A one-sector growth model with consumption standard: Indeterminate or determinate?

In a representative agent, one-sector growth model in which the discounting is decreasing in the consumption standard measured as the current average consumption flow, Drugeon (1998) establishes local indeterminacy. This paper extends Drugeon's setup in the discount rate. In our setup, the consumption standard is a habit stock that a weighted average of the whole history of average consumption flows in the past. Local indeterminacy emerges only when the speed of habit formation tends to infinity; otherwise, local indeterminacy cannot appear, no matter how large the habit affects the discount rate.