The monetary endogenous growth model in which money is introduced into the system via a transactions-cost technology. Motivation to pursue social status, the relative magnitudes of the intertemporal elasticity of substitution and the production technological parameter are crucial for determining the stability property of the model. When a strong enough motivation to pursue social status, resulting in the growth rate of money supply and economic growth rates are positively correlated, because reducing the opportunity cost of holding money, increase people's willingness to hold money, thereby reducing transaction costs and promote economic growth. If the motivation for the pursuit of social status, inadequate or does not exist, so that the transaction costs increase, inhibit economic growth. But whether or not a strong motivation, People to pursue the degree of social status and economic growth rates are positively correlated.