Gas Prices in Perspective

The Haunting

Gas prices haunt Americans. The price of a barrel of oil and a gallon of gas are daily news items. Drivers groan as they watch the gas pump price gauge count past $40 (or $50, or $100), although being able to punch in their phone number or swipe a card to get a three cent discount makes them feel like children on Christmas. There are thousands out there who would go out of their way to fill-up at a station that is four or five cents cheaper, or get a little too excited when they find out their credit card is offering double cash back on gas purchases for the next few months.

At times, I feel myself caught up in the fray as well. I consistently survey the gas stations dotting my commute (and just about everywhere else I drive) to find the best deals, and I know exactly how many miles I can go after my gas light comes on so I can delay the fill up as much as possible. I find myself wondering how premium-only sports car owners can get by filling up at the more expensive stations. I mean, with gas prices the way they are, they stand to save big by filling up at cheaper stations or by downgrading to a car that takes regular octane fuel, right? Not so fast – some red peppers, investigation and straightforward statistics might have something to say on the subject.

Misguided Price Obsession

My wife has a memory that would make a team of Simon-playing elephants jealous. She remembers birthdays like everyone is her favorite aunt and she frequently catches grocery stores overcharging her for food items. Once, while at Wal-Mart, she noticed the red peppers were especially expensive at $2.28. Oddly, Randalls, the typically more pricey venue, had them listed much cheaper at $1.23. Kroger had the cheapest price of all at $0.99 each – more than 55% savings over Wal-Mart.

But wait, that means that buying just one red pepper at Kroger instead of Wal-Mart would save more money ($1.29) than 25 gallons of gas priced a nickel cheaper. If I buy two red peppers in the same manner, I would save enough money to fill up my Accord with premium (instead of regular) and have enough leftover for a candy bar. Could it be that this American gas-price obsession would be better served on items other than petrol? Have we been scrambling to fill up our pockets with pennies around the fountain while quarters are ripe for the taking inside? With my curiosity piqued and feeling somewhat annoyed at myself and others for this seemingly misguided price obsession, I decided to do some investigating.

The Plan

According to the U.S. Department of Labor, the average U.S. household in 2004 spent a relatively prominent amount on gasoline, ranking up there with electricity and clothing, but this direct comparison is insufficient for my purposes. To validate the gas price fixation I had to first quantify the monetary savings possible through obsession-motivated activities and then compare this to another, similarly quantified expense. I came up with two factors to help in this pursuit: the savings factor (SF) and the variation factor (VF).

Table 1: Average household expenditures in the U.S. in 2004

SF is unit-less and can be used to compare the potential monthly savings available within a given geographical area by switching from the most expensive location to the cheapest location. For example, given that ProductA prices vary from $21.95 to $23.99 within the distance AverageConsumer is willing to travel to obtain ProductA, the SF of ProductA (SFA) is about 0.0850. If ProductB, on the other hand, has prices varying from $0.25 to $0.39 over a similarly defined area (i.e., the distance AverageConsumer is willing to travel to obtain ProductB), it results in an SFB of approximately 0.3590. After obtaining these SFs, the potential monthly savings on each item can be compared using the average amount spent on each item each month. If AverageConsumerspends $20 on ProductA and $5 on ProductB per month, the potential monthly savings (SFsave) figure to be $1.70 and $1.79, respectively. The comparison, then, shows ProductB to be more “worthy” of cost saving activities, as SFsaveB is greater than SFsaveA.

VF is also unit-less but is used to compare the variance in the price distributions rather than the direct savings. It is calculated by dividing the standard deviation (σ) by the mean (μ) of the price distribution. Continuing the example above, if σA=$0.73 & μA=$22.45, and σB=$0.07 & μB=$0.29, the VFs turn out to be VFA=0.0325 and VFB=0.2414. Multiplying these by the respective monthly costs from above results in VFsaveA=$0.65 and VFsaveB=$1.21. As VFsaveB is greater than VFsaveAProductB still proves to be more “worthy.”

