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So, in terms of a table, you know, let's just take a strong prior and lets think about what's going to be the effect in terms of profits as we start thinking some of these different pricing strategies. Now, I don't want to move to an optimum pricing strategy, what I'd like to do right now is just think about regions, the city, the suburban and the stores that were close to a club-warehouse, their competitors. So what happens is they price the city stores higher, suburban stores in the middle and the stores that are close to their competitors they push the prices down. And basically, it's like a 10 percent increase in price or a 10 percent decrease in price across these zones. So, what their xxxx is going to get, is a .66 percent increase in profits over this yearly. What I'm trying to do here with this probability greater than 90 percent of the uniform, I'm just trying to think about - I got these 2 distributions, I've got the posterior profit function for the uniform strategy. What I do is I take the 90 percentile and I just think about, well, what's the mass that's above that point from one of these new strategies. So I'm just trying to get at the notion, can I measure this profit increase? Or is it going to be like a 50/50 guess that I'm going to make higher profits. So the point is, that yes, I'm going to be pretty confident that I'm going to be increasing my profits here. So the category elasticity zones - what would be a better thing to do is to go back to that - one of the first slides that I put up with the map of the category price elasticities. What I can do for my model is compute some kind of elasticity that tells me well, what's the effect on sales if I were to increase all my prices by 1 percent. So in some cases, as I said, that category elasticity is -2, so in that city store, what that would imply is if I were to increase my prices by 1 percent, I would drop my total movement by 2 percent. So if anything, I would want to decrease my prices in those stores and then I would want to go out and I would want to look for the stores that are price insensitive and I'd want to increase my prices there. So, just as a rough plot, that would make sense and what would happen is that you would come out with something in the category elasticity zones. So, what you would do there, is you would get 2 percent increase in profits, or 1.91 percent. Now I should mention that these are gross profits. So if the gross profits are about 25 percent what I'm doing is I'm giving a 2 percent in that gross profit of 25 percent. Now it may sound like a lot, but what's happening to the retailer is that the gross margin is about 25 percent, what I pay out to my wholesaler, but if you think about this at the final outcome, the bottom line, their profit margin is typically like 2 percent. So if their total profit margin is about 2 percent and you're taking about a 2 percent increase in gross profit margin of 25 percent, this 2 percent really adds up to something.
Now what's happening is the conclusion from the plots that we should increase prices overall. So what we should do is - let's forget about having decreasing prices and let's just think about having two zones, one base price and another where we increase the prices. So in that case what you get is a xxxx of 6.8 percent. Let's look beyond that and say, let's just change the entire pricing structure that this retailer is following and let's just increase all the prices up by 10 percent. So in that case you get a 21 percent increase in profits. So all this, the retailer is reluctant to move from where they're at in doing a 10 percent increase. Yes, this does make some big differences the way that consumers might perceive this store. And some of these things might be outside of the effects of this model. I don't have competitive data in here, so it's a concern and we're going to try to address that concern in the upcoming slides. But what I'd like to say, is that the conclusion is that you want to increase prices. And you could do a big increase in profits by increasing prices.