Consider the following production technology: Y=L^1/3, where Y is output and L is labor input (effort). Normalize so that the unit price of the output is one. Let the wage (cost per unit of labor) be w.
i) Derive the efficient (first-best) level of effort. [Hint:- the information problem that arises with the contracts that we will examine is that the peasant's effort cannot be observed by the landlord. This is why he cannot contract directly on the level of labor effort. When deriving the first-best level of effort we avoid this problem by assuming that the landlord, who owns the land, supplies the labor as well.]
ii) Now assume that the peasant puts in the labor effort, while the landlord either rents out the land, hires the peasant for a fixed wage, or enters into a sharecropping arrangement with him. The terms of these contracts were described above. Derive the labor effort with each contractual arrangement, assessing how it compares with the first- best.
iii) Show the result you derived above graphically [Hint:- plot output and total cost on the Y-axis and labor effort on the X-axis].
