Shrouded Attributes, Consumer Myopia, and Information Suppression in Competitive Markets
The Quarterly Journal of Economics, 2006 · paper · Economics
A theoretical model of markets with add-on prices, such as printer ink, where some consumers are myopic. It shows firms can profitably hide add-on prices even under strong competition, and competitors cannot profitably educate consumers.
Checked: PDF from nber.org, fetched 5 Oct 2026. Page numbers are those of that PDF.
4 findings
Substance Proof of Proposition 4 asserts "First, it is clear that if a firm shrouds, the add-on price is the monopoly price p̂m", with p̂m defined in Eq. (9) from the effort-adjusted demand q̂S(p̂) of a sophisticate "who knows she will face a price p̂". A shrouding firm's hidden add-on price cannot move sophisticates' period-1 effort, so p̂m need not be its best response, and the "if" direction of "supports a Shrouded Prices Equilibrium if and only if B ≥ 1" can fail.
- p. 20 Eq. (9) and statement of Proposition 4
supports a Shrouded Prices Equilibrium if and only if B ≥1
- p. 19 Section III.B, definition of q̂S
equilibrium add-on demand of a sophisticate who knows she will face a price
- p. 31 Proof of Proposition 4, first step
First, it is clear that if a firm shrouds, the add-on price is the monopoly price
Only the authors can say what is right here.
Judge's note: I checked p.18 (PDF 19), p.19 (PDF 20), p.20 and the proof on p.30 (PDF 31). In the model, shrouding means no consumer observes the add-on price (p.~8). Sophisticates choose effort ê in period 1 to maximise an expectation, and footnote 42 ties effort to Ep̂, the believed add-on price. Proposition 4 states that beliefs at shrouding firms are p̂ = p̂m. Eq. (9), however, maximises over p̂ using q̂S(p̂), the demand of a sophisticate who knows p̂ in advance, so effort moves with p̂. When a shrouding firm changes its hidden p̂, beliefs and effort stay put, so its real objective holds ê at ê(p̂m). The proof gives no argument for its claim that p̂m is still optimal. I reworked the reviewer's counterexample. Take û = (1−ê)q̂ − q̂²/2 + 1.8ê − 1.5ê², with ĉ = 0 and α = 0.5. The cross-partial is −1, which fits the paper's leading case. Effort is ê = 0.4 + 0.5p̂ (second-order term −2) and q̂S = 0.6 − 1.5p̂. The myopes' demand is q̂M = 1 − p̂. The Eq. (9) objective p̂(0.8 − 1.25p̂) peaks at 0.32 with value 0.128. On the corner region the best value is 0.125, so p̂m = 0.32 is unique. At p̂m, B = 0.0896/0.0768 ≈ 1.17, which is ≥ 1. With effort fixed at 0.56, the shrouding firm's add-on profit is p̂(0.72 − p̂). That gives 0.1296 at p̂ = 0.36, more than 0.128 at 0.32. Base demand does not change because the price is unobserved. So the vector (10)–(11) is not an equilibrium even though B ≥ 1. The two definitions coincide only when effort does not respond, e.g. at a corner as in the discrete model. The authors should say whether p̂m is meant as a fixed point with effort held at its equilibrium level.
Second check: another model agreed
Report a problem with this finding
Reference or label Footnote 2 cites "Laibson and Yariv [2005]" but the only reference-list entry is "Laibson, David, and Leeat Yariv, ... mimeo, University of California, Los Angeles, 2004."
- p. 3 footnote 2
See Becker [1957] and Laibson and Yariv [2005].
- p. 35 References
mimeo, University of California, Los Angeles, 2004.
- p. 35 References
Laibson, David, and Leeat Yariv, “Safety in Markets: An Impossibility Theorem for Dutch Books,”
- p. 3 footnote 2
Laibson and Yariv [2005]
Judge's note: Footnote 2 on PDF p3 reads 2005; the single Laibson–Yariv entry on PDF p35 is dated 2004. A text search finds no other Laibson–Yariv entry. Which year is right is for the authors, but the mismatch is plain.
