Discounting and divergence of opinion

The objective of this paper is to adopt a general equilibrium model and determine the socially e¢ cient discount factor, risk free rate and discount rate when there are heterogeneous anticipations about the growth of the economy as well as heterogeneous time preference rates. Among others we tackle the following questions. Is the socially e¢ cient discount factor an arithmetic average of the individual subjectively anticipated discount factors ? More generally, can the Arrow-Debreu prices, the risk free rates, the subjectively expected socially e¢ cient discount factors and discount rates be obtained as an average of the individual subjectively anticipated ones ? Can beliefs dispersion be analyzed as a sort of additional risk or uncertainty leading to possibly lower discount rates ? Is it socially e¢ cient, when diversity of opinion is taken into account, to reduce the discount rate per year for more distant horizons ? If so, what is the trajectory of the decline ?