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For example:

A shop sells sandwiches. They find that if they sell $3$ types of sandwiches they sell more than they would if they only sold $2$ types of sandwiches. However the increase in turnover between $2$ and $3$ is much greater than the increase in turnover between $99$ types of sandwiches and $100$ types.

What is the mathematical function for this and how would I calculate it please?

Thanks in advance

DonAntonio
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Michael Keown
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  • Ok, I have figured out it is diminishing marginal returns, but still not sure how to calculate it, especially with other variables...time of day, how many sandwiches the shop next door offers etc – Michael Keown Mar 26 '13 at 13:07

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There is no way to calculate it. You can collect real data (say from other sandwich shops) and create a model, but without that you can't say anything.

Ross Millikan
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  • so its basically a case of getting as much data together and trying to get a causal relationship through trial and error? – Michael Keown Mar 26 '13 at 15:14
  • given that I do have the real data (it is not a sandwich shop btw), do I have to try to make asumptions that remove the variables? A better question is how, given a set of data, do I go about trying to find a causal relationship? If you give me a sequence 1, 3, 6, 10, 15 I know instinctively what the next number is, but assuming I didn't, how do I go about trying to find it? – Michael Keown Mar 26 '13 at 15:21
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    @MichaelKeown: I always start by plotting and looking at it. It might look linear and you can use a linear regression. It might look quadratic like your triangular numbers. – Ross Millikan Mar 26 '13 at 15:29