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Utility maximizing

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Intros
Lessons
  1. Utility Maximizing Overview:
  2. Using a Spreadsheet
    • List all the possible combination of goods
    • Find the total utility of each
    • Add the utilities
    • Find the highest total utility
    • An Example
  3. Choosing the Margin
    • Marginal utility per dollar of good x
    • Marginal utility per dollar of good y
    • Setting them equal
    • An Example
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Examples
Lessons
  1. Understanding Method 1: Using a Spreadsheet
    Pencils are $2 each, and erasers are $4 each. Suppose you have an income of $12, and the utility you gain from each good is shown in this table:

    Quantity (per pencil)

    Total Utility

    Quantity (per eraser)

    Total Utility

    0

    0

    0

    0

    1

    50

    1

    40

    2

    80

    2

    75

    3

    90

    3

    95

    4

    100

    4

    110

    5

    105

    5

    120

    6

    107

    6

    125


    Use a spreadsheet to find the choice which maximizes utility.
    1. Candy are $4 each, and Chocolate are $8 each. Suppose you have an income of $16, and the utility you gain from each good is shown in this table:

      Quantity (per candy)

      Total Utility

      Quantity (per chocolate)

      Total Utility

      0

      0

      0

      0

      1

      35

      1

      50

      2

      65

      2

      90

      3

      85

      3

      120

      4

      100

      4

      130

      5

      110

      5

      135

      6

      115

      6

      137


      Using a spreadsheet to find the choice which maximizes utility.
      Topic Notes
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      Knowing a person’s budget line and utility, how can we maximize the utility? There are 2 methods.


      Using a Spreadsheet


      Assuming all income is used,
      1. Write out the possible combinations of goods from the specified income.
      2. Write out the total utility gained from each number of good.
      3. Add the utilities together from both goods
      4. Find out which combination of good gives the most total utility.

      Choosing the Margin

      Recall that we learned about finding the marginal utility last section. We can put it to use this section!

      Assuming all income is used, the consumer maximizes their utility between two goods when


      MUxPx=MUyPy\large \frac{MU_x}{P_x}=\frac{MU_y}{P_y}

      Where:

      1. MUxMU_x is the marginal utility of good x.
      2. PxP_x is the marginal utility of good x.
      3. MUyMU_y is the marginal utility of good y.
      4. PyP_y is the marginal utility of good y.