The effect of vertical integration by an input monopolist on the price of the final product and the derived demands are examined when the production is of CES and the demand for the final product is of constant elasticity. The results are proved by analytical methods. Specifically, when the elasticity of substitution is less than one, the price of the final product can decrease but, regardless of any conditions, the derived demand for the nonmonopolized input decreases. However, that of monopolized input decreases if and only if the elasticity of substitution exceeds the elasticity of demand.