A BABYLONIAN lamp, by modern standards, shed little light on its surroundings. Nearly 4000 years later it sheds far more on an issue of great interest: the pace of mankind's material progress. In a new paper, William Nordhaus of Yale University starts by asking what may seem a dull question: do statisticians measure prices accurately? To find out, he studies the economic history of light from Neolithic times to the present. His answer and its implications are startling.
Traditional estimates have failed to track the fall in the price of light, especially over the past 200 years. As a result, they overstate today's price, relative to the price in 1800, not by a few percentage points, nor even by a factor of one or two, but by a factor of about 1000. Even by the standards of economics, that is a large error. The implications are of corresponding size. If the prices of other things are measured as badly as the price of light, it follows that traditional estimates of economic growth are way off the mark.
Economists are familiar with the difficulty of measuring changes in prices over time. It seems easy to measure the price of, say, a ball-point pen. But suppose that. a new version comes along that costs twice as much and lasts four times as long. If it catches on, the price of a pen has doubled—but the price of pen-services, as it were, has halved. This second price is the one that should be used to calculate the change in living standards. However, it is often difficult to observe. You need to know not just the change in the prices of the goods but also the change in the services that the goods provide. Measuring that is especially hard when the range of services itself changes over time. (Compare the communication-services provided by a modern telephone with those of one from the 1950s, for instance.)
Mr. Nordhaus points out that light has a useful property in this respect. Its service— illumination—does not vary. Babylonians used lamps for much the same reason that modern Americans use incandescent bulbs. With diligence and great ingenuity, Mr. Nordhaus has collected data on the light-services provided down the ages by: burning sticks; fat-and-oil- burning lamps; candles (tallow, sperm-oil, etc); gas lights (various); kerosene lamps; and the many different kinds of electric light. (The unit of measurement is the lumen; a wax candle emits about 13 lumens, a modern 100-watt bulb on 110 bolts about 1,200.) Mr. Nordhaus has also collected data on the prices of these sources of light: the price of a candle, the price of a given quantity of gas or electricity, and so on.
Putting the two together yields a true measure for the price of light. In nominal terms, the price of 1,000 lumen-hours has fallen from about 40 cents in 1800 to about one-tenth of a cent today. The black line in the chart plots this series as an index. (The sharp fall at the end of the line marks the introduction of the compact fluorescent bulb.) In real terms, of course, the fall is even sharper: 40 cents in 1800 is worth more than $4 in today's money. Compare this with a price series calculated using the conventional methods of official statistics—that is, by looking at the prices of goods that provide light rather than at the price of light itself. Mr. Nordhaus stitches together such a series from a variety of official sources. According to this measure, the price of light has fallen in real terms since 1800, but has gone up by 180% in nominal terms (as shown by the white line in the chart). In other words, conventional estimates would put the price of light in 1800 at about four-hundredths of a cent per 1,000 lumen-hour. Mr. Nordhaus' first series shows that the price of light in 1800 was about 1,000 times dearer than that.
This staggering difference is par@ an illustration of the effect of compound interest. It represents a drift of roughly 3.6% a year between the official and the t

A.)
B.)
C.)
D.6%