Q9. A tiny village has twelve people. Each villager can choose to either hunt rabbits in a nearby forest, or else go to work in a mill. Wages in the mill are $6/day. Rabbits sell for $1 each. If H villagers go rabbit hunting, the total number of rabbits caught is given by R(H) = 10H - H2 per day, and the rabbits are divided equally among the hunters. Villagers prefer to hunt unless they expect to earn higher wages at the mill. a) Suppose the villagers choose individually if they want to hunt or work at the mill. How many will choose to hunt? What will be the total earnings for the entire village? [3 marks] b) Now work out what is the socially optimal number of hunters. With that number of hunters, what will the aggregate earnings of the village be now? [3 marks] c) Explain in words why there is a difference between the individually-determined and socially optimal number of hunters. Under what general conditions might you expect this difference between these two to go away or reverse? How would the function R(.) need to change for this to happen? [4 marks]