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Title: On Learning and Growth
Authors: Mirman, Leonard J.
Reffett, Kevin
Santugini, Marc
Keywords: Brock-Mirman environment
Dynamic programming
Optimal growth
Issue Date: 2013-10
Series/Report no.: Cahiers du CIRPÉE;2013-3
Abstract: We study the effect of learning on optimal growth. We first derive the Euler equation in a general learning environment without experimentation. We then consider the case of iso-elastic utility and linear production, for general distributions of the random shocks and beliefs (i.e., no conjugate priors) and for any horizon. We characterize the unique optimal policy function for this learning model. We show how learning alters the maximization problem of the social planner. We also compare the learning model with the deterministic and stochastic models. This work builds on the work on learning and growth in a Brock-Mirman environment initiated by Koulovatianos, Mirman, and Santugini (2009) (KMS) for the Mirman-Zilcha model (with log utility and Cobb-Douglas production). While the Mirman-Zilcha model provides some insights about the effect of learning on growth, it also hides many important features of learning that the model in this paper takes account of. In other words, compared to the Mirman-Zilcha model, we show that the case of iso-elastic utility and linear production yields a more profound effect of learning on dynamic programming and thus optimal behavior.
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