Question

1. 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).

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

   2. 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.

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

Answer 1

The net income of farmer who has his own land

Expected net income =Y1= 0.3(125)+0.7(75)= 37.5+52.5 = $90

The farmer who works for someone else

Expected income before rent = 0.3)(250) + 0.7(150) = $180

expected Net income after rent= $180-100 = $80

Expected utility of farmer 1 = U1= (90)^1/2 = 9.49

Expected utility of farmer 2 = U2= (80)^1/2 = 8.94

Expected utility of farmers is the square root of their net income , so the utility derived of both the farmers is almost the same as compared to the net income.

Both the farmers face the risk of a bad crop which is 70 % but the farmer who works for someone would have to pay a fixed rent irrepsective of his earnings., This farmer is at a higher gain and loss because he would have to pay to the owner irrespective of the incoime he earns .He can increase his productivity and his income minus the rent would be his reward. But there exist lesser chances of having a change in the technology or pattern of crop etc because he is not the owner.

Whereas the farmer who has his own land is earning more than this farmer , but has to bear all the costs and benefits completely. If he is experimenting with the cropping pattern or irrigation techniques , all consequences would completely fall on him and he wont be accountable for it to anyone. This gives him an opportunity to adopt new ideas and innovate his techniques.

(You can comment for doubts )