This paper develops a two-country, two-currency search model to study how monetary policy and government transaction strategies affect the circulation values of the two currencies. Government agents follow exogenous trading policies, only accept and hold domestic currency. When domestic currency inflates slightly, increasing the trading probabilities of government and private agents, domestic currency appreciates due to increased demand for domestic currency as long as private agents accept and hold domestic and foreign currencies. As the domestic inflation rate goes up the decrease in the rate of return of domestic currency becomes the dominant effect, and thus the domestic currency value declines. When government demand for overseas goods is very large, foreign sellers accept domestic currency even if the cost of verifying this domestic currency is high. Therefore, domestic currency becomes an international currency.