We are trying to setup a contest at my school where contestants have to pay to enter and compete. We have enough money to cover a grand prize, as well as other minor prizes. According to my naive understanding of supply and demand, the higher the price of the ticket, the less likely it is that people will enter the contest. However, if we don't set the price high enough, we won't generate enough revenue to make up for the cost of the prizes.
This is the first time I've ever tried to do this, so I don't have any data on how to set the price for maximum profit and/or maximizing the likelyhood of breaking even. We want to develop a business model to allow us to continue running this contest in the future, with prizes getting larger and larger each year. But before we can do that, we have to be successful with this first contest. How can we determine the optimal price of the ticket? Are there any particular case studies which have tested hypotheses of the optimal price as a function of the demand and/or the value of the grand prize?
To put into some context, here are some of the contest details:
The idea is to have a so-called "sales pitch" contest, where an independent panel of professionals from business, science, and humanities judge the quality of their "million dollar idea" presentations. There are $500, $150, and $50 first, second, and third prizes for this contest. We hope to obtain a 30-50% profit from the sales. The target audience is college students, but especially graduate students.
Obviously, as we increase the prize money, more people will be interested. But we also don't want to get "too many" such that we cannot guarantee a spot for everyone to participate in the 1 day contest. Are there any good theoretical/mathematical tools we can apply to predict the demand based upon the price in this context?
We haven't conducted any market studies on our target demographic. Are there any published case studies on university students to work from?