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a significant variation across studies and within studies across different groups. There is no convergence toward an agreed-on or unique rate of impatience. In the literature they survey, rates range from –6% to 55700%. This variation could stem from differences in the time horizon. Because it is unlikely that consumers use the same discount rate per period when discounting utility over different time horizons. Strotz (1956) was the first economists to discuss horizon-dependent discount rates. Empirical study shows that agents discount future happiness at a rate that declines with the time at which the happiness will be introduced. Generally, people use “hyperbolic discounting”, which means declining discount rate with respect to time-horizon, rather than exponential discounting. This may lead to time inconsistency problem that is recently becoming a “hot” topic.
When agents use different rates of impatience to discount their future utility, it is not clear which discount rate should be used, for example, for public investments. This raise the more general question of the aggregation preferences in a group. We consider a general model where each agent maximizes a time additive lifetime utility. The discount rate is heterogeneous in different groups and it may depend on either the time of receipt( hyperbolic discounting) or on current assumption. Agents may also have different instantaneous utility functions. We assume that the agents is able to allocate consumption within the groups in a Pareto-efficient way. Time additivity is essential to define a concept of impatience. Rubinstein (1974) also examined the question of aggregating heterogeneous rates of impatience, but he derives a solution only for exponential and logarithmic utility function in a two period model.
One of the contribution of this paper is that

This paper proceeds as follows. In section 2, we describe the model, and in the model we define local index of conformism and  In section 3, We show the efficient sharing rules and choose a representative agent .In section 4,  the individual assets demand

 

 

2 Description of the model

We consider an economy consists of N groups of consumers. To keep the model simple, consumption externalities only take place within each group, but not between groups. Agents have heterogeneous preferences that are indexed by  .
We assume agent of type   live infinitely long, so his life-time utility function is:
                  (1)
 is the discounted utility received by agent of type  consuming c at time t, where c(t) is the agent’s consumption at time t and C(t) is the average consumption in her group at time t.
We have some assumption about u: u is twice differentiable with respect to (c, C, t) and that  is strictly negative . If   is decreasing in t, consumers are impatient, which means that at any given consumption level they value future marginal utility
   
Let   characterizing the distributions of characteristics  in group i,
i= 1,….N. Let   denote the proportion of agents of group i in the economy.
  The groups must take a decision towards a collective risk. As mentioned in introduction, this can be a portfolio choice, or a investment decision to reduce a global risk. 本论文由英语论文网提供整理，提供论文代写，英语论文代写，代写论文，代写英语论文，代写留学生论文，代写英文论文，留学生论文代写相关核心关键词搜索。