Consider the Tragedy of the Commons game from thechapter with two shepherds, Aand B,wheresAandsBdenote the number of sheep each grazes on the commonpasture. Assume that the benefit per sheep (in terms of mutton andwool) equals500-sA-sBimplying that the total benefit from a flock ofsAsheep issA(500-sA-sB)and that the marginal benefit of an additional sheep (whichis defined by the first partial derivative with respect tosA ofthe total benefit function) is500-2sA-sB.Assume that the marginal cost of grazing sheep is100.
- Compute the flock sizes and shepherds’ total benefit inthe Nash equilibrium.
- Draw the best-response unction diagram corresponding toyour solution.
- Suppose A’s benefit per sheep drops to450-sA-sB,which means that his marginal benefit becomes450-2sA-sB.B’s benefit per sheep does not change. Compute the new Nashequilibrium flock sizes. Show the change from the original to thenew Nash equilibrium in your best-response functiondiagram.
