Information space conditions for the first-order approach in agency problems

When the principal is risk-neutral, the optimal contract for the agent which is derived using the first-order approach depends on the signals of the agent's effort only through the information variable (i.e., the likelihood ratio of the signals). By analyzing the principal-agent problem based on the information variable rather than the signals, we derive three new sets of conditions under which the first-order approach is justified. We show not only that they are more general than any sets of conditions in the existing literature, including Conlon's conditions in the multi-signal case and Jewitt's conditions in the one-signal case but also that they do not require the monotone likelihood ratio property (MLRP) for the density function of the signals. We also derive a set of conditions which applies when the principal is risk-averse and show that those conditions are more general than Conlon's corresponding conditions.