1. Suppose a gym faces inverse demand p(qi) = a-bqi from each of N identical customers, and costs represented by C(Q) = cQ. Without competition, this would imply that , and.
The is one contract the gym offers.
1. 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 second option look like? (That is, what are the optimal F and f?)
2. How does the optimal two-part tariff change when $t per-unit tax is introduced? (Assume that inverse demand is p(q) = a-bq, and costs are represented by C(q) = cq.)