A firm is hiring a contractor to build-out a new office space.

The likelihood of the contractor completing the job on time, p, depends on the number of additional labor hours they hire to work on the job, e, which the firm does not observe.

The chance of completing the job on time is P = (e+20)/(e+200)

If the contractor does not complete the job on time, it will cost the firm $25,000 to find temporary office space while they wait for the job to be completed.

The contractor’s estimated profit on the contract excluding additional labor is $50,000.

It costs the contractor $10 per hour for additional labor.

The firm has decided to include an on-time completion bonus to the contract to encourage the contractor to hire additional labor to finish the new office space on time.

Questions

a) How many additional hours of labor would the contractor hire if they were offered a $3000, $4000, and $5000 on-time completion bonus?

b)What is the pattern between the contractor’s expected profit, the probability of on-time completion, and the firm’s expected cost?

c) What is the optimal on-time completion bonus for the firm?

d) What is the tradeoff the firm faces in determining the optimal bonus?