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What's the cross-price elasticity? In this case, as I said, I'm going to have this system of demand equation. So I'm essentially saying that the log of movement for brand lot is equal to the constant, plus the prices of all the other brands. In this case, it's the price of Tropicana, the price of Minute Maid, and the price of all the other brands (all twelve brands that are in the category). I also include a feature, a deal and a lag. Now these last three matrices are only the diagonal elements, so I'm not measuring all substitution between, like feature effects. So I'm not saying that there's differential effects if Tropicana is promoted - I'm not saying feature effect is going to help an incremental effect on Minute Maid sales. I'm just trying to concentrate on this matrix, which is the matrix across price elasticities. Just to give you a sense, since I've got 12 equations, I've got 12 brands, I've got 12 equations, I've got 12 prices here, so first of all this is going to be a vector of 12 different values. This elasticity matrix is going to be 12 times 12 or 144 values. There I have 12 and 12. So the idea is that I've got a lot of parameters in the model. But if you look at the amount of data, I also have a lot of data.
For moredetail about the model here.
So this model is going to capture the general market structure. It's not going to impose any structure on the way brands are competing with one another. In this case, therefore, I'm not going to go out and say if Minute Maid changes their price, the only brand it's going to have an effect on is Tropicana. I'm trying to say that I know from theory that there's going to be substitution between these brands, but I don't know exactly what brands are competing heartily with one another and which ones aren't. While obvious from a Bayesian perspective, this is going to be a simplifying assumption and I might want to go back and put some of that information in there because I did have some notions. But for right now I want to just concentrate on this cross 4 problem, and this general market structure is going to be really good for this cross 4 problem because I don't want to assume that in one store Tropicana is competing and then in another store it also has similar competition packets. Because what may be interesting at this point from a marketing perspective is that Minute Maid and Tropicana are competing really highly and in another store they're not competing at all. What's important is that Minute Maid is competing with its premium brand. I'm really interested in is this general structure, and it's going to give me a lot of effects here. It's going to give me the zone and cross-price effects; it's going to give me feature effects; and it's going to give me in-store deal promotions, live time series and promotional effects. So this really is capturing a lot of what we would expect to see in the market. While I'm not saying this is going to be perfect model, it's simple, it fits in nicely with theory, and it has some good economic motivations like the household production function and this general model within a brand competition. Yes?
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