Question

Six families raise goats that use an acre of a common field for feeding. Eacg goat eats 1/N of the grass in the field, where N is the number of goats that hte families own in total together. Cream production for each goat is given by c = 64^(1-(N/18)), where c is the number of buckets of cream produced per goat. A familys profit is the total cream production of the goat that it owns individually. is raising three goats per family a Nash Equilibrium? Justify. (No need to for Calculus)

Answer 1

No, it is not a nash equilibrium for each family to raise 3 goats. A family can do better, given all other families raise 3 goats, by increasing the number of goats it raises beyond 3. This problem is an example of a problem fo commons where a common resource is overutilized. The output per goas decreases as the number of goats increase, but the total output is still higher for each family. The optimum point is not socially optimum as there are no marginal costs which should be there as society is worse off.