Optimization of warden's activity

Optimization of warden's activity
Let's take a look at the mathematical task:

If there is no charge for the tour then the total consumer surplus is: 79$

CS = 20 + 14 + 30 + 15 = 79 $

The warden would have to offer 15 $ to get three people to postpone their visit (Jon, Jack & Fran). If one considers the people who abstain from visiting the caves on that day as suppliers, their total surplus will be: 3 + 1 + 0 = 4 $.

Under the compensation scheme the people who truly want to take the tour are singled out. Thus, the scheme offers better satisfaction of individual preferences and leads to a higher level of efficiency.

The warden can inform the visitors that he will stick to the first-come, first served system unless other visitors want to buy out the places of the previous ones. He also should add that the price of buying out will be deduced from the reservation price (we assume that there is perfect information and all the visitors know each other's valuations of the visit). In such a case Penny will buy out Jon for 14 $, reducing the wardens benefit by the same amount. Faith will buy out Jack for 15, reducing the warden's income by the same amount. The people bought out can make a reservation for the same amount for the next day (or whenever convenient). This way the warden 'loses' 29 $ instead of the 45 $ under the compensation scheme, and still gains 28 $ more than in the first come first served approach. Fran would lose her place anyway under the first come first served system. Everybody is better off.

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