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In this study, we apply "the equilibrium price" to investigate the efficiency and the elasticity of Taiwan securities trading market. The "the equilibrium price" of each transaction are used to represent the true price of the security. The intra-daily tick-by-tick data of the Taiwan security market is used to obtain the equilibrium prices. Empirical transaction of the two companies Uni-President Enterprises Corporation and Formosa Plastics Corporation are studied. Time-series models of the equilibrium price and the transaction price are established. The time lengths returning to the equilibrium status are also studied, called the efficiency time. Based on the results, we discuss the efficiency of the two stocks. In order to understand the impact of the efficiency time, linear regression models of the efficiency time are built. Furthermore, the variance ratios of the two stocks are also investigated to study their market efficiency. Finally, the elasticity of demand and the elasticity of supply are studied and their Markov chain models are established. The results show that the two companies stay more time in the inelastic states.