Practical question about wine and pricing from a non-math expert I work at a restaurant with a fancy wine list but I have noticed that there doesn't seem to be any method to the way the wines are priced.
Ideally you would want your expensive wines to have a much lower markup and your less expensive wines to have a steeper markup.  The list I inherited is all over the place and it seems both inelegant and bad for business.  I think there must be a way to figure out a function for a curve that I could apply to the bottles based on their cost that would determine price.
If I have a bottle that costs me only 10 dollars, it should be around a 300 percent markup (30 dollar menu price).  30 dollar bottles should be about 200 percent, and get lower and lower but never getting below 150 percent.  If the y-axis is the markup as a decimal, and the x-axis is the cost of the bottle, then the coordinates would be something like (10,3), (30,2), (400,1.5).  The last one is just because we have no bottles that exceed $400 cost per bottle. ( guess it could just be an asymptote but I don't know how that works.

Here's a function that behaves pretty close to the way you're describing: $$m(x)=\frac{16.7}{x+0.83}+1.5$$ where $x$ is the cost of the bottle in dollars, and $m(x)$ is the markup of the bottle, expressed as a decimal. It has a horizontal asymptote at $m=1.5$, so you'll never get a markup lower than 150 percent.
For example, it gives a markup of 3.04 for a price of \$10, a markup of 2.04 for a price of \$30, and a markup of 1.54 for a price of \$400.
