
This paper analyzes self-control problems in intertemporal consumption of a sin good where current consumption imposes a negative externality on one’s future selves due to the existence of present-biased preferences. We introduce the negative externality dubbed ‘internality’, which is augmented by the cumulative distribution function of the sum of previous consumption. We show that the shot-run self with self-control problem over consumes the sin good compared to that of the long-run self without present-biased preferences. Further, we investigate the effectiveness of self-bargaining with the presence of an external control devise as possible punishment. The short-run self faces three possible options: do nothing, accept the long-run self’s offer, or reject the offer. In the latter case an external control devices is implemented. It is shown that successful self-bargaining depends on the efficiency of the control device.
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