Problem Set 3 Part 1 on Public Goods

Public Finance PADM5006

1.Suppose you are deciding how many acres of local land to preserve for parks in a particular community. There are 200 community members who each receive a marginal benefit of monetary value, "P" such that P=9-3q, where q is the number of acres of park in their community.After 3 acres they would be satiated and P=0.Suppose there are another 3 community members who enjoy parks more and receive a marginal benefit of P=300-50q.After 6 acres they are satiated and P=0.So, there are a total of 203 demand curves. Each acre costs $1200 to preserve. Assume all 203 people can enjoy the preserved park land at the same time, i.e. the enjoyment is not rival.

A)What equation would represent the Social Marginal Benefit (like a combined demand curve if the people could coordinate) for the 200 community members who each receive a marginal benefit of monetary value, "P" such that P=9-3q ?

B)What equation would represent the Social Marginal Benefit (like a combined demand curve if the people could coordinate) for the other 3 community members who enjoy parks more and receive a marginal benefit of P=300-50q?

C)What equation(s) would represent the Social Marginal Benefit (like a combined demand curve if the people could coordinate) for all 203 community members?

(Hint: If some people become satiated their individual marginal benefit should not fall below 0.They would just not get any additional benefits.)

D)What equation would represent the SMC of each acre of land?

E)Show graphically the Social Marginal Benefit (like a combined demand curve if the people could coordinate) for all 203 community members and the SMC.(There may be a kink(bend) if some people are satiated before others.)

F)What is the efficient number of acres of park to preserve for this community?

Show your answer algebraically and graphically.

G)How large is the economic surplus this would create?

Show your answer algebraically and graphically.