a note on forecasting demand for special offers in a magazine

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A Note on Forecasting Demand for Special Offers in a MagazineAuthor(s): Max K. AdlerSource: The Journal of Industrial Economics, Vol. 2, No. 1 (Nov., 1953), pp. 44-50Published by: Blackwell PublishingStable URL: http://www.jstor.org/stable/2097390 .

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A NOTE ON FORECASTING DEMAND FOR

SPECIAL OFFERS IN A MAGAZINE

by MAX K. ADLER

i. Introduction. This note is specifically concerned with the

problem of forecasting the demand for commodities which are the

subject of 'special offers' by a particular journal. The main part of

the note will discuss the technique of forecasting which has been

evolved. There are, however, two aspects of wider significance.

First, that the techniques which have been developed may be

applicable in the forecasting of demand for other commoditiesoffered for sale through other channels; attempts at such more

general use may enable further improvements and modifications in

the forecasting methods. Second, apart from this technical interest

to statisticians forecasting demand, there is the point that the

methods which have been developed seem to imply certain generali-

zations about consumers' behaviour in particular situations, and it

may be of interest to economists to consider them.

2.

The Problem. The journal Woman s a weekly magazine with acertified circulation of over 2,500,000 copies per week. It costs 4id.and is read by over 6,ooo,ooo women and girls aged sixteen and over

in the British Isles. The publishers claim it to be the largest women's

magazine in the world. One feature of the journal is that from time

to time it arranges for its readers to acquire commodities which it

offers on special terms. These offers cover broadly three types of

commodities: cosmetics, household goods, and articles of clothing.

The offers are always made in feature articles and not in advertise-

ments. Readers who wish to purchase the offered article or articles

are asked to send in a coupon together with a postal order for the

amount asked for. On the coupon readers give their name and

address and indicate their particular choice, if more than one

variety is offered.

Whether or not the problem of maximizing profits arises,

the publishers of Woman obviously do not wish to make losses on

the offers. It is necessary to give firm orders to the manufacturers

a considerable time before the offers appear in the journal. Manyoffers are taken up by readers in their hundreds of thousands; large

quantities are, therefore, involved, and a wrong judgement on the

size of the order to be placed with the manufacturers can involve

sizeable losses. These can arise in two different ways:

(i) If the demand is overestimated, a certain number of the

44 t



FORECASTING DEMAND FOR SPECIAL OFFERS 45

articles offered are left in the hands of the publisher whohas to disposeof therdin the best possible way.

(ii) If the demand is underestimated, a large number ofreaders who have sent for the offer cannot be satisfied.Since the buyer sends the money when applying, theclerical work connected with returning the individualamounts is very heavy and, togetherwith the postage, also

very expensive, quite apart from the loss of goodwill.Originally, decisions about the magnitude of orders depended onthe businessacumen of the personshandling the offers. The questionarose how far it was possible to use market research and statistical

methods to answerbeforehandhow many readerswould be likely tosend for any particular offer.

3. Methodof ForecastingAdopted.For offers which had alreadybeen made, of course, the total sales were already known. It was

thought that these statistics could be used to forecast the sales of anew offer, if it were possible to establish its relative standing withconsumers as compared with previous offers. For this purpose, itwas decided to use a questionnaire presented in interviews to a

cross-section of the female population.1 A 'pull' of the feature pagecontaining the offerwhose sales are to be forecastis obtained severalweeks ahead of publication. The investigator shows a copy of this

pull to the respondent and gives her a chance to absorb its con-tents. A seriesof questionsis then asked, mainly in order to presentthe respondent,step by step,with a pictureof the real situation whenan offer is sent for. The pertinent questionsare as follows:

If you saw this announcement in Womanwould you say that thisoffer interested

youor not?

If you saw this offer in Woman,do you think you would be

preparedto cut out the coupon and send the money for the offer?If it happened that by the time you came to send for the offer

somebody had cut out the coupon, would you make the effortof buying another copy in order to send for this offer?

In addition to questionsas to marital status and occupation, andthe interviewers' assessment of age and social class, the respondentsare askedwhether, during the last week prior to the interview, theyread or looked through a certain number of weekly journals, one ofwhich is Woman.

In this way, the amount of interest and buying intentions is

obtained, broken down not only by the usual age and class groups,but also by readers of Woman nd by non-readers. Thus it becomes

1 In fact, the surveys were carried out in the Greater London area only, in order to savecosts. The size of the sample was in each case Iooo, stratified by age and class. Onlyfemales aged sixteen or over were interviewed.



46 MAX K. ADLER

possible to assess the relative standing of the offer, compared with

previous offers, and the various differences of acceptance within the

age and class groups, and by readership of the journal. However,

this assessment is necessarily very broad, and does not lend itself to

a numerical statement as to the number of items of the particular

offer that will be bought by the readers of the journal.The introduction of 'barometer scales' helped the statistical

technique to be refined. These are charts containing a picture of a

barometer with readings from o to iOO. Two copies are used in each

interview. The first, bearing next to the points marked iOO, 75, 50,

25, and o, words which indicate the degree of interest in descending

order2 is used to ascertain the degree of initial interest in the offer.The second is used later in the interview, after the respondent has

stated that she would send for the offer, to indicate the strength of

her wish to obtain the article.

