1) for past a) , why was the average product taken and why was not things such as marginal product was taken?

2)

for the socially optimum number, why was that formula used?

* A small village has six people. Each can either sh in a nearby lagoon or work in a factory. Wages in the factory are 4/day. Fish sell in competitive markets for 1 apiece. If L persons fish the lagoon, the total number of fish caught is given by F = 8L - 212 per day. People prefer to fish unless they expect to make more money working in the factory. a. If people decide individually whether to fish or work in the factory, how many will fish? What will be the total earnings for the village? b. What is the socially optimal number of fishermen? With that number, what will the total earnings of the village be? c. Why is there a difference between the equilibrium and socially optimal numbers of fishermen? ANSWER: a. The average product in fishing is F/L = 8 -2L. People choosing independently will fish until 8 - 2L = w = 4, which solves for L = 2. Total earnings will be (8 . 2 - 2 . 22) . E1 = E8 from fishing and E4 . (6 - 2) = E16 from factory work, making the total earnings 24 per day b. The socially optimal number is the one for which the marginal product in fishing is equal to the factory wage. MP = dF/dL = 8 - 4L = w, 8- 4L = 4, which solves for L = 1. Earnings from fishing will be (8 . 1 - 2 . 12) . E1 = E6, while earnings from factory work will be E4 . (6 -1) = 20, making total earnings equal to 26 per day. c. The disparity between individual and social optimality results from the fact that individual decision makers fail to take into account the fact that an extra person fishing reduces the catch of those who were already fishing