Consider the Tragedy of the Commons game from the chapter with two shepherds, A and B, where sA and sB denote the number of sheep each grazes on the common pasture. Assume that the benefit per sheep (in terms of mutton and wool) equals

300 – sA – sB

Implying that the total benefit from a flock of sA sheep is

sA (300 – sA – sB)

And that the marginal benefit of an additional sheep (as one can use calculus to show or can take for granted) is

300 – 2sA – sB:

Assume the (total and marginal) cost of grazing sheep is zero since the common can be freely used.

a. Compute the flock sizes and shepherds’ total benefits in the Nash equilibrium.

b. Draw the best-response-function diagram corresponding to your solution.

c. Suppose A’s benefit per sheep rises to 330 – sA – sB. Compute the new Nash equilibrium flock sizes. Show the change from the original to the new Nash equilibrium in your best-response function diagram.