Second check: another model agreed
Report a problem with this finding
Wording Appendix 1: "all firms have the same σ" uses a symbol σ that is not defined anywhere in the paper.
- p. 27 Appendix 1, paragraph 1
all firms have the same σ
Only the authors can say what is right here.
Judge's note: Viewed page 27 and searched extract/main.txt for σ: this is its only occurrence. The demand microfoundation uses only F, f, v, p and ε; no scale parameter σ is introduced. Only the authors can say what was meant (possibly a leftover noise-scale parameter).
Second check: another model agreed
Report a problem with this finding
Wording Proof of Proposition 4: "As the pre-deviation profit is µ, the firm does not want to deviate iff (24) Π ≤ µD(0), as µD(0) is the pre-deviation profit" gives the same quantity as µ and as µD(0).
- p. 32 Proof of Proposition 4, before eq. (24)
As the pre-deviation profit is µ, the firm does not want to deviate iff
- p. 32 Proof of Proposition 4, after eq. (24)
as µD (0) is the pre-deviation profit
Only the authors can say what is right here.
Judge's note: Viewed page 32. The sentence wrapped around eq. (24) names the pre-deviation profit twice with different values. By Lemma 1 (page 27), µ is the per-customer margin p − c and the firm's profit is µD(0), which is what (24) uses. The first clause is therefore mislabelled or redundant; inequality (24) and the result are unaffected.
Second check: another model agreed
Report a problem with this finding
33 minor (typos and the like; most checked by the judge only)
Wording The introduction says the HP printing cost "is not easily accessible on the company's web site" and is reachable by "a complex sequence of links", while Section II refers to "The Hewlett-Packard decision to omit the deskjet price per page on their web site".
- p. 4 Introduction, top of page
From each printer’s homepage, one must follow a complex sequence of links to uncover the cost of printing.
- p. 8 Section II, first paragraph
The Hewlett-Packard decision to omit the deskjet price per page on their web site
Judge's note: Both passages read on the images (PDF p4 and p8). "Omit" is looser than the introduction's description of information that is present but hard to reach. It is probably shorthand for not displaying it prominently, so this is a wording inconsistency only.
Second check: another model agreed
Report a problem with this finding
Wording Roadmap says "All proofs are presented in appendices." but the "Proof of Proposition 2" is given in full in Section II.D of the main text.
- p. 8 Introduction, roadmap paragraph
All proofs are presented in appendices.
- p. 16 Section II.D
Proof of Proposition 2. The social welfare loss is proportional
Judge's note: PDF p8 has the roadmap sentence; PDF p16 has the complete proof of Proposition 2 ending in a QED box. A text search finds appendix proofs only for Lemma 1 and Propositions 1, 3 and 4. A minor overstatement in the roadmap.
Second check: another model agreed
Report a problem with this finding
Wording Footnote 43 says "Condition B ≥ 1 is α ≤ α†, reproducing the result of Proposition 1", but Proposition 1 states the strict condition "α is less than α†", and Section III.C says the ratio "is greater than 1".
- p. 20 footnote 43
Condition B ≥ 1 is α ≤ α†, reproducing the result of Proposition 1.
- p. 13 Proposition 1
If the fraction of sophisticated consumers α is less than α†
- p. 22 Section III.C, end
will be shrouded if its debiasing ratio B = (1 − α) p/e is greater than 1
Judge's note: Read on the page images. Proposition 1 (PDF p13) uses strict inequalities on both sides and is silent on α = α†. Proposition 4 and footnote 43 (PDF p20) use B ≥ 1 and α ≤ α†. Section III.C (PDF p22) uses "α < 1 − e/p̄" and "greater than 1", while Section III.D uses "iff B ≥ 1". The boundary is therefore stated both weakly and strictly. It is a knife-edge case with no effect on the results. The footnote also says "section 2" although sections carry Roman numerals.
Second check: another model agreed
Report a problem with this finding
Wording Equation (10) in Proposition 4 uses a double-hatted q(p̂) that the main text never defines; the definition "We define the average demand in the add-on market" appears only at equation (21) in Appendix 2.
