A quick reductio for the "three times" framing is to notice that if, having already decided to buy a phone, you were to convert $250 from your bank account into phone-purchasing credit, then the prices change to $500 and $0, and the question changes to whether the more expensive phone is infinity times better. That version of the question makes no sense, so dividing the two prices by each other don't make sense either.
Related: after extensive testing, I bought a thousand dollar laptop even though I had a perfectly good one. Why? The increase in typing speed from having a mechanical keyboard was so large that the time savings more than covers the cost. This was mildly surprising to me as I had never purchased anything for more than maybe $500 except my car.
For curiosity, which laptop did you like the keyboard enough to spend 2x as much on? I spend that much extra for screen quality and size, but I carry a separate keyboard when I'm typing a lot.
Useful framing, but don't forget to factor in opportunity cost - spending $750 on the new phone instead of $250 on an old model means you have $500 less available for some unexpected opportunity. Note that having savings for such opportunities, assuming you don't get direct enjoyment from money, means you're losing enjoyment-hours on whatever you'd otherwise have spent on.
It's around this point in my modeling of such choices that I tend to give up and fall back to general principles: for things I use often, I buy either the cheapest option, or the best option. Compromise bugs me every time I use it, so the hedonic difference between cheap and ok is small, and betweek ok and good is large.
We can break this problem up into two parts by partitioning your budget into a spending and saving component.
You can get a diminishing marginal utility curve for spending, by looking at what your total purchases would be at different budgets. Then you can estimate marginal expected value of cash on hand (the complement of your spending budget spending). Then you hold enough cash for the curves to intersect, and spend the rest.
In practice this isn't always tractable, but usually it's overdetermined anyway since the vast majority of decisions are strongly inframarginal.
The appropriate calculation is whether the marginal value of the upgrade is > $500, where the value of $500 is the marginal value of having that additional money.j
This is a slightly tangential question, but is value generally accepted as being inclusive of risk?
The LessWrongy framework I'm familiar with would say that value = expected utility, so it takes potential downsides into account. You're not risk-averse wrt your VNM utility function, but computing that utility function is hard in practice, and EV calculations can benefit from some consideration of the tail-risks.
Cross-posted from Putanumonit.
Follow-up to Shopping for Happiness.
My old Galaxy smartphone recently gave up the ghost, and I upgraded to the new model for $750. My friend was surprised when I told him. The old model is now available for $250, is the new one really three times better?
“Three times” better can mean several things, but in my post on spending money wisely I came up with the metric that should guide purchasing decisions: happiness gained per unit of time spent experiencing a thing, or :-)/hr. By this metric, since the new phone costs 3x as much, unless it provides 3x the :-)/hr it’s worse in terms of $/:-). That means I’m getting less happiness per dollar spent.
I like my new phone a lot: the screen is bigger, the battery lasts all day and night, I can use it for blogging. It brings me at least 25% more :-) than the old phone. But, it doesn’t make me 200% happier. And yet I feel like I’m getting a good deal.
When my friend asked how I would justify this decision I warned him not to trust my explanation – since I already bought the phone, any justification may just be a post hoc rationalization. That caveat aside, my justification is that the price of the phone is a red herring. What I really care about is the value.
Ask yourself: how much would you be willing to pay for your smartphone if it was the only model available for sale?
Whether they “ruined a generation” or not, but I think that smartphones are awesome and immensely improve my life. If I had to choose between no phone at all or a Galaxy smartphone, I’d pay at least $4,000 for the old model and $5,000 (25% more) for the new one. That means I’d be willing to pay $1,000 more for the upgrade, and they only charge me $500 more ($750 vs. $250) for it. The fact that smartphones cost less than what I’m willing to pay is just a wonderful bonus born of engineering ingenuity and market competition.
I square this with the $/:-) disparity by noting that my goal is to maximize :-) over all the money I spend, not in each category separately.
Consider a toy example of a world in which only two product categories exist: jackets and smartphones. You have $1,000 to spend, and four products to choose from:
Given the constraint that you can only enjoy one smartphone at a time, the most happiness is bought by purchasing the Galaxy Note 9 and a regular jacket – 5,500 :-). The S7 does better in terms of $/:-) but it doesn’t leave you with great options for the remaining $750. It’s better to spend more on categories of products where you get a lot of :-) and spend the minimum in low-value categories instead of looking to optimize within each category separately.
This example is not too far from the real case for me. The fact that I’d be willing to pay ~10x the asking price for a smartphone is a sign that smartphones (along with soap, tea, and underwear) are high-value categories. If I have enough money to buy great things in each of those I should do that before looking elsewhere. For things that I value little compared to their average price (cars, jewelry, whiskey) even a good within-category deal is a bad deal overall.
Decomposing Value
One more thing to consider is that the value of a purchase is made up of several factors. Marketing theory usually breaks those into four types:
Companies use this breakdown to market product to consumers, but as a consumer, you can flip this around to figure out what you’re looking for and how much it’s worth. For example, I can decompose the value of a tailored suit:
This means that I’d be willing to pay up to $2,350 for a good suit (thankfully, I can find one for a fraction of that price), but I won’t pay much extra for a suit that is slightly better looking for me or does a better job of keeping me warm – most of the suit’s value is social.
In rich countries, people tend to spend a lot more money on social value than on other kinds. Making me warm in New York costs a lot less than making me cool.
For an opposite example, I almost always buy the cheapest overnight airline tickets I can find, even if an airline with great food and service costs only 10% more. The value of a plane ticket to me is almost purely functional – getting me to another city. I don’t care to pay more than $15 for an in-flight meal, let alone hundreds of dollars for business class or more polite flight attendants.
Advanced Putanumonit users don’t have to limit themselves to the four types of value described above. You can goal factor any purchase and break it down to your personalized components of value. And after doing this exercise, truly advanced and enlightened users may decide not to spend their money on anything except peanut butter. Unfortunately, I’m not there yet.