[This paper develops a general, competitive model of commodity differentiation. The structure analyzed is sufficiently rich to admit the basic structures of many of the common models of commodity differentiation as special cases. Thus, the model provides a unifying framework within which alternative formulations of strategic product choice can be compared. It is shown that competitive equilibria exist under only mild restrictions on the underlying economic structure and vary continuously with endowments. Finally, some results relevant to all models of commodity differentiation featuring price taking consumers are presented. The results are shown to point to some potentially important methodological restrictions.]

F. R. MACAULAY' and other writers2 have noted a tendency for changes in the square roots of common-stock prices to be constant regardless of price level. This phenomenon has naturally suggested that when such prices are represented graphically the charts be designed so that vertical distances from the origin are proportional to the square roots of the prices indicated in the margins. There is some reason to believe that charts of this kind might also be useful in plotting other kinds of data. Assume that n sales are distributed at random over 1/p firms during some interval of time, and that u1, u2, *, u1/, are the actual numbers of sales made by the different firms F1, F2, , Fil, Then, a priori, the probability that a particular firm will make one of these sales is p, and the mean and variance of the u's will tend to be

IT IS OFrEN THE CASE that an individual's decision is at least partly based on information received from another. And when the agents' payoffs depend on both the former's decision and on the latter's information, there is an incentive for the individual to attempt to bias the decision maker's decision in his or her favor by strategically manipulating the information transmitted. In a seminal paper, Crawford and Sobel (1982) (hereafter, C/S) study such strategic information transmission in the context of an abstract sender/receiver game. Variants of the Crawford and Sobel model have been applied widely, and as the application varies so often does the interpretation of type. In some cases, type refers to a preference parameter given by Nature-as, for example, in bargaining theory (e.g., Farrell and Gibbons (1989), Matthews (1989)), whereas in other settings-for instance, legislative decision making or expert testimony -type refers to more or less technical information concerning how decisions map into final consequences and, as such, is acquired information (e.g., Gilligan and Krehbiel (1987), Milgrom and Roberts (1986)). When the information has to be acquired, it is natural to suppose the acquisition is costly; for otherwise, there is no reason why such information is asymmetrically distributed. So long as the receiver can observe surely-or, at least, accurately infer-whether the sender is informed, and so long as messages are cheap-talk, there is no issue here for strategic information transmission (save whether to become at all). However, there are many circumstances when it is inappropri- ate to assume the receiver has such knowledge. One possibility is that a receiver may know that a sender has some relevant informa- tion, but be uncertain of the quality of this information. A second, perhaps more important, possibility is that a receiver is unable to tell whether a (potential) sender is uninformed. Inter alia, this problem constitutes the rationale for of the law being inadmissible as a legal defense (were it admissible, then informed miscreants would mimic uninformed transgressors); leads voters to be skeptical of politicians claiming ignorance of illegal arms deals; and makes the SEC sensitive to problems in distinguishing insider trading from legitimate good judgement. So there is an intrinsic asymmetry in that it is generally possible for, say, senders to verify possession of at least some information, but it is typically prohibitively difficult to verify any lack of knowledge