MIT utility function the value of each “util” is about $2.46,

 http://www.mit.edu/~hauser/Papers/NoteonConjointAnalysis.pdf


N C O U R S E W A R E > P. 1 Note on Conjoint Analysis John R. Hauser Suppose that you are working for one of the primary brands of global positioning systems (GPSs). A GPS device receives signals from satellites and, based on those signals, it can calculate its location and altitude. This information is displayed either as text (latitude, longitude, and altitude), as a position relative to a known object (waypoint), or, increasingly, a position on a map or navigational chart. GPSs come in many versions. Some mount in cars and trucks and provide driving directions. Others are used in navigation on the oceans or lakes. And some are handheld, useful for hiking, camping, canoeing, kayaking, or just walking around the city. We will suppose that it is your job to decide which features the new handheld GPS will have. Each feature is costly to include. Including the feature will be profitable if the consumers’ willingness to pay (WTP) for that feature exceeds the cost of including that feature by a comfortable margin. Simplified Conjoint Analysis Illustration We’ll simplify the problem for illustration. First, let’s assume that all consumers have the same preferences – the same WTP for each feature. This assumption does not hold in real markets, hence we will have to consider pref- M I T S L O A N C O U R S E W A R E > P. 2 erences either by segment or as some distribution across all potential consumers. We do this by estimating a conjoint model for each consumer or by estimating how WTP varies across consumers. Second, let’s assume that there are no engineering constraints. The GPS can have all of the features or none of the features and the costs are additive. Finally, we will assume there are only three features of interest, plus price: • Accuracy – the GPS can locate your position within either 10 feet or 50 feet • Display color – the screen either displays colors (for a map) or is black & white • Battery life – the battery lasts either 12 hours or 32 hours • Price – the price can vary between $250 and $350 With four things varying (3 features plus price), at two levels each, there are 2x2x2x2 = 24 = 16 possible combinations. Suppose that we create pictures of each of the sixteen GPSs and have consumers evaluate all sixteen GPS “profiles.” They might rate each potential GPS on a 100-point scale where 100 means most preferred. This is a rudimentary conjoint analysis task. Naturally, great care would be taken to make sure that consumers understood the features and that the task were realistic. (We show examples later in this note.) The data, for a single consumer, might look like that in Table 1. The first column indicates the consumer’s preference for a particular combination of features and price. (These are the data as indicated by italics.) The next four columns indicate whether or not the rated GPS has that feature-price combination. A ‘1’ indicates the feature is at its “high” level, e.g., 10 feet rather than 50 feet, and a ‘0’ indicates a feature is at its “low” level, e.g., 50 feet rather than 10 feet. Not surprisingly, the data (‘4’) indicate that consumer prefers least an inaccurate GPS, with low battery life, a B&W screen, and priced at $350. The data suggest (‘99’) that the same consumer prefers most an accurate GPS, with a long battery life, a color screen, and priced at $250. M I T S L O A N C O U R S E W A R E > P. 3 Table 1. Preference Ratings for 16 Handheld GPSs Preference Accuracy Battery Color Price Rating 10 vs. 50 feet 32 vs. 12 hrs Color vs. B&W $250 vs. $350 4 0 0 0 0 41 0 0 0 1 18 0 0 1 0 60 0 0 1 1 33 0 1 0 0 74 0 1 0 1 49 0 1 1 0 86 0 1 1 1 11 1 0 0 0 55 1 0 0 1 27 1 0 1 0 66 1 0 1 1 41 1 1 0 0 85 1 1 0 1 58 1 1 1 0 99 1 1 1 1 The goal of conjoint analysis is to determine how much each feature contributes to overall preference. This contribution is called the “partworth” of the feature. In this rudimentary conjoint analysis, we can use ordinary leastsquares (OLS) regression as is available in Excel under tools/data analysis/regression. 1 An abridged output is shown below. The partworths are the regression coefficients. For example, the partworth of 10 feet (vs. 50 feet) is 9.6 indicating that the consumer gets 9.6 “utils” if the accuracy of the GPS is improved. Similarly, the regression estimates that the consumer gets 40.6 “utils” if the price is reduced from $350 to $250.2 Table 2. Regression to Estimate Partworths for Features and Price Coefficients Standard Error t-statistic Intercept 2.7 1.0 2.7 10 feet vs. 50 feet 9.6 0.9 10.9 32 vs. 12 hours 30.4 0.9 34.5 Color vs. B&W 14.9 0.9 16.9 $250 vs. $350 40.6 0.9 46.1 1 You may need first to add the Analysis ToolPak under the tools/add-ins menu. 2 Statistically, the regression does quite well. The R2 is 0.99 and all coefficients are highly significant as indicated by their high t-statistics. M I T S L O A N C O U R S E W A R E > P. 4 With this regression we compute the consumer’s willingness to pay (WTP) for each feature. Because the consumer gets 40.6 “utils” when the price is reduced by $100 ($350 Æ $250), the value of each “util” is about $2.46, which we obtain by comparing the difference in price to the difference in the price-partworths: $100/40.6. We now compute the WTP for accuracy. It is approximately $23.65, which we as obtained by (9.6 utils)*($2.46/util). Similarly, the WTP for increased batter life is $74.88 and the WTP for a color screen is $36.70. These partworths are approximate rather than exact numbers because there is measurement error when the consumer provides his or her preferences on the questionnaire. This measurement error translates into uncertainty in the estimates of the partworths as indicated by their standard errors. Nonetheless, if we asked enough consumers to complete a conjoint analysis exercise, we could gain greater statistical power and obtain estimates of the partworths that are more accurate.