Budgeting and Percents: It's all Relative

News Item: Gas Prices Soar

In late summer and early fall of 2005, gas prices in the United States skyrocketed from an average of about $2 per gallon ($2/gal) to about $3 per gallon ($3/gal) in the aftermath of hurricanes Katrina and Rita, as well as in the face of limits to the growth of global oil supplies. The latter are expected to persist and prices of $3/gal or higher may return.

What would the "effect on your pocketbook" be? The answer to this question depends on your situation, a fact you will quantify in the exploration below.



Suppose that gasoline prices increase by 50% during a 12 month period. How will this affect your budget? To answer that question, you'll want to know, "what percent of my current budget does gasoline take up?" If you choose to drive a lot (or are forced to due to your employment situation) or if you own a car with a low miles-per-gallon (mpg) rating, your gas monthly costs will be higher.

A somewhat less obvious factor, however, is your income. If your income is lower, then for any given level of gas spending on dollars, it is a higher percent of your total income. Let's suppose the price of gas average $2/gallon this year, and will average $3/gallon next year (a 50% increase).

A. Sally and Wendy

Soccer-mom Sally owns a very large SUV that gets 10 mpg (miles per gallon). Working class Wendy owns a smaller, more efficient car, that got 20 mpg when new but gets only 15 mpg today since it's now an old car.

Both Wendy and Sally have somewhat long commutes of about 30 miles each way. If their work commute is two ways times 5 days per week, their weekly mileage for work related driving is __________ per week. You also know that Sally's annual salary is $60,000 while Wendy's is $18,000.

On the next page, after reading each step through very carefully, you will fill out a comparative table for Sally and Wendy. Before you do so, list several (at least two) findings you expect a comparison of effects of the price of gas on them:

___________________________________________________________________________

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Soccer-mom Sally Working-class Wendy
Gallons of gas used for weekly commute:
__________
Gallons of gas used for weekly commute:
__________
Converting at (roughly) 4 weeks per month,
_____gal/mo for work commute
Converting at (roughly) 4 weeks per month,
_____gal/mo for work commute
At $2/gallon, monthly cost of
work commute: $_____
At $2/gallon, monthly cost of
work commute: $_____
Monthly income excluding taxes:
$__________
Monthly income excluding taxes:
$__________
What percent of income excluding
taxes goes to commute? ____%
What percent of income excluding
taxes goes to commute? ____%
At $3/gallon, monthly cost of
work commute: $_____
At $3/gallon, monthly cost of
work commute: $_____
What percent of income excluding
taxes goes to commute? ____%
What percent of income excluding
taxes goes to commute? ____%
By how many percentage points did
the gas part of the budget increase? ____%
By how many percentage points did
the gas part of the budget increase? ____%

Your Notes:

B. What's the "gas bite" for lower-income Americans?

Let's now answer to the above questions for an American who is among the "working poor" -- a lower-income American (call her Rachel Ragamuffin) whose annual salary is $12,000. Assume she has the same type of car as Working Class Wendy, and drives the same number of miles per week

C. How does the "gas bite" cut into the rest of your budget?

  1. Soccer-Mom Sally: -- effect of gas prices on the rest of her budget (solutions included for first calculations)
    • Her total (pre-tax) monthly budget is: $5,000
    • ..and at $2/gal gas, under above assumptions, she spends: $240 per month. ($2 × 120 gal/mo)
    • So her budget for "the rest" would be $5,000 - $240 = $4,760

    • However at $3/gal gas, she spends ______
    • So her budget for "the rest" would $5,000 - $___ = $____

    • Conclusion: When gas went from $2/gal to $3/gal, her budget for "the rest" decreased from $____ to $____. This is a decrease by $____.

    • Our job is to find out what percentage decrease is it, when going from $4,760 [down by $120] to 4,640

    • We know that Sally's budget for "the rest" must be cut by a percent determined by the fraction 120÷4760 (we divide by 4760, since the cut is cut from the initial $4,760)
    • Thus, her budget for "the rest" must be cut by ≈  ______ [the "≈ " symbol means "approximately equal to"]

  2. Working Class Wendy -- effect of gas prices on the rest of her budget:
    • Her total (pre-tax) monthly budget is ______
    • ..and at $2/gal gas, under above assumptions, she spends: $____/mo
    • So her budget for "the rest" would $____-$___ = $____

    • However, at $3/gal gas, she would spend ______
    • So her budget for "the rest" would be $____-$___ = $____
    • Conclusion When gas went from $2/gal to $3/gal, her budget for "the rest" decreased from $____ to $____
    • So when gas prices increased from $2/gal to $3/gal, the money Wendy has available for "everything else" decreases by $_____

    • Our job is to find out what percentage decrease is it, when going from $_____ [down by [$80]] to $_____.
    • Wendy's budget for "the rest" must be cut by a percent determined by the fraction _____÷_____ (Again, we divide by the initial amount she had available for "everything besides gas" before it decreased)
    • The bottom line? We find out that Wendy's budget for "the rest" must be cut by ≈  ___%

  3. Rachel (lower-income/working poor) -- effect of gas prices on the rest of her budget:
    • Her total (pre-tax) monthly budget is $______
    • ..and at $2/gal gas, under above assumptions, she spends: $___/mo.
    • So her budget for "the rest" i.e. for "everything else" would $____-$___ = $___.

