The manager of a firm receives an engineering report claiming that an additional hour of capital would add twice as much output as would an additional hour of labor. According to the firm's accountants, an hour of capital costs 3 times more than an hour of labor.

Question

(i) Is the firm on its expansion path? Why or why not?
(ii) Suppose the firm is under contractual obligations to keep its output at current levels. What long-run adjustment (if any) should the manager make in the firm's employment of labor and capital?
(iii) Sketch an isoquant-isocost diagram that illustrates the situation described in part ii. Label the initial situation "A" and the post-adjustment situation "B." The scale of your diagram does not need to be accurate.

Answer 1

(i) No, the firm is not on its expansion path. The engineering report shows that the value of MPK is twice that of MPL, so MRTSLK = MPL/MPK = 1/2 hour of capital per hour of labor. The accounting report shows that the value of PK is 3 times that of PL, so PL/PK = 1/3 hour of capital per hour of labor. Thus MRTSLK ? PL/PK, but the two values must be equal for the firm to be on its expansion path.
(ii) We can conclude that the isoquant is steeper than the isocost since MRTSLK > PL/PK, so the manager should employ more labor and less capital in the long run.
(iii) The firm will move down a fixed isoquant onto a lower isocost. This situation is shown in the accompanying diagram, which is not drawn to scale.