₀. For a given price p₁^r1, the DE reduces to zero and, for any p₁ > p₁^r1, the DE remains zero: the consumer would simply buy the same quantity of the old product, and none of the new one. Hence, p₁^r1, the reservation price, is the maximum price consumers are willing to pay for the new product. The condition for a consumer to buy a strictly positive quantity of the new product is p₁ < p₁^r1. Since p₁^r1 is the price for which the expenditure functions with and without the new product are equal, i.e. the level of p₁ for which the DE is equal to zero, if one is able to estimate d(·), p₁^r1 can be recovered by setting d(·) to zero and solving for p₁. Notice that the reservation price p₁^r1 is a function, among other variables, also of the price of the old product.

The second possibility is that the new product replaces the old one. Then the demand curve shifts, due to the quality change. If the quality cannot be described by a linear consumption technology,⁶ the choice for the consumer is how much to buy of the new product, if any. Since the old product is no longer available, the reference utility is the one reached when neither the old nor the new one are available (call it v_n), as compared to the utility when the new product is available. The relevant expenditures are in this case e₀(P, v_n(P, s, M)) and e₁(P, p₁, v_n(P, p₁, s, M)), where p₀ is no longer an argument in either, and the conditions for purchase remain d(·) >0, or p₁ < p₁^r2, where p₁^r2 is the reservation price for this situation. In this case, p₁^r2 is not a function of the price of the old product, which is no longer available.⁷

Since the price consumers are willing to pay depends on the quantity chosen, the new demand curve should be estimated to assess how much they would pay for different quantities. A researcher might then set a particular quantity chosen for the product in asking the question (e.g. ‘How much would you be willing to pay if you were to buy a quantity X?’, or, equivalently, ‘How much would you buy of this product if the price were Y?’). Different quantities should be prompted in the elicitation question (or, equivalently, the quantities respondents would buy for different prices of the new good should be asked).⁸ If consumers are asked to state how much they would pay for a given quantity of the new product, the response is the value of the inverse demand function of the new product evaluated at the relevant quantity.

The consumer will buy q₁⁰ rather than q₀⁰ if WTP(·) > 0.⁹ To assess the maximum price the consumer is willing to pay for the change, conditional on choosing q₁⁰, consider that when the WTP is equal to zero, the consumer is indifferent between buying q₀⁰ of the old product and buying q₁⁰ of the new one. Hence, if one is able to estimate the WTP function, by setting the WTP function to zero and solving for p₁, one can recover the quantity-constrained reservation price (p₁^*1) consumers are willing to pay for buying quantity q₁⁰ of the new product. The condition for a consumer to buy the quantity q₁⁰ of the new product can also be expressed as p₁ < p₁^*1. Hence, p₁^*1 identifies the point on the new demand curve corresponding to q₁⁰. In other words, p₁^*1 is the MWTP corresponding to q₁⁰.

The condition for choosing to consume q₁⁰ rather than nothing is WTP(·) > 0, or p₁ < p₁^*2, where p₁^*2 is the constrained reservation price obtained by setting WTP(·) to zero and solving for p₁. Again, p₁^*2 identifies the point on the new demand curve corresponding to q₁⁰. Unlike p₁^*1, p₁^*2 is not a function of p₀.

These considerations help to clarify the problems with the current literature on WTP for a new product or for a quality improvement of a market good. Studies in the literature are usually silent as to the quantity involved, and simply ask the price, or the premium relative to the regular quality, that consumers are willing to pay. The problems are (i) it is unclear whether p₁^r or p₁^* is the variable of interest, and responses are most likely a mixture of both, (ii) if the variable of interest is p₁^r, then it should be made clear that what is asked is the price for which consumption becomes zero, (iii) if it is p₁^*, then the relevant quantity should be specified, (iv) whether the new good totally replaces the old one or not should be specified, since this makes the difference between p₁^r1 and p₁^r2, and between p₁^*1 and p₁^*2, (v) when asking the WTP in terms of a price premium, the usual approach disregards the shift in the demand curve of the old product and (vi) even when the quantity is implicitly set at the existing level of the old good, when p₁^* is estimated it only identifies the point on the demand curve corresponding to q₁⁰.

Whether the issue of quantity adjustments to quality changes, or to new goods embodying quality changes, is relevant, and to what extent, depends on the specific case. It is certainly relevant in the case of divisible goods that are purchased by weight, such as fruits, vegetables, beef at the butcher's and so on, since quantity adjustments are possible and costless. In other cases, the critical issues are whether or not a quantity adjustment is possible for the consumer, and, if it is, whether or not he actually does adjust purchased quantity in the light of changes in quality. In most cases examined in the environmental valuation literature, no quantity adjustment is possible, quality levels are mutually exclusive and a only a yes–no choice is possible. An example is in the classic paper by Bishop and Heberlein (1979) on WTP for early season goose-hunting permits, where hunters can only purchase (or not purchase) one hunting permit. A similar case occurs with durable consumer goods like cars, refrigerators and so on. Though there is no impediment to purchasing more than one item, consumers usually decide whether to purchase a car, and which one, not how many cars and for all practical purposes this case can be treated as a yes–no choice. For such discrete goods, the marginal WTP is not defined, due to the discontinuity. Rather, total WTP for a quality change is determined as the DE function evaluated without and with the relevant change (i.e. the compensating measure for the change, if the ‘without’ situation is the reference utility). If the choice is between purchasing one unit or nothing, total WTP is obviously the unit price the consumer would be willing to pay. Responses to an elicitation question in terms of price therefore do identify consumers' behaviour. By definition, the quality change cannot involve any quantity change but the 0–1 shift. These are the situations in which the discrete choice random utility models (RUM) (McFadden, 1974) have been typically applied.

