The Shape of Code

We are told that computers are now orders of magnitude cheaper than they once were. Computers have changed an awful lot over the last 70 years; how is the functionality supported by different computers normalised such that the price of computers from long ago can be compared with today’s computers?

One approach is to narrow the question down to calculating the cost of performing some basic operation, e.g., numerical calculation or sorting a list of values. Nordhaus’s famous paper: Two Centuries of Productivity Growth in Computing uses this approach.

The primary advantage of the cost-of-operation approach is that it can be made to work across the complete range of computing platforms. The major disadvantage of this approach is that it focuses on the performance of the cpu/memory, ignoring the ability to store large amounts of data and perform I/O (which is most of the cost of some computer systems).

The US consumer price index (CPI) uses Hedonic regression to adjust the average price of a product family whose quality changes over time (the CPI is used to track inflation, and so every price needs to be for a product identical to the exemplar chosen at some start date). Hedonic pricing models are also used to understand how specific features within a product category (e.g., housing, automobiles, or electronics) contribute to the price. The term hedonic is derived from hedonism, and was first used in a 1939 paper analysing the price/quality of automobiles.

The 1979 paper “Hedonic Prices and the Structure of the Digital Computer Industry” by R. Michaels (cannot find a downloadable copy) appears to have kick-started the computer/hedonic research rabbit hole (the 1969 book “The Economics of Computers” by W. F. Sharpe covers computer costings in detail). Hedonic regression estimates the value of a product by braking it down into its major components which are used as the explanatory variables in a regression model that predicts the product price on given dates, e.g., for mainframe computers: price, cpu speed, amount of memory, number/size of hard disks, number of tape drives and card readers.

While mainframes and microcomputers share some characteristics (e.g., cpu, memory, and discs), they address different markets with very different requirements (e.g., mission-critical requires high reliability and tape backups). Different Hedonic regression models need to be fitted for each.

Gathering a representative sample of information on all the major components of a product, preferably for each year, is a lot of work. Many papers make use of information from proprietary databases. A lot of historical information is now available in scanned trade publications, but LLMs are not yet good enough to reliably extract detailed information from scanned documents (e.g., they sometimes ignore information, rather than hallucinating). I am waiting for the error rate to decrease.

The analysis in the book chapter Computer Processors and Peripherals by R. J. Gordon spends a lot of time dealing with the issues around potentially inconsistent data sources. The final price index (table 6.7) shows that the normalised price of mainframes decreased by a factor of 922 between 1951 and 1983 (23% per year, for 33 years). That is, the equivalent 1951 mainframe purchased in 1983 would have been cheaper by a factor of 922. In practice, prices did not decrease by a factor of 922, rather some combination of price/quality of the average mainframe changed by this factor (where quality is some combination of faster cpus, more memory and other factors). For an analysis of computer related products see the book “Price Measurements and Their Uses” by Foss, Manser, and Young.

The price of microcomputers (or computers as we call them today, as there is little public perception of any other type of computer) has decreased, but by how much (in the Hedonic sense)?

The first Hedonic analysis of microcomputers was Cohen’s 1988 Master’s thesis, for personal computers between 1976 and 1987. I think Cohen is pushing product family boundaries to treat the 8-bit computers introduced before the IBM PC in August 1981 (which did not include a hard disk until 1983, and did not really become a 16-bit computer until the IBM AT in 1987) as being comparable with later microcomputers. Cohen’s analysis found positive/negative swings in the adjusted prices of the microcomputers.

The paper Price and quality of desktop and mobile personal computers: A quarter-century historical overview by Berndt, Dulberger and Rappaport claim that there was an average annual 27% decline in microcomputer prices between 1976 and 1999. Again, my comments on pre-1987 microcomputers applies. A later paper (appendix table 1) shows average actual prices increasing until 1991 and decreasing thereafter, with the averages of cpu frequency, memory capacity and hard disk size continually increasing. There was little difference in the prices at the start(1976)/end(2002) of the period analysed, but a huge difference in the quality characteristics. While writing my Evidence-based software engineering book, I emailed Berndt for the data, which a co-author kindly made available. Unfortunately, I found that much of the data was confidential (the name of a company that sold computer sales data appeared in the files), and could not be publicly shared 🙁

Hedonic analysis of computers appears to have become unfashionable around the start of 2000. More recent papers analyse products such as mobile phones and cloud services. Please leave a comment if you know of any recent hedonic analysis of computer prices.

The only detailed microcomputer price data I know of consists of 6,259 detailed prices collected by Stengos, and Zacharias over 35 months, starting in January 1993, from the adverts in PC Magazine.