The Manchester SchoolVolume 89, Issue 3 p. 310-314 ERRATUMFree Access Erratum This article corrects the following: Price and quantity competition with network externalities: Endogenous choice of strategic variables Ryo Hashizume, Tatsuhiko Nariu, Volume 88Issue 6The Manchester School pages: 847-865 First Published online: September 16, 2020 First published: 29 April 2021 https://doi.org/10.1111/manc.12364AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat In the article by Hashizume and Nariu (2020), the following errors were published. (On page 847) The Correspondence section should be Ryo Hashizume, Faculty of Art and Design (Correspondence Education), Kyoto University of the Arts: 2–116 Uryuyama, Kitashirakawa, Sakyo-ku, Kyoto, Japan. Email: rhashizum@gmail.com. (On page 850) Equations 1 and 2 should be (1) (2) (On page 851) Equations 3, 4, 5, 6-1, and 6-2-3, 4, 5, 6-1, and 6-2 should be (3) (4) (5) (6-1) (6-2) (On page 852) The maximization problem of firm i is expressed by (On page 852) Equations 7, 8-1, and 8-2 should be (7) (8-1) (8-2) (On page 853) Equations 9, 10-1, 10-2, 11-1, 11-2, 12-1, 12-2, 12-3, and 12-4-9, 10-1, 10-2, 11-1, 11-2, 12-1, 12-2, 12-3, and 12-4 should be (9) (10-1) (10-2) (11-1) (11-2) (12-1) (12-2) (12-3) (12-4) (On page 854) Equations 13-1, 13-2, 13-3, and 13-4-13-1, 13-2, 13-3, and 13-4 should be (13-1) (13-2) (13-3) (13-4) (On page 857) Proposition 2 should be as follows: where ∂f(e, n)/∂n < ∂f(e, n)/∂e ≦ 0. Proof.From (8-1)–(8-2) and (10-1)–(10-2), it follows that πPP/πQQ = (1 − b2)(qPP)2/(qQQ)2. Let di = d, i = 1, 2, and then we have Hence, we obtain the result: πPP/πQQ ⋛ 1 1 – b2 ⋛ [f(e, n)]2. By simple calculation, we get ■ (On page 859) Equations 14-1 and 14-2-14-1 and 14-2 should be (14-1) (14-2) (On page 862, 863) Under Section A2 | Proof of Lemma 1 should be (i) From (8-1), (10-1), and (12-1)–(12-2), we get (ii) From (8-1) and (10-1), it follows that (iii) From (8-1), (10-1), and (12-1), we have (iv) From (8-1), (10-1), and (12-1)–(12-2), we get which lead to by (A1)–(A3). (On page 863, 864) Under Section A3 | Proof of Proposition 1 should be (i) From (8-1) and (10-1), we have where A(n) is defined in the proof of Lemma 1-(ii). First, let us check the positivity of the coefficient of di. Multiplying the coefficient by (1 − n), we obtain where the inequality follows from (1 − n)2 > (en – b)2 by (A1) and (2 − n)(2 – n – b2) − (1 − n)(3 – n – b2) = 1 – b2 > 0. Hence, the coefficient of di is positive. Noting that A(n) ≧ 0 for any n ∈ [0, 1), holds if en ≦ b. Similarly, we have holds if en ≦ b. Now, we consider the case where en > b. For the more efficient firm's price, we have On the other hand, for price of the less efficient firm, we get Therefore, we get the desired result. (ii) Suppose that en ≧ b. From (8-2) and (10-2), it follows that . Hence, we only need to show . By (8-1) and (10-1), we get where the inequality follows from (DQ/DP) ≧ [(2 − n)/(2 − n – b2)]2 and [(2 − n – b2)di + (en – b)dj]/ [(2 − n)di + (en – b)dj]> (2 – n – b2)/(2 − n), by en ≧ b. Here, we have where the inequality is due to n ≧ b. As a result, we obtain . (iii) From (ii), the statement is true if en ≧ b. Hence, it suffices to show that when en < b holds. From (8-2) and (10-2), we get ■ (On page 864) Under Section A4 | Proof of Corollary 1 should be Let e = 0. From Proposition 2, we have Hence, the necessary and sufficient condition for πPP > πQQ is given by < n. ■ (On pages 864, 865) Under Section A5 | Proof of Proposition 3 should be From (12-1)–(12-4), it follows that If en > b, we have From (A3), (1 − n)dj> (b – en)di holds, and we have On the other hand, by applying a similar argument for the less efficient firm, we have These have been corrected in the online version of the paper. We regret any inconvenience caused by these errors. REFERENCE Hashizume, R., & Nariu, T. (2020). Price and quantity competition with network externalities: Endogenous choice of strategic variables. The Manchester School, 88(6), 847– 865. https://doi.org/10.1111/manc.12343Wiley Online LibraryWeb of Science®Google Scholar Volume89, Issue3June 2021Pages 310-314 ReferencesRelatedInformation