Consumer Biases Firm Response - phd-finance.uzh.ch€¦ · – Real estate auctions (Ashenfelter and Genesove, 1992) – Sports: Free agents in baseball (Blecherman and Camerer, 1996);

Biasesin theMarket

ConsumerBiases— systematic

— persistent

Firm Response— contractdesign

— productdesign

Canwe explainotherwisepuzzlingcontractdesign?

Examples:— Options= responseto CEO overconfidence?

— Wagecompression= responseto preferencesforequality/ loss aversion(with wageof co-workerasreferencepoint)?

ContractualResponse

= Evidencefor prevalenceof biasesin themarket

— Consumersdisplaybiasesoutsidethelaboratory.

— Consumerbiasesaffectmarketoutcomes.

+ IntegratingBehavioralEconomicsinto ContractTheory

+ IntegratingOrganization

BehavioralEconomicsinto Industrial

• Basic assumption

— Everyone ‘born’ with biases

— Effect of biases lower if:

∗ learning

∗ advice

∗ consulting

∗ specialization

• For which agents are these conditions likely to besatisfied?

— Firms

— In addition, firms are likely to be aware of biases.

• manytasks

• limited opportunitiesforlearning

• small stakes

• arbitrageis difficult

• specializationof production

• continuousfeedbackfromcapitalmarkets

• largestakes

• competition— entry of newfirms.

Consumers

• limited information • hiring of consultants

• Implications?

• Study biases in the market

• Four major instances:

— Interaction between experienced and inexperiencedagents (noise traders)

— Interaction between firms and consumers (con-tract design, price choice)

— Interaction between managers and investors (cor-porate finance)

— Interaction between employers and employees (or-ganizational economics / labor economics)

— Interaction between politicians and voters (polit-ical economy)

Auctions

• Wide-spread and popular price mechanism in many market and for many centuries (Cassidy, 1967)

• Standard explanation– identifies bidder with highest private value vi

– revenue maximization and efficiency = core reasons for popularity of auctions (Milgrom, 1987)

• Alternative explanation– identifies bidder with highest inclination to overbid, i.e. to bid

more than private value (bi > vi) or alternative price (bi > ) – potential for overbidding = additional reason for popularity

Evidence on Overbidding?

• Conjecture of overbidding in many settings:– Ancient Rome: legal debate whether auctions are void if the

winner was infected by “bidder's heat” (calor licitantis). – Overbidding in contested mergers (Hietala, Kaplan, and Robinson,

2003; Malmendier and Moretti, 2007) and for new issues (Ritter, 1991; Loughran and Ritter, 1995)

– British spectrum auctions (Klemperer, 2002)

– Real estate auctions (Ashenfelter and Genesove, 1992)

– Sports: Free agents in baseball (Blecherman and Camerer, 1996); Drafts in football (Massey and Thaler, 2006)

Identification of “overbidding” problematic ORunclear whether “overbidding” reflects agency problems.

Evidence on Overbidding?

• Cleanest evidence from experimental economics– Large and persistent overbidding in SPAs and (only short-term) overbidding

in first-price auctions relative to RNNE (Kagel, Harstad, and Levin, 1987; Kagel and Levin, 1993; Cox, Roberson, and Smith, 1982; Cox, Smith, and Walker, 1988).

– Debate about motives in literature• Spite motives? (Morgan, Steiglitz, and Reis, 2003)• Joy of winning? Fear of losing? (Cooper and Fang, 2006; Delgado, Schotter,

Ozbay, and Phelps, 2007)• Bounded rationality? (Cooper and Fang, 2006)

But: Need explanations for overbidding in laboratory SPA auctions, which would also predict overbidding in ascending English auctions.

Different approach Lee and Malmendier (2008): Rather than disentangling the reasons for overbidding in the lab (using lab experiments), test for overbidding in the field and its possiblereasons.

Research Question (1)

1. Do we observe overbidding outside the laboratory?– Often hard to identify, esp. in private-value settings.– Private value vi unobservable.

2. What are the causes of observed overbidding? (Different from those identified in the lab?)

Causes of Overbidding

• Quality differences (or perceived quality differences)• Shipping quality or shipping cost differences• Switching costs

– Costly to identify/return to alternative offer outside the auction.• Utility of Winning (Bidding fever)

– In the “heat of an oral auction” or in the last minutes of an internet auction bidding beyond individual valuation.

– Valuation increases over the course of the auction bidding beyond ex-ante valuation.

– Including: quasi-endowment effect• Limited Memory/Attention

– Valuation forgets alternative outside option over the course of the auction bidding beyond ex-ante valuation.

