Contrast the production functions given below:
a. Suppose that the production function faced by a 30-weight ball bearing producer is given by Q = 4K0.5L0.5, where MPK = 2K- 0.5L0.5 and MPL = 2K0.5L- 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 MPK = 4L and MPL = 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?