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In the Bewley models, the endowment is faced to idiosyncratic risks. But contingent claims markets is restricted or completely excluded by assumption and so households couldn’t insure themselves against these risks. Consequently, households will have strong motive to precautionary saving for self-insurance. Households’ only option is to “self-insure” by managing a stock of a single asset to buffer their consumption against adverse shocks. The bewley models differ mainly with respect to the particular asset that is the instrument for self-insurance: fiat currency, credit (such as IOU's, bank deposits, government bonds and so on) or capital. In these models if the interest rate would be equal to the rate of the time preference then asset and consumption diverge to infinity and so monetary equilibrium doesn't exist. Therefore these 1 This paper is a final thesis of the PhD programme at the Isfahan university. 2 Corresponding Author International Journal of Academic Research in Business and Social Sciences August 2013, Vol. 3, No. 8 ISSN: 2222-6990 521 www.hrmars.com/journals models conclude that the use of Friedman rule can be misleading in an incomplete market setup. Therefore these models reduce the interest rate so that asset and consumption converge and consequently the monetary equilibrium exists. In this paper we extend the bewley models and construct a heterogeneous model with idiosyncratic risks and borrowing constraint where agents hold money and bearing interest assets as government bonds for precautionary motives and self-insurance. We show that the consequences of bewley models in this condition are still true: There should be the interest rate lower than time preference ( r ) to insure the existence of monetary equilibrium. With sufficient uncertainty in the income and interest rate sequences, consumption will grow without bound even if the rate of interest is equal to or greater than the discount rate. Introduction This paper describes a version of what is sometimes called a "savings problem" (Chamberlain and Wilson, 2000). A consumer wants to maximize the expected discounted sum of a concave function of one-period consumption rates. However, the consumer is cut off from all insurance markets and almost all asset markets. The consumer can only purchase nonnegative amounts of a single risk-free asset. The absence of insurance opportunities induces the consumer to adjust his asset holdings to acquire “self-insurance.” Self-insurance occurs when the agent uses savings to insure himself against income fluctuations. On the one hand, in response to low income realizations, an agent can draw down his savings and avoid temporary large drops in consumption. On the other hand, the agent can partly save high income realizations in anticipation of poor outcomes in the future (Sargent and ljungqvist, 2004). Bewley models The bewley models are the class of models were invented by Bewley (1977, 1980, 1983, 1986), to study a set of classic issues in monetary theory such as inside and outside money, a free banking regime, the criticism of Friedman’s optimal quantity of money (Sargent and ljungqvist, 2004). Bewley (1983) was the first to derive the properties of a model were money was used as a self-insurance device to cope with some idiosyncratic risk. He notably shows that Friedman's rule cannot hold in such a framework. If the interest rate is close to the discount rate, the money demand explodes because of precautionary motives (Jelloul, 2007). The equilibrium thus necessitates a low rate of interest such that r thereby violating the Friedman rule (Huggett, 1993). Imrohoroglu (1992) used numerical simulation to compute the welfare cost related to inflation by using the steady state average utilities. In this paper we extend the bewley models and construct a heterogeneous model with idiosyncratic risks and borrowing constraint where agents hold money and bearing interest assets as government bonds for precautionary motives and self-insurance. We implement along the lines of Aiyagari (1994) and Imrohoroglu (1992) a model with two assets that can be used as store of value. International Journal of Academic Research in Business and Social Sciences August 2013, Vol. 3, No. 8 ISSN: 2222-6990 522 www.hrmars.com/journals The Model The present model describes a particular type of incomplete markets model. The models have a large number of ex-ante identical but ex-post heterogeneous agents who trade a single security. We use a general equilibrium framework and infinite horizon savings problem. We assume that the government augments the nominal supply of currency over time to finance a fixed aggregate flow of real transfer T.The government budget constraint at t≥0 is: (1( 1(1 ) t t t T T g Where g is the rate of money supply growth. We consider a continuum of agents with distinct money and bonds holdings. Every agent occupies a state s at time t with a probability ( | ) s s of transiting to a state s' at t + 1. The sequence of household’s endowment evolves according to an m-state Markov chain. Each period t, every agent receives a wage depending on its state. If the realization of this process in time t is equal to i s , then the income of household is equal to i s . The households for selfinsuring themselves can some cash money or to adjust its bond holdings by paying a transaction cost ( ). Money and bonds holdings are nonnegative so no borrowing is allowed. The agent's sequence of consumption and money holding and bond holding is 0 { , , } t t t t c m b . Bond has a net rate of interest i and fiat currency has an implicit rate of return 1 1 t t p r p . Agents hold 0 t m money and 0 t b bonds at the beginning of period t. households decide to consume t c to maximize their intertemporal discounted utility: (2) 0 ( ) t t t t U E u c |
