Suppose that a firm's production function is given by the Cobb-Douglas function q= (K^a)(L^ß) and that the firm can purchase all the K and L it wants in competitive input markets at rental rates v and w, respectively.
a. Show that cost minimization requires vK/a=wL/ß
b. Assuming cost minimization, show that total costs can be expressed as a function of q, v, and w of the form TC=(Bq^1/a+ß)(w^ß/a+ß)(v^a/a+ß) where B is a constant depending on a and ß.