The Price is Wrong: Numeracy and Mental Accounting with Percentage Changes

1. The Price is Wrong: Numeracy and Mental Accounting with Percentage Changes Haipeng (Allan) Chen Akshay R. Rao Howard Marmorstein Michael Tsiros

2. A man by the name of Smith was walking home from work when he spotted a $5 bill on the pavement. He looked around, picked it up, and put it in his pocket. His other pocket already contained a $10 bill. Smith smiled. “My wealth has increased by 50%,” he said to himself. Unfortunately, the pocket that held the $5 bill had a hole in it. When Smith got home, he discovered to his dismay that the $5 bill was missing. “That’s not so bad,” he said. “Earlier, my wealth increased by 50%, now it has decreased by only 33%. I’m still ahead by 17%!” Reported in 200% of Nothing (Dewdney 1993, p. 9)

3. A 60% decrease followed by a 70% increase on the standardized test scores in the state of California seemed to cheer up a lot of people. Reported in 200% of Nothing (Dewdney 1993, pp. 9-10)

4. “The depression took a stiff wallop on the chin here today. Plumbers, plasterers, carpenters, painters and others affiliated with the Indianapolis Building Trades Unions were given a 5% increase in wages. That gave back to the men one-fourth of the 20% cut they took last winter.” The New York Times, quoted in How to Lie with Statistics (Huff 1954, p. 111)

5. Importance of numerical ability (numeracy) Consumers have difficulty… Calculating unit prices (Russo 1977) Computing net cost (e.g., $400 down, $49/mo, 60 months, Estelami 1999) Calculating price differences (Thomas and Morowitz 2008) Recalling prices (Lee and Monroe 1999) Updating reference prices after promotion withdrawal when presented in % off vs. $ off format (DelVecchio et al. 2007)

6. Attempts to measure numerical ability (numeracy) • Understanding basic math facts and relationships (e.g., 1 in 10 vs. 1 in a 100, Lipkus et al. 2001) • Preference for numerical information (PNI) scale (Viswanathan 1993). However, PNI is moderately and not consistently correlated with objective numerical ability. • Numeracy has only recently began receiving attention in CB • Double discounting (20% + 25% vs. 40%, Chen and Rao 2007) • Perception of the difference between 100 and 150 is influenced by whether it is provided as 50% increase or 33% decrease (Kruger and Vargas 2008)

7. In this paper … We examine the success of the value pack vs. % off in a field study (actual choices by motivated consumers) We develop a numerical ability with percentages scale (NAPS) We examine different offers (value pack vs. % off) with actual consumers and link it to NAPS and PNI scales We develop and test a model which reconciles inconsistent findings in the mental accounting literature (integrating or segregating mixed gains)

8. STUDY 1 (Field Experiment) • Store:Upscale kitchen appliance store • City demographics: • Population: ~ 30,000 (86% White) – metropolitan area: over 4 million) • Median HH Income: ~ $66,000 • Education: ~ 40% with BS or higher (over 25 years old) • Median Age: 34 years old • Data collection: 1/7/08 - 5/3/08

9. STUDY 1 (Field Experiment)The Value Pak (Fruits & Passion Hand Lotion) Sales: .31 units/day vs. .54 units/day

10. Study 2 Mall intercept (Professional MR company) • 120 adults (East coast) • $3 reward • Average HH income ($30K – $50K) Discount (between subjects): Value pack vs. $ discount Offer I. Toothpaste (Your favorite brand) Regular price: $3.89 for 8 Oz. Special this week: Get 50% more free. Get 12 Oz for the 8 Oz price. Offer II. Toothpaste (Your favorite brand) Regular price: $3.89 for 8 Oz. Special this week: 35% off the regular price.

11. Numerical Ability with Percentages Scale (NAPS) – Study 2 1) If a price is reduced by 40% and then reduced further by 10%, what is the total percentage discount you are getting? a) 44% b) 46% c) 48% d) 50% e) 52% 2) If the annual percentage yield (APY) on a certificate of deposit (CD) is 5%, what is the total percentage return on this CD in 5 years? a) 23.5% b) 25% c) 26.5% d) 28% e) 29.5%  3) You receive a “convenience check” in the mail from one of your credit card companies (that is, you have an opportunity to take a loan). The offer states that you can borrow $10,000 at an annual percentage rate of 1% for the next 4 months. After that, the interest rate will go up to 8.99%. In addition, there is a one-time transaction fee of 3% on any amount you borrow. Assuming that you borrow $10,000 now and pay back the loan right before the rate adjusts higher, approximately what is the effective annual interest rate on this $10,000 loan? a) 1% b) 4% c) 7% d) 10% e) 13%

12. Measures – Study 2 DV: Attitude toward the offer 5-item scale (adapted from Burton and Lichtenstein 1988) I think the offer on my favorite brand of toothpaste is: Bad 1 2 3 4 5 6 7 Good Unattractive 1 2 3 4 5 6 7 Attractive Not beneficial 1 2 3 4 5 6 7 Beneficial Unfavorable 1 2 3 4 5 6 7 Favorable I don’t like it 1 2 3 4 5 6 7 I like it a = .93 & .95

