Concave and Convex Functions

3.1.3 of The Economy 1.0 & The Economy #2

For a function to be concave what does that mean?

-Where the function of two variables where the line segment between any two points on the function lies entirely below the curve, representing the function.

Illustrate how a function can be concave in mathematical terms.

LHS: The function of the average (of two values)

RHS: The average of the function (of two values)

-Similar yet so different

Suppose that Jason’s production function is this.

Scenario 1: He spends first term doing nothing, and then studies 9 hours every day in his second term

Scenario 2: Spends 4.5 hours on studying on both terms

Which will give me a higher grade ultimately?

Scenario 1: First term will produce a grade of 0, and the second term will produce a grade of 60. Overall, an average grade of 30.

Scenario 2: First and second terms produce a grade of 42.5, thus producing an average grade of 42.5

Why? Because this produces the concave mathematical formula

Scenario 1 was the average of the function of the two terms

Scenario 2 was the function of the average of the two terms

What does this production function infer? What would the marginal product look like?

-This would be seen as a convex function, meaning that the marginal product is increasing, not diminishing.

-Thus, this means that every hour spent studying adds more grade points than the hour before.