Filling up gas tank with same $amount My econ teacher told us that his father would always put in$10 of gas in his car no matter what the price of gas was.

He showed that mathematically his father would come out on top. I know that there are a lot of ways people discuss about how much you should fill your tank (some say fill it up all the way you'll save, etc) but that has more to do with how the car works. The fixed rate of spending I believe was more tied into the fluctuation of gas prices.

Does anyone know the formula/way to describe what my econ professor taught us? It's been too long and I forgot it.

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Back then $10 likely filled the tank :) regardless, the theory is that were I to put in$10 into my tank through any time period, over time I would save more money than if I always filled the tank to a certain level, i.e. always topping it off, or always filling it halfway, etc.

Anyone know how to prove that?

russ_watters
Mentor
I don't know why this would be true, much less significant. A couple of effects I can think of:

1. Not filling your tank all the way means you are storing less gas, which means you are loaning the gas company less money and therefore earning interest on the money that stays in your bank account. So, for example, if it averages $20 to fill your tank, you're holding$10 more in your bank account and earning interest on it.

2. Gas prices tend to rise with time, with or without an inflation adjustment. So buying later means buying at a higher price; filling your tank means investing in gas futures.

3. I'm not sure if the constant  is significant to your prof's logic, but over time, your $10 will mean buying less gas, so the amount you are storing for the gas company is dropping. So if your$10 started off buying you a full tank and now only buys you a half tank, you have "saved" $10 a few pennies at a time by buying less gas each time. Of course, this is not permanent in and of itself. Then again, I made it permanent recently by trading-in a car with an empty tank of gas while buying my new car with a full tank. So essentially the car dealer unintentionally gave me$60 worth of gas.

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phyzguy
There is a similar investment strategy called dollar cost averaging. The idea is you buy a fixed dollar amount of stock every month, say $100. Then, you buy more shares when the stock is down, and fewer shares when the stock is up, which reduces your average cost per share of buying the stock. Whether it is an effective strategy or not is debatable, but some people swear by it.. Edit: I just ran some numerical simulations that show that this does work. Assume the price of gas has no long term trend, but fluctuates randomly with a normal distribution. If the average price of gas is$4.00 with a sigma of $0.50, you will pay an average price of$3.93 with this strategy. If the sigma is $1.00, you will pay an average price of$3.68.

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BWV
There is a similar investment strategy called dollar cost averaging. The idea is you buy a fixed dollar amount of stock every month, say $100. Then, you buy more shares when the stock is down, and fewer shares when the stock is up, which reduces your average cost per share of buying the stock. Whether it is an effective strategy or not is debatable, but some people swear by it.. Edit: I just ran some numerical simulations that show that this does work. Assume the price of gas has no long term trend, but fluctuates randomly with a normal distribution. If the average price of gas is$4.00 with a sigma of $0.50, you will pay an average price of$3.93 with this strategy. If the sigma is $1.00, you will pay an average price of$3.68.
Dollar cost averaging is a losing strategy assuming stocks have a higher expected return than cash, the market is just as likely to crash after the last dollar is averaged in than it is after a lump sum investment, leaving the difference the opportunity cost of holding cash during the DCA period.

Your simulation does not say much because the mean is known. Basically in it you "know" the avg price of a gallon of gas is 4 so naturally one would buy as little as possible when the price is over $4. Does he factor in the fact that he actually drives the car?$10 on Monday and $10 on Friday is basically the same as$20 on Monday.

I don't see how this works when considering recurring costs...

There is a similar investment strategy called dollar cost averaging. The idea is you buy a fixed dollar amount of stock every month, say $100. Then, you buy more shares when the stock is down, and fewer shares when the stock is up, which reduces your average cost per share of buying the stock. Whether it is an effective strategy or not is debatable, but some people swear by it.. Edit: I just ran some numerical simulations that show that this does work. Assume the price of gas has no long term trend, but fluctuates randomly with a normal distribution. If the average price of gas is$4.00 with a sigma of $0.50, you will pay an average price of$3.93 with this strategy. If the sigma is $1.00, you will pay an average price of$3.68.
I'm almost positive this is what my econ prof was speaking of. I was thinking about it last night and realized why this would be a viable strategy... you beat me to it!

Whether this is up for debate or not wasn't my original question. Was just trying to remember the theory. But thank you all for the input.

Note: I'm a math major now, so the realities of how a car works or whether or not one even drives the car don't matter to me! ;)

BWV
Like most economic problems, it becomes a tautology based on debatable assumptions. If you assume the price of gas will appreciate with inflation and an individual cannot earn an after-tax risk free rate of return on savings >= the rate of inflation (certainly true today) then the optimal strategy is to keep the tank full

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srfriggen said:
I'm a math major now, so the realities of how a car works or whether or not one even drives the car don't matter to me! ;)
As an engineer, this hurts my head haha

AlephZero
$10 on Monday and$10 on Friday is basically the same as $20 on Monday. It's not quite the same, because you might not have$20 on Monday (suppose you get paid on Thursdays for example), and even if you do have the $20 on Monday, only spending$10 on gas means you have the option of spending the other $10 on something else. For example if you car breaks down you could spend the$10 on a taxi, but you can't give the taxi driver $10 worth of gas from your broken down car. An economist would say "money is fungible, but gasoline is not". I don't see how this works when considering recurring costs... I guess this was supposed to be an example of dollar cost averaging, but it's a poor example IMO. The biggest flaw is that if you drive a constant mileage per day and the price of gas rises, you have to spend$10 more often than you did before, or you will soon run out of gas.
The biggest flaw is that if you drive a constant mileage per day and the price of gas rises, you have to spend $10 more often than you did before, or you will soon run out of gas. This was my first thought,$10 doesn't buy a whole lot of gas these days...