Abstract: This paper analyzes the character of the long-run cost function with Cobb-Douglas production function.We explain the economical meaning of all kinds of parameters,and analyze the extremum condition of the long-run cost function under constant factor production elasticity and factor price.It is concluded that if the firm inputs the factor in equal quantity,then the long-run cost will be maximized.The paper points out that the firm must avoid the equal quantity of the factors inputting.

Key words: Cobb-Douglas production function, long-run cost function, maximized long-run cost