(Solution) - A fisherman at Hardin Lake can catch 20 fish per -(2025 Original AI-Free Solution)

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A fisherman at Hardin Lake can catch 20 fish per day, provided he has the lake to himself. Two fishermen can catch 19 fish apiece per day, and three can catch 18 fish apiece per day. Other numbers are given by the table:
Number of Fishermen Fish per Day per Fisherman
1 ............. 20
2 ............. 19
3 ............. 18
4 ............. 17
5 ............. 15
6 ............. 13
7 ............. 10
8 ............. 7
The opportunity cost of a day at the lake is 7 fish (i.e., the alternative activity is asvaluable as 7 fish).
a. How many fishermen come to the lake? How many fish do they catch? What is the social gain from the existence of the lake?
b. What is the optimal number of fishermen at the lake? What is the social gain if this optimum is achieved?
c. What entrance fee leads to the optimal outcome?