A plot of land is owned by a Landlord but worked by a Tenant. If the Tenant provides effort L he incurs a cost C(L), which increases at an increasing rate with L. The value of output from the plot is given by the production function y = {g(L) + x with probability 0.5 g (L) -x with probability 0.5 where g(L) increases at a decreasing rate with L, and z represents random variations in output due to climatic conditions. The variance of output is therefore x^2. The Landlord is risk neutral but the Tenant is risk averse with a "coefficient of risk aversion" given by r. The Landlord can monitor the output produced by the Tenant, but cannot observe or infer the amount of effort she exerts. Using the above information, write down the "expected utility index" of the two parties under (1) a wage contract, (2) a rental contract and (3) a sharecropping contract in which the tenant receives a share s of the output produced and the landlord get the rest In each of these contracts describe how the risk is allocated between to two parties. What about the incentives faced by the Tenant to exert effort