Question

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 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 of 1/2). However, he must pay a rent of 100. Calculate the expected net income of both farmers. Assume that their utility function takes the following form: U=y1/2, 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?

Answer 1

Consider the given problem here the expected net of the “owner farmer” and the “rent farmer” are given below.

=> 125.05+75*0.5 = 100, for the owner farmer.

Now, for the rent farmer it is given by.

=> (250-100)*0.5+(150-100)*0.5 = 150*0.5+50*0.5 = 100. So, here the expected income for both the farmer is same. Now, the utility function is given by, “U=Y^0.5”. So, the expected utility of owner farmer is given by.

=> 0.5*(125^0.5) + 0.5*(75^0.5) = 9.92 = EU(owner).

Similarly, the expected utility of rental farmer is given by.

=> 0.5*(150^0.5) + 0.5*(50^0.5) = 0.5*(125^0.5) + 0.5*(75^0.5) = 9.66 = EU(rental). So, if we compare these two results we get that the “owner farmer” having more expected utility compare to the “rental farmer”. So, depending on the utility function the “rental farmer” is taking more risk compare to the rental farmer.