ECON 100 Marginal Utility Answers

St. Charles Community College 
Econ 100     Survey Economics
Answers to Class Discussion Problem

The Problem:

There a student named Anne who attends a community college in a Midwestern town.  She knows she needs to control her expenses, so she allows herself a monthly entertainment budget of $30 per month for entertainment.  She has two favorite activities that take up this budget.  She and many of her friends enjoy line dancing at a local club that has a country and western theme.  She also enjoys attending the games of a local minor league baseball team.  She has gotten to know some of the players, and many of her friends also attend these games.

The data shown below offers an insight into the total utility that each of these events Offer Anne.  Assume that admission to the club costs her $4.00 per visit, and ball game tickets are $7.00 per game.

Questions:

  • Complete the chart.
    Answer: Allocation of Expenditures per Month between Two Alternative Activities

    Trips To The Club Per Month Total Utility Marginal Utility (MU)  Price Per Visit (P) Marginal Utility Per $ (MU/P)
    1 16 16 $4.00 4.00
    2 27 11 $4.00 2.75
    3 35 8 $4.00 2.00
    4 41 6 $4.00 1.50
    5 44 4 $4.00 1.00
    6 46 2 $4.00 .50


    Trips To Baseball Games Per Month Total Utility Marginal Utility (MU) Price Per Visit (P) Marginal Utility Per $ (MU/P)
    1 21 21 $7.00 3.00
    2 33 12 $7.00 1.71
    3 42 9 $7.00 1.29
    4 48 6 $7.00 .86
    5 51 3 $7.00 .43
    6 51 0 $7.00 0
  • Explain how Anne will maximize her satisfaction (utility) given these facts and her budget.
    Answer:
    • In making her decisions, our heroine is guided by two microeconomic principles:
      1. She has an entertainment budget of $30.00 per month (A budget constraint.
      2. MUx/Px = MUy/Py  (The utility maximization equation).
    • Her first choice is to visit the western club to enjoy line dancing.
      1. MUx/Px = MUy/Py    -->   16/4 > 21/7    -->     4 > 3. 
      2. She has now used up $4.00 of her $30.00 entertainment budget.
    • She now chooses to attend a ball game because:
      1. MUx/Px = MUy/Py       -->   11/4 < 21/7   -->   2.75 < 3. 
      2. She has now used up another $7.00 of her budget leaving $19.00 left for the month.
    • Her next outing (her third) is to go back to the club for more line dancing.
      1. MUx/Px = MUy/Py    -->   11/4 > 12/7  -->   2.75 >  1.71. 
      2. She now has used up another $4.00 of her budget leaving $15.00 remaining for the month.
    • Her fourth social outing will be to visit the club again.
      1. MUx/Px = MUy/Py     -->    8/4 > 12/7    -->   2.00 >  1.71. 
      2. She has now used up another $4.00 leaving her with a monthly entertainment budget of $11.00 per month.
    • Her next outing (her fifth) will be to the next ball game.
      1. MUx/Px = MUy/Py     -->   6/4 < 12/7   -->  1.5 <  1.71. 
      2. She has now used up another $7.00 leaving her remaining budget at $4.00. 
    • Her next outing (her sixth) will be to the western club again.
      1. MUx/Px = MUy/Py     -->   6/4  > 9/7  -->      1.50  > 1.28. 
      2. She has now used up another $4.00 which means that she has exhausted her entertainment budget for the month.
    • Comments:
      • The problem ended because Anne had used up her monthly entertainment budget.
      • Had the problem been constructed in such a manner that Anne had been left with $3.00 in her budget after the fifth outing, the problem would have ended there since Anne wouldn’t have sufficient funds to make either choice.
      • If the problem had been constructed in such a manner that Anne had been left with $4.00, and the calculations came out in a manner indicating that Anne should rationally choose the ballgame which cost $7.00, then, logically, she would choose to go to the club even though the calculations showed that did not maximize her utility.