Gossen's second law

Gossen's Second “Law”, named for Hermann Heinrich Gossen (1810–1858), is the assertion that an economic agent will allocate his or her expenditures such that the ratio of the marginal utility of each good or service to its price (the marginal expenditure necessary for its acquisition) is equal to that for every other good or service. Formally,

${\displaystyle {\frac {\partial U/\partial x_{i}}{p_{i}}}={\frac {\partial U/\partial x_{j}}{p_{j}}}~\forall \left(i,j\right)}$

where

• ${\displaystyle U}$ is utility
• ${\displaystyle x_{i}}$ is quantity of the ${\displaystyle i}$-th good or service
• ${\displaystyle p_{i}}$ is the price of the ${\displaystyle i}$-th good or service