The Road and Maritime Services (RMS) Department considers outsourcing a highway repair project to a new contractor. The project is rather routine, but the contractor is new.

1. If the objective of RMS is to control the cost of the project, should RMS offer a cost-plus (CP) or fixed price (FP) contract?
2. If the objective of RMS is to shorten the completion time of the project, under what circumstance, should RMS offer a fixed time fixed price contract or a time-dependent bonus contract?
3. The contractor has two options to undertake the highway repair project. The details of these two options are listed in the following table. Hint: Part c) is unrelated to part a) or b).

Option ID	Contractors Cost	Completion Time
1	3	F-distribution with mean 30
2	6	Log-normal distribution with mean 20

RMS wishes to induce the contractor to choose option 2 (which is the socially optimal choice). Due to moral hazard, RMS can neither observe nor verify what option the contractor uses. Instead, RMS offers to pay the contractor P(t)=f-bt, where f is a fixed payment, b is a linear penalty rate, and t is the project completion time. The contractor is risk-neutral and has a reservation value of 2. Derive the incentive compatibility (IC) constraints and individual rationality (IR) constraint to induce the contractor to take option 2.