4. We consider N farmers who can each produce at zero cost as much wheat as they want. If the kth farmer produces gig, the total quantity produced is Q: q1 + q2 + glg+ + gubThe price of wheat is determined by p = ehlQ). (a) What is the appearance of the global recipe |'|[Q] = gg'bQ) for Q 2 0? (b) Using the previous point, show that the strategy of producing one unit of wheat is dominant for each farmer. Deduce that the corresponding profit of a farmer is el'lN). (c) Suppose the farmers agree that each will produce (1/N) wheat unit. Still based on the first point, show that the total profit is then maximal. check that the profit of each farmer is (Um). Can such an agreement be honored in the absence of an explicit contract? (d) Why is this N-player game a generalization of the prisoner's dilemma? Note: This game is an illustration of the "tragedy of the commons"