Final answer:
The marginal rate of technical substitution (MRTS) given the marginal product of labor (MPL) as 15 and the marginal product of capital (MPK) as 10 is 1.5. This means the firm can substitute 1.5 units of capital with 1 unit of labor to keep output constant.
Step-by-step explanation:
The marginal rate of technical substitution (MRTS) is defined as the rate at which a firm is able to substitute one input for another while keeping the level of output constant. In this case, you have given the marginal product of labor (MPL) as 15 and the marginal product of capital (MPK) as 10.
The MRTS is calculated by taking the ratio of the marginal products of the inputs. Hence, the marginal rate of technical substitution between labor and capital (MRTS L,K) is given by:
MRTS L,K = MPL / MPK
Substituting the given values:
MRTS L,K = 15 / 10 = 1.5
Therefore, the MRTS is 1.5, meaning that the firm can replace 1.5 units of capital with 1 unit of labor to maintain the same level of output.