Quality is an important variable of non-price competition between firms. In this thesis,we assume the quality of products is determined by the material used and the cost of product design,which are called the quality functions. To analyze how a firm decides its expenses on product design and material,we focus on two industry structures: monopoly and vertical product differentiation markets. In the monopoly market,the quality function is assumed as constant elasticity of substitution,and the firm's decision when equilibrium is achieved is investigated by computing the costs on material and product design. On the other hand, in the vertical product differentiation market,we assume there are two kinds of firms in the market: a monopoly firm producing high-quality products,and many other perfect competition firms producing low-quality products. The decisions of firms under equilibrium condition are discussed and comparedwhen the quality functions are in the form of Cobb-Douglas and Leontief.