1. Consumer search and
price dispersion
Trial lecture during Ph.D. defense of
“Essays in Industrial Organization and Search Theory “
by
Øyvind N. Aas

2. Outline of talk
1. Motivation and questions
2. Theory
3. Empirics
4. Policy
Feb 5, 2016 Trial lecture - Øyvind N. Aas 2

3. Observations
Feb 5, 2016 Trial lecture - Øyvind N. Aas 3
iPhone 6sGalaxy S6
Cindy Michelle

4. Feb 5, 2016 Trial lecture - Øyvind N. Aas 4

5. 43 “Specific brands”
Trial lecture - Øyvind N. Aas 5
Mean
(product)
Min
(product)
Max
(product)
Standard deviation 2,19 0,456 6,09 NOK
Coefficient of
variation 0,09 0,03 0,3199
Max - min 5,26 1 13,5 NOK
Histogram of savings by moving
from max to min
0,319
0,03 = 10,6

6. Motivating questions
1. How can identical products have different
prices?
2. What determines the prices and why are
the different dispersion across products?
3. Policy implications
• M&A regulation?
• Platform design?
Feb 5, 2016 Trial lecture - Øyvind N. Aas 6
1. Inefficient
2. Inequality
𝑃𝑟𝑖𝑐𝑒
𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦
Fig. Price 0.5l Coca Cola
𝑆
𝐷

7. Setup
• How agents meet: random or direct matching?
• How are contracts determined: bargaining or
price posting?
• Sequential search (e.g., buying a house) vs.
nonsequential (e.g. job applications)
Feb 5, 2016 Trial lecture - Øyvind N. Aas 7
$100,-

8. Search again<𝜃 𝑅
Stop searching≥𝜃 𝑅
Basic setup
• Ex. consumer searching for the
best quality of a product
• No centralized market
• Optimal stopping rule
Feb 5, 2016 Trial lecture - Øyvind N. Aas 8
𝑢𝐽 𝜃 𝑢𝐽′ 𝜃 > 0
𝑢𝐽 𝑅
1 − 𝛽
= 𝑢𝑗 0 + 𝛽
0
𝑅 𝑢𝐽 𝑅
1 − 𝛽
𝑑𝐹 𝜃
+𝛽
𝑅
∞ 𝑢𝐽 𝜃
1 − 𝛽
𝑑𝐹(𝜃)
𝑢𝐽 𝑅 − 𝑢 𝑗 0 =
𝛽
1 − 𝛽 𝑅
∞
𝑢𝐽 𝜃 − 𝑢𝐽 𝑅 𝑑𝐹(𝜃)
Marginal cost
(less interesting conversation)
Marginal benefit
(more interesting conversation)
Michelle in a bar
Different men in the economy

9. Theory
• Suppose centralized market for
lemon, with cost $1. Value = $10.
• Suppose 𝜖 > 0 cost of finding the
price in a store
• Diamond paradox: 𝜖 > 0 drastically
changes the equilibrium
Feb 5, 2016 Trial lecture - Øyvind N. Aas 9
Equilibrium price = $1
Price = $1 Price = $2
Price = $1+ 𝜖 Price = ($1+ 𝜖) + 𝜖
Equilibrium price = $10
Price = $1 Price = $1

10. Theory
• Diamond (1971, JET), search costs lead to uniform price
• How can price dispersion come about as an equilibrium
result?
• Reinganum (1979,JPE), Varian (1980,AER), Carlson and McAfee
(1983,JPE), Stahl (1989,AER), Stahl (1996,IJIO)
• Burdett and Judd (1983,ECTA) What are crucial conditions
to generate price dispersion in an economy with identical
consumers and firms?
• Answer: Ex post heterogeneity in consumer information
Feb 5, 2016 Trial lecture - Øyvind N. Aas 10

