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Van Westendorp Price Sensitivity Analysis is currently one of the most common approaches to understanding price preferences in market research. Survey respondents are asked to report the prices at which they would feel a given product is 1) so cheap that they would doubt its quality, 2) is a good buy for the money, 3) expensive but is not out of the question, and 4) too expensive; the resulting data are then used to develop estimates of ‘acceptable’ and ‘optimal’ price ranges for the product. Though easy to implement, Van Westendorp has serious drawbacks in terms of the assumptions it requires and the kinds of inferences it can make. To circumvent these limitations, we propose a framework that leverages conjoint experimentation to deliver more rigorous pricing insights with fewer assumptions. 

This post walks through an original survey experiment comparing Van Westendorp to conjoint and offers insight into how to implement a conjoint-based pricing approach, either on its own or in conjunction with Van Westendorp. Using a well-known, mid-market denim retailer as the putative company, we randomly assigned 2,000 people in the U.S. to complete either a Van Westendorp question set about their jeans or a series of conjoint tasks evaluating profiles of said jeans, where price is varied alongside other characteristics. Below, we report the findings from this exercise and highlight the strengths of conjoint vis a vis Van Westendorp.

Limitations of Van Westendorp

Though the Van Westendorp (VW) framework is simple in that it relies on a limited set of intuitive questions, it is unlikely to accurately reflect how consumers actually respond to price in the market for the following reasons:  

Figure 1 below plots the results from the VW arm of our experiment. The derived range of acceptable prices for a putative pair of the company’s jeans ranges from $30 to $42, and the optimal price point is located at $33. The point of indifference is at $36, where the same proportion of customers feel that the product is getting too expensive as those who feel it is a bargain. These prices fall far below the standard range for a pair of the company’s jeans, which tend to range between $70 and $130 at full price. Nearly all respondents in our survey consider the lower bound of the real price range, $70, so expensive that they would not consider purchasing these jeans. And yet, the company has operated at this price point (adjusting for inflation) profitably for decades. Our data is weighted to Census values along a series of dimensions and does not skew exceptionally lower income such that we could attribute these low values to an artifact of sampling.

Figure 1: Van Westendorp Price Sensitivity Meter

These price ranges indeed cast doubt on respondents’ capacity to understand and accurately and honestly articulate price preferences. While people will, of course, try to go as low as they can with respect to price in an unconstrained setting, that is precisely the point: in addition to VW’s myriad other shortcomings, it also does not establish the constraints businesses face in pricing, including price floors. Moreover, a meaningful proportion of our sample assigned to the VW condition reported intransitive price preferences. Though these respondents are not included in the analysis above, they reveal that without forcing transitivity in the survey programming, reported price preferences are wont to be inconsistent and may not converge to reasonable distributions. It’s important to note that outside of this behavior, the respondents were otherwise attentive and offered high-quality responses, certainly in part due to our proprietary screening procedures. Given these limitations, we turn to demonstrating the comparative advantages of using conjoint experiments to understand price.

Leveraging randomization via conjoint experiments

Conjoint analysis measures the preference and importance that respondents place on the different elements of a product or service, represented in (typically) pairs of hypothetical profiles, among which respondents choose. Pricing analysis can be done via conjoint experiments through the inclusion of a price characteristic that varies across profiles. The conjoint framework does not make the same strong assumptions that Van Westendorp does about how people perceive, understand, and report price sensitivity. Below, a non-exhaustive list of its advantages: 

The price levels varied in the conjoint arm of our experiment were $50, $70, $90, and $110, reflecting the most common current price points based on a review of the company’s website across both the men’s and women’s sections. Additionally, each profile included information about the fit of the jeans (slim fit, straight leg, wide leg), their color (black, dark blue, light blue), and whether or not the jeans had rips as part of the style. These, of course, are common characteristics one would know about a pair of jeans in addition to their price.

Figure 2 below plots the average marginal component effects (AMCEs) of the jean attributes randomized in the conjoint condition. AMCEs represent the marginal effect of an attribute averaged over the joint distribution of the remaining attributes and are causally identified by virtue of the fact that attribute levels are randomly assigned to profiles (Hainmueller et al., 2014b). That is to say, randomization allows us to directly infer the causal effect of price on selection decisions – an impossibility in non-randomized pricing frameworks like VW. We can interpret each AMCE as the change in the probability of a profile being selected if a given attribute level is present in a profile, compared to a baseline attribute level. 

