Company P has commissioned an economic torecast trom consultancy A in order to choose the optimal level of investment in a new project. The profitability of the project depends on the level of investment I 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 I. The company believes that random variable is uniformly distributed on the interval [0,10]. The payoff to the company from investment I in state is P(I)=1000(I)2 The consultancy is paid a fixed amount F regardless of what it reports. However, it has a hidden stake in the outcome of the project; its payoff if the company invests I in state is A(I)=F(I1.05)2 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. a. Will the consultancy report truthfully? Why or why not? [4 marks] b. What would you expect equilibrium to look like? [4 marks] c. Find an equilibrium in which the consultant's 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 IHigh or ILow. Find these investment levels and the 'trigger level' of the consultant's report above which the company will choose the high level of investment. [10 marks] e. Are there more efficient equilibria (where the consultant's 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] f. 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 consultant's information)? [5 marks].

1. Company P has commissioned an economic torecast trom consultancy A in order to choose the
optimal level of investment in a new project. The profitability of the project depends on the level
of investment I 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 I. The company believes that random variable is uniformly distributed on the interval
[0,10]. The payoff to the company from investment I in state is P(I)=1000(I)2 The consultancy
is paid a fixed amount F regardless of what it reports. However, it has a hidden stake in the
outcome of the project; its payoff if the company invests I in state is A(I)=F(I1.05)2 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. a. Will the consultancy
report truthfully? Why or why not? [4 marks] b. What would you expect equilibrium to look
like? [4 marks] c. Find an equilibrium in which the consultant's 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 IHigh or ILow. Find these investment levels and the 'trigger level' of the
consultant's report above which the company will choose the high level of investment. [10
marks] e. Are there more efficient equilibria (where the consultant's 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] f. 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 consultant's information)? [5 marks]