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Our goal is to construct a system of demand equations. Demand - the amount that I sell - is basically going to be a function of my pricing strategy and of my promotional strategy. In this case, you have all these individual stores, and the hierarchical nature of problem is to measure the price sensitivity for each particular store.
Obviously, the stores are all in the Chicago market, so the first question to ask is ``are there any differences between one store and another store?'' In the United States you get segregation in housing markets, people tend to cluster towards themselves. First, I return to some previous work we did and show that yes, you can observe these things at the store level. Now we want to start thinking about improving our estimates for each of the individual stores using a hierarchical model. The idea is to start pulling all these stores back, towards some kind of average value. Once we've done that we want to evaluate the differences in price sensitivities and carry it through a decision-theoretic context. This means to think about, ``what our posterior profit function is going to be and once I know what the posterior profit looks like, what does that imply about what will be a good pricing strategy?''
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