Three Essays on Microeconomic Dynamics

Abstract

The following three essays discuss dynamics under uncertainty. The first two chapters discuss the question of how one agent can learn about another in an environment with repeated interaction. The third chapter centers on the optimal time to implement a policy in a scenario with stochastic features.

In the first chapter I develop a model of learning in which the focus is on the process of gradual learning. In particular, I examine the question of how the dynamic learning process can improve the long run acquisition of information. The model is based on a repeated interaction between two agents, an Investor and an Associate, where cooperation by both is needed in order to develop a project. The Investor can learn about the Associate by offering different levels of investment in order to infer something about the Associate's type through his response. If the Associate defaults, then he has a short term gain but the interaction is over. The model looks to find the long term level of investment in this interaction. The model can be viewed in a variety of ways, for example as trust development. It can explain why in some cases, even after a long interaction, the level of trust and hence the associated investment will not increase above a certain threshold.

One concept that is relevant in this chapter is the notion of "monotonicity". Monotonicity means roughly that the interaction in every period should be informative. If this happens, then the investment realized by both agents increases gradually, and the amount of information necessary for determining the next period investment is reduced.

The second chapter develops an application of the theory proposed in the first chapter. In this chapter the idea further elaborates upon the theory by using a particular functional form, a Cobb Douglas function. Additionally, this chapter discusses how the requirements of the theorems of the first chapter are related to the fundamentals of the model and develops new results. For example, one result with empirical implications is: a more patient Investor will not necessarily learn more in the long term than a less patient one.

The third chapter analyzes a different problem. Here, an authority has the chance to implement a costly policy, facing the risk that with some probability a similar policy is imposed externally. The question is: what is the best way to implement this policy? Should one just wait until the change is imposed or should one commit to some policy in the future? The difference between both cases is described and we analyze how the parameters of the model affect the optimal solution of the policy maker. Finally, I analysis the effects of time length between the announcement and the implementation. I then characterize an "optimal announcement time" for this model.