I construct a model of a speculation for an economy with boundedly rational agents. Speculation is defined as a trade for gains from price change while investment is defined as a trade for consumption. In a model without boundedly rational agents, the equilibrium price exactly reflects the underlying value of the good traded whether the agents trade for price gain or for their own consumption. However a model of speculation with boundedly rational agents produces fundamentally different equilibrium from that of investment. The price rises higher than the fundamental value of the asset. Moreover the price may rise even higher than the level which equals the expectation of boundedly rational agents since the extra premium can be justified by the higher rate of price rise. In particular the paper shows that rational agents are responsible for the amplification of the price bubble since the price rises higher than the expectation of boundedly rational agents alone. Hence price bubble in the asset market occurs due to the cooperation of rational agents once there exists uncertainty as to the existence of boundedly rational agents.