Question

2) (4 points) Suppose that a firm is producing in the short run using a combination of labor and capital. At their current point of production, the MPL = 100, MPK = 6000, w = $25 and r = $2000. In the long run, is the firm minimizing costs? If not, how should they change around their use of K and L to minimize costs while producing the same quantity? Discuss.

Answer 1

Here in this question , the marginal rate of substitution (MRTS) of the firm is :-

MPL/MPK = 100/6000 = 1/60

And the ratio of input prices = w/r = 25/2000 = 1/80

At the optimal level , that is a level where the firm is maximising output with minimum cost , MRTS should be equal to the ratio of input prices.

But here , MRTS is greater than the ratio of input prices. This means , that the firm is not minimizing its cost in producing its maximum level of output. In order to minimize cost , the firm must change the share of its labor and capital in production , that is , it must increase its use of labor and reduce the use of capital , this would decrease the MPL and increase the MPK , which would therefore in totality reduce the value of MRTS. The firm must continue with alteration of labor capital share till the point MRTS becomes equal to the ratio of input prices which is 1/80. At this point , firm would be minimizing its cost in producing the same quantity.