Where h ( \ mathbf { p }, u ) is the Hicksian demand and x ( \ mathbf { p }, w ) is the Marshallian demand, at the vector of price levels \ mathbf { p }, wealth level ( or, alternatively, income level ) w, and fixed utility level u given by maximizing utility at the original price and income, formally given by the indirect utility function v ( \ mathbf { p }, w ).
12.
F ^ i \ left ( p \ right ) and g \ left ( p \ right ) have nice interpretations : f ^ i \ left ( p \ right ) is the expenditure needed to reach a reference utility level of zero for each individual ( i ), while g \ left ( p \ right ) is the price index which deflates the excess money income e ^ i \ left ( p, u \ right )-f ^ i ( p ) needed to attain a level of utility \ bar { u }.
