1.Compare the situation of two farmers, one who owns his land and the other who rents it from a landlord. In good times (which happen with probability 12), the owner-farmer earns an income of 125. In bad times (also with probability 12), he earns an income of 75. The tenant works on a farm that is twice as large and earns an income of 250 in good times and 150 in bad times (both with probability of 12). However, he must pay a rent of 100. Calculate the expected net incomeof both farmers. Assume that their utility function takes the following form: = 1/2, where y stands for the farmer's net income. Calculate the expected utility of both. Compare this result to the calculation on expected income. What do you conclude in terms of the different risks that both farmers face?

2.A private farmer hesitates in considering buying new machines to work on his land. The cost of the new machines is K. Without new machines, the output on his land is Ta, where T stands for land. With new machines, output will be b Ta, where b > 1. Calculate the amount T above which it is profitable to use the new technology.

3.A private farmer has to decide whether to buy new machines to work on his land or not. The cost of new machines s 2,000. The sizeof his land is 500. Without new machines, the output on his land is 500*10=5,000. With new machines, output will be 6,000. Is it profitable for the farmer to buy the new machines?

4.A private farmer has to decide whether to buy new machines to work on his land or not. The cost of new machines is 2,000. Without new machines, the output on his land is 10,000. With new machines, output will be 10,000*. Calculate the minimum level of that makes the machines profitable.

5.Consider two farmers, one who owns land and the other who rents it from someone else. In good times (which happen with probability 0.3), the owner-farmer earns an income of 125. In bad times (which happen with probability 0.7), he earns an income of 75. The tenant works on a farm that is twice as large and earns an income of 250 in good times (prob=0.3) and 150 in bad times (prob=0.7).

a)However, he must pay a rent of 100. Calculate the expected net income of both farmers.

b)Assume that their utility function takes the following form: = 1/2, where stands for the farmer's net income. Calculate the expected utility of both.

c)Compare this result to the calculation on expected income. What do you conclude in terms of the different risks that both farmers face?