So I'm taking an entrepreneurship class, and we're doing a simulation where we run a donut shop. My math is pretty strong (integral and differential calculus level), so I'm trying to use my math skills to give our team an edge.
We are able to buy "market research" to see what the other teams are doing. So we can see their market share, and what they're pricing at. I've used simple algebra to find the actual quantities involved here as well.
Now, what I'm trying to do is find a function that predicts demand as a function of price. I've broken it down by product, since we have 4 different products that we're dealing with.
Now 2 of the products give us information that doesn't make sense. Plotting the points and doing a fit shows that demand increases as price increases. This is obviously incorrect, and since there are so few data points, I think that other factors are influencing what's going on here.
I was able to get something that made more sense however with the third product. I plotted the points and did a fit, and that would be the pink line here:
This is the template function I used for the fit:
I chose a -x^3 function because I knew the general shape would look something like what I was expecting.
FIT [x, - a·x^3 + b]
Now this wasn't great because I'm expecting an vertical asymptote around zero. So I took the ln of both axis of the data, did another fit, and solved for y to get a power model based on the -x^3 function. That's what gives me the red line in the graph above.
FIT [x, - a·x^3 + b]
And the result is your red line on the graph there.
Now my question is, can I expect any accuracy here? Is there better ways of predicting demand with respect to price? There are a lot of factors, but some ability to predict demand will give us a significant advantage.