Why labor and capital display diminishing marginal products

Question

Problem

Contrast the production functions given below:

a. Suppose that the production function faced by a 30-weight ball bearing producer is given by Q = 4 K^0.5L^0.5, where MP_K = 2K^-?0.5L^0.5 and MP_L = 2K^0.5L^-?0.5. Do both labor and capital display diminishing marginal products? Does the production function display a diminishing marginal rate of technical substitution?

b. Suppose that the production function faced by a 40-weight ball bearing producer is given by Q = 4KL, where MP_K = 4L and MP_L = 4K. Do both labor and capital display diminishing marginal products? Does the isoquant you drew in (a) display a diminishing marginal rate of technical substitution?

c. Compare your results. Must labor and capital display diminishing marginal products in order for the MRTS to diminish?

The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.