What causes a decreasing returns to scale?

Decreasing returns to scale occur if the production process becomes less efficient as production is expanded, as when a firm becomes too large to be managed effectively as a single unit.

Can a decreasing function be convex?

Any function f from ( 0 , ∞ ) onto ( 0 , ∞ ) which is decreasing and convex has an inverse g which is positive, decreasing and convex. When f is positive, decreasing and p , q -convex, its inverse g is q , p -convex.

How do you tell if a production function is concave or convex?

A function of a single variable is concave if every line segment joining two points on its graph does not lie above the graph at any point. Symmetrically, a function of a single variable is convex if every line segment joining two points on its graph does not lie below the graph at any point.

What is the relationship between concave and convex?

Concave means “hollowed out or rounded inward” and is easily remembered because these surfaces “cave” in. The opposite is convex meaning “curved or rounded outward.” Both words have been around for centuries but are often mixed up. Advice in mirror may be closer than it appears.

What’s the difference between a straight line and a convex curve?

When the PPC is a straight line, opportunity costs are the same no matter how far you move along the curve. When the PPC is concave (bowed out), opportunity costs increase as you move along the curve. When the PPC is convex (bowed in), opportunity costs are decreasing. Google Classroom Facebook Twitter

Which is the definition of a concave function?

Definition 1.1.1. A function with continuous second-order derivatives defined on a convex set X is concave if and only if its Hessian matrix is negative-semidefinite everywhere on its domain of definition X. Theorem 1.1.1. Let f (x) be a concave function; then it reaches a global maximum at x if and only if /x (x) = 0.

What happens to opportunity costs when the PPC is convex?

When the PPC is a straight line, opportunity costs are the same no matter how far you move along the curve. When the PPC is concave (bowed out), opportunity costs increase as you move along the curve. When the PPC is convex (bowed in), opportunity costs are decreasing.