Consider a production cooperative wish just two farmers. Each farmers chooses independently how much labor to supply to the cooperative. Each unit of labor is supplied at an opportunity cost of w. output is produced by means of a standard production function (exhibiting diminishing returns), with input equal to the aggregate quantity of labor put in by the two farmers. There is no other variable input of production.
A) Draw production and total cost as a function of labor input. Find (diagramnatically) the amount of labor input that maximizes farm surplus.
B) Now returns to the problem where labor is supplied independently. Show that if total output is divided equally among the two farmers, production will fall short of the answer in part (a)
C) Next, suppose that farmer 1 receives a share s > 1/2 of the total ouput, while farmer 2 gets 1 - s (everything else is the same as before). Describe what happens to production and labor efforts as s varies between 1/2 and 1.