Suppose q is produced using three factors of production, z1, z2, and z3. In the short run, the firm takes z1 as fixed and then chooses z2 and z3 to minimize the cost of producing some given level of output. Under what circumstances will an increase in z1 (1) raise short run costs, (2) lower short run costs, or (3) leave short run costs unchanged? That is, if C(w1, w2, w3, z1, q)is a firm's short run cost function, what determines the sign of C/z1? Give an intuitive explanation of your results(HINT: Think about the relationship between the price ratio and the MRTS)