this question is for environmental economics class

Part 1: Welfare in a market with an externality - The citizens of Jakku enjoy the shade from having trees at their private residences with di minishing returns. Suppose the private marginal benet of consumption of trees is: PMB(Q) = 40 7 :6? where Q is the number of trees - Each tree costs citizens $20: PM C (Q) = 20 - The visitors to Jakku from other planets benet from having trees on Jakku because the trees make it easier for the visitors to acclimate to the dust in Jakku's atmosphere. The external total benets of trees for visitors is: ETB(Q) = 2Q 1. What is (i) the competitive equilibrium quantity of trees on Jakku QC and (ii) the socially optimal quantity of trees on Jakku Q3? 2. What are the (i) consumer surplus and (ii) producer surplus at Q\"? 3. What is the external surplus at Q\"? 4. What is the private surplus at Q5? 5. How does the private surplus at the competitive quantity Q'2 compare to the private surplus at the efcient quantity Q\"? Provide economic reasoning for why they differ (or don't differ)