Consider a sharecropping arrangement where farmers earn a shares of output F(L), where L denotes their hours

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Consider a sharecropping arrangement where farmers earn a shares of output F(L), where L denotes their hours of labor. Consider two farmers, where one is more productive than the other. The more productive farmer has costs aL (a < 1). The less productive farmer has costs L. This reflects the fact that the more productive farmer can get more work done in an hour. Calculate the optimal amount of labor for each farmer. Which farmer will work more? Assume that the landlord does not know which farmer is more productive. Assume he is willing to share labor costs so that each farmer only incurs a share s of his labor costs. Which of the two farmers will work more, and how close will effort of the latter be to that in a privately owned farm? What if the farmers are made to incur only a share sa of the cost? Explain the reason for these results.

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