Public goods, please answer all

5 Public Goods In Coconimo County there are three types of people: video gamers (g), trail rumers ( r ), and mountain bikers (b). The different types of people make use of public lands to different degrees and have different benefits for any given size of the public lands in the county. Denote the size of public lands as A acres (so A refers to the quantity of public lands). The total benefits for each type of person are: B9=0Br=10A4A2B6=20A2A2 where the subscripts denote the type of person. The marginal cost of increasing the size of the public lands has a fixed component and a component based on the size of the park. The total cost of A acres of public land is: C(A)=10A+A2 Initially, the government of Coconino County is committed to a policy of not charging different prices across different people. For simplicity, assume that there is only one individual of each type 4 in the county. 1. If the size of public lands were determined by the private market, what would be the market determined price and acreage of public lands in Coconino County? It will likely be helpful to solve this tsing both graphical analysis and math. 2. What condition needs to bold at the socially optimal acreage of public lands in Coconino County (A) ? Explain intuitively what this condition means and why it is optimal. 3. Using the condition you identified above, calculate the socially efficient arreage of public lands, A. Again, it will likely be helpful to solve this using both graphical analysis and math