Figure 5 illustrates the effects of the price changes implied by an optimal constrained micro-marketing pricing strategy with a moderate prior. Each boxplot denotes the store-level price changes for each product. To illustrate the effects of these price changes consider Minute Maid 64 Oz. In over 75% of the stores we would want to increase the price of this product. Certain products have very broad ranges in price movements, like Florida Natural in which the prices in some stores are increased by 10% and others are decreased by 10%. Although it is possible for the average price for any particular product across stores to increase, the revenue and average price across products within a store must remain constant due to our constraints.

Figure: Boxplots of Constrained Optimal Price Changes Across Stores

In section 5 we discussed the sensitivity to the prior in terms of out-of-sample predictions. In this section we can use a more natural metric, profits, to evaluate the sensitivity of the posterior to changes in the prior. It is clear from Table 7 that the posterior is sensitive to changes in the prior, as our prior becomes weaker the store specific differences grow and we find larger store-level demand differences. Yet whatever the strength of our prior beliefs, we still reach the same substantive conclusions that store-level differences in price sensitivity can be measured and translated into profitable micro-marketing strategies.