# An Experimental Study of the Relationship Between Responses to Price Changes and the Price Level For Shoes

##### Citation:

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Nonyelu G. Nwokoye (1975) ,"An Experimental Study of the Relationship Between Responses to Price Changes and the Price Level For Shoes", in NA - Advances in Consumer Research Volume 02, eds. Mary Jane Schlinger, Ann Abor, MI : Association for Consumer Research, Pages: 693-704.
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[Nonyelu G. Nwokoye is a doctoral candidate in Marketing at the University of Massachusetts, Amherst. His thanks go to Kent B. Monroe for his valuable counsel in all phases of the study and to Alan G. Sawyer and David Finn for their assistance in administering the experiment.]

The responses of subjects to shoe price changes were studied using the concepts of price tolerance and discount limit. Price tolerance was defined as the largest price increase that would make a shopper still consider purchasing; discount limit was defined as the largest price decrease that would make the shopper still believe the original price. While price tolerance generally increased with price level, the increase was nonlinear but appeared to be highly sensitive to the ending digit of the price. There was strong evidence that discount limit increases linearly with price. Price tolerance was significantly less than discount limit for most price levels, indicating that subjects were more sensitive to price increases than to price decreases.

How do consumers react to price changes? Are consumers more sensitive to price increases than to price decreases? How much of a price change is necessary to invoke a behavioral change? Reliable answers to the above questions have practical implications for price-setting.

If intuition suggests that a $1 price increase is more apparent on $10 item than on a $100 item, does this imply a systematic relationship between the perception of price increase and the price level? Weber's law has often been invoked when researchers discuss perception of price changes. Weber's law states that the increment in stimulus intensity needed to produce a just noticeable difference (JND) in response is directly proportional to the stimulus.

Researchers disagree on whether Weber's law could be assumed in pricing and response relationships derived from it (see Kamen and Toman, 1971; Monroe, 1971; Gabor, Granger, and Sowter, 1971). The major problem is that Weber's law cannot be directly tested for price, because, as has been articulated by Stapel (1972), everybody can notice even a one-cent difference. This suggests that there is no JND for price, and that experimental methods which depend upon the JND concept would not be directly applicable in pricing studies. One way out of the problem is to operationally define the smallest change in price that will induce a well-defined behavioral change in the buyer.

This paper reports the results of a study in which changes in price for shoes (plus or minus about a level) obtained from subjects' responses were related to price level over a wide range of prices. Directional effects were also examined to see if price sensitivity is different for price increases as compared to price decreases. Such differences have been reported by other workers using other methods (e.g. Pessemier, 1960; Uhl, 1970).

HYPOTHESES

Price increases and decreases are first defined and given particular labels. For price increases from a level, price tolerance is defined as the largest increase in the price of a particular product offer that will make a shopper still consider purchasing that product offer. For price decreases from a level, discount limit is defined as the largest decrease in the price of a particular product offer that will make a shopper still believe the initial price. The above definitions imply that the shopper knows and accepts the initial going price of the product offer.

The following hypotheses are set up:

Hypothesis 1: For a given market segment and product class, price tolerance increases linearly as price level increases.

Hypothesis 2: For a given market segment and product class, discount limit increases linearly as price level increases.

Hypothesis 3: For a given market segment and product class, price tolerance is less than discount limit for each price level.

Hypotheses 1 and 2 are suggested by analogy to Weber's law. Hypothesis 3 derives from the fact that price is a sacrifice a buyer makes for acquiring a product, and it is assumed that a buyer would want a price increase (if one must be made) to be as small as possible, and a discount (if one is promised to be as large as possible.

METHOD

Using the product class shoes, mean price tolerance and discount limit were determined for 180 University of Massachusetts undergraduate students in a laboratory setting. Two completely randomized designs were used -- one design for price increases and the other for price decreases. In each design, price treatments were 15 price levels ranging from $3 to $50 for a pair of shoes, and 6 subjects responded for each price level. Since the product class was being studied, no particular type of shoe was specified. Each subject was presented with a scenario which, for both price increases and decreases, began as follows:

Shoes come in a wide range of prices, depending on the type and quality of shoe.

Suppose you are out one day shopping, and as you pass by a shoe store you recall that for a while you have been thinking of buying a new pair of shoes. Then you enter the store and find a pair of a certain type and quality that you want. Assume that the price of the shoes is $P, and it is a price you can pay. However, on this day you do not plan to spend the $P on shoes, so you leave the store and decide to return a few days later to pick them up.

For price increases, the scenario ended thus:

When you come back to the store you find that the price of the shoes has been increased. What is the highest price you will still consider paying? Assume that your mind is not rigidly fixed on having that Particular pair.

For price decreases, the scenario ended thus:

When you come back to the store you find that the price of the shoes has been reduced. What is the minimum price that will make you still believe the original price?

