This paper examines the possibility of economic slump with the liquidity trap in a sticky price model. The main findings of the paper are: First, the appearance of recessions and depressions with liquidity traps is observed as equilibrium paths if the government conducts a contractionary monetary policy. Second, the model exhibits the indeterminacy of equilibrium paths. Finally, expansive monetary policy is an effective tool to escape from the liquidity trap, although fiscal stimulus causes full crowding out.