In Parkland County there are three types of people: Couch Potatoes, Joggers, and Bicyclists. There are 2 people of each type in the county. The different types of people exercise different amounts and have different marginal benefits for any given size of public park. the marginal benefits for each type of person are: MBCP (A) =0
MBJ (A) =10-A/2
MBB (A)=20-A
where subscripts denote the type of person. The cost of A acres of park can be expressed as:
MC(A) =10+2A.
(1)Suppose the county government informs the voters that for each unit of A, each person will pay a tax of $10. What would be each person's preferred size of A?
(2)Suppose that the government of Parkland decides that it wants to provide the efficient size of park. Further suppose that the government decides it is now willing to charge different types of people a different tax to meet this goal and that it can tell different types of people apart. How much will the government charge each person?