13. Results – Study 2 Value pack is perceived as better than the % off discount (t119 = 3.99, p < .01). Actually the % off discount is slightly better. The least numerate (getting all 3 questions wrong) judged the value pack as representing a better deal (t63 = 4.70, p < .01) whereas the more numerate (getting 1 or more correct) judged the two deals as similar (t55 = 1.11, p > .20). When we used both the NAPS scale and the PNI scale as independent variables in a regression on the attitude towards the offer, the model estimates are as follows: AO = - .413 + .392 NAPS - .064 PNI While the coefficient for NAPS is significant (p = .035), the coefficient for PNI is not (p = .55). Therefore, as expected, people’s numeracy with percentages is predictive of their attitude towards the offer.

14. Mental Accounting Implications • Segregate gains (+$20, +$20) vs. (+$40) • Integrate losses (-$40) vs. (-$20, -$20) • Integrate mixed gains (+$20) vs. (+$40, -$20) • Segregate mixed losses when the gain is small (e.g., (-$40, $+1) vs. ($-39)) but integrate mixed losses when the gain is relatively large • Mr. A bought his first New York State Lottery ticket and won $100. Also, in a freak accident, he damage the rug in his apartment and had to pay the landlord $80. • Mr. B bought his first new York State lottery ticket and won $20. • Who was happier? (22 A 61 B 4 no difference) • (Thaler 1985)

15. Boundaries in Mental Accounting While integrating mixed gains works for numbers, it reverses for percentages. For example: Mr. A’s couch & chair was priced originally at $1,300 but is now reduced by 3.8%. Mr. B’s chair was priced originally at $300 and his couch was priced at $1,000. His chair is now reduced by 33%, and his couch is now increased by 5%. (Heath et. al. 1995)

16. Study 3 Stimulus: • A: 33% price reduction on $1,000 airline ticket, and 5% price increase on $300 airline ticket • B: 28% price reduction on $1,300 (both airline tickets) Objectively: A < B Thaler (1985), i.e., MA of $ • v($330) + v (-$15) < v($364) different mental accounts • v($330 - $15) < v($364) same mental account Heath et. al. (1995), i.e., MA of %age • v(33%) + v(-5%) < v(28%) different mental accounts • v(33% - 5%) = v(28%) same mental account

17. Error-based predictions But, do people realize A < B? It depends on numeracy. For those who realize A < B (same as Thaler): • v($330) + v (-$15) < v($364) different mental accounts • v($330 - $15) < v($364) same mental account For those who don’t (same as Heath et al.) • v(33%) + v(-5%) < v(28%) different mental accounts • v(33% - 5%) = v(28%) same mental account

18. Stimuli – Study 3 “You are considering two trips. One trip is from Miami to Philadelphia while another is from Miami to Rome. The price was $300 for the Miami - Philadelphia trip and $1,000 for the Miami – Rome trip. At travel agent A, the price from Miami to Philadelphia has now been raised by 5% but the price from Miami to Rome has now been lowered by 33%. At travel agent B, the total price of $1,300 for the two trips has now been lowered by 28%.”

19. Stimuli – Study 3 Manipulation: • Easy to segregate (One trip with friends for fun and the other for a job fair) • Easy to integrate (Both trips with friends for fun) Net effect of the price change: • 28% • 24% • Other, please specify _________________ N = 126 DV: Happiness for buying the tickets from agent A or agent B (15-point scale)

20. Results – Study 3 58% chose option (a) 28% (i.e., low in numeracy) 28% picked option (b) 24% (i.e., high in numeracy) Numeracy : (F(1,104) = 16.54, p < .01) Numeracy X Mental account : (F(1,104) = 5.43, p < .05) Participants high in numeracy preferred the pure gain (12.03 vs. 8, t104 = 6.16, p < .01) regardless of ease of segregation When easy to segregate, participants low in numeracy indicated they would be happier with pure gain (10.19 vs. 8, t104 = 3.40, p < .01) When easy to integrate, participants low in numeracy indicated they would be equally happy with the two options (7.46 vs. 8, t104 = .85, p > .20)

21. Contributions Numerical ability with percentages scale (NAPS) Numeracy interacts with mental accounting affecting evaluations of price promotions Low numeracy produces framing effects Numeracy affects the editing stage when dealing with percentages while loss aversion affects the evaluation stage Public policy prescription may depend on whether preference for segregating mixed gains is a computational error or a perceptual bias)

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23. Future Research Directions Further development and refining of the NAPS scale Hard wiring of the brain -- is our brain designed to handle frequencies (integers) better than percentages (fractions)? Can we identify parts of the brain that may handle percentages and train them? fMRI and other technological advances may help in this process.