Theoretical Framework

• Second-price private-value auction– Denote bidder i’s private value as vi

– Denote bidder i’s bid as bi

– Denote second-highest bid as pw

• Optimal bidding strategy (Vickrey 1961)

Empirically: Since vi unobservable, overbidding (bi > vi) unobservable.

Adding Fixed Price

• 2nd stage: Unlimited market supply of identical good at fixed price .

• Initial assumption: No transaction costs of bidding and then switching to fixed price.

• Proposition 1.a: A PBE of game with fixed price:Bid in auction.Iff not winner and vi > , buy at fixed price.

• Proposition 1.b: For all realizations of valuations and in all PBE’s, the auction price is weakly smaller than the fixed price: .

Implications

In rational benchmark model without switching costs, auction price should never be higher than .Empirically: > is sufficient for overbidding.Actual overbidding frequency is higher for two reasons:1. Bidders may bid above vi.2. Winning bidder bids above .

Reasons for Bidding above Fixed Price?

1. Transaction / Switching CostsE.g. costly to switch from auction to fixed-price webpage once a bidder has started bidding.

If cost high enough, then conditional on entry into the auction.

2. Limited Memory/AttentionIf cost high enough, then conditional on entry into the auction.

3. Utility of Bidding ? Utility of Winning, e.g. premium πi.

4. Bidding Fever, e.g. perceived premium .

Switching Costs

• Proposition 2.a: There is a PBE of the game with infinite switching costs, in which player i bids conditional on entering the auction.

• Proposition 2.b: For all realizations of valuations and in all PBE’s, the auction price is weakly smaller than the fixed price:

eBay Auctions• Proxy bidding

– Bidders submit “maximum willingness to pay”– Quasi-second price auction: price outstanding increased

to prior leading maximum willingness to pay + increment.

• Fixed prices (“Buy-it-now”) without auction– Immediate purchase.– Listing on same webpage, same list, same formatting.– About 1/3 of eBay listings

Key ingredient for analysis.Persistent presence of buy-it-now price as a

(conservative) upper limit of bids

Data Set 1

• Collected data of all auctions and Buy-it-now transactions of Cashflow 101 on eBay from 2/11/2004 to 9/6/2004.

• Cashflow 101: board game with the purpose of finance/accounting education.

• Retail price: $195 plus shipping cost ($8.47) from manufacturer (www.richdad.com).

• Two ways to purchase Cashflow 101 on eBay– Auction (quasi-second price proxy bidding)– Buy-it-now

Sample

• Buy-it-now offers of the two retailers– Continuously present for all but six days.

(Often individual buy-it-now offers present as well; they are often lower.)

– 100% and 99.9% positive feedback scores.– Same prices $129.95 until 07/31/2004; $139.95

since 08/01/2004.– Shipping cost $9.95; other retailer $10.95.– New items (with bonus tapes/video).

Listing Example (02/12/2004)

Listing Example – Magnified

Pricing:

[Buy Now] $129.95

Pricing:$140.00

Overbidding

Given the information on the listing website:• (H0) An auction should never end at a price

above the concurrently available purchase price.

Distribution of Final Prices42% are above “buy-it-now” (mean $132.55; SD 17.03)

0

10

20

30

40

50

60

90 100 110 120 130 140 150 160 170 180Final Price

Freq

uenc

y

Alternative Explanations

1. “Noise”: Are these penny-difference?2. Shipping costs and Sales Tax3. Failure to understand / retrieve fixed prices4. Quality differences (I): quality of item5. Quality differences (II): quality of seller6. Concerns about unobserved wording differences

between auctions and buy-it-now posting.7. Concerns about consumers’ understanding of

buy-it-now posting.




buy-it-now posting.

Distribution of Final Price0

.01

.02

.03

.04

Den

sity

80 100 120 140 160 180Final Price

(Dashed Line at $129.95)Subsample with fixed price of $129.95

Distribution of Final Price0

.01

.02

.03

.04

Den

sity

80 100 120 140 160 180Final Price

(Dashed Line at $139.95)Subsample with fixed price of $139.95

Table III. Overbidding

Variable Obs. Mean Std. Dev. Min. Max. Overpayment (Final Price) 166 0.28 16.70 -48.95 47.55

Overpayment (Final Price)> $0 166> $10 166> $20 166> $30 166

100%64%39%14%6%

Fraction of Total Number of Auctions

Fraction of Overbid Auctions

42%27%16%




buy-it-now posting.