- p. 20 Proposition 4, eq. (10)
p = c − (p̂ − ĉ) q̂(p̂) + µ
- p. 31 Appendix 2, eq. (21)
We define the average demand in the add-on market
Judge's note: On PDF p20, equation (10) prints q with a double hat. Section III.B (PDF p19–20) defines only q̂^S and q̂^M. A text search finds the average-demand definition only in the proof of Proposition 4, equation (21), on PDF p31. The meaning can be inferred from equation (9), so this is a small gap in exposition.
Second check: another model agreed
Report a problem with this finding
Wording "This no-advertising result contains a boundary condition that determines when advertising will appear: B ≥ 1." B ≥ 1 is the condition under which shrouding (no advertising) holds, as the next sentence says.
- p. 20 after Proposition 4
a boundary condition that determines when advertising will appear: B ≥1.
- p. 20 next sentence
Advertising does not arise when the cross-subsidies to sophisticates are larger
Only the authors can say what is right here.
Judge's note: Read on PDF p20. Proposition 4 says the Shrouded Prices Equilibrium holds iff B ≥ 1, and the following sentence says advertising does not arise when cross-subsidies exceed distortions. Taken literally, the printed sentence gives B ≥ 1 as the condition for advertising to appear, which is the reverse. It can be read loosely as naming the boundary, so I treat it as a wording defect; intended wording was probably "will not appear" or B < 1.
Second check: another model agreed
Report a problem with this finding
Wording Appendix 1 says "all firms have the same σ" although σ is never defined, and announces "The following Proposition characterizes the symmetric equilibrium" when the result that follows is labelled Lemma 1.
- p. 27 Appendix 1, first paragraph
all firms have the same σ.
- p. 27 Appendix 1, first paragraph
all firms have the same σ
- p. 27 Appendix 1, before Lemma 1
The following Proposition characterizes the symmetric equilibrium.
Only the authors can say what is right here.
Judge's note: Read on the PDF p27 page image. A search of the text layer finds σ only in this one sentence, and the noise is described only through F and f, so the symbol is undefined; only the authors can say what was meant. The statement introduced as "the following Proposition" is labelled "Lemma 1", which is a cosmetic mislabel. The same paragraph also prints the noise subscript as both ε_ai and ε_ia.
Second check: another model agreed
Report a problem with this finding
Typo Acknowledgements print "Glenn Ellison, Sarah Ellison" while the reference list prints "Ellison, Glenn, and Sara Fisher Ellison"; the first name is spelled two ways.
- p. 1 acknowledgements
Glenn Ellison, Sarah Ellison
- p. 34 References, Ellison and Ellison 2004
Ellison, Glenn, and Sara Fisher Ellison
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: that the person thanked next to Glenn Ellison is the same person as his co-author in the reference list, and which spelling is correct. Both spellings are on the page images (p1 and p34); the paper itself does not say they are the same person.
Second check: none (judge only)
Report a problem with this finding
Typo Stray comma in "Debiased Hilton customers, get a $100 hotel room" (p5) and misplaced space in "Barry Nalebuff ,Aviv Nevo" (p1).
- p. 5 para 5
Debiased Hilton customers, get a $100 hotel room
- p. 1 acknowledgements
Nalebuff ,Aviv Nevo
Judge's note: Both seen on the page images. Punctuation only.
Second check: none (judge only)
Report a problem with this finding
Typo "rational consumers will expect the worse from a firm that shrouds" should read "the worst".
- p. 4 second paragraph
rational consumers will expect the worse from a firm that shrouds
- p. 4 para 3
will expect the worse from a firm
Judge's note: Seen on the PDF p4 image. Wrong word form in the idiom; cosmetic.
Second check: none (judge only)
Report a problem with this finding
Typo Misspellings and slips: "Tranparents’s add-ons" (p5), "We call c the the marginal cost" (p19), "applies to each attributes" (p22), "nutrtitional labelling" (also "occassionally", "outweight") (p25), "(Cambrige, UK:" (p34), "Consumer Mispreceptions" (p37).
