THE LOGISTIC SUBSTITUTION MODEL

The method is the one found by Prof. Marchetti and his collaborators (AtE Apr.78). In 1970, Fisher and Pry of General Electric Research in Schenectady, N.Y., found that there is a surprisingly consistent pattern in the way that a new product penetrates a market and displaces its competing predecessor. The pattern holds for the most varied products, and for a free market as well as for a planned economy such as the USSR'S. Marchetti found it also holds for energy sources, and he generalized the formula for several sources competing at a time.

The actual mathematics is elementary: If F is the fraction that a certain energy source claims out of the total (say, coal, with a fraction of 0.35 or 35%), then the logarithm of the ratio F/(1 - F), plotted against time, converts the figure above into the one below, fraction (F) in which the actually recorded values (jagged records) follow the calculated ones (smooth curves) very closely.

The agreement is, in fact, stunningly good: What these curves say is that the rise and decline of energy sources in history is governed by something that cannot be perturbed by such puny episodes as World War I, World War II, Suez 1956, or the 1973 oil embargo. What perturbations there are deviate from the curve only temporarily and soon return to it again.

"It is," says Marchetti, "as if the system had a schedule, a will, and a clock." (The "schedule," incidentally, is quite similar for every energy source: Its share takes about 100 years to advance from 1% to 50% of the total energy consumption.)

Prof. Marchetti and his collaborators at the International Institute of Applied Systems Analysis in Austria have now tried the method with many variations. They found it works for individual countries (US, West Germany, France, Britain, Japan, and others); it works for individual sectors (electricity generation, residential energy use, etc.); and it works even when given only sparse data.(*)

Computer buffs can now get the evaluation program in FORTRAN (but not the data base).(**)

* C. Marchetti and N. Nakicenovic, The dynamics of energy systems and the logistic substitution model, IIASA Report RR-79-13, Dec. 1979. $8.50 from IIASA Publications Dept., 2361 Laxenburg, Austria; or (for unknown price) from NTIS, 5258 Port Royal Rd., Springfield, VA 22161.

** N. Nakicenovic, Software package for the logistic substitution model, $7 from addresses as above.