Suppose that, in a village, it costs a yuan to buy a cow. How much milk the cow produces will depend on how many other cows are grazed on the common land. We'll let f(c) =c2 be the value of the milk produced if there are e cows grazed on the common. The price of the milk is assumed to be 2 yuan. (a) What is the market value of the milk per cow? (b) What is the profit maximizing problem for the entire village? Solve it and find the optimal number of cows for the village. (c) What is the marginal revenue if an individual villager decides to add a new cow? (d) When entry is free, show the condition when entry stops and the final number of cows. (e) Compare the results of (d) and (b) and tell why it would happen.