The paper by Goeller and Weinberg addresses the problem of long-run resource availability on the basis of empirical data different from, and as pertinent as, those that have been drawn upon in the economic literature. The authors have gone through the entire periodic system examining all the elements plus some important compounds, to determine the flow of their extraction in 1968, and estimate for each the total resources potentially available according to a rather generous definition of potential sources--the atmosphere, the ocean and a mile-thick crust of the earth. The ratio of total resources to demand in that year is expressed for each element in years to go until exhaustion at the constant 1968 rate of extraction--a simple signal of relative abundance or scarcity. Through the entire list and in the cases where there is a clear indication of a finite life time, the authors trace the important uses and possible substitutes in these uses. On the basis of their scrutiny of these geological and technological data, Goeller and Weinberg pronounce the principle of infinite substitutability: With the exception of phosphorus and some trace elements for agriculture, mainly cobalt, copper and zinc, and finally the CH_x (coal, oil and gas), society can exist on near-inexhaustible resources for an indefinite period. This line of thought suggests that when you look very far into the future quite a different type of information becomes important. Traditional econometrics doesn't help us much here. There is a type of thinking here that draws on basic scientific notions and knowledge, and that economists might well take note of.

An abstract of this article, from a report by the authors, may be found in EAPA 1: 02316. It is re-announced here because of its better availability in Science. (LMT)

This paper uses a model of the valuation of bonds bearing call options, together with observed market yields on callable bonds, to infer information about the uncertainty associated with interest rate expectations. A dynamic programming solution of the model simultaneously determines both the bond price and the issuer's optimal refunding strategy, given the relevant data describing the bond and the market's expectations of future interest rates. Application of the valuation model in reverse, for quarterly average data for 1969-76, generates a time series representing the uncertainty which the market associated with its expectations of future interest rates during this interval, given the then-prevailing yields on new issues of utility bonds and industrial bonds callable after 5 years and 10 years, respectively. This uncertainty, parameterized as the standard deviation of a truncated normal distribution, fluctuated between 1/2 percent and 3/4 percent between 1969 and early 1974, then rose to sharply higher levels from mid-1974 through mid-1975, and has fluctuated between 3/4 percent and 1 percent since late 1975.

I. Introduction, 323.—II. Formulation, 325.—III. An example, 326.—IV. Consistent price schemes, 328.—V. Back to the example, 332.—VI. Relaxing the assumptions, 333.—VII. Concluding remarks, 334.

20, 3 leaves : ; Includes bibliographical references. ; Cover title.;"January, 1978."