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The individual's marginal utility of money is 1 = 2 units of utility. What is the maximum quantity of the good that the individual can buy when its price is 6.

Economics

ScanSolve AI Answer

Answer

D\text{D}

Step-by-step solution

4 steps

To determine the maximum quantity of the good the individual can buy, we need to compare the marginal utility per dollar of the good with the marginal utility of money.

  1. Calculate the Marginal Utility (MU) for each unit of the good.

    Marginal Utility (MU) is the change in total utility from consuming one additional unit.

    • MU for 1st unit: 24−0=2424 - 0 = 24 units
    • MU for 2nd unit: 45−24=2145 - 24 = 21 units
    • MU for 3rd unit: 63−45=1863 - 45 = 18 units
    • MU for 4th unit: 78−63=1578 - 63 = 15 units
    • MU for 5th unit: 90−78=1290 - 78 = 12 units
    • MU for 6th unit: 99−90=999 - 90 = 9 units
  2. Calculate the Marginal Utility per dollar (MU/P) for each unit.

    The price of the good is $6.

    • MU/P for 1st unit: 246=4\frac{24}{6} = 4 units of utility per dollar
    • MU/P for 2nd unit: 216=3.5\frac{21}{6} = 3.5 units of utility per dollar
    • MU/P for 3rd unit: 186=3\frac{18}{6} = 3 units of utility per dollar
    • MU/P for 4th unit: 156=2.5\frac{15}{6} = 2.5 units of utility per dollar
    • MU/P for 5th unit: 126=2\frac{12}{6} = 2 units of utility per dollar
    • MU/P for 6th unit: 96=1.5\frac{9}{6} = 1.5 units of utility per dollar
  3. Identify the Marginal Utility of Money (MUM).

    The problem states that the marginal utility of money is 1=21 = 2 units of utility. So, the MUM is 2 units of utility per dollar.

  4. Apply the utility maximization rule.

    An individual maximizes utility by consuming a good up to the point where the marginal utility per dollar spent on the good equals the marginal utility of money (MU/P = MUM). The individual will purchase units as long as MU/P ≥\ge MUM.

    • For the 1st unit, 4>24 > 2. Buy.
    • For the 2nd unit, 3.5>23.5 > 2. Buy.
    • For the 3rd unit, 3>23 > 2. Buy.
    • For the 4th unit, 2.5>22.5 > 2. Buy.
    • For the 5th unit, 2=22 = 2. Buy.
    • For the 6th unit, 1.5<21.5 < 2. Do not buy.

    The individual will buy a maximum of 5 units.

    The final answer is D\text{D}.

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