I have been discussing with colleagues a recent article in the American Journal of Agricultural Economics, Zhen, et al. on Predicting the Effect of Sugar-Sweetened Beverage Taxes on Food and Beverage Demand in a Large Demand System. One issue we discussed was whether diet and sugar sodas were complements or substitutes. As a reminder, substitutes means that as one price goes up, people buy more of the other product. A complement means that that as one price goes up, people buy less of both goods.
Are they substitutes or complements? I would suggest that it’s an empirical question. Zhen, et al. mention research that finds that the two types of sodas are complements (Dharmasena and Capps, 2012, for those playing at home).
If someone is buying diet soda, I would not expect the prices to affect their decision within the ranges of price movements we usually see. Price may lead them to switch to other low-calorie drinks (water, tea) or other diet foods, but the significant calories in a sugar soda probably represent large dis-utility to the diet-conscious consumer. On the other hand, consumers of sugar drinks have already rejected the diet drinks and probably switch to other good-tasting drinks (energy drinks, flavoured milk).
Me, I can’t stand diet drinks and price won’t make me switch. I will drink water instead.
We could also think about the purchase scenario. When consumers buy soft drinks, perhaps they are buying them for a group: a family or a party. They buy both diet and sugar drinks to cater to the different tastes in the group. Higher and lower prices change the total amounts but have little effect on the ratio.
There are two methodological issues that can affect these sorts of estimates. First, there is significant correlation in the diet and sugar soft drink prices. Companies tend to price both types the same. That correlation would make it difficult (or perhaps impossible) to estimate cross-price elasticities (XPE). Secondly, a common assumption is that XPEs are symmetric. That is, the diet–> sugar XPE is the same as the sugar–> diet XPE. That may not be the case. A diet drinker may be reluctant to change, but a sugar drinker may be quite price sensitive. If we assume symmetry (which is common) then we won’t estimate the different XPEs.