Initially, some might not see the value of including this second factor, but I found it to be the best way to compare the effortrequired to bring about savings. To illustrate, imagine there are 100 stores selling ProductX within an area fitting the previously discussed conditions. 99 of them are selling it for $1.00 and one of them for $0.50, resulting in an SF of 0.5. If the distribution is changed, however, and 50 of the retailers price ProductX at $1.00 and 50 at $0.50, the SF would remain 0.5. It’s true the potential savings in the area is the same in both instances, but the effort required to bring about those savings is much higher in the former case than in the latter. This fact, intuitive in this example, can be revealed in more complicated data sets by comparing the VFs. For the above cases, the former VF (0.0503) is much less than the latter VF (0.3350), confirming the obvious. Further confirmation of the method is obtained by considering a third case in which 99 prices are $0.50 and one is $1.00. This price distribution results in a VF of 0.0990, correctly indicating an increased degree of difficulty over the more evenly distributed case.

Using these two factors I can effectively quantify and compare just about any expense, from gas prices to utilities, food to clothes, cigarettes to diapers. Among all of the expenses, though, there is one that haunts me almost as much as (if not more than) the cost of gas: Pharmacies. Not because I shop there often, however, but because everyone else seems to. I set out to investigate how these two expenses, gasoline and pharmaceutical items, compared using my bi-factor method described above.

Quantifying Gas Savings

First, I needed to find what the average person spends on gasoline per month. The freshest data available was from 2004. According to the Energy Information Administration, the average cost of gas in the U.S. that year was $1.85 per gallon of regular grade and the average gas mileage of a new, light-duty vehicle was 21 mpg. Assuming that gasoline made up the vast majority of the “Gasoline and motor oil” expense listed, I calculated the average yearly cost to be about $1,500. Dividing this figure by twelve resulted in the approximate monthly petrol cost ($gas) of $125.

Next, I needed to calculate the gas price distribution within a reasonable area. Starting with the intersection of US Highway 290 and Barker Cypress Rd in Houston, TX, I surveyed all 43 gas stations within a 5-mile radius – a distance large enough to include all but the most obsessive petrol penny pinchers. The results ranged from $2.82 at Power Fuel and Super Clean to $2.99 at Texaco, Exxon and two different Shells (see Figure 1).

Figure 1. Gas station locations within 5 mile radius of
intersection of US290 & Barker Cypress Rd in Houston.
Table 2. Prices at gas stations
within 5 mile radius of
intersection of US290 & Barker
Cypress Rd in Houston.

This data resulted in a mean price (μgas) of $2.90 per gallon with a standard deviation (σgas) of $0.05. This equates to a VFgas of 0.0177 and a VFsavegas (VFgas * $gas) of $2.22. The high and low prices lead to an SFgas of 0.0569 and an SFsavegas (SFgas * $gas) of $7.11.

Although the price of gas will vary over time, I felt I could safely assume VFgas to be relatively constant and also to be fairly representative of other areas.

Table 3. Distribution and factor values for gasoline
prices within 5-mile radius of Barker Cypress &
USHwy 290 in Houston, TX on August 8, 2006.

Pharmaceutical Savings

The inflated nature of the prices within seem to be common knowledge, and yet customers flock to them because they’re close – a behavior that directly contradicts the idea of passing up a convenient but expensive gas station in favor of an inconvenient cheaper location. Could there be some order to this madness?

I visited two convenience stores close to the center of the same five mile radius used previously, both located on Barker Cypress south of Hwy 290, and questioned the employees as to which items were purchased most. A friendly, yet somewhat uncomfortable, manager at Walgreens listed milk, pet food, Gatorade, Sudafed/Benadryl, Tylenol/Advil, batteries, and Prilosec. Another employee at the same store suggested cough/cold items as the most popular. At CVS, the cashier listed Diet Coke and Benadryl. I compiled these to form my “investigation list” – along with a couple of other things like shampoo, glass-cleaner, and chips, which rounded out a reasonably complete cross-section of pharmaceutical store stock.

