Indirect utility function

In economics, a consumer's indirect utility function v ( p , w ) {displaystyle v(p,w)} gives the consumer's maximal attainable utility when faced with a vector p {displaystyle p} of goods prices and an amount of income w {displaystyle w} . It reflects both the consumer's preferences and market conditions. In economics, a consumer's indirect utility function v ( p , w ) {displaystyle v(p,w)} gives the consumer's maximal attainable utility when faced with a vector p {displaystyle p} of goods prices and an amount of income w {displaystyle w} . It reflects both the consumer's preferences and market conditions. This function is called indirect because consumers usually think about their preferences in terms of what they consume rather than prices. A consumer's indirect utility v ( p , w ) {displaystyle v(p,w)} can be computed from his or her utility function u ( x ) , {displaystyle u(x),} defined over vectors x {displaystyle x} of quantities of consumable goods, by first computing the most preferred affordable bundle, represented by the vector x ( p , w ) {displaystyle x(p,w)} by solving the utility maximization problem, and second, computing the utility u ( x ( p , w ) ) {displaystyle u(x(p,w))} the consumer derives from that bundle. The resulting indirect utility function is