Most textbooks in finance are apparently embarrassed by the Modigliani-Miller (MM) theorem on capital structure. The intense controversy it has provoked in academic circles over the past sixteen years makes it hard to ignore, and yet many textbook writers seem to be unable to distill anything from it that might be of interest to their readers. A typical example might begin by laying out the economist's conventional perfect market assumptions and showing that the theorem may be derived deductively from these assumptions. It is then observed that markets are not perfect and it is implied that perfect market theorems, while perhaps interesting to ivory-tower academics, are of no use to a businessman who has to act in imperfect real-world markets. (For example, Weston and Brigham [16], in their appendix to Chapter 11, on p. 339 state: “Given their assumptions, their theoretical arguments were quite correct. However, their assumptions have been questioned extensively, and very few authorities today accept the MM position.”) We are then returned rather uneasily to the traditional world of U-shaped cost of capital curves, in which managers are required to examine such holy relics as financial break-even charts (Van Home [15, p. 231]) or to exercise judgment about the stockholders' utility preferences (Weston and Brigham [16, p. 258]) in order to make their debt/equity decision.

I. The basic theory in terms of the consumer problem, 532.—II. Applications of the main theorems, 543.

Paul Samuelson and Subramanian Swamy in their survey of index-number theory in this Review emphasized that The fundamental point about an economic quantity index, which is too little stressed by writers, Leontief and Afriat being exceptions, is that it must itself be a cardinal indicator of ordinal (p. 568). In a later article in this Review John Pencavel has endeavored to compute real wage indices in this sense. He interprets each of his indices as an of the individual's welfare (p. 93). His two series of real wages are derived from an estimated indirect Stone-Geary utility function which incorporates nonlabor income of the wage earners and an endogenous work-leisure choice. In one series the increase in real wages over the period 1934-67 was substantially less than the index of money wages deflated by the Consumer Price Index or the Bureau of Labor Statistics series of real spendable weekly earnings of production workers, whereas in the second series the increase was substantially greater than in these other series over the same period. He has also constructed an index of real nonlabor income. My contention is that none of these indices is a true quantity index, but a genuine true quantity index can be obtained from the indirect utility function by using a slightly different definition of income. Moreover, this can be done for any regular utility function. For a family of functions which includes the Stone-Geary, this index is equal to an index of deflated incomes and is the canonical dual of the true price index. For any utility function one can obtain a quantity index of real income across incomeprice situations directly and simply by taking the ratio of the indirect utility function in period t to that at the situation in a base period 0. That is,