Of all attributes, differences in price levels are most notable. Compared to a $50 price point, a $110 price point leads to a 25 percentage point decrease in the probability of a jean being selected. A $90 and $70 price point lead to 14 and 8 percentage point decreases in the probability of a jean being selected, respectively. Perhaps most interestingly, a $70 price point leads to a relatively small decrease in demand compared to a $50 one, especially considering the suggestion of the Van Westendorp model that $70 is unacceptable for nearly all respondents. The other attributes of the jeans can be interpreted in the same way and may offer insight into the dimensions underpinning demand in addition to price. 

Figure 2: Average Marginal Effects of Conjoint Attributes

We can also evaluate the marginal means of the conjoint attributes instead of effects relative to an attribute’s baseline value, as in Figure 3. Marginal means (sometimes called ‘win rates’) have a direct interpretation as probabilities: a marginal mean of 0 means respondents choose profiles with that feature level with a probability of 0, and a marginal mean of 1 means they choose it with a probability of 1.¹ This presents a straightforward way to evaluate price elasticity, or how demand changes as price changes – something we cannot do with a Van Westendorp.

Figure 3: Marginal Means of Conjoint Attributes

We can likewise use the conjoint framework to evaluate how the effects of price change as different additional features of the product change, or how the effects of additional features change as price changes. Suppose this company was interested in how the effects of price vary across whether jeans have rips as a style feature, specifically whether people are less likely to pay higher prices when jeans have rips. We plot the effects of attributes, including price, by style in Figure 4 below. Evidently, whether jeans have rips or not has little bearing on preferences over price: the effects of prices are consistent across both attribute levels, and any slight differences between them are not statistically significant, as evidenced by the right-most pane of the figure. Powerfully, these interactions between features have causal interpretations due to the fact that all features are randomly assigned to profiles. In the same way, we could additionally subset conjoint analyses by respondent segments too and evaluate whether meaningful heterogeneity in price preferences exists across segments; while respondent-by-attribute interactions don’t yield causal inferences, they offer insight into what respondent characteristics predict certain price preferences.

Figure 4: Attribute Effects by Price

Possibilities for a conjoint-based pricing approach

We can also integrate a conjoint approach with a VW analysis, which might be especially useful when introducing new products. Indeed, we can use a VW analysis to elicit unprompted and unconstrained price evaluations in a first survey, and then pipe these into the pricing attributes – either as is or adjusted based on strategic considerations – into a conjoint experiment in a second survey. Even if price ranges are left unaltered, the conjoint framework still confers all of its aforementioned benefits, including the unique capacity to observe choices and estimate price elasticity. 

Similarly, we can use values from the third VW statement (“getting expensive, but not out of the question”) to derive a pseudo-demand curve to complement our conjoint estimates. A typical demand curve illustrates the proportion of people willing to pay $X or more for a product and moving down the curve allows us to identify how many additional people we can bring into the market by reducing price. Here, by plotting the cumulative distribution of that third statement we can make similar inferences. Figure 5 below plots an example using the VW arm of our experiment. Here, we see that around 25% of respondents say they would be willing to pay $50 or more for the jeans.

Figure 5: Pseudo-Demand Curve

Conclusion

Motivated by an original survey experiment, we have outlined the theoretical and empirical shortcomings of a Van Westendorp approach to pricing and the ways in which a conjoint design overcomes them. By randomly assigning attributes, including price, to product profiles, conjoint experiments are unique among pricing frameworks in allowing us to estimate the causal effects of price while offering added realism, predictive validity, capacity to estimate elasticity and insight into critical heterogeneities, whether of the effect of price by other attributes or by respondent segments, or both. A conjoint pricing framework can also make space for integration with Van Westendorp: the latter can be used to derive initial price ranges that are then piped into the former to generate unconstrained price ranges and then observe their performance in a more powerful setting. 

References

Hainmueller, J., Hangartner, D., & Yamamoto, T. (2014a). Do survey experiments capture real-world behavior? External validation of conjoint and vignette analyses with a natural experiment. Proceedings of the National Academy of Sciences, 112(8), 2395-2400.

Hainmueller, J., Hopkins, D. J., & Yamamoto, T. (2014b). Causal inference in conjoint analysis: Understanding multidimensional choices via stated preference experiments. Political analysis, 22(1), 1-30.

¹Because our 4 price levels can co-occur across a pair of profiles (for instance, it is possible to see $50 in both profiles in one task), our actual range for this attribute can only vary between (¼)*(¼) = 0.06 and 1-0.06 = 0.94.

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