The Lost Mountains of northern Iowa are inhabited by the rare Marshallian deer. Patches of grass are far apart

in this rugged land. If a deer finds a fresh patch of grass and spends h hours grazing it, it gets the square root

of h units of grass. The deer compete for grass. When there are n deer, it takes a deer n 2 minutes to find a

fresh patch. A deer can survive if it gets 1 unit of grass every 200 minutes.

a. Find the average cost in time of a unit of grass if a deer gets y units of grass from each patch.

b. How much time will an efficient deer spend in each patch when there are n deer? (Hint: Minimize aver-

age cost.)

c. Since there is free entry into the deer business, the equilibrium population is the maximum number of

efficient deer who can survive. How many is this?