The Production Function

What must be an essential feature for all production functions?

-That if the input is 0, then the output must be 0.

-Thus, if the input is greater than 0, the output must be greater than 0

With this production function, what is happening to

f(x)

f’(x)

f’’(x)

If we say x = number of farmers, and f(x) = grain produced

-We can see that as you increase the number of farmers, the amount of grain being produced rises. Thus, as x rises, so does f(x)

-We also see that as x increases, so does y in a way that its slope is positive. Thus, we can say that f’(x) > 0

-Finally, as we see x increasing, we see that the gradient gets less steep and flatter. Thus, we can say that f’’(x) < 0

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