In some cases for non-durable market goods also it can be assumed that the quantity is fixed to one, and the discrete choice RUM framework can be used. This is when the choice is discrete and mutually exclusive among different brands at every purchase occasion (e.g. weekly purchase of detergent). Utility in the RUM framework is assumed to have a deterministic component (characteristics of the different brands, including the price, and consumers' characteristics), and a random component, so that choices are not necessarily the same on different purchase occasions. The crucial point is that, to assess WTP for a particular brand in terms of price, the quantity purchased must be fixed, regardless of the characteristics, which also implies that the different brands are mutually exclusive. One should therefore be careful in defining purchase occasions and in assuming that the purchased quantity is fixed, particularly when the interest is in predicting consumers' reactions to a new product. In particular, if a new, higher quality and more expensive good becomes available, a consumer might deliberately decide to buy it once in a while, and to buy the usual good the rest of the time. In this case, the consumer does not make different choices in the different purchase occasions as a result of the stochastic nature of the utility function, but as a rational, deliberate choice (possibly with random components as well).¹⁰ Arguably, this might be a relevant issue particularly for non-durable market goods sold in discrete quantities, such as many foods and wine. The different brands may be mutually exclusive on a single purchase occasion, but this does not rule out the possibility of choosing the optimal brand bundle over a longer time span. If this is the case, then measuring WTP for the higher quality good in terms of its price (or of its price premium) would suffer the same problems identified above.

3. Estimation issues

There remains the issue of analysing market behaviour concerning market goods that either are continuously divisible goods, or are not mutually exclusive with respect to other goods on each purchase occasion, or whose purchase is planned over more than one purchase occasion so that quantity adjustments are at work over a time period. This more generally covers all situations in which variations in the aggregate demand are all not only due to shifts at the extensive margin where individuals are shifting from one alternative to another, but also at the intensive margin (McFadden, 1974). When a new quality good is introduced, one ideally would need to estimate its demand function to make predictions on consumption levels at different prices. With an estimated demand function, one is able to determine the MWTP for any desired quantity level (p*) and, provided the good is not essential, its reservation price (p^r). Of course, since it is impossible to estimate the demand function for the new good from actual market data, stated preference techniques have to be used.¹¹ Estimates of the demand functions can be obtained by asking consumers how much of the old and of the new product they would buy at different prices, provided that enough variation in prices is ensured. Alternatively, respondents might be asked to state the maximum price they would be willing to pay for given quantities, though the former format is probably much more familiar to consumers. Note that the two formats are based on alternative assumptions about the origin of the random disturbance (demand or MWTP). Blend and van Ravenswaay (1999) and Burrell (2002) use open-ended questions on the quantities that would be purchased of both the regular and the new product at given prices of both to estimate demand functions. Open-ended responses in terms of quantity directly reveal the points on the individual demand functions corresponding to the prospected prices. However, in the environmental valuation literature the open-ended format has been questioned on several grounds. Some of the problems of the open-ended format are linked to the public good nature of environmental goods, and do not apply to market goods, e.g. incentive compatibility. Nevertheless, some problems may remain with an open-ended format, due to the cognitive effort required to give a precise response about the quantity of a divisible good that would be purchased. A closed-ended format may then be an alternative, and using the same approach the question could be formulated as a dichotomous choice (such as ‘If the price of the old and of the new products were p₀ and p₁, would you buy at least quantity y₀ of the new product?’). If the demand function is assumed to have a deterministic and a random component such that y = f(P, p₀, p₁, s, M) + e, where y is the demand, then the probability of a ‘yes’ response to proposed prices p₀ and p₁ and quantity y₀ is Pr(yes) = Pr[y₀ − f(P, p₀, p₁, s, M) < e]. By assuming a statistical density function for e, the demand function can be estimated by maximum likelihood methods. Since a dichotomous choice response brings forth less information than an open-ended format, the number of questionnaires must be substantially larger than when using an open-ended format.

A different approach was taken by Sanogo and Masters (2002), who estimated the WTP for a quality change taking into account the quantity–quality trade-off. They set an experiment in which respondents were given a quantity of a good and were allowed to trade it for a larger quantity of a lower-quality good. Dividing the market value of the former (pq) by the quantity accepted determines the price p' of the lower-quality good and the difference (p − p') can be used to estimate the WTP for the characteristics differentiating the two goods. Nevertheless, as these authors noted, this is only an approximation of the WTP, since the marginal WTP for the higher-quality good is assumed to be its price, which is only true if it is actually purchased, and not given as in this case. Moreover, even if the lower-quality good is actually purchased, when a new substitute product becomes available, the demand for the former shifts and this modifies its marginal WTP.

