An agriculture cooperative has 10 members. Each member has two options: fish in a nearby lake or work on a farm earning 400 UAH a day. Fish can be sold by the cooperative in a town nearby for 40 UAH per kg. If L cooperative members fish in a particular day, the total amount of fish caught is given by F=130L−20L2. Cooperative members love fishing and prefer this activity unless they can earn more by working on the farm. a) Suppose each member of the cooperative decides individually whether to fish or work on the farm. How many kilograms of fish will the cooperative members catch? What will be the total revenues for the cooperative (money from sold fish and earnings on the farm)? b) Suppose, instead, the head of the cooperative decides on the allocation of members between activities. What will be the optimal number of members that will do fishing in this case? How will this affect the total earnings of the cooperative?
c) Is there a difference between answer to (a) and answer to (b)? Why? Explain d) Suppose the head of the cooperative decides to discourage fishing by a unit tax per kg. How much the tax should be to achieve the same number as in b (approximately)? e) Suppose the wage earned on a farm increases to 600UAH a day while price of fish goes down to 20UAH, how will this change your answers to a? Calculate and explain