Ten villagers graze cows in a common field. It costs 10$ to buy a cow and its
Question:
Ten villagers graze cows in a common field. It costs 10$ to buy a cow and its only value is the milk it produces. With c cows grazing on the field, total value("BENEFIT") of their milk is 100c^(1/2)(hence the total value of milk per cow is 100c^(1/2/c)). The total benefit is increasing in c (upward sloping) because each additional cow generates revenue(which goes to the villager who owns the cow) but the slope is decreasing c because for every additional cow in the field, there is less grass available for the other cows, who therefor wont produce as much milk. The marginal benefit per additional cow grazing the field is 50c^(1/2)
1. How many cows should the village raise to maximize total profits(what is optimal c^(*).
2. How many cows will the village raise since each villager only considers her own proits(what is the market outcome)?