Table III. Overbidding (with shipping costs)

Variable Obs. Mean Std. Dev. Min. Max. Overpayment (Total Price) 139 2.69 14.94 -28.91 45.60

Overpayment (Total Price)> $0 139> $10 139> $20 139> $30 139 25%

100%66%48%35%

73%48%35%

Fraction of Total Number of Auctions

Fraction of Overbid Auctions

Sales Taxes

1. Buyers from same state as the professional sellers may not buy at the fixed price in order to avoid sales taxes.• Aside: Buyers owe their own state's sales tax also when buying

from a different state, but they may not declare their purchase.

2. The two fixed-price retailers located in different states, Minnesota and West Virginia. • Since both have at least one listing most of the time, bidders from

one of these states can choose the other fixed price. • Overbidding even after adding sales tax (6.5% for Minnesota, 6%

for West Virginia) to fixed price and 0% to the auction price. • For example: a buyer from Minnesota would pay $138.45,

including sales tax, for an item purchased from the Minnesota-based retailer; 28 percent of final prices lie above this threshold




buy-it-now posting.

Failure to retrieve

• Could search does not retrieve the fixed-price listing?• The buy-it-now items should appear in virtually all

searches since descriptions of the fixed-price items are more detailed and without typos.– Survey (four waves in 2005, 399 subjects, mostly Stanford

undergrad or MBA students):– 92 percent start search by typing a core word, typically item name– 8 percent first go to the appropriate item category, in this case

“boardgames”, and then search within this category.With either method, the fixed-price listings are retrieved. If the search includes additional qualifiers, these listings are generally

more likely to be retrieved than most auction listings due to their extensive item descriptions.

Failure to understand

• They are intuitively designed and similar to other internet fixed prices.

• Survey– 90.5% of subjects who have used eBay have come

across the buy-it-now.– 100% of subjects who have used buy-it-now were

satisfied with their experience.

• Will show later: overbidding not restricted to eBay novices.




buy-it-now posting.

Quality of Item• Have ruled out observable quality differences: fixed-price

items brand-new + all bonuses + money-back guarantee; auction items not.




buy-it-now posting.

Seller X

Feedback Score: 2849 Positive Feedback: 100% Members who left positive feedback: 2849 Members who left negative feedback: 0 All positive feedback received: 2959

Recent Feedback: Past Month Past 6 Months Past 12 Months positive 52 365 818neutral 0 1 1negative 0 0 0

Seller Y Feedback Score : 3107 Positive Feedback: 99.90% Members who left a positive: 3111 Members who left a negative : 4 All positive feedback received: 3333

Recent Feedback: Past Month Past 6 Months Past 12 Months positive 112 666 1316neutral 0 2 2negative 0 0 1

Table II. Retailers' Information

Data Set 2: Cross-Section of Auctions

• Does the observed overbidding generalize beyond Cashflow 101?

• If so, to what types of items and what types of bidders does it generalize?

Data Set 2: Cross-Section of Auctions

• Automatized download of 3,863 auctions of a broad range of items with simultaneous fixed prices, available at the time of the last bid.

• Selection criterion: homogenous items!– Ensures comparability of auction price and fixed price.– Non-trivial: used from new items, accessories, bundles, and multiple

quantities.– search features including “new”, price limits (e.g. excluding accessories),

NOT (excluding bundles), OR (“4gb” versus “4 gb”)Constrain

• 103 different items:– electronics, computer hardware, - financial software, – personal care, cosmetics, perfume/colognes, - automotive products– sports equipment, - home products, – entertainment products and books

Overbidding in the Cross-Section

42% 39%32%

59% 56%

35% 39%45%

72%

48%

24%

0%

68%

0%10%20%30%40%50%60%70%80%90%

100%

Cashflo

w 101 (N

=166)

Consum

er ele

ctron

ics (N

=435)

Compute

r hard

ware (N

=190)

Financia

l softw

are (N

=152)

Sports e

quipment (N

=55)

Personal

care

(N=28

2)

Perfum

e / co

logne (

N=77)

Toys /

games

(N=16

4)Boo

ks (N

=398)

Cosmeti

cs (N

=21)

Home prod

ucts (N

=29)

Automotiv

e produ

cts (N

=9)DVDs (

N=74)

• Age– toys for kids (Elmo), – teenagers (games and playstations), – adults (electronics).

