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R>We analyze this problem in the Arrow-Debreu framework. We assume that there is a complete set of Arrow-Debreu securities in the economy. The equilibrium price of Arrow-Debreu security in state s is denoted  , which means that agent   must pay   ex-ante to receive one unit of the consumption good if and only if state s occurs. We normalize prices in a way such that 
We assume rational expectation in each group. Thus the equilibrium for group   requires that
                             (2)
Let   denote the proportion of agents of group   in the economy.
The market clearing condition is
          
This can be written as
                     ,        (3)
 where we interpret   as the average wealth in the economy at time t.

(1)  local index of conformism
Let’s see some consumption externalities in the utility function  , in addition to the former assumption that the utility is increasing and concave with respect to one’s own consumption level, our model allows for  , which means agent is jealous of the other agents in her group; and   which means that the agent is altruistic to others. Finally, we assume  . It means that an increase in average consumption in the group increases the marginal utility of one’s own consumption. It also means that the agents want to “keep up with the Joneses”. We can also use the term “conformism”. We define the local index of conformism in the Gollier’s way:
  (4)
Here is a bit different from Gollier, because our model introduced time concept, while his model is only static and independent of time.
  Here we have some explanation about index of conformism  . From the definition, we know that   is the increase in one’s own consumption that leaves one’s marginal utility unchanged after a unit increase of the mean consumption in the economy. We say that an agent is anti-conformist if   is uniformly negative. And we say that an agent is conformist if   is strictly in between 0 and 1. Finally, he is “over-conformist” if  is uniformly larger than 1. The simplest case of consumption externalities is additive of consumption:
 . (5)
In 1999, Campbell and Cochrane and in 2002, Shore and White considered this kind of conformism. In this case, the degree of conformism  is equal to a constant . Also following Gali(1994) and Carroll, we will illustrate our model by using special case of multiplicative externalities.
 (6)
for the widely used increasing and concave utility function  . Here we may compute: 
 
 
 So the index of conformism
 
         
when  ,    =
Hence    =   = (7)
From the expression, we can see that   is an index of the degree of consumption externalities. When  =0, then  =0, which means there is no externality. And when utility function has the form of  , the agent focuses only on his consum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。