Stated choice (SC) methods (Louviere et al., 2000) are now a popular alternative to CV in the environmental valuation literature and have also been used in the marketing literature. This methodology is typically employed for discrete choice situations, since its core is the preference revealed by choices between alternatives. Therefore, it suits the analysis of choices among mutually exclusive goods with different characteristics on single purchase occasions very well. Though different qualities of a market good are discrete characteristics, it is not immediately evident how different purchased quantities could be treated as characteristics. Sometimes package size has been introduced as a choice characteristic in marketing studies using SC methods (Louviere et al., 2000, Ch. 10), but as a mode of purchase linked to deal-proneness rather than as a measure of quantity. The essence of the method is comparing choices between discrete alternatives and choices must be mutually exclusive, exhaustive and of a finite number (Train, 2003). One might consider each quantity–price combination as an alternative, but if the relevant good is continuous and quantity can be adjusted, then the number of alternatives is infinity. Only when the good is discrete and there is a finite number of price–quantity alternatives (not a frequent situation) can SC methods be used, since each of them is a mutually exclusive choice. We note nevertheless that in these cases the usual assumption of a linear utility function cannot be maintained. Take the simplest case of a good x possessing characteristic b, such that b = αx, and assume a linear utility finction u = β₁b + β₂ (M − px) = β̇₁αx + β₂ (M − px), where M is income and p the price of the good, so that (M − px) is expenditure on other goods. Assume further there is a finite number (J) of x_i and p_i price–quantity alternatives. Then the marginal WTP is −β₁/β₂ for any price–quantity alternative, a highly unrealistic assumption since it would imply constant MWTP, i.e. a horizontal demand curve. Models allowing for non-linear utility (Hensher, 1998) should then be used. Overall, there seems to be limited scope for SC methods when quantity can be adjusted, while it remains a useful tool when analysing mutually exclusive choices in single purchase occasions.

A further alternative is estimating the DE function (Corsi and Novelli, 2003). In this study, by adding random components to the DE function for a new product when the old one remains available (equation (3)) and to the WTP function when consumers are constrained at the old consumption level (equation (6)), the functions are estimated by maximum likelihood techniques. Then, setting them to zero, p^r1 and p^*1 are obtained. With the estimated DE equation, the percentage of consumers that, at different price levels, are likely to purchase some organic beef is also estimated.

Estimation of the DE function provides less information than estimation of the demand function for the new good. Both methods allow estimation of the reservation price of the new good (p^r) and of the maximum price consumers would be willing to pay for a given quantity (p*). However, estimation of the demand function provides in addition an estimate of the overall quantity consumers would buy for any price of interest, while estimation of the DE function only allows an estimate of the share of consumers likely to buy a positive quantity of the good at any price of interest, which is obviously less informative. Nevertheless, the DE function approach has some merit, especially in terms of the lower cognitive effort required of respondents. When a new product is proposed, assessing it hypothetically and deciding what quantity to buy of both the old and the new product requires a strong cognitive effort from respondents.¹² When the new product is a close substitute for an existing product, it is much easier for respondents to take former consumption as a reference, and to decide whether they would buy the same, a greater or a smaller quantity of the new product, or nothing at all. There is probably a trade-off here between the reduced information that can be obtained with the DE approach and the accuracy of responses that could be gathered with the alternative approach of estimating the demand function. The survey instrument can also be important, since a telephone survey requires easy-to-answer questions, while personal interviews are probably needed to secure reliable responses to detailed questions on the quantities consumers would purchase at different prices.

4. Summary and conclusions

This paper discussed the issue of how to estimate the maximum price consumers are willing to pay, and how to predict consumers' behaviour, when a quality improvement is embodied in a market good and consumers can adjust the quantity purchased. It has been argued that current practice, which typically does not specify a quantity when asking consumers the price they are willing to pay for a new quality product, fails to identify consumers' likely behaviour. The situations in which, and the extent to which, the issue of quantity adjustment as a reaction to quality changes applies is a matter of empirical analysis. It is nevertheless clear that it is the researcher who has to show whether, in the specific case to be analysed, quantity adjustments are possible or not.

The discussion covered both theoretical and econometric approaches for assessing through stated preferences methods the likely behaviour of consumers facing a new quality of product. Whatever approach is chosen, it has, nevertheless, to be stressed that from a theoretical and methodological point of view, when the quantity of the good for which WTP has to be evaluated can be adjusted by consumers, the traditional setting of CV has to be adapted. This mainly concerns market analyses, but it has also more general implications for the evaluation of environmental goods, and it should be taken into consideration whenever the trade-off is not between a given change in quality of the environmental good and a lump sum or a price change keeping quantity constant, but rather between a change in the quality of the environmental good and a change in its price, allowing for quantity changes.

Acknowledgements

I wish to thank the editor and three referees, who provided valuable comments and advice that greatly improved the paper. Remaining errors are obviously mine.

References