    • However, at $3/gal gas, she would spend $____/mo
    • So her budget for "the rest" would $____-$___ = $___
      [Question for students: Is this realistic? Is this amount really enough to pay for "everything other than gas" ?]
    • If gas goes from $2/gal to $3/gal, then, Rachel's budget for "the rest" would decrease from $___ to $___
    • So if gas prices increase from $2/gal to $3/gal, the money Rachel has available for "everything else" decreases by $___=$___ = $__

    • Our job is to find out what percentage decrease is it, when going from $_____ [down by [$80]] to $_____.

    • Rachel's budget for "the rest" must be cut by a percent determined by the fraction _____÷_____ (Again, we divide by the initial amount she had available for "everything besides gas" before it decreased)
    • The bottom line? We find out that Rachel's budget for "the rest", which was already lower than Sally's and Wendy's to begin with, must be cut by ≈  ___%

    Summarizing Your Findings:
    How can we quantify "by how much" each person's gas bill goes up
    (Despite the fact that Soccer-mom Sally's car gets the lowest mileage)?
    Soccer-mom Sally Working Class Wendy Rachel (Working Poor)
    Monthly gas bill goes up by
    2.4 percentage points
    (I.e., from ______% to _____%)
    Monthly gas bill goes up by
    5.33 percentage points

    (I.e., from ______% to _____%)
    Monthly gas bill goes up by
    8 percentage points

    (I.e., from ______% to _____%)
    By how much must her budget for "Everything else" decrease?
    (Even putting aside that Rachel's "Everything else" budget was lower than Wendy's -- and Wendy's lower than Sally's -- to begin with)
    Budget for "everything else" must
    decrease by ___%
    Budget for "everything else" must
    decrease by ___%
    Budget for "everything else" must
    decrease by ___%


    D. How big a difference?

    It is commonly estimated that roughly 66% (or two-thirds)of a household's budget is spent on food and shelter (rent or mortgage, heat/utilities, etc).

    We already saw how what income level you have affects what percent of your income gas "eats up". But since you have to eat and have shelter, and if your situation is that you have to drive to work, this brings up a new question: how big an effect does one's income have on on what percent of your budget is left over for "everything else" -- everything excluding food/shelter and gas? To explore this, fill out the table below.

      Total Budget Gas Food/Shelter "Everything else"
    Soccer-mom Sally:100%7%66% ________% or about what fraction? ____
    Working-class Wendy:100%16%66% ________% or about what fraction? ____
    Rachel100%24%66% ________% or about what fraction? ____

    Does this shed light on the frequently-heard comment that gas prices "bite hardest" in lower-income communities? Not only is Working-class Wendy's total budget lower than Soccer-mom Sally's total budget, but Wendy also has a smaller percent (or that smaller budget) leftover for "everything else" than Sally has. In fact, by what fraction is Wendy's budget-percent for "everything else" lower than Sally's?

    The answer: Wendy's budget-percent for "Everything else" is about 20% while Sally's is about 30% so Wendy's budget-percent for Everything Else is about one-third lower than Sally's. Instead of having about 3/10 of her budget for "Everything else", as Sally does, Wendy's budget is both lower in absolute terms and, on top of that, the percentage of that (lower) budget available for Everything Else is also lower.

    By what fraction is Rachel's budget-percent for "everything else" lower than Wendy's?

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    What would be the effect on your own life if the percentage of your budget available for "Everything else" was similarly cut?

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    By what fraction is Rachel's budget-percent for "everything else" lower than Sally's?

    How significant does that (perhaps modest looking) "8 percent" difference seen earlier seem now, in terms of how it would affect Rachel's life? How does our choice of which numbers to look at affect how we see, or which aspects are clear within, a given real-world life situation?

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    Disclaimer: as many have pointed out, gasoline is environmentally destructive and "should cost more, not less". This is an important issue, however economic and other forms of equity are another dimension; does society lower fossil fuel usage in an equitable way (such as offsetting higher a gas tax with tax cuts having a lower-income focus), so everyone conserves, or do the wealthy continue to drive polluting SUVs while the poor can't afford to drive to work? The above exploration is structured to help you analyze (and to numerically quantify) some economic impacts of higher prices for gasoline as they manifest in personal budgets. Many other dimensions are certainly worthy of being explored elsewhere. If you wish to explore such dimensions (or how they inter-relate) you may ask your instructor in this or a future course, about the potential for such an assignment. In the meantime what your thoughts in brief on balancing economic equity with protecting the environment for ourselves and future generations?

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    Created 2000-2006 by Dr. Harel Barzilai. Some rights reserved. Reproduction and use with attribution for noncommercial educational purposes is permitted and encouraged. Details at http://creativecommons.org/licenses/by-nc-sa/2.0/   Acknowledgement: Part of this work was made possible with kind support (Fall 2005-Spring 2006) from the Professional Development Mentors Program (PDMP) at Salisbury University, a collaboration of the Faculty Development and the Learning Technology committees.