^{page 68 note (1)} L. Needleman, ‘The demand for domestic appliances’, National Institute Economic Review no. 12, November 1960, pages 24-44 and C. St J.O'Herlihy, G. Fane, K. M. Gwilliam and G. F. Ray, ‘Long-term forecasts of demand for cars, selected consumer durables and energy’, National Institute Economic Review no. 40, May 1967, section prepared by Gwilliam on pages 44-54.

^{page 68 note (1)} In the remainder of this article the term ‘penetration’ is used with the meaning given to ‘saturation’ in the previous articles. ‘Saturation’ is here used to apply to the tailing-off part of the penetration curve as it approaches 100 per cent (that is to say the point at which the number of sets owned is equal to the number of households).

^{page 68 note (2)} Throughout the article deliveries include imports, purchases include those made by rental companies and no distinction is made between ownership in the strict sense and renting.

^{page 68 note (3)} Gwilliam, op. cit., pages 47-8.

^{page 69 note (1)} For the second period the lower variant thus differs by 1/2 per cent a year from that suggested in the first section of the article. In the present case it was felt that a wider range between the alternatives would yield more illuminating results.

^{page 71 note (1)} Strictly speaking the data (from the Family Expenditure Survey) relate not to income but to total expenditure on all items. But the risk of distortion if the latter is inflated for in dividual households by above-average expenditure on electrical appliances has been met by the use of groupings of, on average, 100-120 families, based on income ranges (for a view of the role of income ranges as an instrumental variable in this context see N. Liviatan, ‘Errors in variables and Engel curve analysis’, Econometrica, July 1961, pages 336-362).

^{page 72 note (1)} As for example in S. J. Prais and H. S. Houthakker, ‘The analysis of family budgets’, Cambridge Department of Applied Economics, Monographs 4, 2nd impression, CUP, 1971 (especially pages 88 et seq.). For the 1970-71 relationship, however, the coefficients are equally consistent with the view that total household expenditure on electrical appliances depends on the household's total income regardless of size: the form shown in table 3, namely E/p=K(Y/p) ^1.50 p ^0.43, where E is expenditure on electrical appliances, Y is income, p is household size and K is a constant, is easily transformed to E=KY ^1.50 p ^-0.07, so that the coefficient on p, which retains its standard error of 0.13, is no longer significantly non-zero at 95 per cent.

^{page 74 note (1)} As Needleman concluded ten years ago at a much earlier stage in the saturation process (op cit., page 26): ‘The rates at which ownership has grown in different countries have … varied idiosyncratically’.

^{page 74 note (2)} The life expectancy (n) is approximately given by the formula n°=n*S_t-n*/Σ R_t-1, where S_t-n* was the stock of durables in use n* years previously, R_t-i was the number of replacement purchases i years previously, and n* is that number of years deduced by inspection to be the closest integral value to the actual value of n. The values assigned to R and S for each durable are entirely derived from data on the number of appliances delivered each year and the number of households owning or renting appliances; the latter being taken to be equal to S. Secondary purchasing, which has been occurring increasingly over recent years at least for vacuum cleaners and televisions, is thus ignored. To the extent that it has taken place, S_t-n* will be understated and R overstated and the calculated value n° will thus be too low. But except perhaps in the case of television sets the resulting error in n° is unlikely to be of any importance (secondary purchasing ten to fifteen years ago, the principal range of n°, will not have been of an order to impart more than marginal bias to S_t-n*); and it is worth noting that the life expectancies calculated in this way generally remain markedly constant (to within six months) between one year and the next (apart from the large once-for-all jump in the life-length of televisions early on).

A further minor distortion may be caused by deliveries of washing machines to launderettes and of deep freezers and refrigerators to grocers and supermarkets.

^{page 76 note (1)} A variation in growth rates between, say, 3 per cent and 5 per cent in a particular year is likely, however, to have less effect than a period of abnormally unfavourable economic conditions, which could cause a large amount of replacement buying to be deferred to a later year. This applies to a lesser extent to initial purchases also.

^{page 76 note (2)} This is a similar rationale to that given by Needleman (op. cit., Appendix, section 14).