Next, I sought out all locations within the same previously defined boundary from which a consumer could purchase the items on the list: Target, Walmart, Randalls and Kroger. I then surveyed the price of each item, disregarding any sales or member card discounts.

Figure 3. Survey of grocery and pharmaceutical stores within the same five-mile radius.
C=CVS, K=Kroger, R=Randalls, T=Target, WG=Walgreens & WM=Walmart.
Table 4. Prices for common pharmaceutical items. High price of each item in red, low price in green.

Comparison Results

Table 5. Variance analysis of pharmaceutical item prices.

After calculating both factors and their savings counterparts for each pharmaceutical item, the comparison was obvious. The average VFpharm value was more than ten times larger than VFgas, and even the item with the lowest VF (VFindigestion medication=0.0551) was more than three time larger. The highest VFpharm (VFsports drink=.2819) was so large that VFgas was virtually negligible. It seemed obvious, then, that the effortrequired to save money on pharmaceutical items would be much less than that required to save a proportional amount on gas.

The SF comparison yielded similar results. The average SFpharm was 0.2928, meaning that you would have to spend significantly less on pharmaceutical items to be able to save as much money within the studied 5-mile radius as you could on gas. In other words, if I, like the average consumer in 2004, spent $125 a month on gasoline at gas station #42: the Shell station on Huffmiester and Cypress Rosehill, I could save $7.11 (SFsavegas) of that by switching to gas station #18: the Power Fuel on Fallbrook and 1960. If I spent an equal amount ($125 monthly) at Walgreens, however, I could save as much as $36.60 (SFsavepharm) of that each month by switching to Walmart or Target.

Figure 4. Mean (μ) and standard deviation (σ) of price distribution of pharmaceutical items and gasoline within 5-mile radius.
Figure 5.Savings Factor (SF) and Variation Factor (VF) of price distribution of pharmaceutical items and gasoline within 5-mile radius.

What about those who only occasionally visit their neighborhood Walgreens, though? If someone dropped by CVS only once a month to pick up an item on sale, the money saving potential might not be there, but what if they spent $25 a month? $40? $75? Exactly how much does the consumer have to spend monthly at the average pharmacy to have the same savings potential as gasoline? To find out, I equated SFsavegas to SFsavepharm and solved for $pharm:

  1. SFsavegas = SFsavepharm
  2. SFsavegas = $pharm * SFpharm, average
  3. $pharm = SFsavegas / SFpharm, average
  4. $pharm = $7.11 / 0.2928 = $24.28

So, if I spend about $25 a month at a convenience store, I stand to save more money by switching to someplace like Walmart or Target than I would by switching to a cheaper (or even the cheapest) gas station. Doesn’t seem like much for a whole month, does it? It’d take only one package of Prilosec and one of Tylenol to put me over. Or, two packages of diapers and glass cleaner would do the trick. Or a bag of dog food and M&Ms once every other week or so. Dropping $25 at Walgreens or CVS is nothing.

Unavoidable Conclusions

Given the heavily skewed comparison, is my “haunting” over? Definitely. Although I rarely shop at pharmacies, I find comfort in knowing there are myriad places that could readily yield more savings if given the same amount of penny-pinching effort as many usually exert to save on petrol.

Why the disproportionate emphasis on gas prices in our culture, then? Although some cite a failure of politicians or media populists to account for inflation and purchasing power changes, I think it is simply because gas prices are in your face. As a cartoon recently stated in the Cincinnati Enquirer, “Actually, most prices look outrageous when you put them on tall signs in big numbers.” The numbers are big and I see them every day. I almost can’t help but track them, and I probably won’t stop – I just won’t bother going out of my way to buy the cheapest stuff, not until I see some major changes in VFgas and SFgas, at least

 

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