On the closed-form solution of an endogenous growth model with anticipated consumption

Abstract

This paper derives a closed-form solution of the AK endogenous growth model with logarithmic preferences and anticipated future consumption which enters additively into effective consumption. We get an explicit representation of the time paths of the economic variables in level by resorting to Gaussian Hypergeometric functions. We compare the model with anticipated future consumption to the model with habit formation. The maximum utility attainable in the model with anticipation is shown to be higher than the one attainable in the model with habits. Using the derived explicit expressions, we perform some comparative-dynamics and -statics analyses with respect to relevant parameters. Numerical simulations complement the theoretical results. Thus, this work provides further support to the usefulness of especial functions in the study of economic dynamics.