• Political affiliation– books of liberal authors (Obama)– books of conservative authors (O'Reilly)

• Price levels– cheap versus expensive financial software (Quicken 2007 Basic versus Home

Business), – cheap versus expensive navigation systems (Garmin Streetpilot C320, Garmin GPS

C330 Navigation System, and Garmin GPS C550 Navigation System), – cheap versus expensive iPods (shuffle, nano, and 80gb), and digital cameras

(Canon A630, SD600, and SD630)

• Gender of consumer– perfumes of the same brand for men and women, – personal care products for men (electric shaver, hair tonic) and women (hair

straighteners, cosmetics)– iPods of different colors (blue, green, silver versus pink)

Overbidding by Target Consumer

Overbidding by Target Consumer

Sample Sample212 165160 13685 6872 58

435 36420 1821 16

114 98159 13334 2610 9

Target ConsumerWithout Shipping With Shipping

% Overbidding % OverbiddingMale 38% 45%Female 33% 29%Kids 28% 54%Teenagers 61% 31%Adults 39% 37%Liberal 40% 17%Conservative 33% 38%Cheap 45% 36%

Most expensive 40% 56%

Expensive 38% 48%More expensive 41% 35%

“Over-bidders”

How many over-bidders generate 42% over-bid auctions?

Quantify• What % of auctions end up overbid?• What % of bidders ever overbid?• What % of bidders mostly overbid? • What % of bids are overbids?(Using data with bidding history.)

Table VII. Market Amplification

Observations (Percent)Auction-level sample

Does the auction end up overbid? No 78 56.52%Yes 60 43.48%

Total 138 100.00%Bidder-level sample

Does the bidder ever overbid? No 670 83.02%Yes 137 16.98%

Total 807 100.00%

Table VII. Market Amplification

Observations (Percent)Bidder-level sample

Does the bidder mostly overbid? No 715 88.60%(more than 50%) Yes 92 11.40%

Total 807 100.00%Bid-level sample

Is the bid an over-bid? No 2,101 89.29%Yes 252 10.71%

Total 2,353 100.00%Overbidding is defined using the final price.

“Disproportionate” Influence of Overbidders

• Inherent to the nature of auctions: Bidders making any kind of upward-biasing “mistake” is most likely to be the winner.

Models of shopping cost / search cost.• Overbidding important empirically even if exerted

only by minority.• “Generalizes” winner’s curse to private value

setting.Alternative motivation for success of (online) auctions.

What explains overbidding?

• Results rule out benchmark model without transaction costs.

• Switching-cost explanation implies the expected auction price should be significantly lower than the fixed price (Proposition 2.b).

• Finding 3 (Overpayment on Average). The average auction price is higher than the simultaneous fixed price, by $0.28 without shipping costs and by $2.69 with shipping costs.- The difference without shipping costs, $0.28, is not significant

(s.e.=$1.30 and 95 percent confidence interval of [-$2.27;$2.84]).- The difference with shipping costs, $2.69, is significant (s.e.=$1.27

and 95 percent confidence interval of [$0.19;$5.20])- Both differences are significant relative to calibrated expected

auction price ($125.52 for the χ²-distribution and $119.95 for the uniform distribution).

What explains overbidding? (III)

• Transaction costs of learning about the BIN price:Unexperienced eBay users might not (yet) take BIN listings into account since they either have not understood how they work or have a harder time identifying them on the screen.

• Implication: overbidding should decrease with experience.

• Finding 4 (Effect of Experience). The prevalence of overbidding is the same for more experienced and less experienced auction winners.

Overbidding by Experience

0.00%

10.00%

20.00%

30.00%

40.00%

50.00%

60.00%

70.00%

80.00%

90.00%

100.00%

Below Median (<=4)(N=83)

Above Median (>4)(N=83)

Limited Attention / Memory

• Prediction of Limited Attention / Memory:1. Overbidding more likely the further away next BIN listed on screen2. Overbidding more likely the lower first BIN listed on screen3. The effect of distance to BIN stronger for first than for later bids

• Test of Limited Attention / Memory: – Transform data set to data of “choices available at each bid”– Perform conditional logit analysis

• Utility of bidder i from choosing item j∈{0, ..., J }: y*ij = bxij + eij

– xij is a vector of observable characteristics of the item– eij represents unobservable factors

• Let j be the choice for bidder i that maximizes his utility: yi = argmax(y*

i0 , ..., y*iJ ).

