I. The invention, 475. — II. The innovation: domestic lag, 475. — III. The innovation: international lag, 476. — IV. Explanation of the lag, 478. — V. Conclusion, 481

Learning curve model, Capital Budgeting, Productivity, Innovation

I. The basic issue, 457. — II. Status of the United States industry compared with the world industry as a whole, 458. — III. The United States and European industries compared, 461. — IV. Technological and economic complications in the decision process, 465. — V. The United States and Japanese industries compared, 470. — VI. The significance of 1962, 471. — VII. Conclusions, 473.

T HE DEMAND for consumer durables has been of particular interest to economists because of cyclical and irregular variations in purchases. Sales cycles of considerable amplitude are associated, in part, with the accelerator effect of an annual consumer purchase-stock I ratio of less than 1.00, in combination with the consumer's ability to exercise considerable discretion in choosing the time for making replacement purchases. One cluster of consumer durables household laundry appliances has not been subjected to extensive study, yet seemed to offer promising possibilities for analysis.2 Viewed technically, four products comprise the cluster: the wringer washer, the automatic washer, the combination washer-dryer, and the dryer. The principal item in this group is the washer and, since 1952, the automatic washer. From an economic viewpoint, the components of this cluster can be classified according to their market maturity and according to their complementary or competing relationship to one another in purchase and in use. We shall define a product as one for which there has not previously been a close substitute. The washing machine of the 1920's was new in its use of nonhuman sources of energy electricity or gas. We do not include in any portion of our analysis laundry equipment which was totally dependent upon manual operation even though its use may have continued after introduction of the electric and gas machines. A product can be said to have reached market maturity when the rate of increase in its use by consumers has begun to decline. With a durable good, this occurs when the rate of increase in ownership begins to decline.3 We shall define an innovation as a major change in the attributes of a product. The automatic washer and combination washerdryer can be classified as innovations, representing major changes in the electric washer, in contrast to relatively minor improvements in the wringer-such as drains, timers, electric wringers -and later in the automaticsuch as programmed temperature, speed, and dispenser controls. To the consumer, the marginal utility of an innovation is far greater than that of an improvement. The demarcation between the two can be established best in terms of consumers' market behavior toward the product or their use of it. A successful innovation in durable goods is one which causes the ownership (and use) rate to rise to a level equal to or greater than that of its predecessor, and this usually occurs at the expense of the predecessor product. An abortive innovation is evident when product ownership rises but then declines before reaching the level achieved by the predecessor product. A declining product is identified by an absolute decrease in rate of ownership. The meaning of competing and complementary products in this study is consistent with that in general use in demand analysis. * Scientific Paper No. 2539 (Washington Agricultural Experiment Stations, Pullman), Project 1496. The author is indebted to Shaikh M. Ghazanfar, who assisted in all phases of the statistical analysis and was responsible for many of the calculations and for all of the graphs; to Rosemary Baker, who was responsible for assembling many of the original data; and to Jagjit Dhesi, who assisted in the calculations. Henry J. Carey and the late Marguerite Cook of the Market Research Department of Merchandising Week, were kind in providing considerable statistical data from their files, and Guenther Baumgart, President of the American Home Laundry Manufacturers' Association, generously made available the association's annual reports of distributors' sales of laundry appliances by states. The author is especially grateful to her colleagues, William Iulo and Harry McAllister, who, through a number of constructive criticisms, helped to correct and refine the analysis and increase the clarity of presentation. 'Throughout this paper, stock and inventory refer to consumer stocks (or inventories) rather than business stocks (or inventories) unless otherwise indicated. 'The most extensive study which has been published is by Spencer and Mattheiss [22]. More limited attention has been given to washing machines in [2] and [7]. Historical reviews can be found in [20] and [21]. 'Since in this paper both ownership and purchases are specified as a proportion of number of households or of population, the relevant rate of change is rate of change in ownership ratio. Members of the appliance industry commonly refer to this ownership ratio as saturation level

A new method is proposed for deriving skew distributions of business finn sizes from the assumption of Gibrat's Law. The growth of the firm is decomposed into an industry-wide component and an individual component, the latter governed by a one-period Markov process. The model is fitted to data on the recent growth of large American firms. A NUMBER of stochastic models, embodying various forms of Gibrat's law of proportionate effect, have been shown to generate skew distribution functions resembling the actual size distributions of business firms. (See [2] and references cited there.) In a previous paper [1] we presented some results of the simultation of such a model permitting serial correlations over time in the size changes of individual firms. The aim of the present paper is to carry further the analysis of autocorrelated growth, by proposing an economically meaningful scheme for its analysis, and applying the scheme to some data on large American firms. In studying business firm growth, we often encounter cases where a firm suddenly acquires an impetus for growth. Perhaps by innovating in production or marketing processes, or perhaps as an effect of new management staffs or techniques, the firm grows much more rapidly than the other firms in the industry, as measured, say, by the ratio of the current firm size to its size in the previous time period. Thus, we may observe that, while most of the firms in the industry are growing at, say, 5% a year, some firms grow 10%. Furthermore, a firm that grew 10% last year is likely to grow more rapidly than average again this year as a result of the carry-over effects of an innovation that occurred in a previous year on operations in subsequent periods. This carry-over becomes more and more likely as we shorten the length of the time period we are considering from a year to a month, week, or day. Moreover, on the average, a firm which grew rapidly in one year subsequently retains a greater share of the industry assets (or market share if sales are used as a measure of firm size) from that time on than do firms that have enjoyed only the average industry growth. Therefore, not only the growth rate over and above the average growth rate, but also the period when the extra growth took place are important factors in the individual firm's growth relative to the industry growth. In this paper, we develop a model to represent such characteristics of firms' growth, so that the process may be analysed further. In the final section we estimate the key parameter of the model for the recent growth of large American business