11. Burdett and Judd (1983,ECTA), noisy sequential search
11
(MC = MB)
𝑝 = min 𝑝 𝑚
, 𝑧
𝑐 =
0
𝑧
𝑧 − 𝑝 𝑑𝐹𝑝
1. Competitive price? Not an
equilibrium, incentive to deviate
2. Any price above competitive? Not an
equilibrium, since incentives to
undercut and sell to consumers with
two price quotes
3. Discontinuity in demand schedule, so
a pure strategy equilibrium cannot
exist
𝑝 − 𝑟
𝑘=1
∞
𝑘𝑞 𝑘[1 − 𝐹𝑝 𝑝 ] 𝑘−1
= 𝑞1 𝑝 − 𝑟
𝑝, 𝑝𝐹(𝑝)
If 𝑞1 = 1, all observe only one price (Diamond result)
If 𝑞1 =0, all observe at least two prices (competitive result)
If 𝑞1 ∈ 0,1 , probability observe at least two prices
Pay c>0 to receive k
prices with prob. 𝑞 𝑘
Ex post heterogeneity in consumer information
Prediction (Janssen & Moraga-Gonzalez,2004):
More companies in the economy will lead to higher prices
$10
$4

12. Empirics:
Estimating search costs from prices
• Search costs can alter equilibrium predictions and policy
implications. So how empirically significant are they?
• Given prices, can we say something about the search cost
among consumers?
• Hong and Shum (2006) methodology to estimate search
costs
• Main takeaway: prices are sometimes sufficient to estimate search
costs, because of equilibrium restrictions (optimality conditions
from consumers and firms) which rationalize observed prices.

13. Main idea
Probability of minimum
price of
No. of
prices
sampled
$2 $3 Expected
min price
Marginal
Expected
gains Δ
Δ − 𝒄
(0,25)
2 pepl.
Δ − 𝒄
(0,06)
4 pepl.
Δ − 𝒄
(0,03)
4 pepl.
1 0,5 0,5 2,5
2 0,75 (=1-0,25) 0,25 2,25 0,25 0,0000 0,1875 0,2422
3 0,8750 0,1250 2,1250 0,1250 -0,1250 0,0625 0,1172
4 0,9375 0,0625 2,0625 0,0625 -0,1875 0,0025 0,0047
5 0,9688 0,0313 2,0313 0,0313 -0,2188 -0,0313 0,0013
Feb 5, 2016 Trial lecture - Øyvind N. Aas 13
𝑃𝑟 𝑝 𝑚𝑖𝑛 = 3 = 1 − 1
2
2
= 0,25
Constant search costs: c, first sample free,
Choose obs, so that EMB = MC
0%
20%
40%
60%
80%
100%
0 0,05 0,1 0,15 0,2 0,25
Estimatedsearch-costcdf
Seach costs
Search-cost distribution

14. Methodology, Hung and Shum (2006)
• First, from the empirical price distribution, compute the cutoffs Δ𝑖
• Second, define
• 𝑞1 = 1 − 𝐹𝑐(Δ1) : proportion of consumers with one price quote
• 𝑞2 = 𝐹𝑐 Δ1 − 𝐹𝑐(Δ2) : proportions consumers with two price quotes
• 𝑞3 = 𝐹𝑐 Δ2 − 𝐹𝑐(Δ3)
• 𝑞 𝐾 = 1 − 𝑘=1
𝐾−1
𝑞 𝑘 : proportions of consumers with K price quotes
• Use indifference conditions from Burdett and Judd (1983), to estimate
𝑞1, 𝑞2, …, 𝑞 𝐾−1
Π 𝑝 = 𝑝 − 𝑟
𝑘=1
∞
𝑘𝑞 𝑘[1 − 𝐹𝑝 𝑝 ] 𝑘−1 = 𝑞1 𝑝 − 𝑟 = Π(𝑝)
• Sort prices, 𝑝 = 𝑝1 ≤ 𝑝2 ≤ 𝑝 𝑛−1 ≤ 𝑝 𝑛 = 𝑝
• Let K ≤ 𝑛 − 1 denote max number of prices sampled
Feb 5, 2016 Trial lecture - Øyvind N. Aas 14

15. Methodology, Hung and Shum (2006)
• Given K ≤ 𝑛 − 1 , we have 𝑛 − 1 indifference conditions
𝑞1 𝑝 − 𝑟 = 𝑝𝑖 − 𝑟
𝑘=1
𝐾
𝑘𝑞 𝑘[1 − 𝐹𝑝 𝑝𝑖 ] 𝑘−1 , 𝑖 = 1, ⋯ , 𝑛 − 1
• Where, 𝑞 𝐾 = 1 − 𝑘=1
𝐾−1
𝑞 𝑘 and 𝐹𝑝 𝑝 = 0, so replace
𝑟 =
𝑝 𝑘=1
𝐾
𝑘𝑞 𝑘 −𝑝𝑞1
𝑘=1
𝐾 𝑘𝑞 𝑘 −𝑞1
• Empirical likelihood (alt. MLE)
Feb 5, 2016 Trial lecture - Øyvind N. Aas 15