- p. 5 first paragraph
Tranparents’s add-ons
- p. 5 Introduction, curse-of-debiasing paragraph
unecessary costs
- p. 4 Introduction, second paragraph of page
will expect the worse from a firm
- p. 8 Introduction, top of page
make an more informed choice
Judge's note: Each checked on a page image or high-resolution crop. "Cambrige" is clear in crop C005-i, and the text layer shows the same misspelling in the Fudenberg–Tirole entry. The other items bundled here ("unecessary", "expect the worse", "an more", "is may") are also real and are covered under C006, C003, C011 and C015.
Second check: none (judge only)
Report a problem with this finding
Typo "they know how to avoid unecessary costs" should read "unnecessary".
- p. 5 third paragraph
avoid unecessary costs
- p. 5
they know how to avoid unecessary costs
Judge's note: Seen on the PDF p5 image.
Second check: none (judge only)
Report a problem with this finding
Typo Adjacent references spell the same author two ways: "Hossain, Tanjim, and John Morgan" (2006) and "Hossain, Tanjin, and John Morgan" (2005); the text also has "unecessary costs" (p. 5) and "occassionally adopted" (p. 25).
- p. 35 References, Hossain and Morgan 2006
Hossain, Tanjim, and John Morgan
- p. 35 References, Hossain and Morgan 2005
Hossain, Tanjin, and John Morgan
- p. 35 References
Hossain, Tanjin, and John Morgan, “Shrouded Attributes and Information Suppression
- p. 35 References
Hossain, Tanjim, and John Morgan, “...Plus Shipping and Handling
Judge's note: Viewed page 35: consecutive entries read "Tanjim" and "Tanjin" with the same co-author, so one is a misspelling. The page alone does not say which, though the inconsistency is objective. The crops for pages 5 and 25 confirm "unecessary" and "occassionally"; the page 25 line also shows "nutrtitional". The "Cambrige" item is covered in C037.
Second check: none (judge only)
Report a problem with this finding
Typo Footnote 10: "their introductory balance (which accumulate at a 0% interest rate)"; the singular antecedent calls for "accumulates".
- p. 6 footnote 10
(which accumulate at a 0% interest rate)
Judge's note: Seen on the PDF p6 image. The earlier parallel clause "credit card charges (which may accumulate ...)" is plural and correct; the second has the singular "balance". Cosmetic grammar slip.
Second check: none (judge only)
Report a problem with this finding
Typo "but instead make an more informed choice" should read "a more informed choice".
- p. 8 first paragraph
instead make an more informed choice
- p. 8 first paragraph
make an more informed choice
Judge's note: Seen on the PDF p8 image.
Second check: none (judge only)
Report a problem with this finding
Typo "the degree of competion in the industry" should read "competition".
- p. 12 Section II.B, demand function paragraph
the degree of competion in the industry
- p. 12 Section II.B, Period 1
degree of competion in the industry
Judge's note: Seen on the PDF p12 image.
Second check: none (judge only)
Report a problem with this finding
Typo "welfare analysis of the Shrouded Price Equilibrium" uses a different form from the defined term "Shrouded Prices Equilibrium".
- p. 16 II.D intro
welfare analysis of the Shrouded Price Equilibrium
Judge's note: Seen on the PDF p16 image. The same page (Proposition 2 and its proof) and the rest of the paper use "Shrouded Prices Equilibrium". Cosmetic terminology slip.
Second check: none (judge only)
Report a problem with this finding
Typo Footnote 38: "In some cases is may be natural to assume" should read "it may be"; the same footnote has "Shrouded Prices Equlibrium".
- p. 17 footnote 38
In some cases is may be natural to assume
- p. 16 Section II.D, first sentence
welfare analysis of the Shrouded Price Equilibrium
- p. 17 Footnote 38
In some cases is may be natural
- p. 17 Footnote 38
Shrouded Prices Equlibrium does not depend on it.
Judge's note: Both slips seen in footnote 38 on the PDF p17 image. The "Shrouded Price Equilibrium" item also listed here is handled under C014.
Second check: none (judge only)
Report a problem with this finding
Typo Footnote 38 misspells "Equilibrium": "Shrouded Prices Equlibrium does not depend on it."
