The correct answer is $\boxed{\text{B}}$.
The marginal productivity of capital (MPK) is the additional output that is produced when one more unit of capital is used, holding all other inputs constant. The marginal rate of technical substitution (MRTS) is the amount of capital that must be given up to increase labor by one unit, holding output constant.
In this question, we are given that the MPK is 4 units of output and the MRTS is 2 units of capital per unit of labor. This means that if we increase labor by one unit, we must give up 2 units of capital in order to keep output constant.
The marginal productivity of labor (MPL) is the additional output that is produced when one more unit of labor is used, holding all other inputs constant. We can calculate the MPL as follows:
$$MPL = \frac{MPK}{MRTS} = \frac{4}{2} = 2$$
Therefore, the marginal productivity of labor is 2 units of output.
Here is a brief explanation of each option:
- Option A: 1/2. This is incorrect because the marginal productivity of labor cannot be negative.
- Option B: 4. This is the correct answer.
- Option C: 6. This is incorrect because the marginal productivity of labor cannot be greater than the marginal productivity of capital.
- Option D: 8. This is incorrect because the marginal productivity of labor cannot be greater than the marginal productivity of capital.