Question: Suppose a gym faces inverse demand p(qi) = a - bqi from each of N identical customers, and costsrepresented by C(Q) = cQ. Without competition, this would imply that
qi = (a- c)/2b , and p = (a+c)/2 .
The is one contract the gym o?ers.
There is another contract available, though, where the client agrees to give the gym a sum of money,F, out of which the gym would then pay clients f dollars for each workout. What does this secondoption look like? (That is, what are the optimal F and f?)