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: \(u\left( x_1,x_2 \right)=4x_1x_2\)