Indirect utility function; reduce utility bills
In economics, a consumer’s indirect utility function
<math>v(p, w)</math> gives the consumer’s maximal utility when faced with a price level <math>p</math> and an amount of income <math>w</math>. It represents the consumer’s preferences over 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 <math>v(p, w)</math> can be computed from its utility function <math>u(x)</math> by first computing the most preferred bundle <math>x(p, w)</math> by solving the utility maximization problem; and second, computing the utility <math>u(x(p, w))</math> the consumer derives from that bundle. The indirect utility function for consumers is analogous to the profit function for firms.
Formally, the indirect utility function is:
- Non-increasing in prices, because an increase in prices cannot open up an available bundle that would provide more utility;
- Non-decreasing in income, because when income rises, at worst you could consume the same bundle;
- Homogenous with degree zero in prices and income; if prices and income are all multiplied by a given constant the same bundle of consumption represents a maximum, so optimal utility does not change.