16. Empirics
Feb 5, 2016 Trial lecture - Øyvind N. Aas 16
0
0,2
0,4
0,6
0,8
1
0 1 2 3
Estimatedsearch-costcdf
Search costs ($)
Estimated search-cost distributions
Lazer
Stokey
Billingsley
Duffie
63.3% have search
costs above Δ1 = $2.90
𝑞1, … , 𝑞 𝐾−1 𝐹𝑐(Δ2) = 𝐹𝑐 Δ1 − 𝑞2
𝐹𝑐(Δ3) = 𝐹𝑐 Δ2 − 𝑞3
𝐹𝑐 Δ1 = 1 − 𝑞1
Moraga-Gonzalez and Wildenbeest (2008)
Personal computer memory chips (www.shopper.com)
Kingston KTT3614
Kingston KTT3614

17. Discussion
• Caveats:
• Obfuscation (not all prices are «true» price)
• Search technology
• Production costs
• «Differentiated products» across firms (e.g., return, shipping, handling,
etc.).
• Hortacsu and Syverson (2004) importance of search frictions and product differentiation (e.g., mutual index funds + hedge fund)
• Distribution of search costs have shifted over time, average search costs have gone down, upper percentile tends to increase, more novice
investors entering
• Moraga-Gonzalez and Wildenbeest (2008), oligopoly with ML, Monte Carlo for robustness and counterfactual with tax increase
• 15% sales tax reduces search intensity so consumers carry more than propotional increase, firms profit rise
• Policy affects both firms prices and consumers search intensity
• Wildenbeest (2011), product differentiation (61%) and search costs (41%) among retail chains in the UK.
Feb 5, 2016 Trial lecture - Øyvind N. Aas 17

18. Matvareportalen
• Competition Authority: the portal facilitates price cooperation (collusion)
(bad for consumers)
• Consumer Protection Agency (CPA): the portal promotes competition
(good for consumers)
Feb 5, 2016 Trial lecture - Øyvind N. Aas 18
“Matvareportalen kan bli forbudt”
– Bergens Tidene Oct, 27 2015
Vs.

19. • “The portal facilitates collusion” (illegal price cooperation)
𝑡=0
∞
𝛿 𝑡Π1 𝑝1𝑡, 𝑝2𝑡
• 𝛿 < 1 discount factor, close to 1 more patience
• Two firms, choose prices simultaneously each period
• 𝑝 = 𝑐 is one equilibrium
• 𝑝 𝑚 as the monopoly price, symmetric trigger strategies, FE,PO
Matvareportalen – Competition authority
Feb 5, 2016 Trial lecture - Øyvind N. Aas 19
𝑝𝑖𝑡 =
𝑝 𝑚 𝑖𝑓 𝑝𝑗𝑡−1 = 𝑝 𝑚
𝑐 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
𝑝 = 𝑝 𝑚 in t=0
Collusion alternative

20. Matvareportalen – Competition authority
• Information lags, it takes two periods before deviation is detected
• Information lags softens punishment, strenghtens incentives to deviate.
• More transparency, easier to sustain collusion, higher prices
• Worse for consumers, better for firms.
Feb 5, 2016 Trial lecture - Øyvind N. Aas 20
Π 𝑚
2
1 + 𝛿 + 𝛿2 + ⋯ ≥ Π 𝑚
Π 𝑚
2
1
1 − 𝛿
≥ Π 𝑚
→ 𝛿∗ ≥
1
2
Π 𝑚
2
1 + 𝛿 + 𝛿2 + ⋯ ≥ Π 𝑚 1 + 𝛿
Π 𝑚
2
1
1 − 𝛿
≥ Π 𝑚
1 + 𝛿
→ 𝛿∗ ≥
1
2
>
1
2
(Collude≥Deviate)

