Conclusion

So, just to get you the results, let's just start there.

Category Profit Changes Under Optimal Pricing Strategies

The following table gives results.

Let's start with a strong prior. If I go to this optimal constrained strategy instead of my uniform pricing strategy, my yearly profits are going to increase by about .44 percent, if I'm saying that all of the stores have to follow the same pricing strategy. Remember, when I put these constraints on I could think about having constraints for the entire chain level, so we have to ask if the store can come up with a new pricing strategy for all the stores that still keeps the average price the same and still keeps the total sales the same. In that case, it's really difficult, but they can do a little better. Now suppose they say that all the stores can choose a different pricing strategy. In that case, I'd get a 2.74 increase in profits and compare that to .44 percent increase; you see that you can get a lot better with these micro-marketing strategies. Dominic's is concerned about a .66 percent increase in profit, and now you're talking about a 2.74 percent increase in profit, so this is really going to be important to them and you could really make a difference in their gross profits.

Again, in terms of some kind of measureability, it looks like these are definitely measurable. You may not think these constraints are such a good idea -- you can still think about coming up with an optimal strategy without these constraints. In this case the slope of the profit function is not exactly what I would have chosen, but to come up with it beforehand, I -- there was not a lot of curvature in the profit function and you tend to just increase all the prices. So, you get a 24 percent increase and profits would be uniform; if you do it at the micro-marketing level, you come up with almost a 26 percent increase in profits. What I did in this optimal unconstrained sense that I don't have these average prices, the total movement, the total revenue, but I still have a constraint that I'm only willing to pick about 10 percent -- I'm going to allow my prices to changes by plus or minus 10 percent. There still is a bound on pricing, but I haven't made it as great.

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Boxplots of Constrained Optimal Price Changes Across Stores

Let's think about what exactly this pricing strategy would look like for an individual store and what it would look like across all the stores. Here I've thought about -- here are my twelve brands, and what about the price changes. I can either decrease it by 10 percent or increase it by 10 percent. The x's denote what I would do for one individual store. For this store I would want to increase my price by about 8 percent on Tropicana Premium, and for Tropicana Premium 96 oz I would want to decrease it by about 5 percent. Then I would want to treat Florida Natural about the same. I'd want to increase Tropicana by 10 percent, and on and on. If you average all these price effects, you'd see that about half are above and half are below. And if you weighted them by the movement you'd find out that the average prices remain unchanged. On top of that, (I can't illustrate it, but it's still there) the revenue from having these price changes would also remain unchanged. Essentially you're trying to give people an incentive to switch to more profitable brands for you. To go back to the questions of fairness from the beginning, although it might be unfair just to increase all the prices by 10 percent, it might have some dramatic effects, but if I changed the price gap between Minute Maid and Tropicana in some stores and in other stores I leave them together, it doesn't seem to make a lot of difference. Now, what I've done to the box plots is to illustrate the overall change across all the stores. In this case, Tropicana can go anywhere from decreasing by a percent to increasing it by 10 percent. The idea is that you see a lot of dispersion across the stores, so what would be a good pricing strategy for them to follow?

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Summary and Future Directions

Let me summarize some of the things I think are really compelling about this. You started out thinking about trying to measure store elasticities, or these individual parameters, but I think this hierarchical model is really elegant. It really summarizes how we should do it, and from a frequentists perspective it really would have been difficult -- not impossible -- but very arbitrary - how would we have described these relationships. It would have been difficult to estimate them.

Some conclusions are given here.

The next problem is taking this problem, this measurement perspective of price elasticities, mapping into the profit function, and then thinking about the consequences in terms of pricing policies. So it really puts it back into the retailer's decision framework. Some future directions are given here. I'll now finish up and open it up to discussants.

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