The profits from the optimal constrained and unconstrained pricing strategies are reported in Table 7 for each prior. The constrained strategy holds average store price and revenues to their values under a uniform strategy. We also add a bound of 10% on any price changes, to guarantee that any solution will be in a relevant range. This bound reflects the price range the retailer was willing to entertain in controlled experiments. These optimal values are computed numerically using the NAG subroutine E04VCF since an analytical solution to the optimal price is not known for this model. The column titled ``Uniform Chain Pricing Strategy'' are those profits earned by the retailer following an identical pricing strategy in each store. Whereas the column titled ``Micro-Marketing Pricing Strategy'' are those earned by the retailer when the price solution for each store is allowed to be store specific. To gain some insight into the spread between the marginal posterior profit distributions, we compute the probability this new strategy will exceed the 90th percentile of the uniform price strategy. The probability of all micro-marketing strategies exceeding a uniform price strategy is greater than .99, which shows these gains will be noticeable after considering the natural variation of the profit distribution.

  
Table: Category Gross Profit Changes under Optimal Pricing Strategies

Using a moderate prior we would realize a .42% increase in gross profits if the retailer moved to a better uniform pricing strategy that did not change average store prices or revenues. The actual price changes implied by this strategy are small. This reflects the difficulty in finding a new pricing strategy that generates more profits than the uniform strategy and retains the current average prices in each store. On the other hand if we allow each store to follow its own pricing strategy than the retailer can realize a 3.46% increase in gross profits. If we were to change the prior and assume that store level differences have greater commonalities, we would expect that micro-marketing profits would increase by 2.74%, while under a weaker prior that assumes fewer commonalities profits would increase by 4.29%.

Lifting off these constraints, but still allowing each store to have its own prices, we could generate a profit increase of 29.08%. If we were to only allow uniform price changes without any constraints we would still increase profits from the current uniform strategy to 26.55%. This 2.53% profit increase from the uniform unconstrained to the micro-marketing unconstrained represents the incremental contribution of micro-marketing. It is purely a micro-marketing effect since no chain-wide price differences occur.