# I just wrote my first LaTeX document!

I feel like a professor now! (Oh boy.)

So yeah, it’s kinda long (5 pages; too long for a single blog post), but if you’re interested, feel free to download the PDF below.

The content is an analysis on how to get the most bang for your buck. If you’re somewhat stingy like me, it’ll be an enjoyable read. Feel free to critique and comment… let me know about any errors. (I’m sure there’ll be some.) It’s not completely 100% done yet, but it’s good enough to post, I suppose.

PDF –> UtilityvCost

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For those who don’t feel like opening the PDF, but who are still stingy, a relevant, non-mathematical snippet:

Eqs. (18)–(20) combine the price and the price-dependent quality factors, and they state: if the percent increase of quality is larger than the percent increase of price, maximum satisfaction gets closer to maximum utility for higher prices. If, on the other hand, the percent increase of quality is smaller than the percent increase of price, maximum satisfaction gets farther away for higher prices. So higher prices are not always bad, but again one needs to weigh the factors. And in different situations, the results may end up quite different, because of how you assess the quality.

For instance, consider food. How much more quality will a fancy five-star restaurant give you, compared to *decent* family-owned joint? Probably a lot. But how much more expensive will it be? A LOT. But what if you’re a food connoisseur? In that case, you will find much more quality from top-notch food than someone who is just eeking out a living. So you might want to opt for fancy restaurants more often than a college student–you’ll get more bang for your buck that way, while for the college student, that may not be the case.

Now we take the same question and ask how hungry we are. Are we not very hungry at all, decently hungry, or starving? If you’re not hungry, fancy food and decent food will taste about the same, and neither will taste too awesome. So the percent increase in perceived quality will not exceed the percent increase in price. Likewise, if you’re starving, all food will taste amazing…and again your perception of quality will not increase a lot no matter how awesome the food truly is. The middle case is probably when you want to go to the fancier, pricier restaurants, because you will be able to best differentiate top-notch foods from marginal-quality foods.

In cases where your perception of quality changes very little with price–either from ignorance (no shame!) or the fact that the good is made the same everywhere–Eq (12) reduces to Eq (8). And then the cheaper item will always give you more bang for your buck, as we originally hypothesized.

P.S. Reason for my excitement: I LOVE LaTeX’s font and overall appearance… like omg. Don’t be hatin.