Question

Suppose the production function for a fim is given by: q4L05k 05. f the firm currently has 10 units of capital (K) Suppose the production function for a firm is given by: q-4L.K. · lf the firm currently has 10 units of capital (K) and 10 units of labor (L), then calculate the Marginal Rate of Technical Substitution (MRTSLK). (Round to the nearest two decimal places if necessary.) Answer:

Answer 1

Production function is as follows -

q = 4L^0.5K^0.5

Calculate the marginal product of labor (MPL) -

MPL = dq/dL

MPL = d(4L^0.5K^0.5)/dL

MPL = 2K^0.5/L^0.5

Calculate the marginal product of capital (MPK) -

MPK = dq/dK

MPK = d(4L^0.5K^0.5)/dK

MPK = 2L^0.5/K^0.5

Calculate the marginal rate of technical substitution (MRTS_LK) -

MRTS_LK = MPL/MPK

MRTS_LK = (2K^0.5/L^0.5)/(2L^0.5/K^0.5)

MRTS_LK = K/L

Firm is currently using 10 units of capital (K) and 10 units of labor (L).

So,

MRTS_LK = 10/10 = 1

Thus,

The Marginal Rate of Technical Substitution (MRTS_LK) is 1