Establish demand curve with infrequent sales I sell variations of an item on eBay. It is an unusual commodity which I purchase in bulk lengths and then cut to various sizes. They come in about 20 types, which I then sell as 10 different lengths, giving a total of 200 variations.

My goal is to determine what price I should charge for each, to maximise monthly profit.

The problem is I only make an average of one sale per day. I have no idea how I can establish a demand curve for the products, given such limited data. (Some variations I only get one sale per 18 months!)

What techniques could I use for this problem?

How could I go about establishing the most profitable price for each of the variations, with such limited information? (Given known costs). 

The only clear idea I have is this:


Treat all 200 variations as a single product, and vary all their prices simultaneously, to derive a single demand curve. So for example, one month I might set all prices to generate 10% profit on top of the costs, then next month, set all prices to generate 20% profit, and so on, and this way establish what price generates the highest monthly profit.


But the variations tend to have wildly different applications, as well as, I expect, alternative products that can satisfy the customers' requirements, and so on - so having a single demand curve could leave significant profits untapped.

The only other idea I have is to profile the demand curve for each item in a different way:


For each product, take an example: one that only sells approx every 6 months on average: On each sale, if the time since the last sale was 6 months, I divide the total profit made on that item by 6 - or for a product that sold twice in one month, multiply by two. And then each time there is a sale I can some how establish the demand curve for it. 


But the snag is for a product that sells infrequently, the demand curve could be static, but obviously this does not mean it would sell, say, once every 6 months like clockwork. So it could take years to establish a demand curve for that variation.

I'm wondering if I should entirely forget about the demand curve and concentrate instead on a marketing-oriented approach, for example:


Surveys: (How I would phrase this I'm not sure - I doubt customers would tell me the maximum they'd pay!)
Market research: plot graphs of how much other retailers/distributors charge for each variation. (Although I have seen very few indeed that sell small lengths such as those that I offer)
What you're looking for is the price elasticity of demand of your product.  That is: by how much will your sales rise or fall depending on how you manipulate price?  It depends on what you're selling and, like you said, each variation of your product will have a different elasticity.  So, say you increase prices by 5% and experience a %5 decrease in sales; your price elasticity of demand would be -1 (unit free).  

The strategy you outlined to parse out the price elasticity sounds reasonable from a data collection standpoint, albeit a bit risky.  I might change the price of just one of your variations (maybe one that sells somewhat more frequently)  to assess the sensitivity your customers are to price changes.  However, if your product's elasticity is high, your sales might drop dramatically or stop altogether.