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14(264+0.275y)=λ=0.275 (296+x4)\tfrac{1}{4}(264+0.275y) = \lambda = 0.275\,(296+\tfrac{x}{4})

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produces first-order conditions 14\tfrac{1}{4}(264+0.275y) = λ\lambda = 0.275\,(296+x4\tfrac{x}{4}) , which reduce, after clearing terms, to a single tangency condition independent of the budget size:

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14(264+0.275y)=λ=0.275 (296+x4)\tfrac{1}{4}(264+0.275y) = \lambda = 0.275\,(296+\tfrac{x}{4})

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

produces first-order conditions 14\tfrac{1}{4}(264+0.275y) = λ\lambda = 0.275\,(296+x4\tfrac{x}{4}) , which reduce, after clearing terms, to a single tangency condition independent of the budget size:

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  • xx: the writing.
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