Illustration by James Yang

For decades corporations have struggled to predict consumer behavior. A key element of tactical marketing has been the analysis of how changing the price of one product affects the sales of competitors. For example, if Crest slashes the price of its toothpaste by 10 percent, Colgate's market share may shrink by 5 percent. But the market share of Aim, which is favored by children, may not be as sensitive to Crest's price reduction.
       It sounds simple, but assessing the effects has been tricky. Marketers want to know the magnitude of these price effects and whether there is any pattern to them. "For business people this concept, known as cross-price elasticity, is central because it tells them how competitive various products are," says V. "Seenu" Srinivasan, the Ernest C. Arbuckle Professor of Marketing and Management Science.
       The numbers are very hard to estimate because there are so many things going on at the same time. Typically, multiple products are changing prices all at once. "It's very hard to tease out what exactly is happening," says Srinivasan. So far, the preferred method of measuring these cross-price elasticities has been econometric analysis, which involves tracking the market shares of different brands, observing the prices, and relating the two. Unfortunately, this method turns up incorrect answers a significant portion of the time.
       A different type of analysis developed by marketers examines so-called row-conditional brand-switching probability, which measures the amount of switching between brands. For example, of all those who bought Colgate last time, what fraction of people will buy Crest next time? Supermarket scanner panel data is used to track buying. The difficulty with this approach is that it reveals switching patterns but it doesn't provide explicit information about the effect of price discounts.
       However, Srinivasan, working with Randolph Bucklin, associate professor of marketing at UCLA's Anderson School of Management, and Gary Russell, associate professor of marketing at the College of Business Administration at the University of Iowa, has developed a new theory to assess competition more accurately. For the first time, the three researchers have connected the economic analysis of cross-price effects with the marketing analysis of brand-switching probabilities. The researchers discovered that under certain realistic assumptions, cross-price elasticities are exactly proportional to row-conditional brand-switching probabilities.
       The new theory gives marketers much more flexibility and precision. "It opens up a whole lot of possibilities for marketing," says Srinivasan. "We can show there is this theoretical connection and we can demonstrate it's true with real data." Indeed, the researchers demonstrated their theory using data from real marketing databases.
       For instance, using data from the liquid laundry detergent market, Bucklin, Russell, and Srinivasan showed that if Tide decreases its price by 10 percent, then the market share of Wisk will go down by 3.1 percent. On the other hand, if All were to drop its price 10 percent, Wisk's share would slip 0.8 percent. ("All does not have that much effect because it is a low-share brand," says Srinivasan.) Then they presented data showing that of those who purchased Wisk last time, 15.6 percent purchased Tide and only 4.6 percent of them bought All. Since the ratio of 15.6 to 4.6 is approximately equal to the ratio of 3.1 to 0.8, the researchers found that there is a high correlation between switching probabilities and the cost-price elasticities.
       "Intuitively you can see a connection between them, but mathematically it hasn't been shown before," says Srinivasan. "Using this theory together with traditional econometric methods you can get results that are much more accurate than just using econometric methods."

--Barbara Buell

"A Relationship Between Market-Share Elasticities and Brand-Switching Probabilities," Randolph E. Bucklin, Gary J. Russell, and V. Srinivasan, Journal of Marketing Research, Vol. 35, February 1998