Each subject was given an individual price scale on which a mark was to be made. For price increases, the scale began from the initial price and increased in steps of $0.25 to a terminal price at least 200 percent higher for initial prices in the range $3 to $15, and- to at least 50 percent for initial prices in the range $18 to $50. For price decreases, the scale began from the initial price, decreasing in steps of $0.25 to $0 for initial prices in the range $3 to $15, and to a terminal price at least 50 percent lower for initial prices in the range $18 to $50. In all cases, the price scale was wide enough for any respondent.

The scenario and price scale were contained on one sheet of paper. The 180 sheets (6 increases and 6 decreases about 15 price levels) were randomly stacked using a random number table and then serially handed out to the subjects.

Since prices were unambiguously specified, problems of sensitization could be serious if repeated measures of price tolerance and expected discount were attempted on the same subject. Thus, each subject responded to only one price change.

DATA ANALYSIS AND RESULTS

Price tolerance or discount limit was defined as the absolute difference between the initial price and the subjects' price response, i.e.

|Pi - Pr|

where

Pi is the initial price

Pr is the price response

Price tolerance was obtained for each subject responding to a price increase, and discount limit for each subject responding to a price decrease. For each price level, mean price tolerance was computed for the group of subjects responding to increases from that price and mean discount limit was computed for the group responding to decrease from that price. These are shown in Table 1. Mean price tolerance as a percentage of price and mean discount limit as a percentage of price were computed for each price level and are also shown in Table 1. Acceptable price increases ranged from 5 percent for a price level of $45 to 64 percent for a price level of $3, with most values below 15 percent. Believable price decreases ranged from 17 percent to 47 percent.

One-way ANOVA was performed on both sets of data. F-tests showed that price level was not significant in explaining the variation of price tolerance (p > 0.10) but price level was significant in explaining variation of discount limit (p < 0.005).

Figure 1 shows price tolerance as a function of price. There is a wide scatter of points, making the hypothesized linear relationship unlikely to hold. However a simple linear regression fit produced the equation:

Y = 1.53 + 0.04P (1)

where Y is mean price tolerance and P is price level. The slope coefficient was positive and significant ( p < 0.05). Proportion of variance explained (R-squared) was 0.34 giving a correlation coefficient of R = 0.58. Thus, the hypothesized positive correlation between price tolerance and price level was weakly supported.

MEAN PRICE TOLERANCE AND MEAN DISCOUNT LIMIT AND THEIR PERCENTAGES FOR FIFTEEN PRICE LEVELS

MEAN PRICE TOLERANCE VERSUS PRICE LEVEL

MEAN PRICE TOLERANCE VS. PRICE LEVEL BROKEN INTO THREE PLOTS

MEAN DISCOUNT LIMIT VERSUS PRICE LEVEL

On closer inspection of the plotted points in Figure 1, it appears that price tolerance for price level ending in the digit 0, 5, or some other digit, follow different patterns. This led to drawing three plots as shown in Figure 2. Except for the price level of $3, price tolerance for prices not ending with the digits O or 5 appears to follow a linear trend as price increases up to p = $23. For price levels ending with the digit 0, price tolerance rises from $1.0 for p = $10 and in the price range $20 to $50 shows little variation, staying roughly within $3 - $4. For price levels ending with the digit 5, price tolerance increases from $1.0 for P = $5 and stays fairly flat at a value roughly $2.25 in the price range $15 to $45.

Apparently, the structure of the number system is a factor to be included in explaining the response of the subjects to price changes.

A graph of mean discount limit versus price level is shown in Figure 3. There is less scatter of points and a more definite linear trend than in Figure 1. The linear regression equation obtained was:

Y = 0.76 + 0.22P (2)

where Y is mean discount limit and P is price level. The slope coefficient was positive and significant ( p < 0.01). Proportion of variance explained (R-squared) was 0.89, giving a correlation coefficient of R = 0.94. Thus, the hypothesized positive correlation between discount limit and price level was confirmed. The high R-squared, confirmed by a significant F-test of the ANOVA, indicates that price level alone is highly effective in predicting discount limit.

Unlike the case of price tolerance, no clear cut patterns of discount limits are revealed when they are grouped according to the ending digit of the price level.

Hypothesis 3 states that mean price tolerance is less than mean discount limit at each price level. Columns 2 and 4 of Table 1 show that this is true except for P = $3 in which the relationship is reversed. Significance of the difference of means was tested at each price level. In ten of the fifteen cases the values were significant beyond the 0.05 level, two cases were significant beyond the 0.10 level, and three cases (at $3, $20, and $30) were not significant. Thus, there is support for the notion that buyers are more sensitive to price increases than to price decreases.

