(Updated 1999 Dec 17)
On Buying a Computer
Background: I bought a Pentium-100 in 1995 for $2800, and it was an acceptable machine for about three years. I decided it was time for a new computer in 1998 when I saw that even games in the "classics" section of the computer store couldn't be run on my machine.
Twenty-eight hundred dollars over three years seemed on the high side, so I wanted to decide ahead of time how much to spend. In 1997, I tried fitting a price-versus-time curve to a reciprocal function: 1/t + c. I made a math error in my first attempt, and when I re-examined the problem a year later, it turns out choosing a mathematical function was unnecessary.
I used examples which are now dated, so I'm simply going to append my original document which I sent to a couple of people. My model has three main assumptions:
I don't consider what happens if one of the first two conditions is false.
I spent part of a Saturday reinvestigating the problem, and I think I have a simpler, more intuitive way to attack the problem. The calculus derivation I tried earlier not only was complicated, but assumed a model for prices changes that may or may not have been correct, and you had to estimate the useful lifetime of the computer. Even without any computational error on my part, the errors of approximation would have built up, and for no good reason. Now, I think that the most important thing to know is the estimated lifetime of the computer. In the example calculation I did, I measured it in months, and oddly, the lifetime is great enough that it's difficult for the final answer to be way off. I'm assuming, as last year, that one buys a computer at regular intervals, when the previous computer becomes obsolete. As before, the quantity that one wants to minimize is still dollars per unit time. Let's say the computer costs $1500 and has a lifetime of 33.333 months. (25 months would be easier to divide by, but around three years is a better estimate of a computer's lifetime I think.) The cost per unit time would be $45.00/month. To reiterate, this is the number we wish to minimize. Let's say that we re-evaluate after a one month period, so that the useful lifetime decreased to 97.00% of those 33.333 months. Let's also say that the price decreased to R% of its old cost. The new cost per unit time would now be $45.00(N/97). If R, the ratio of the new price to the old price, is less than 97, the cost per unit time has decreased (good), and if R>97, then the cost per unit time has increased (bad). What I picture is that when a new type of computer is introduced, it'll be expensive, and the price will drop precipitously after a while, 'cause these business people at Intel, for example, will be releasing something even better in a couple of weeks to make your old stuff obsolete. In this case, the ratio of recent-to-prior price R will be lower than the fractional decrease in lifetime, and this pattern will hold true for quite some time, a time during which the cost per unit time will steadily decrease. So, when a new type of computer comes out, it will usually be the case that it is better to wait. Eventually though, the price will level off, at which time the relative price change R will be greater than the change in lifetime, and I suspect this trend will continue until that type of computer is no longer sold. In this second phase, the cost per unit time will be increasing. The ideal time to buy would be the point where the cost per time has just stopped decreasing and has just started to increase. This statement smells of calculus, but I'm trying to describe it in intuitive terms. As I wrote above, I figure for most computers of the type one is likely to find in stores, the useful lifetime will be about 30-36 months for me. I buy my games from the "classics" section of the computer store, so that number may differ from person to person. The cool part about that number of months is that you have to be pretty far off before the errors mean anything. When the lifetime remaining is 33.333 months, the fractional change in lifetime per month is (1 - 1/33.333=) 97.00%. When it's 30 months, that figure is (1 - 1/30=) 96.67%. When it's 36 months, the number is (1 - 1/36=) 97.22%. To be off by a whole percent in either direction, you have to be down to 25 months or up to 50 months, and I think estimating lifetime is within that accuracy is quite attainable. I saved CompUSA flyers for a couple of months to follow price changes. The systems advertised from week to week didn't stay the same, so I had to guess to make price comparisons from month to month. Also, prices jumped around erratically, so I used about 2-3 months worth of flyers to get an average change per month. I think my estimates were reasonable. At the low end, for the AMD K6 and Cyrix MII 266 MHz chips, the price in the July-August range had levelled off; I wouldn't have bought one as late as August. At the high end, Pentium II's in the 400-450 MHz range, prices were dropping on the order of 10% per month in the September-October period: better to wait. In between seems to be the way to go. For Pentium II's, MII's, and K6-II's with 300 to 350 Mhz chips, prices in September-October were dropping at around 5%/month (very close to that 3% mark). If I needed to buy a computer today, this is what technology I would shoot for. For what it's worth, they happen to run between $900 and $1400 right now at CompUSA.
Aftermath: I ended up getting in November a K6-II 380MHz for $1600. The total cost would have been less, but I indulged in a DVD ROM and surround sound. I guess some expenses are less subject to objective analysis than others.
Other random thoughts:
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