The sums of the barometer readings are averaged by the number of

respondents in each class and age group, and these averages serve as

weights to be applied to the percentages of those interested, those not

interested, and those who do not know. An Intensity of Interest

Index is obtained by multiplying the percentage of those interestedby their average interest score.

When the Intensity of Interest Scores for two or more similar

offers are compared it can be seen at a glance which offer has the

highest acceptance. The acceptance of the various age and class

groups can also be ascertained in this way, and this may yield useful

pointers for the writing of future offer features.

Although the introduction of the barometer undoubtedly improves

the research findings, it still does not make possible numericalforecasts. For this it is necessary to take account of the sales of

previous offers. It was found that sales forecasts based on an offer

dissimilar to the one to be predicted did not yield accurate results;

therefore all offers were classified in the three groups, cosmetics,household goods, and clothing items, as mentioned before, and

forecasts of the sales of a future offer are based on the findings for a

past offer of the same group.

If the population would react in exactly the same way to the

published offer as the sample of women does to the pull of the offer

feature, it would be quite easy to make a forecast. In this case, each

per cent of those saying that they would send for the offer, would

represent a certain number of sales, and a simple multiplication

would result in an exact sales forecast.

It is well known, however, that the number of people who say that

2Thus, IOO is marked 'Very Interested', and o, 'Not Interested at All'.



FORECASTING DEMAND FOR SPECIAL OFFERS 47

they would act in a certain way is always larger than the number of

people who, in the event, do so act. This is illustrated by the fact that

in respect of a certain offer each percentage point of those saying

that they would send for it yielded 5428 actual sales, while each

percentage point of those who said the same to another, similar,

offer yielded only I469 actual sales. How then can these two

figures be reconciled?

On the basis of experience it was argued that the percentage of

those saying they would send for an offer who will actually do so

will depend on the price, so that the higher the price of a given offer

the lower the percentage who will send. For the purpose of fore-

casting, it was assumed that the percentage would decrease propor-tionately to the rise in price; in other words that, in order to forecast

the sales from a given offer, the percentage of those who say that they

will send for it, both for the offer which serves as forecasting base and

for the offer for which the sales are to be predicted, must be deflated

by the price of each offer respectively.

This deflating factor is taken into account in the following formula.

XO Yp

Xp , whereYo

Xp=the sales of the offer to be predicted;

Xo=the actual sales of the offer that serves as prediction base;

Yp=the quotient of the percentage of readers who said that they

would send for the offer to be predicted, over the unit price of

that offer;

Yo=the quotient of the percentage of readers who said that they

would send for the offer that serves as prediction base, overthe unit price of that offer.

An actual example will make the matter clear. Of offer A, the

offer that serves as prediction base, 240,000 items were sold at the

price of I/3 each, when 45 per cent of the readers of Womanin the

sample said that they would send for the offer. Offer B, the offer

the sales of which are to be predicted, costs 2/- per unit and 38 per

cent of the readers of Women n the sample said that they would send

forit;

how many units will be sold?

xp 240. 38

24 =I27 approx.45

I5

The sales forecastis, therefore I27,000 units.

4. Results of the Forecasting. The practical applications of this



48 MAX K. ADLER

sales forecasting formula are not without interest, for they show both

its successes and its failures. So far, eight forecasts have been made;3

the percentage deviations from the actual sales were as follows:

Offer A - I.53/

B + I.Oi%

C - 4.47%D + I.Oi%

E - 4.2 I%

F + I2.03%

G + 79.I3%

H +I52.55%

On the arbitrary assumption that forecasts with errors up to 5 percent are full successes, forecasts with errors of between 5 and I 5 per

cent are partial successes, while forecasts with an error greater than

I5 per cent are failures, the table shows that the forecasting for

offers, A, B, and D was very good, and that for offers C and E was

reasonably good, while the forecast for offer F was a partial success

only, and those for offers G and H were complete failures.

It is, perhaps, illuminating to discuss the reasons for the partial

success and for the failures. In the case of offer F, the comparableoffer on which the forecast had been based was published about a

year before offer F; the change in the economic climate of the

country between the two dates apparently induced more women in

the higher income groups to send for this relatively cheap offer,while a number of working-class women did not send for it; an

inspection of the Intensity of Interest Scores of the various social

classes fortifies this opinion.

Within the first four days after offer G, a summer dress, couponscame in in a satisfactory manner, and the experts considered that

it was yielding the number of sales as forecast. However, four days

after publication, rain fell heavily and the temperature became very

low, and from then on only a trickle of coupons arrived.

