Suppose that MUY = 14, MUX = 11, PY = 2 and PX = $2. Which of the following statements is correct?

Question

BlackTom AI · Accepted Answer

Utility-maximization requires equalizing the marginal utility per dollar spent across goods: MUx/Px = MUy/Py.

Relevant knowledge points:
- Marginal utility (MU) measures extra utility from one more unit of a good.
- With a fixed budget, the rule for utility maximization (for divisible goods) is to allocate spending so that the last dollar spent on each good yields the same marginal utility per dollar: MUx/Px = MUy/Py. If MUy/Py > MUx/Px, the consumer should buy more of Y and less of X until equality is achieved.

Step-by-step reasoning and calculations:
1. Compute marginal utility per dollar for Y:
   MUy/Py = 14 / 2 = 7.
2. Compute marginal utility per dollar for X:
   MUx/Px = 11 / 2 = 5.5.
3. Compare the two: 7 (for Y) > 5.5 (for X).

Interpretation:
- Because MUy/Py exceeds MUx/Px, each additional dollar spent on Y yields more utility than an additional dollar spent on X. With a fixed budget, shifting spending from X to Y raises total utility until MUy falls or MUx rises enough to restore equality.

Why the correct answer is correct:
- The condition for current utility maximization is not satisfied (7 ≠ 5.5). Therefore the consumer is not currently maximizing utility; they should reallocate spending toward Y.

Why other possible statements would be incorrect:
- The statement that the consumer is maximizing utility is incorrect because the marginal utility per dollar values are unequal.
- A claim that they should purchase more X would be wrong because X gives lower utility per dollar; the consumer should buy more Y and less X.
- Any claim implying indifference or optimality without equal MU/P is invalid.

Conclusion: Since MUy/Py (7) > MUx/Px (5.5), the consumer is currently not maximizing utility, which matches the provided correct answer.

Suppose that MUY = 14, MUX = 11, PY = 2 and PX = $2. Which of the following statements is correct?Single choice

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