4. Mrs. Simpson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents, respectively. At present she is buying these products in amounts such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of bread and milk?

a. yes

b. no

Question

4. Mrs. Simpson buys loaves of bread and quarts of milk each week at prices of $1 and 80 cents, respectively. At present she is buying these products in amounts such that the marginal utilities from the last units purchased of the two products are 80 and 70 utils, respectively. Is she buying the utility-maximizing combination of bread and milk?

a. yes

b. no

BlackTom AI · Accepted Answer

Utility is maximized when the marginal utility per dollar spent is equal across all goods: MU_bread / Price_bread = MU_milk / Price_milk.

1. Relevant knowledge points and concepts
- Marginal utility (MU): the additional satisfaction from one more unit.
- Budget constraint implies consumers equate MU per dollar across goods to maximize total utility.
- Condition for utility maximization: MU_x / P_x = MU_y / P_y.
- If MU per dollar differs, reallocating spending toward the higher MU per dollar good increases total utility.

2. Complete reasoning process step by step
- Given: Price of bread P_b = $1.00; Price of milk P_m = $0.80.
- Given marginal utilities: MU_b = 80 utils; MU_m = 70 utils.
- Compute MU per dollar for each good and compare.

3. Calculations with intermediate steps
- MU per dollar for bread = MU_b / P_b = 80 utils / $1.00 = 80 utils per dollar.
- MU per dollar for milk = MU_m / P_m = 70 utils / $0.80.
- Compute 70 / 0.8: 70 ÷ 0.8 = 70 × (1/0.8) = 70 × 1.25 = 87.5 utils per dollar.

4. Explain WHY the correct answer is correct
- Since MU per dollar for milk (87.5) is greater than for bread (80), Mrs. Simpson gets more utility per dollar by buying milk. To increase total utility given her budget, she should buy more milk and less bread until the marginal utilities per dollar equalize. Therefore, her current combination is not utility-maximizing.

5. Why other options are incorrect
- Option a (yes) is incorrect because it assumes MU per dollar are equal; they are not (80 ≠ 87.5). The other listed options contain no answer text and are irrelevant.

6. Conclusion confirming final answer
- Because MU_m/P_m (87.5) > MU_b/P_b (80), she is not maximizing utility. The correct answer is b.

类似问题

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The utility function for Maurice is U = MIN(4M, C), where M = pints of milk and C = boxes of cereal. Maurice has $90 in income and the price of cereal is PC = $2 and the price of a pint of milk is PM = $1. What is Maurice's utility-maximizing consumption bundle?

Suppose that MUX = Y and MUY = X. The prices of Good X and Good Y are PX = $5 and PY = $4. How many units of Good X does the consumer buy if she has an income of $410?

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