perhaps it wasn't necessary to actually mention who was your competitor
Anyway, a good start would be to plot the data and see how it looks. For instance, if it looks like a straight line, then you have a linear relationship. If it looks like a parabola, you have a square relationship. If it looks like a very quick and steep parabola, it might be an exponential relationship. Once you have decided what the relationship is, you can deduce what the coefficient (or "gradient") is and come up with a formula that links your cost price to the retail price.
Of course, it is highly probable that a relationship actually exists, but depending on how accurate your data is, you might not be able to strictly select one right away, in which case you will need some more data before repeating the attempt.
If I can suggest some keywords, you could look up data analysis and graph reading. And linearization, too.