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Now we'll think about this stuff in terms of how I should change the individual categories, so I'm going to look at one particular store, store number 6, and think about changing all the premium brands and all the store brand prices. This map of essentially gives me what happens if I increase the premium brand prices by 20 percent, and leave the store brand prices constant. This is a price index on each axis. Here's the store brand, here's the premium brands, here's the contour function, and this is just the posterior mean. At each of these points I could show you that there is dispersion around this point. If I want to compute the gradient it means that I would want to start increasing the price of the premium brands and decreasing the price of the store brands. In another store, I'm going to move off in a different direction. Again, there's this overall movement to increase prices, but what's happening here is that I want to increase them both by the same. Here I would want to make the price gap bigger; here I would want to make the price gap about the same. If I went across all 80 stores and just picked up this gradient and I could plot it, it would look like this nice dispersion. Here's the extremes, and then you'd see all these stores that are falling in between these extremes. In some of the stores we would want to decrease it or leave the gap about the same, in other stores you would want to increase this gap. As I said, it's not totally satisfactory just to increase all the prices. What I'd really like to do is start thinking about how there's going to be some kind of a change in the environment if I just simply go out and increase all my prices.
To see other directional profit gradients click here. For more detail click here.
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