Question

1. Imagine a small, grassy mountain pasture discovered by Adam and Betty (both ranchers). Assume the pasture is an open access resource. Both want to graze cattle on the pasture and each knows the other is there and each is fully informed about all payoffs from grazing. Each can choose a light level of grazing or a heavy level of grazing. A heavy level of grazing would cause their cows to grow faster and fatter, but would deplete the resource if they both do it (stunting the growth of the cows). Consider the following payoff matric Light Grazing by B Heavy Grazing by B Light Grazing by A $100 $20 $100 $120 Heavy Grazing by A $120 $40 $20 $40 a. What is the socially optimal outcome? Explain. b. What is the Nash Equilibrium outcome, if there is one? (what will they do if left to themselves) Explain. Your answer should include an explanation of what Nash Equilibrium outcome means. c. is the equilibrium outcome a Prisoner's Dilemma? d. If Adam and Betty are able to communicate and agree to penalize heavy grazing, how large of a penalty for heavy grazing would effectively deterit?

Answer 1

(a) Socially optimum outcome occurs at the point where marginal social benefit(MSB) and marginal social cost (MSC) intersect.

(b) Nash equilibrium is a set of strategies that players act out, with the property that no player benefits from changing their strategy.

Nash equilibrium of the game is (Heavy Grazing by A, Heavy Grazing by B).

Heavy grazing will be done by both when they left to themselves. They will over-exploit the resources.

(c) Yes, the equilibrium outcome is a prisoner's dilemma because they can achieve Pareto superior outcome by choosing light grazing by both i.e. (100,100) but still they both have chosen heavy grazing thinking that one might deviate.