- p. 17 footnote 38
Shrouded Prices Equlibrium does not depend on it.
- p. 17 footnote 38
Shrouded Prices Equlibrium
- p. 17
Shrouded Prices Equlibrium does not depend on it
Judge's note: Read footnote 38 on the full page image of PDF page 17; "Equlibrium" is printed there. The same footnote also has "is may be natural".
Second check: none (judge only)
Report a problem with this finding
Typo Duplicated word in Section III.B: "We call c the the marginal cost of the base good".
- p. 19 Section III.B, last paragraph on the page
We call c the the marginal cost of the base good
Judge's note: The crop shows "the the" on a single line, so it is not a line-break artefact. The text layer agrees.
Second check: none (judge only)
Report a problem with this finding
Typo Number disagreement in Section III.C: "Our Proposition 1 also applies to each attributes."
- p. 22 Section III.C, first line of the page
Our Proposition 1 also applies to each attributes.
- p. 22 Section III.C, top
also applies to each attributes
Judge's note: Seen on the first line of the PDF p22 page image; it should read "each attribute".
Second check: none (judge only)
Report a problem with this finding
Typo Misspelling in Section IV.B: "the usual costs of regulation could easily outweight its possible benefit" (should be "outweigh").
- p. 25 Section IV.B, first paragraph
could easily outweight its
- p. 25 Section IV.B, second paragraph
occassionally adopted such unshrouding policies (e.g. nutrtitional labelling
- p. 25 Section IV.B, second paragraph
report the cost of ink of printed page
- p. 26 Section IV.B, last paragraph
shrouded attributes.. For example, Singapore regulates the mark-up the hotel charge for phone.
Judge's note: "outweight" is printed on the PDF p25 page image. The other items bundled into this cluster are judged in their own clusters: "occassionally" (C024), "nutrtitional" (C025), "cost of ink of printed page" (C026), the double full stop (C027) and "the hotel charge for phone" (C028). This verdict covers "outweight" only.
Second check: none (judge only)
Report a problem with this finding
Typo Misspelling in Section IV.B: "regulators have occassionally adopted such unshrouding policies" (should be "occasionally").
- p. 25 Section IV.B, second paragraph
regulators have occassionally adopted
- p. 25
regulators have occassionally adopted such unshrouding policies
Judge's note: Seen on the PDF p25 page image.
Second check: none (judge only)
Report a problem with this finding
Typo Misspelling in Section IV.B: "(e.g. nutrtitional labelling, energy usage labelling" (should be "nutritional").
- p. 25 Section IV.B, second paragraph
nutrtitional labelling
- p. 25
(e.g. nutrtitional labelling, energy
Judge's note: Seen on the PDF p25 page image.
Second check: none (judge only)
Report a problem with this finding
Typo Garbled phrase in Section IV.B: "report the cost of ink of printed page in a prominent place on the product" (presumably "per printed page").
- p. 25 Section IV.B, second paragraph
report the cost of ink of printed page
- p. 25 Section IV.B, First
cost of ink of printed page
Judge's note: Seen on the PDF p25 page image. The same paragraph later says "ink cost per page", which supports "per printed page" as the intended wording.
Second check: none (judge only)
Report a problem with this finding
Typo Double full stop in Section IV.B: "regulators may impose markup caps on shrouded attributes.. For example".
- p. 26 Section IV.B, paragraph beginning "Finally"
markup caps on shrouded attributes..
- p. 26
regulators may impose markup caps on shrouded attributes..
Judge's note: Two full stops are visible on the PDF p26 page image.
Second check: none (judge only)
Report a problem with this finding
Typo Ungrammatical sentence in Section IV.B: "Singapore regulates the mark-up the hotel charge for phone."
- p. 26 Section IV.B, paragraph beginning "Finally"
regulates the mark-up the hotel charge for phone.
Judge's note: Seen on the PDF p26 page image. Footnote 50 ("hotels price their international phone calls") indicates the intended sense, roughly "the mark-up that hotels charge for phone calls".
