According to Engineer and Shi (1998, 2001) and Berentsen and Rocheteau (2003), the double coincidence of wants problem seems to be not essential to rationalize the use of money in a search theoretic framework. This paper analyzes an endogenous price search model of money where there is universal double coincidence of wants. The existence of a monetary equilibrium depends, essentially, on the asymmetry in the role played by economic agents in the exchange and production processes. In particular, entrepreneurs are assumed to produce a fixed amount of a divisible consumption good by means of labour services provided by workers. Entrepreneurs can offer a co-operative (barter) contract or a monetary contract to workers. Under the co-operative contract real wages are determined in the labour exchange sector, while in the monetary regime real wages are determined in the commodity exchange sector. The monetary contract is proved to be an equilibrium strategy provided that: (i) the workers' labour disutility is sufficiently high and/or (ii) the entrepreneurs' bargaining power in the commodity market is sufficiently large relative to their bargaining power in the labour market. The rationale for money comes from the fact that entrepreneurs use it as an instrument to maximize their output share.