• McFadden (1974): if {eij }j ∈0,1,...J are independently distributed Weibull rv’s, then the probability that item j is chosen is: Prob(yi = j | xi ) = (ebxij)/(∑J

h=0 ebxih)

Table VI. Bidding and Limited Attention

Full First Bids Later Bids Full First Bids Later BidsDistance to nearest BIN listing 1.176 1.106 1.021 1.061 1.006 1.025 1.056 1.013

[rows between] [0.025]*** [0.029]*** [0.028] [0.042] [0.005] [0.028] [0.043] [0.005]**(Price just below)*(Distance to BIN) 0.894 0.868 0.939 0.822 0.933 0.752

[0.160] [0.245] [0.204] [0.128] [0.232] [0.147](Price just above)*(Distance to BIN) 2.083 2.948 1.785 1.372 1.538 1.469

[0.487]*** [0.911]*** [0.670] [0.239]* [0.324]** [0.421](Price far above)*(Distance to BIN) 1.159 0.640 1.325 1.231 0.861 1.261

[0.137] [0.236] [0.152]** [0.118]** [0.346] [0.133]**Price outstanding just below BIN price 1.164 1.326 1.164 1.205 0.835 1.799

[dummy] [0.207] [0.357] [0.279] [0.179] [0.198] [0.347]***Price outstanding just above BIN price 1.747 0.966 2.920 1.861 1.027 3.255

[dummy] [0.453]** [0.381] [1.004]*** [0.412]*** [0.345] [0.992]***Price outstanding far above BIN price 2.152 1.761 2.844 2.746 1.213 5.922

[dummy] [0.449]*** [0.617] [0.781]*** [0.729]*** [0.575] [2.057]***Position on screen 0.988 0.918 0.974 1.000 0.983 0.973 0.998 0.977

[row number] [0.005]** [0.009]*** [0.013]** [0.019] [0.004]*** [0.013]** [0.019] [0.004]***Price outstanding 0.975 0.99 0.983 1.006 0.991 0.981 1.013

[0.003]*** [0.003]*** [0.004]*** [0.005] [0.003]*** [0.005]*** [0.005]**(Price outstanding)2 1.002 0.989 0.988 0.983 0.988 0.991 0.977

[0.002] [0.003]*** [0.004]*** [0.004]*** [0.003]*** [0.004]** [0.004]***Starting Price 0.994 0.994 0.998 0.99 0.994 0.998 0.991

[0.001]*** [0.001]*** [0.001]** [0.001]*** [0.001]*** [0.001]* [0.001]***Auction controls Yes Yes Yes Yes Yes Yes YesExtended time controls Yes Yes Yes Yes Yes YesN 14,043 14,043 14,043 6,712 7,331 14,043 6,712 7,331Pseudo R-squared 0.01 0.14 0.18 0.25 0.15 0.18 0.25 0.16

Full Sample"Just above/below" = +/-$10"Just above/below" = +/-$5

Dependent variable: binary variable equal to 1 for items bid on (at a given time)

Summary

1. Significant empirical overbidding (42-54%).2. A small sample of over-bidders suffices to

generate a large portion of overbidding winners.Auctions exacerbates the effect of overvaluation on market outcomes: “Auctions as the search for fools.”Overbidding may reflect standard search cost or non-standard biases.

3. Limited Attention/Memory of alternative prices explains a significant fraction of overbidding.

4. Experience does not eliminate overbidding.Suggests non-standard explanation for overbidding.

Implications: Firm Response

• Optimal auction design given bidder behavior(revenue-maximization / efficiency)

Allow opportunity to “forget”Don’t give feedback on mistakes.

• Overbidding appear to be easy to induce and to have a large impact on revenues.

Firms can increase profits with simple strategiesMention higher prices (outside prices, former prices in sales, etc.)Generate “lock-in” effect: Get (potential) buyer involved into the transaction, e.g., by submitting bid; outbid notices.

• Market experience does not appear to remedy the bias.Firms do not give feedback, do inform about overbidding.

• time-inconsistentpreferences

• underestimatetime

inconsistency

Givenconsumerbehavior,firms designprofit-maximizingcontracts.

Consumers Contracts Firms

• rational,profit-maximizing

• awareof time inconsistencyofconsumers

Figure 4b. Price per averageattendanceMonthly contracts with monthly fee>=$70

30

25

20

15 -

10 -

0

S ~•S

•

.5 - - ~~55-45, 5-.

~ ~ ~,~S -~ •—•-:-~ •~~& - - S. - - -

55,_S •~‘ ~——-~_____ __5•

•5 S

• 55 - - -- 9 ‘•- - -

,_i~T:-;__~i--~ —~--;-~i‘5 - - _9_S -.

