Resolvent estimates for 2 dimensional perturbations of plane Couette Flow

We present results concerning resolvent estimates for the linear operator associated with the system of differential equations governing perturbations of the Couette flow. We prove estimates on the L_2 norm of the resolvent of this operator showing this norm to be proportional to the Reynolds number R for a region of the unstable half plane. For the remaining region, we show that the problem can be reduced to estimating the solution of a homogeneous ordinary differential equation with non-homogeneous boundary conditions. Numerical approximations indicate that the norm of the resolvent is proportional to R in the whole region of interest.Comment: 16 pages, 4 figures. A mistake in the proof of Theorem 1 was corrected. The presentation was changed a little, and typos were correcte

Learning-by-employing: the value of commitment

We analyze a dynamic principal–agent model where an infinitely-lived principal faces asequence of finitely-lived agents who differ in their ability to produce output. The ability of anagent is initially unknown to both him and the principal. An agent’s effort affects the informationon ability that is conveyed by performance. We characterize the equilibrium contracts andshow that they display short–term commitment to employment when the impact of effort onoutput is persistent but delayed. By providing insurance against early termination, commitmentencourages agents to exert effort, and thus improves on the principal’s ability to identify theirtalent. We argue that this helps explain the use of probationary appointments in environmentsin which there exists uncertainty about individual ability.Keywords: dynamic principal–agent model, learning, commitment.

Evidence about the Potential Role for Affirmative Action in Higher Education

In two recent cases involving the University of Michigan (Gratz v. Bollinger and Gruttinger v. Bollinger), the Supreme Court examined whether race should be allowed to play an explicit role in the admission decisions of schools. The arguments made in support of affirmative action admission policies in these cases and others raise two fundamental questions. First, do students actually have incorrect beliefs about individuals from different races at the time of college entrance? Second, if students do have incorrect beliefs at the time of college entrance, can diversity on a college campus change these beliefs? While a small literature has recently shed some light on the second question, no previous work has been able to provide direct evidence about the first one. In this paper we examine the first question by taking advantage of unique data collected specifically for this purpose.