Consider the case of a landowner and a farmer interested in renting that land. Consider that if the farmer makes effort there will be a production of 100,000 pesos with probability .95. If he makes no effort there is a .30 probability of that state of nature occurring. The bad state of nature implies a production of 40,000 pesos. Such a state occurs with probability 5% in case the tenant makes effort and with probability 70% if he does not make effort. Making effort costs the farmer 5000 pesos.

Moreover, under any state of nature the landowner can pay the farmer's reservation wage of 12000 pesos.

a) Assume that effort is observed and that the farmer's utility function is 100X^(.5). Find the optimal contract, showing the wage and payments for the landowner.

(b) Assume that effort cannot be observed. Find the optimal contract. Be careful to be very clear in stating whether: i. Whether the participation constraint is met. ii. Whether the incentive constraint is met iii. Payments in the bad and good state of nature for the farmer. iv. The payments for the landowner in the bad and good states of nature.

Please a and b