Question

1. If wH=100 and wL=36 and U(w)=w^1/2. Further, let the reservation utility be 7.

(a) What is the minimum probability for which the wage earner accepts the contract?

(b)Let p=3/4. What is the maximum cost of effort for which the tenant accepts the contract?

2. If alpha=1/2 and H=1000 and L=200 what is the minimum rent the landlord charges such that the absolute difference between the rent and the sharecropping contract for the tenant (in the good state) is twice as large as the difference between the sharecropping and the rent contract (in the bad state).

Answer 1

Q1)

(a) Let p be the minimum probability for which the wage earner accepts the contract

Thus, at this p, Expected value of contract = reservation utiltiy

=> p*(100)^0.5 +(1-p)*(36)^0.5 = 7

=> 10p + 6(1-p) = 7

=> 10p + 6 - 6p = 7

=> 4p = 1

=> p = 1/4

If p < 1/4 , wage earner will not accept the contract

(b) Let the cost of effort be x

Cost should be such that, utility from high effort >= utility from low effort

Thus, at the max cost we have, utility from high effort = utility from low effort

=> 3/4 *(100 - cost)^0.5 = 1/4(36)^0.5

=> (100 - cost)^0.5 = 2

=> 100 - cost = 4

=> cost = 96