Question

An agent can exert one of two levels of effort e ( eh,=2 el =1) . Firm gross profits are G = ( Gh=16, Gl = 0) The outcome Gl occurs with a probability of ᴨh =0.75 if action eh is taken and with a probability of ᴨl =0.25 if el is taken. The utility function of the agent is u(w,e) = w1/2 –e and the reservation utility is zero, find the first best contract

Answer 1

The agent has to make a choice between 2 levels of effort eh=2, el=1. High level has a probability of 0.75 and lower level has a probability of 0.25 . under both these probablities the prospect for the product demand again has 3 probablities high , medium and low . Given the high level of probablity of high level of effort and the gross profit G=16, we can get the expected value by multiplying the gross profit with the corresponding probability . Thus high level of effort, the expected value is 16*0.75 = 12 and the low level effort= 16 *0.25 = 4. Hence the agent can make the best decision taking the high level of effort .