DISCUSSION AND IMPLICATIONS

It is clear that the highest price increase that the subjects would accept without changing their choices (price tolerance) is not predictable by price level alone. It would appear that when brand names are suppressed (as in this experiment) and price is responded to as a stimulus, that the structure of the number system as well as the perceived meaning of price strongly affect subjects' responses. Thus, price appears to be multidimensional. The results of this study suggest that: (1) buyers are likely to accept bigger price increases for prices ending with the digit 0 than for prices ending with the digit 5, and (2) variation in the price tolerance for prices ending in the digits 0 and 5 is less than variation of price tolerance for price levels ending in other digits. This latter point perhaps reflects the greater ease of making mental computations with numbers ending in 0 and 5 than with numbers ending in other digits.

The above evidence suggests that for product classes where prices are relatively unstable, pricing a product at $19.95 or $19.99, for example, might lead to greater resistance to a future price increase than if the initial price had been $$20.

The finding that price tolerance is not zero, reflecting a reaction threshold on the part of the buyer, suggests that a seller could get away with some price increase without serious consideration of the competition or the short run effects on demand. To the extent that competing product alternatives in a product class are differentiated the seller has even greater latitude in raising price.

Price level predicted discount limit quite well. This indicates that other factors are relatively less important when a buyer reacts to a discount. The finding in this study that expected maximum discount was generally over 20 percent may depend upon the product class (here shoes). It is plausible that for some products, e.g., luxury items, the buyer does not expect any appreciable mark down, and may even doubt the quality of the product if the price is slashed.

In addition, a seller's fairness or integrity in pricing may be in question, if he applies a discount higher than what buyers expect. Exceptions may be when seasonal, perishable, or obsolete stock must be cleared. Thus knowledge of buyer's average discount limit may provide an approximate discount ceiling.

Some comments on methodology are in order. First, possible limitations in the execution of the study are the rather small size (n = 6) of the experimental groups, and the mixing of male and female subjects in some groups. Women's shoes are generally priced lower than men's shoes and there might be sex differences in response to price changes. Fifty-two of the 180 students were female, but they were not evenly assigned to the thirty groups used. The data for those groups in which both sexes were equally represented were re-examined. There were three such groups for price increases and four groups for price decreases.

Mean price tolerances were significantly different in two cases out of three-- higher for males in one case and higher for females in the other (t-tests). Mean discount limits for females were higher than for males in all four cases of price decreases, but only one case was significant. The small sample sizes cast doubt on these tests. On the whole, sex differences do not appear to have been a major factor in the results.

Another comment on methodology is that if data on price tolerance had been obtained beyond $23 for prices not ending with the digits '0' or '5', it would have been possible to see if the apparent linear increase of price tolerance with price (shown in Figure 2) would continue. Thus, hypothesis 1 might have been confirmed for prices not ending with the digits '0' and '5'.

Before the findings of this research can be generalized, there is need to replicate the study using non-student subjects such as housewives of a given socio-economic class, and trying other Product classes.

SUMMARY

The concepts of price tolerance and discount limit were introduced and used to study subjects' reactions to price changes. Price tolerance was defined as the largest increase in the price of a particular product offer that will make a buyer still consider making the purchase. Discount limit was defined as the largest decrease in the price of a particular product offer that will make a buyer still believe the original price. Mean price tolerance and mean discount limit were obtained for fifteen price levels for shoes. Percentage price tolerance ranged from 64 percent to 5 percent and mean discount limit ranged from 47 percent to 17 percent.

The hypothesis that price tolerance increases linearly with price level was weakly supported. An interesting effect indicating the multidimensional nature of price was revealed in the data. When brand imaged are suppressed or weak and price is responded to as a stimulus, it appears that the size of price increase that buyers will accept is determined as much by the number system (the ending digit of the price) as by the economic meaning of price.

The hypothesis that discount limit increases linearly with price levels received strong support. In 12 out of 15 price levels, mean price tolerance was significantly less than mean discount limit, providing new evidence that buyers are more sensitive to price increases than to price decreases.

REFERENCES

Gabor, A., Granger, C., & Sowter, A. Comments on "psychophysics of prices' Journal of Marketing Research, May 1971, 8, 251-252.

Kamen, J., & Toman, R. "Psychophysics of prices": A reaffirmation. Journal of Marketing Research, May 1971, 8, 252-257.

Monroe, K. B. "Psychophysics of prices": A reappraisal. .Journal of Marketing Research, May 1971, 8, 248-250.

Pessemier, E. An experimental method for estimating demand. Journal of Business, October 1960, 33, 373-383.

Stapel, J. "Fair" or "psychological" pricing? Journal of Marketing Research, February 1972, 9, 109-110.

Uhl, J. Consumer perception of retail food price changes. Paper presented at the First Annual Meeting of the Association for Consumer Research, Amherst, Massachusetts, August 1970.

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##### Authors

Nonyelu G. Nwokoye, University of Massachusetts

##### Volume

NA - Advances in Consumer Research Volume 02 | 1975

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