Edward F. Renshaw, Portfolio Balance Models in Perspective: Some Generalizations that Can be Derived from the Two-Asset Case, The Journal of Financial and Quantitative Analysis, Vol. 2, No. 2 (Jun., 1967), pp. 123-149

These two formulations are different from each other except that a constant H happens to be a Samuelson optimal value. In other words, Strotz's optimization is more constrained than Samuelson's, and Strotz's optimization cannot achieve Pareto optima except in the special case just mentioned.2 Does this difference between the two approaches invalidate Strotz's propositions in section II and section III in his article? If we confine our problem to Pareto optima, Strotz's propositions happen to be meaningful, that is, when H happens to be Samuelson's optimal value. And even in this case the relation between the optimal value of H and Pareto optima is ambiguous, and we must explicitly treat productive services of fixed income assets in the model. But it can be expected that such an approach would introduce complications into the model. Although Strotz's formulation has these difficulties, I believe, Samuelson's comment on Strotz's article, in the Appendix to Aspects of Public Expenditure Theories in this REVIEW, XL (November I958) is valid, that is, changing public goods does materially affect the distribution of income and all decisions have to be made simultaneously.

When any expensive machine is erected, the extraordinary work to be performed by it before it is worn out, it must be expected, will replace the capital laid out upon it, with at least the ordinary profits. A man educated at the expense of much labor and time to any of those employments which require extraordinary dexterity and skill, may be compared to one of those expensive machines. The work which he learns to perform, it must be expected, over and above the usual wages of common labor, will replace to him the whole expense of his education, with at least the ordinary profits of an equally valuable capital. It must do this, too, in a reasonable time, regard being had to the very uncertain duration of human life, in the same manner as to the more certain duration of the machine.2

Since the publication of Bridger Mitchell's article on the Optimal Pricing of Local Telephone Service (1978), it has been assumed that social welfare can usually be increased by moving from a flat monthly rate for local calls to a two-part tariff with a price per call that is somewhat in excess of marginal cost. While a fixed monthly charge for local calls can be considered a regressive head tax (A. M. Henderson, 1947), it does not follow that a two-part tariff will resolve the equity problem. In this paper I use a simple diagram and a two-person revenuemaximizing formula to illustrate one of the more important limitations of usage-sensitive pricing. In the following analysis, it is assumed that there are two types of telephone users. The first type of consumer, D1, is assumed to have a net demand for calls or message units, represented by the linear equation: