$5 or 50% off: How We are Tricked by Percentages When it Comes to our Spending

There has been a certain problem that had been bothering me for a while, and, by “a while”, I mean a few years. This problem was introduced to me in a Vsauce (yeah, I know) video that I watched probably in 7th grade (which, unfortunately, I can’t seem to find), but I think it has a lot to do with how humans understand and interact with money. The premise is, if you are looking for a spatula and all the spatulas you find are $10 and you are offered 50% off a $10 spatula, you would be happy and likely buy the spatula. After all, you just saved $5. However, if you were in the market for a house, and the real estate agent agent generously offered you $5 off, you would probably laugh, and those $5 won’t be even taken into consideration. It seems to make sense, while $5 is 50% of the price of a spatula, it is incredibly tiny when compared to the price of a house. But, as Vsauce pointed out, that’s not really rational. You see, those $5 could still buy 5 Carl’s Jr. value meal cheeseburgers or 27 packets of Top Ramen, and it’s not relevant whether those $5 were saved from the spatula or the house. In short, money isn’t geometric, it’s linear, the same amount of money can buy the same product, no matter how much money you have otherwise (excluding factors like inflation which is rarely cause by one person who has accumulated a giant amount of wealth, with the exception of maybe Mansa Musa). Vsauce pointed out that, evolutionarily, it made sense to measure things geometrically, not linearly because, it’s much more important if there are 1 or 2 tigers about to attack you, an increase of 50%, than 100 or 101, 1%. As Anya said in her earlier blogpost “Marginalism: 1+1 is (marginally) greater than 100+1”, which directly inspired this post, we focus on the percent increase rather than the amount increase when we determine the utility something brings us. Again, this makes sense in a lot of situations, with many products for example. Upgrading your bed from a twin to full, an area increase of about 8 ft but of 40% is much more enjoyable than from a queen to a a king, an area increase of 9 ft but of only 30%. With money however, that is not really the case, as it’s better to have $5 added to your fortune of $1000 than $2 to your fortune of $4 because, no matter how you slice it, those $5 will buy more than $2, even if they are a smaller percent increase. Likewise, saving, or keeping, $5 on a spatula or house will still have you keep $5 more than you would have had if the item was not discounted and that $5 can be used for the same goods. In the same way, saving 60% on a $30 dollar shirt seems like a great deal, after all, it is 60% less than it should have been, but shirt that is 15% to begin with won’t even catch our eye. A high quality sock that is $5, $2 more expensive than an average one, has a opportunity cost of $2 or 40%. If we look at the opportunity cost as a percent, the 40% may not seem worth the better quality, after, all, it is just a sock. However, when you consider that the opportunity cost is only $2, or just over the price of guacamole at Chipotle (sorry, it’s the only example I could think of), and those socks will keep your feet significantly warmer and won’t get holes after wearing them twice, they begins to seem worth it. Our brains can trick us that the opportunity cost is larger or smaller than it really is by focusing on percentages and ratios, which served us well in the past and may still be useful in some situations, instead of amounts. As a rule of thumb, just remember that $1 = $1 and every dollar saved is equal to any other dollar saved, just as one dollar spent is equal to any other dollar spent, irrespective of the percent of the overall price.

Shopping at the Mall: Marginal Analysis, Rational Behavior, & Fallacy of Composition

           A year ago I was shopping at Valley Fair and decided to check out what clothes were available at Abercrombie. I had gone into the store hoping to find a pair of good quality jean shorts, and I ended up finding the perfect pair, as well as finding a dress that I liked. When I went to buy the clothes, I wasn’t aware of just how expensive each item was. Upon learning that each item was sixty dollars, I knew I couldn’t buy both. I had a couple of options. Buy the dress only because it was very unique and couldn’t be found elsewhere. Buy the shorts only because they could be multi purposeful and worn with many different shirts. Buy neither and find shorts in a similar style elsewhere. I ended up buying just the shorts. Even though I found them to be overpriced, I believed I could eventually get my money’s worth, especially considering the high quality of the shorts.

I didn’t know this at the time, but by choosing between the dress and the shorts, I was conducting marginal analysis, which is comparing of marginal benefits and marginal costs. When I was choosing between the dress and the shorts, I had to consider what each clothing items’ benefits were and what each clothing items’ costs were. I had determined that each item’s costs were the same, but that the shorts’ benefits were greater than the dress’s benefits. Therefore, I concluded that buying the shorts would increase my utility, or personal satisfaction.

Another economic perspective I was exhibiting was rational behavior, a type of behavior that reflects “rational self-interest” and pursues opportunities to increase utility. Rational decisions may change as costs and benefits change. Therefore, if the dress were on sale, it is possible I may have bought both the dress and the shorts. Also, rational behavior changes under different circumstances, meaning that if I had gone to the mall on a different day, I may not have made the same decision I made that day. For example, if I had just been invited to a dressy party, it’s likely I would have chosen the dress. Because rational behavior means that choices will vary greatly among individuals, even though I bought the shorts because I determined that it would increase my utility, my friend may not buy those shorts because she could conclude that it would not increase her utility.

This brings us to an important point about a logical fallacy called the fallacy of composition. This is when people believe that a statement that is correct for one person is correct for every person. Again, I decided the buy only the shorts, but someone else may decide to buy both the shorts and the dress, and someone else may decide to buy none. And herein lies why economics is so complicated. There are endless possibilities of what could occur in a certain scenario; therefore, nothing is certain. But it is the job of an economist to try to predict the most likely outcome based on the economic perspective, which includes key topics such as marginal analysis, rational behavior, and the fallacy of composition. Did you notice any other economic perspectives I could have used in making my decision?

 



 

Gaming the System: My personal experience with the unintended consequences of incentive schemes

Watching the video about Steven Levitt's daughter reminded me of a nearly identical experience my aunt had with my young cousin.
My cousin, for some reason, did not like to eat. My aunt was very worried about him and she was trying to figure out how to get him to eat his food so that he would get enough nutrition.
One day, she decided to try paying him to eat his food: every time he would eat something, he would get a dollar.
My cousin was very happy about this, and my aunt was glad to see him eating. But then my cousin realized that he could use eating to extort more money out of my aunt: once, when we were eating lunch together, he would refuse to eat anything until he was given a dollar. He would eat a few carrots, and then stop again and demand more money for eating any more food. My aunt, realizing her incentive scheme was falling apart, decided to stop paying him, realizing he would eventually get so hungry that he would have to eat, dollar or not. Unfortunately, he didn't eat his lunch that day, but fortunately for me, I got to eat his grapes!
Moral of the story: payment is a poor incentive for getting your kids to do what you want them to do (it always backfires).

Marginalism: 1+1 is (marginally) greater than 100+1

When Mr. Stewart introduced marginalism in class, I had a hard time wrapping my head around it. If you were also confused, here's some more information!
Marginal value is the extra utility derived out of each additional unit of a service or good. For example, if you earn $1 per day, and suddenly your mom gives you an additional $1 per day, that is a very high marginal value: you've just doubled your daily money!
However, if you make $100 per day and then your mom gives you another $1 per day, the marginal value is pretty low: you've only increased your income by 1 percent instead of 100 percent.
In both scenarios, your mother is giving you the same monetary value ($1). The difference in the scenarios, however, is the value of one additional dollar relative to what you already have. In the first case, one extra dollar is very valuable because that will result in a 100 percent increase in your income. In the second case, one extra dollar is pretty useless because you're only increasing your money by 1 measly percent.
Both gifts from your mother are the same dollar value, but in the first case, it's a high marginal value and in the second case, it's a low marginal value.

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