The case of offer H is a very curious one. There are several

reasons for the failure of the forecast for this offer. One reason was

the omission of a key word from the questionnaire. But the main

reason, the existence of which was unknown at the time of the

forecast, consisted in the fact that underneath the coupon for the

offer another coupon was printed with which the readers could placea regular order for the magazine with a newsagent. Both coupons

appeared under the same headline which, to casual readers, seemed

to indicate that they could send for the offer only when, at the same

8 Since this paper was prepared two more forecasts have been made; in both cases theerror was less than 4 per cent.



FORECASTING DEMAND FOR SPECIAL OFFERS

time, placing a regular order for the magazine; many readersmayhave had still in their minds the pre-warpracticeof a numberof pub-lishers who coupled free and special offers with the taking out of a

subscriptionfor aJournal. Since the coupons appeared on a laterpage that also contained advertisingmatter, it is certain that largenumbers of readers refrainedfrom sending for the offer, erroneouslybelieving that they committed themselves to much more than was,in fact, indicated.

The partial successonly of forecastingoffer F and the breakdownof forecasting in the cases of offers G and H show clearly how thesuccessful use of the forecasting formula can be vitiated by un-

predictable changes in relevant factors.5. Extension f theFormula'sUse. The forecastingformula may,

however, be used for an additional plrpose, for the forecastingofhow demand will be affected by changes in the price at which theoffer is made. Thus by successive substitutions a table can beconstructedfrom which the total sales, the total turnover and thetotal profit at each price level can be read.' The formula assumessales to decreasein strictproportionto the increasein price; in other

words,the

publicis more sensitiveto a

priceincreaseat a lower than

at a higherprice. Given this, it could lead to a policy of maximizingprofits by raising the price and sacrificinga number of sales.

However, these results should not be taken too far. Each com-

modity has, in the mindsof the buying public, a lowest and a highestprice limit; this is true even if the public themselvesare only vaguelyaware of it. If the price is below this limit, fewerpeople will buy the

commoditythan would be shown by the formulathroughcontinuoussubstitution because a number of potential buyers will grow sus-

picious of the quality of the commodityoffered. On the other hand,buyers' resistance will be experienced if the price is beyond the

psychological limit. Where these actual limits are cannot bediscovered by the application of the sales forecastingformula. In

addition, competition restricts,of course, the price range at which4 As an example, the following table shows the substitutions beginning with a price of

Is. 3d. to a price of is. gd. for the same article.

Price Profit Total Total Totalper Unit per Unit Sales Turnover Profit

sh d. 'ooo £Is. 3d. 2 226 14,125 1,883Is. 4d. 3 213 14,200 2,663Is. 5d. 4 200 14, 67 3,333Is. 6d. 5 189 14, 75 3,938Is. 7d. 6 179 14, 70 4,558Is. 8d. 7 170 14,167 4,958Is. gd. 8 162 4,175 5,400

It can be seen that with increasing price total sales fall proportionately, while the totalmoney turnover remains stable. Therefore, total profits increase very rapidly.

D

49



50 MAX K. ADLER

a certain commodity can be marketed. The experiencefrom whichthe formula has been constructed has been fromcommodities sold asspecial offers, and, therefore, having the attraction that their priceswere below hose at which they would regularly be available throughordinary channels of distribution. It does not follow that such resultswould obtain for prices which were higher than 'outside' competitiveprices. As in so many other fields of economic activity research canprovide only a base for decision; the decision itself has to be made bythe businessman whose experience tells him how far he can go.

6. Conclusion.Forecasting is generally agreed to be one of themost important tasks of the statistician in business. The attempt at

forecasting,as describedin this note, is by no means exact, but thepractical results have been sufficiently good to serve as a guide tothe decision makers, provided no unpredictable elements makethemselves felt.

Beyond its practical usefulness, however, and subject to thequalifications made earlier, the relative success of the forecastingformula suggests two general conclusions. The first is that a con-sumer' intention of buying a commodity is lesslikely to be negatived

for low-priced commodities than for high-priced ones, so that theremay be more uncertainty of consumer conduct for commoditieswhose pricesare high in relationto normal budgets. This conclusionis outside the scope of usual economic theory, which is concernedwith actual happenings and not with intentions.

The second conclusion is that for high-priced commodities, priceincreaseshave less effect on the stability of demand intentions than

similar absolute increases will have on lower-priced commodities.

The economist would perhaps expect this, since the same absoluteincrease in price has lower proportional significance the higher theinitial price of a commodity.

A further interesting point is the implication of the forecastingformula that the effective demand for special offersof this kind hasunit elasticity. This has had its empirical justification - theore-

tical justification is another matter and without further evidence

can only be speculative.It would be interesting to have the forecasting formula here

described'applied to other businesses and to other methods of

selling. It seems likely that it would be useful to them, perhapsadapted and modified as necessary. The author would be pleasedto co-operate with other market researchpractitioners f they would

experiment with its use.

LONDON

a note on forecasting demand for special offers in a magazine

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