Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems

I extend Holmstrom and Milgrom's model by allowing the agent to control privately or publicly the diffusion-rate process, and show that the optimal contract is still linear. I discuss the conditions under which conflicts over the choice of diffusion rate do and do not arise. As an application, I examine project- selection problems of a firm. Conflicts between the manager and investors arise because giving the manager too much incentive to work to increase the profit from ongoing operations can induce him to be too conservative in project selection, possibly resulting in optimal contracts with low sensitivities.