| In this dissertation I explore the impact of learning (and thus the possibility of experimentation) in economic environments.; In the first chapter (joint with Lones Smith) we characterize the behavior of value functions in a general class of experimentation problems near fixed points of the belief space. In particular, we provide an exact asymptotic formula for the value function and its first two derivatives in the neighborhood of a, fixed point, valid for discount rates above a given threshold. The asymptotic behavior of the value function and its first derivative is not particularly interesting—they both behave like constants. However, we show that the second derivative of the value function explodes at a geometric rate. We provide a simple formula for the rate of expansion (not simply a lower or upper bound).; In the second chapter (also joint with Lones Smith) we consider a standard dynamic version of Becker's (1973) classic static matching model, and discover a robust failure of Becker's global result. We show that as the number of production outcomes grow, assortative matching is neither efficient nor an equilibrium for high enough discount factors. Specifically, assortative matching fails around the highest reputation agents for ‘low-skill concealing’ technologies. Our theory implies the dynamic result that high-skill matches (like the Beatles) eventually break up. Our results stem from two findings: (a) value convexity due to learning undermines match supermodularity; and (b) for a fixed policy in optimal learning, the second derivative of the value function explodes geometrically at extremes (an application of the theory in the first chapter).; In the third chapter I develop a dynamic model of technological adoption in the presence of switching costs. Firms receive information about the productivity of a new technology, with which they update their prior beliefs in a Bayesian fashion. This model is used to explore the impact of uncertainty on expected adoption thresholds. If learning is only the product of experience, I find that uncertainty speeds adoption, regardless of the magnitude of switching costs. If some information is revealed even when the firm is not using the new technology, I find that there is a boundary such that for switching costs below this boundary the possibility of learning speeds adoption of the new technology; the opposite holds for switching costs above this boundary. I then provide some comparative statics on the adoption thresholds. |