-545 - - - - S -

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Month

25

~20

~15

~10

,~ 5

0

Fi2ure 4a. Price per averageattendanceAnnual contractswith annual fee>=S700

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Month

Markets

1. Goodswith immediate costsand delayedbenefitsrelative to best alternative activity (Investment Goods)

- health club attendance,vacation time-sharing

2. Goodswith immediate benefits and delayedcostsrelative to bestalternative activity (Leisure Goods)

- credit card borrowing, cellular phonecalls

3. Contracts with automatic renewal & costly cancellation- credit card, newspaper,mail order

2 Behavioral IO: Contracts

2.1 Self-Control — The Basics

(Based on DellaVigna and Malmendier, QJE, 2004).

MARKET (I). INVESTMENT GOODS

Firm

• Monopoly• Two-part tariff: L (lump-sum fee), p (per-unit price)• Cost: set-up cost K, per-unit cost a

Consumption of investment good

Payoffs relative to best alternative activity:

• Cost c at t = 1, stochastic— non-monetary cost

— experience good, distribution F (c)

• Benefit b > 0 at t = 2, deterministic

Figure Ia. Timing of simple model.

Period 0 Period I Period 2

Payoffs:-c-p b

Agentaccepts

Firm offers Agent(L~p) rejects

Payoff:-L

Agent doesnot consume

Payoff: Payoffs:0U 0

INTERTEMPORAL PREFERENCES

Hyperbolic discounting (Strotz, 1956; Pheips-Poliak, 1968;Laibson, 1994; O’Donoghue-Rabin, 1999):

Ut =ut+~~ 0 ut+s

with ~3< 1. Discount function: 1, /36,

(1) Time inconsistency

Discount factor for self t is

/362 ~3,

• /36 between t and t + 1 > short-run impatience;

• 6 between t + I and t + 2 ~> long-run patience.

(2) Overconfidenceabout time inconsistency

Agent believes futures selves have discount function:1, ~6, ,362 ~ ...,with ~ � /3.

Partially naive hyperbolic (/3,,~, with/3</3< 1

<1

j\(~~ye

(O’Donoghue-Rabin, 2001)

6)

I I

CONSUMER BEHAVIOR.

• Long-run plans at t = 0:

Consume ⇐⇒ βδ(−p− c+ δb) > 0

⇐⇒ c < δb− p

• Actual consumption decision at t = 1:

Consume ⇐⇒ c < βδb− p (Time Inconsistency)

• Forecast at t = 0 of consumption at t = 1:

Consume ⇐⇒ c < β̂δb− p (Naiveté)

FIRM BEHAVIOR. Profit-maximization

maxL,p

δ {L−K + F (βδb− p) (p− a)}

s.t. βδ

(−L+

Z β̂δb−p−∞

(δb− p− c) dF (c)

)≥ βδu

Solution for the per-unit price p∗:

p∗ = a [exponentials]

−³1− β̂

´δbf³β̂δb− p∗

´f (βδb− p∗)

[sophisticates]

−F³β̂δb− p∗

´− F (βδb− p∗)

f (βδb− p∗)[naives]

Features of the equilibrium

1. Exponential agents (β = β̂ = 1).Align incentives of consumers with cost of firm=⇒ marginal cost pricing: p∗ = a.

2. Hyperbolic agents. Time inconsistency=⇒ below-marginal cost pricing: p∗ < a.

(a) Sophisticates (β = β̂ < 1): commitment.

(b) Naives (β < β̂ = 1): overestimation of con-sumption.

Figure 2a. Optimal level ofp: pricing of overconfidence.

* costc

Figure 2b. Violation of asvmDtoticallv boundedneaks(ABF~condition.

f(c)

18bb_p* /Sb-p

cost C

46

Existence of solution for p~

• Could p~—~ —oo?

• Figure 2b. Sufficient condition for existence of p~.

• Rule out unbounded peaks on the tails of f(c).

Asymptotically Bounded Peaks (ABP)

There is a pair (M, z) E 1R2 such that

f(y”) <Mf(y’) for all y’, y”

with z < y’~< y”~and y’ y” > 0.

All standard distribution functions satisfy ABP.

PERFECT COMPETITION.

Price per unit p~as under monopoly:

below marginal-cost pricing

• perfect competition 1~•p*I~

• bid down lump-sum fee L*

Proposition 1 (Investment Goods)

(1,) Under a regularity condition,

the profit-maximizing per-unit price p~satisfies

p*p*

= aif/3=land

< aif/3<1.

(ii) In the case of perfect competition,

L* = Kif/3=land

L* > Kif/3<l.

MARKET (Ii). LEISURE GOODS

Payoffs of consumption at t = 1:

• Benefit at t = 1, stochastic

• Cost at t = 2, deterministic

~> Use the previous setting:

—c is “current benefit”,

b < ü is “future cost.

