A communal vegetable garden has been set up by the council for 68 members of a small self- sustaining community. Each of the 68 members can either contribute towards taking care of the garden or leave the upkeep to the other community members. Even if an individual chooses not to help out, they still have access to the growing vegetables. It's estimated that the benefit of the garden increases proportionally with the number of caretakers, so that B(n) = 4n. The payoff to a participant, P(n), is estimated to be 228-2n 1. Graph the shirk function and the participate function on the same graph to show the collective action scenario described above. Label all important points on your graph and show all relevant calculations. [6 marks] 2. Does this game represent an Assurance game? Why or why not? Explain fully. [4 marks] 3. Suppose there is a thunderstorm overnight that ruins a large portion of the vegetable garden. The expected payoffs therefore change so that P(n) = 190-1.5n, P(n+1) = 188.5-1.5n, S(n) = 3n, and S(n+1) = 3n+3. Given this information, derive an equation in terms of n for each of the total payoff functions T(n) and T(n+1). [3 marks] 4. Derive the expressions for marginal private gain and marginal social gain. If there are 31 community members already contributing toward the vegetable garden, is it worthwhile for one additional member to now help with the upkeep of the garden? Explain in terms of the benefit to society and the benefit to the additional member. [7 marks] 5. At what point will the total social benefit be maximised? [2 marks]