Utility function

Summary

Utility

• The state of being useful, profitable, or beneficial
• Economics / philosophy:
• Well-being, satisfaction, pleasure, or happiness.
• The ability of a commodity to satisfy needs or wants
• The satisfaction experienced by the consumer of that commodity.
• We will use: Utility is a measure of preferences of a consumption bundle.

Utility function

• A utility function is a rule that assigns a real number to every possible consumtion bundle.
• A utility function in a two goods model:
• Domain: $R_+^2$ , the collection of all points $\left( x_1,x_2 \right)$ where $x_1≥0$ and $x_2≥0$
• Codomain: $R$ .
• Notation, $u=u\left( x_1,x_2 \right)$ .
• Example: $u\left( x_1,x_2 \right)=4x_1x_2$