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A consumer's preferences for two goods, X and Y, are represented by the utility function U(X, Y) = X^0.5 * Y^0.5. The price of good X is $2, the price of good Y is $4, and the consumer has an income of $100. To find the combination of goods that provides the highest satisfaction given the budget, what is the optimal quantity of good X the consumer should purchase?
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A consumer's preferences for two goods, X and Y, are represented by the utility function U(X, Y) = X^0.5 * Y^0.5. The price of good X is $2, the price of good Y is $4, and the consumer has an income of $100. To find the combination of goods that provides the highest satisfaction given the budget, what is the optimal quantity of good X the consumer should purchase?
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- Point A: A combination where the decision-maker can afford more of both goods without exceeding their constraint.
- Point B: A combination on the boundary of what is affordable, but where the personal value the decision-maker places on one more unit of the first good (in terms of the second good) is greater than its market trade-off rate.
- Point C: A combination on the boundary of what is affordable, where the personal value the decision-maker places on one more unit of the first good (in terms of the second good) is exactly equal to its market trade-off rate.
- Point D: A combination that would provide higher satisfaction than any affordable combination, but is not affordable.
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