Product pricing question

#1
Hello all. It's been a long time since I've been on this forum. Glad I was able to find it again.

I'm afraid my stats experience is limited to the basics... normal distribution, dispersion, confidence intervals, regression. I have mostly worked in a production environment and have done studies on supply chain operations, but little else.

I was given a problem in relation to an opportunity that came up, and wanted to get some input. I was given 60 weeks of weekly data relating to four competing products, A,B,C and D. I assumed these were something like Coke, Pepsi, Dr. Pepper and Sprite. For each of these, I was given the price for each week, the product cost that week and the weekly sales. I was then asked to "apply appropriate statistical models and get back to me with your results." The implication there, I think, was something along the lines of an optimum pricing for maximum profit, or something like that. One product, D, had a lower cost than the others, so I assumed it represented a store brand.

Well, I've not done product pricing before, but I used Excel and got a regression equation for each product (and one overall, which should just be the sum of the others, right?). Then, I looked at the distribution of sales for each product at particular prices that were common to determine the effect on sales and profit of a price change (I remember from economics that is called elasticity). But, as far as finding the optimum pricing scheme... well, I wasn't sure where to go with that. I also looked at product sales mix and broke out the weeks into quartiles by performance. I compared overall sales volume with total profit and found that the occasional huge increases in volume didn't increase weekly profit, because the sales were driven primarily by price cuts (promotions, I suppose). I found that the product mix of the best performing weeks was almost identical to that of the worst performing, except that there was a shift of 4% of the sales from one product to another, and the other two remained constant (something like 25-25-25-25 to 29-25-21-25, for example). I definitely don't know how to properly analyze product mix... is that Chi-Square analysis??

I did my best and sent it back... but haven't heard anything. I was wondering if I could get some input on what you might have done, whether you think what I did was OK, and if someone could point me in the right direction for product pricing statistics. Whether I get the job or not, I would like to learn this... as I am not even sure what he meant by "appropriate statistical models."

THANKS for any help.
 
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