True or False with explanation (explanation determines credit).

a. (5) A production function with constant returns to scale can exhibit diminishing marginal product of its inputs.

b. (5) Suppose a production function only uses one input, labor. If production displays constant returns to scale, then it does not exhibit diminishing marginal product of labor.

c. (5) Suppose a production function utilizes both capital (K) and labor (L) as inputs. For this production function, an increase in L (holding K constant) leads to an exact proportional increase in output. That is, for instance, increasing L by a factor of two yields twice as much output. Then, this production function must display increasing returns to scale.