This paper has investigated the role of search and matching frictions in a monetary model and examined if the Friedman rule, advocating a rate of deflation equal to real interest rate, is still right. We defined a dynamic programming problem in which money is situated in the model by cash in advance constraint, and used a numerical method (value function iteration method) to solve the pre-mentioned problem. Also, in this paper, the concept of the homogenous agent is substituted by the heterogeneous agent, and there are two groups of agents, namely unemployed and employed agents. The difference between the two divergence groups is indicated by different constraints in this study. According to our model, the Friedman rule will not maximize the aggregate welfare of the assumed society with this new friction. It is noteworthy that the parameters of the numerical model have been derived from the United States economy and the essay is theoretical. The results can be applied in different economies with their specific parameters. Also, the study offers some implications to central banks. JEL Classification: E52, E24, C78.