1 esults:

1. Exponential agents.

Marginal cost pricing: p~= a, L* = K (PC).

2. Hyperbolic agents tend to overconsume. ~—~>

Above-marginal cost pricing: p~> a.

Initial bonus L* < K (PC).

(a) Sophisticates: commitment device.

(b) Naives: underestimation of usage.

Corollary I (Leisure Goods)

(i) Under a regularity condition,

the optimal price per consumption p~satisfies

= aif/3=land

~* > aif/3<1.

(ii) In the case of perfect competition,

= Kif/3=land

< Kif/3<1.

L*

L*

EMPIRICAL PREDICTIONS

Two predictions for time-inconsistent consumers:

1. Investment goods (Proposition 1):

(a) Below-marginal cost pricing

(b) Initial fee (Perfect Competition)

2. Leisure goods (Corollary 1)

(a) Above-marginal cost pricing

(b) Initial bonus or low initial fee (Perfect Competi-tion)

Field evidenceon contractsInvestment goods

A. US Health club, industry ($11.6bn revenuein 2000)

• Survey of all health clubs in Bostonarea (100 clubs) — Table 2• Most common contract design:

- monthly and annual fee & initiation fee- no per-visit fee’

• Estimated marginal cost: $3-$6+ congestioncost

+ Below-marginal-costpricing of visit.

• Small transaction costs

• Reverseprice discrimination

HealthClab IndustryTop 8 Clubs (revenues as of 2000)

Revenues (m$) Employees US States

(1) (2) (3)

3. Town Sports InternationalNewYork, NY

4. WellbridgeDenver, CO

5. Life Time Fitness Inc.Prairie, MN

6. TCA Club ManagementChicago, IL

7. The Sports Club Co.Los Angeles, CA

8. Crunch Fitness InternationalNew York, NY

Concentration Indexes

Herfindahi index (*10,000) 152.65

Concentrat‘ion Ratio 4 20.25%

32.55%

lable 1. US

1. Baily Total FitnessChicago, IL

2. 24 Hour Fitness WorldwideSan Francisco, CA

1,007 20,000

943 26,300

225 6,400

175 5,000

101 3,000

85 2,200

77 2,400

73 2,200

28

15

9

12

6

16

4

5

Concentration Ratio 50

Table 2a. Health club industry.Menu of contracts

Typeof contractMonthly

(1)Annual

(2)

Per-visit

(3)

Average fee in $:per visit

per monthperyearff1 ttiatlOfl fee

057.59

0128.40

00

594.2373.32

11.30000

Menu Of contracts:No. of health clubs

- Frequent contract- Infrequent contract

Cancellation procedure:

Automatic renewal- cancel in person- cancel by letter- cancel by phoneAutomatic expiration

Sample: I club per firm

1111

573324

53

47

6

5151

23 (12 certified)

62

N=67

51

2‘49

N=67

9 (6 certified)

I38

N=67


B. Vacation time-~sharingindustry ($7.5bn salesin 2000)

• Booking a holiday:immediate transaction costof booking

- delayedpleasurablevacation

• Common contract (RCI, Hapimag): Point System- high initial fee: $11,000(RCI)- minimal feeperweekof holiday: $140(RCI)

+ Below-marginal-costpricing of holiday apartments.+ High initial fee.


C. Theater-classicalconcerts• Attendanceof cultural event:

- immediate transportation and logistic costs- delayedpleasurableexperience,culture

• Common contract: seasonalsubscription

D Educational institutions• Education:

- effort cost, forgonewages

- acquireusefulknowledge

• Typical contract: yearly tuition and no feeper lesson/course

Field evidenceon contractsLeisure goods

A. Credit card industry ($500bnoutstanding debt in 1998)

• Credit card borrowing:- higher immediate consumption- lower future consumption

• Resalevalue of credit card debt: 20% premium (Ausubel, 1991)• No initial fee,bonus(car/ luggageinsurance)

+ Above-marginal-costpricing of borrowing+ Initial bonus for transactors

Table 3b, Credit card industry. Representativecontracts

(1)

Prime + 12.99%12.99%

+ 6.50%+ 3.98% to+ 11.98%+ 7.99%to+ 12.99%+ 9•99%

IntrOdUctoryinterest rate

(APR)

(3)

2.90%*3.90%*9.90%*

0%

3.90%

1.70%*0%

7.90%

Length ofintroductory

offer(4)

9 months6 months9 months6 months

6 months

6 months6 months6 months

Regular interestrate (APR)

