The consumer's expenditure minimization problem results in the same optimal basket as the consumer's utility maximization problem if the required level of utility for the expenditure minimizer is the same as the maximized utility for the utility maximizer.

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This is known as the expenditure minimization theorem, which states that if the consumer's level of utility is the same for both the expenditure minimization and utility maximization problems, then the optimal basket of goods purchased will be the same for both problems. This is known as the duality of consumer theory, where the solutions to the consumer's utility maximization problem and expenditure minimization problem are equivalent if the same level of utility is achieved.

The Consumer's Expenditure Minimization Problem Results in the Same Optimal