the level of investment and on a random variable (the state of the market). The consultancy can determine the correct value of , and will write a report informing the company, which will then choose . The company believes that random variable is uniformly distributed on the interval [0,10]. The payoff to the company from investment in state is

(|) = 1000 ( ) The consultancy is paid a fixed amount regardless of what it reports. However, it has a

hidden stake in the outcome of the project; its payoff if the company invests in state is (|) = ( 1.05)

Assume that F is fixed by law (i.e. not chosen by the company or the consultancy) and is small enough that the contract (commission) will always be offered and accepted.

Will the consultancy report truthfully? Why or why not? [4 marks]

What would you expect equilibrium to look like? [4 marks]

c. Find an equilibrium in which the consultants report is ignored; what will the company invest? [5 marks]

d. Now find an equilibrium in which the company responds to the report by making either a high or a low investment or . Find these investment levels and the trigger level of the consultants report above which the company will choose the high level of investment. [10 marks]

Are there more efficient equilibria (where the consultants report conveys more useful information i.e., where the investment level is more sensitive to the report? For extra credit, can you find a formula for an equilibrium with three levels of investment? [10 marks]

Finally, can you describe an alternative fee structure for the consultant that would lead to an efficient outcome (where the company makes maximum use of the consultants information)? [5 marks]