Andrew Breyer and Jack Edy are independent dairy farmers who share a common plot of

land on which their cows graze. If there are few cows on the land, then the cows are well fed

and produce a lot of milk; as more cows graze the land, the cows become somewhat less well

fed and produce less milk. You can approximate this relationship with the function m=120-10C where

, where m is milk production in gallons per day by each cow, and C is the total number of cows grazing on the land.

a. Suppose Breyer chooses to graze 2 cows on the land. How many cows should Edy graze

if he wants his cows to produce as much milk as possible?

b. Suppose Breyer chooses to graze 6 cows. Now how many cows is Edy's milk-

maximizing number?

c. Plot Edy's reaction function - his optimal number of cows as a function of Breyer's

choice. Since the problem is symmetric, plot Breyer's reaction function too. It's fairly

straightforward with a game table. Use Excel if needed.

d. In equilibrium, how many cows does each graze? How much milk does each cow

produce per day? How much is produced by each farm?

e. In a brilliant leveraged buyout, Breyer acquires Edy's farm; the resulting merged farm is

the only user of the grazing land. How many cows should Breyer choose to graze on the

land now? How much milk does the farm produce?

f. Explain why your answers to d and e are different.