Question

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

Answer 1

Expected net income of landowner farmer:

1/2*(income in good time) +1/2*(income in bad time)

= 1/2*(125) + 1/2*(75) = 1/2(200) = 100

Utility = y1/2 = 1001/2 = 10

Expected net income of land renter farmer:

1/2*(net income in good time) +1/2*(net income in bad time)

1/2*(250 -100) + 1/2*(150 -100) = 1/2*(150) + 1/2*(50) = 1/2(200) = 100

Utility = y1/2 = 1001/2 = 10

Thus, we see that the expected income and utility of both farmers are the same. But there is a major difference in the risks that they face. Farmer with own land gets higher, 75 in a bad time as compared to the farmer who is renting land who gets 50. Thus the land owner is better insured against bad time. But at the same time, the land renter gets higher income on the good times, 150 against 125 for the land owner. Thus, the risks are different in good and bad times for both the farmers despite getting the expected income and utility.