Essays on dynamic incentives

This dissertation studies the design of optimal incentives for agents that make many decisions over time. If an agent is able to allocate resources between consumption and saving, then his optimal choice involves equating the marginal value of consumption with the marginal return from saving. However, if the agent also must make a discrete choice (such as whether to cover-up some bad news), then there is a technical problem: the return from saving is not a differentiable function. The second chapter develops envelope theorems that establish that this problem is irrelevant. The non-differentiable points only occur at suboptimal choices, and first-order conditions equating marginal cost with marginal benefit do in fact apply. The third chapter studies dynamic incentives arising from monetary policy in a setting where agents use money to smooth out a fixed cost of labor participation. The envelope theorem from the second chapter establishes that the marginal value of holding money is differentiable at optimal choices. The socially optimal monetary policy given by the Friedman rule leads the agent to equate the marginal utilities of consumption across time periods, so that the fixed cost is perfectly smoothed out over time. If monetary policy is inflationary, then a hot potato effect distorts the agents\u27 incentives away from constant consumption. The fourth chapter studies optimal incentives in moral hazard problems in which the agent may dynamically suppress signals and replace them with counterfeits. This form of fraud may affect the design of optimal contracts drastically. For example, if fraud is costless and produces perfect counterfeits, then there is complete market failure. This chapter studies how the possibility of fraud affects the design of incentives. It establishes that in optimal contracts, the principal deters all fraud, and does so by two complementary mechanisms. First, the principal punishes signals that are suspicious, i.e. appear counterfeit. Second, the principal is lenient on bad signals that the agent could suppress, but does not