Evaluating Optimization Methods for Atypical Preferences
A student is tasked with finding the optimal consumption bundle for a consumer whose preferences are represented by the utility function U(X, Y) = 2X + Y. The consumer has an income of $100, the price of good X is $4, and the price of good Y is $2. The student attempts to solve the problem by finding the point where the slope of the indifference curve is equal to the slope of the budget line. They calculate the Marginal Rate of Substitution (MRS) as 2 and the price ratio (Px/Py) as 2. Based on the fact that MRS = Px/Py, the student concludes that they cannot find a unique solution because the condition holds for every possible bundle. Critically evaluate the student's approach and conclusion. Is their reasoning sound? Explain the economic and geometric relationship between the indifference curves and the budget constraint in this specific case, and justify what the consumer's actual optimal consumption choice(s) would be.
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Evaluating Optimization Methods for Atypical Preferences
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