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basic setup[ edit ] suppose the consumer's consumption set , or the enumeration of all possible consumption bundles that could be selected if there were no budget constraint, has l commodities and is limited to positive amounts of consumption of each commodity. let x be the vector x={xi;i= ,...l} containing
u ( x ∗ ) {\displaystyle x(p,i)=\operatorname {argmax} _{x^{*}\in b(p,i)}u(x^{*})} . finding x ( p , i ) {\displaystyle x(p,i)} is the utility maximization problem. if u is continuous and no commodities are free of charge, then x ( p , i ) {\displaystyle x(p,i)} exists,[ citation needed ] but it is not...
https://en.wikipedia.org/wiki/Utility_maximization_problem