Second check: none (judge only)
Report a problem with this finding
Typo Appendix 1 says "The following Proposition characterizes the symmetric equilibrium." but the result that follows is labelled "Lemma 1" and proved under "Proof of Lemma 1".
- p. 27 Appendix 1, sentence before Lemma 1
The following Proposition characterizes the symmetric equilibrium.
Judge's note: Viewed page 27. The sentence is immediately followed by Lemma 1 and its proof; no Proposition follows. The label in the lead-in sentence is wrong; the mathematics is unaffected.
Second check: none (judge only)
Report a problem with this finding
Typo Appendix 1: "We interpret ε_ia as a tremble" reverses the subscript order of the shock, which is written ε_ai in the line before and in the demand expression D_i.
- p. 27 Appendix 1, first paragraph
We interpret εia as a tremble
Judge's note: Viewed page 27. The image shows U_ai = v_i − p_i + ε_ai and "where ε_ai is i.i.d.", then "We interpret ε_ia". The reversal is in the PDF itself, not an extraction artefact.
Second check: none (judge only)
Report a problem with this finding
Typo Proof of Proposition 4: "it prices of the add-on efficiently" contains a stray "of".
- p. 32 Proof of Proposition 4
it prices of the add-on
Judge's note: Viewed page 32. The image reads "When a firm faces only sophisticated consumers, it prices of the add-on efficiently." The extra word is in the PDF.
Second check: none (judge only)
Report a problem with this finding
Typo References, Ausubel: "American Economic Review, VXXXI (1991), 50-81." prints a malformed Roman-numeral volume; the list's other AER entries imply LXXXI.
- p. 33 References, Ausubel 1991
Review, VXXXI (1991), 50-81.
- p. 33 References, Ausubel
American Economic Review, VXXXI (1991), 50-81.
- p. 33 References, Ausubel
VXXXI (1991)
Judge's note: Viewed page 33: the image shows "VXXXI". It is not a valid Roman numeral. The same list gives AER as LXXII (1982) on page 35 and LXXIX (1989) on page 37, which puts 1991 at volume 81 = LXXXI. The fix follows from the paper's own entries.
Second check: none (judge only)
Report a problem with this finding
Typo References misspell the place of publication twice: "(Cambrige, UK: Cambridge University Press, forthcoming)" (Ellison) and "(Cambrige, MA: MIT Press, 1991)" (Fudenberg and Tirole).
- p. 34 References, Ellison (forthcoming)
(Cambrige, UK: Cambridge University Press, forthcom-
- p. 34 References, Fudenberg and Tirole
(Cambrige, MA: MIT Press, 1991)
- p. 37 References, Spence
Consumer Mispreceptions, Product Failure, and Producer Liability
- p. 34 References, Ellison forthcoming
Cambrige, UK
Judge's note: Viewed the crops for both entries and page 34; both show "Cambrige", and the text layer agrees. The same Ellison line spells "Cambridge University Press" correctly. The "Mispreceptions" item also raised under this cluster is handled in C040.
Second check: none (judge only)
Report a problem with this finding
Typo References, Salop and Stiglitz (1977): the title is printed as "Bargains and Ripoffs: A Model of Monopolistically Competitive Price," and appears to be missing its final word.
- p. 36 References, Salop and Stiglitz 1977
A Model of Monopolistically Compet- itive Price,”
Only the authors can say what is right here.
Judge's note: Rests on outside knowledge: the published title is believed to end "...Monopolistically Competitive Price Dispersion". Viewed page 36: the title as printed ends at "Competitive Price,", which reads as incomplete. The missing word cannot be verified from the files.
Second check: none (judge only)
Report a problem with this finding
Typo References, Spence (1977): "Consumer Mispreceptions, Product Failure, and Producer Liability" misspells "Misperceptions".
- p. 37 References, Spence 1977
Consumer Mispreceptions, Product Failure, and Producer Liability
- p. 37 References, Spence 1977
Consumer Mispreceptions
Judge's note: Viewed page 37: the image shows "Mispreceptions", and the text layer agrees. It is a plain misspelling in the PDF.
Second check: none (judge only)