## Does the utility function represent convex preference?

The characteristic of utility functions that represent convex preferences is quasi-concavity. A function u : X → R is quasi-concave if, for every x, y with u (x) ≥ u (y ) and every α ∈ (0, 1), u (αx + (1 − α) y) ≥ u (y ) .

## How do you know if preferences are convex?

Preferences are convex if and only if the corresponding utility function is quasi-concave. Assume preferences satisfy completeness, transitivity, continuity and monotonicity.

What is a concave utility function?

In expected utility theory for choice under uncertainty, cardinal utility functions of risk averse decision makers are concave. In microeconomic theory, production functions are usually assumed to be concave over some or all of their domains, resulting in diminishing returns to input factors.

### Can preferences be represented by a utility function?

A consumer’s preferences can be represented by a utility function if they satisfy properties P. 1 through P. 4, and one additional property called continuity. Continuity is probably the least intuitive property of preferences, yet it is not implausible.

### What is concave preference?

The shape of indifference curves depends upon the preferences of the individual. There are two broad classes, convex and concave. Indifference curves are convex if the individual likes to consume the two goods together. They are concave if the individual prefers to consume them separately.

What do you understand by convex function and concave function?

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.

## How do you know if a utility function is convex?

A utility function is quasi–concave if and only if the preferences represented by that utility function are convex. A utility function is strictly quasi–concave if and only if the preferences represented by that utility function are strictly convex.

## What type of preference is the utility function?

Utility function measures consumers’ preferences for bundles of goods or services. Ordinal utility ranks a customer’s choice by preference, and cardinal utility assigns a numeric value to each preference to determine how much more one good is preferred over another.

What is a concave and a 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.