21. Matvareportalen – CPA
• “The portal promotes competition”
• Suppose 𝜆 fraction of informed consumers
• More informed consumers, decreases the lower bound, 𝑝 =
1−𝜆
1+𝜆
• More competition for informed consumers, expected price falls
• More transparency, lower prices
• Better for consumers, worse for firms.
Feb 5, 2016 Trial lecture - Øyvind N. Aas 21
𝑝
1 − 𝜆
2
+ 𝜆 1 − 𝐹(𝑝) =
1 − 𝜆
2

22. • Petrikaite (2016) Collusion with costly consumer search
• Q: how does stability of collusion relate to market transparency from the
viewpoint of the consumers
• Sequential search, Stahl (1989) homogeneous prod., 𝑢 = 𝜈 − 𝑝
• No price>𝑝 𝑟, so indifference condition for competitive eq.
• Lower bound, and CDF
Matvareportalen – collusion and search
Feb 5, 2016 Trial lecture - Øyvind N. Aas 22
𝑝
𝑝 𝑟
𝑝 𝑟 − 𝑝 𝑑𝐺 𝑝 = 𝑠 (MB = MC)
𝑝 𝑟
ℎ 𝑝 , 𝑠
𝑝
ℎ(𝑝)
𝑠
As search cost increase, consumers
becomes less picky
𝑝
1 − 𝜆
2
+ 𝜆 1 − 𝐹(𝑝) =
𝑝𝑟 1 − 𝜆
2
= Π∗
𝑝 =
𝑝 𝑟 1 − 𝜆
1 + 𝜆
𝐹 𝑝 = 1 −
𝑝 𝑟 − 𝑝 1 − 𝜆
2𝜆𝑝
(Competitive profits)

23. Matvareportalen – collusion and search
Feb 5, 2016 Trial lecture - Øyvind N. Aas 23
Collusion ≥ Deviating
𝑣
2
1
1 − 𝛿
≥
𝑣
2
1 + 𝜆 +𝛿
𝑝 𝑟 1 − 𝜆
2
1
1 − 𝛿
→ 𝜹∗
≥
𝒗𝝀
𝒗 𝟏 + 𝝀 − 𝒑 𝒓 𝟏 − 𝝀
Π 𝑐 =
𝒗
𝟐
Π 𝑑 = 𝑣 𝜆 +
1 − 𝜆
2
=
𝒗
𝟐
𝟏 + 𝝀 Π∗ =
𝒑 𝒓 𝟏 − 𝝀
𝟐
𝑣
2
1 + 𝛿 + 𝛿2 + ⋯ =
𝒗
𝟐
𝟏
𝟏 − 𝜹
NPV collusion
𝑣
2
1 + 𝜆 + 𝛿
𝑝 𝑟 1−𝜆
2
1 + 𝛿 + 𝛿2
+ ⋯ =
𝒗
𝟐
𝟏 + 𝝀 +𝜹
𝒑 𝒓 𝟏−𝝀
𝟐
𝟏
𝟏−𝜹
NPV deviating
1
0
𝒔 ↑→ 𝒑 𝒓 ↑→ 𝜹∗ ↑
Less transparency leads to
less sustainable collusion
More transparency leads
to more sustainable
collusion

24. • Suppose transparency is related to fraction of shoppers
(i.e., 𝜆)
• More transparent, higher 𝜆
• More shoppers implies less demand from uninformed
• More shoppers implies lower bound goes down, so reservation
price goes down
• Competitive profit goes down, but rate is lower with more
shoppers
Matvareportalen – collusion and search
Feb 5, 2016 Trial lecture - Øyvind N. Aas 24
− ↑ ↓
For more shoppers, inc. deviating profit > red. comp. profit 𝜹∗
↑ with 𝝀 More transparent, less
sustainable collusion
𝜹∗ ↓ with 𝝀 More transparent, more
sustainable collusion
For fewer shoppers, inc. deviating profit < red. comp. profit
1
1
𝜹∗ ↑ with 𝝀
2
0𝜹∗
↓ with 𝝀
𝑣
2
1
1 − 𝛿
≥
𝑣
2
1 + 𝜆 +𝛿
𝑝 𝑟 1 − 𝜆
2
1
1 − 𝛿