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Some Observations on the Index Number Problem

Econometrica 1963 31(3), 391 open access
A Laspeyres index of total input in the electric power industry was constructed. The nature of the bias imbedded in such an index, and its relation to the Paasche index and its bias, are investigated. Means to evaluate the actual size of the bias and means to reduce it are devised.

Optimal Timing of Innovations

The Review of Economics and Statistics 1968 50(3), 348 open access
The article shows that innovations are induced, since they become more profitable with the expansion of output. The amount of resources devoted to innovating activity, however, is in general not the optimal one because of the pressure of two opposing forces. On the one hand, competition between potential innovators tends to make this amount too large, on the other, the inability of innovators to capture all the benefits tends to make the amount too small. When all benefits are captured by the innovator either there is no economic growth due to innovations or else innovators are the sole beneficiaries from that growth. When benefits are diffused the innovation will always lead to economic growth, but only by sheer coincidence will it lead to maximum growth, which may be missed because the innovation is introduced either too early or too late. The rate of growth is always positive if the innovation is introduced too late. It may fall to zero with too-early introduction or even become negative if innovational activity is subsidized.

Assets, Subsistence, and The Supply Curve of Labor

American Economic Review 1973 open access
The supply curve of labor is now accepted as a matter of course by most economists. It has no doubt been perplexing to observe that the most commonly employed types of utility functions do not yield such curves under the usual textbook analysis of the problem.1 Particular preference maps have been found that generate backward bending curves;2 however, they are nonparametric, leading to difficulties of estimation, and upon closer examination seem to imply counter-intuitive results. We will show that taking into account the wealth position of an individual on the one hand and survival consideration on the other greatly expands the variety of shapes that can be derived for the supply curve from some simple utility functions. The use of a specific simple utility function also implies some severe restrictions on the form the supply curve can take, rendering it testable. Empirical evidence is shown to support the conclusion that the supply curve is monotonic. We will also show that the notion that the aggregate supply curve of labor slopes down rests, in part, on an error of aggregation, and that the empirical evidence usually cited in support of the negative slope, when correctly interpreted, cannot be so construed.