This study examines how monetary policy affect the relationship between inflation and unemployment. Using a framework with microfoundations to study how public employment and government consumption are effect unemployment. In this model, government agents, subject to the same restrictions, matching and term of trade as private agents. The measure of government agents in the labor market and goods markets will affect the behavior of the private agents, and change the Philips curve. We found that a higher government consume will crowding out effect than the private consume in the goods markets. And a higher wage premium of public sectors versus private sectors result in a higher unemployment rate. This model shows that the government should reduce the intervention on the market under a positive slope of the Philips curve.