CitibankMBNAFirst USAChase Manhattan

Bank of America

Household Bank

PrimePrimePrimePrimePrimePrime 2.90% 6 months

Providian Prime + 3.24% 0% 3 monthsPrime + 10.24% 0% 2 monthsPrime ±13.24% 0% 2 months

Capital One 9.90% N/A N/A14.90% 2.90%* 6 months

___ ____ ______ 19.80% N/A N/ADiscoverAmerican Express

13.99%9.99%

Prime + 7.99%


B. Mobile phone industry ($52.5bnrevenuein 2000)

• Cellular phonecalls:

convenient,latest gadget

- future costof foregoingproductiveactivities

• Surveyof contractsfor majorUS companies(Table4)

• High marginalpricebeyondmonthly allowance

+ Abovemarginalcostpricing of minutesbeyondmonthly limit

Table 4. MObile phone industry, Menu of contracts

Monthly Monthly Averageallowance fee in $ price per

minute in ~(I) (2) (3)

Price of (4)/(3)additional

minutes in(4) (5)

AT&T’

SprintPCS

450 59.99 13.3650 79.99 12.3

900 99.99 11.1

1,100 119.99 10.9

1,500 149.99 10.0

2,000 199.99 10.0

20 19.99 100.0200 34.99 17.5

350 39.99 11.4

450 49.99 11.11,000 74.99 7.5

353525252525

40

40

40

40

40

2.632.842.25

2.29

2.5

2.5

.40228

3.50

3.605.33


C. Gambling industry

• Las Vegashotels and restaurants:

• Price rooms and mealsbelow cost, at bonus

• High price on gambling

+ Above marginal costpricing of addictive leisure goods

Summary of empirical findings

1. Investment goods:Below-marginal costpricing

High initial fee

2. Leisure goods:Above-marginal costpricing.

Initial bonus or low initial fee

Interpretation:Time-inconsistentpreferencesOverconfidenceabout self-control (more plausible)

WELFARE EFFECTS

Result 1. Self-control problems + Sophistication ⇒First best

• Consumption if c ≤ βδb− p∗

• Exponential agent:— p∗ = a

— consume if c ≤ δb− p∗ = δb− a

• Sophisticated time-inconsistent agent:— p∗ = a− (1− β)δb

— consume if c ≤ βδb− p∗ = δb− a

• Perfect commitment device

• Market interaction maximizes joint surplus of con-sumer and firm

Result 2. Self-control + Partial naiveté ⇒ Real effectof time inconsistency

• p∗ = a− [F (δb−p∗)−F (βδb−p∗)]/f(βδb−p∗)

• Firm sets p∗ so as to accentuate overconfidence

• Two welfare effects:— Inefficiency: Surplusnaive ≤ Surplussoph.

— Transfer (under monopoly) from consumer to firm

• Profits are increasing in naiveté β̂(monopoly)

• Welfarenaive ≤ Welfaresoph.

• Large welfare effects of non-rational expectations

Result 3. If agents can generate more surplus “in the“outside the market” (Sb — c — a >11),

then

• market interaction with sophistication ~ increase inconsumer welfare.

• market interaction with naivete ~ may decrease inconsumer welfare.

Here:

market” than

Decrease in consumer welfare under perfect competition

Ntatlon

Consumer Wet are U under n~xxiopo1y

J/3.5b_p*(Sb_p* - c)dF(c)]

Firm profits [1 under monopoly

S

S

(Sb—a—c)dF(c)+

(Sb_p* —c)dF(c) —SK—8~a

Joint surplus S= U/fl + [1

(Sb—a—c)dF(c)—5K

/36b_p*

4

Three approaches to welfare analysis:,

1. Preferences of initial self: u = u0 + $ ~t>i ~ut

2 Long-run preferences u = u0 + ~It�1 ~

3. Preferences of all selves

APPROACH3

Result 1. Sophistication =~ Pareto optimality

• Firm maximizes profits s.t. l.R.

• Cannot improve welfare of consumers and firm

Result 2.

provementPartial naiveté ~ Possibility of Pareto im-

• Firm maximizes profits s.t. ‘wrong’ i.R.

• Welfare of later selves?

GefletIIZ21ti~OI1

• Gen’eia I “b~iasesin the market.”

1. Consumers have “technological deviation.”

2. Firms have technology to overcome this devia-tion.

3. Consumers may have biased beliefs.

• In this paper,

1. Consumers have bounded sell-control.

2. Firms have commitment technolgoy to overcomebounded self-control.

3. Consumers may be overconfident about futureself-control.

4

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