Question

A firm has a technology that relies on only one input (call it x). The output of the firm (call it y) increases as you increase x but at a diminishing rate. Based only on the information provided then y=100*exp(-x) would be a valid representation of this firm’s production function.

Answer 1

If the output of the firm (call it y) increases as you increase x but at a diminishing rate, then y=100*exp(-x) wouldn't be a valid representation of this firm’s production function, because at x = 0, 1, 2 and 3 the output is y = 100, 36.78, 13.53 and 4.98 respectively, so according to this production function the output of the firm (y) decreases as you increase x.