A comparison between the wholesale model and the agency model with different launch strategies in the book supply chain

Abstract

Electronic books’ pricing model and launch strategy are main issues concerned by the members of the book supply chain. Inspired by this fact, this paper establishes analytical models to investigate the publisher’s and the bookstore’s optimal decisions combined with pricing models (the agency model or the wholesale model) and launch strategies (the simultaneous launch strategy or the delaying launch strategy) of electronic books in a book supply chain. Additionally, we analyze the impacts of exogenous parameters on the publisher’s and the bookstore’s optimal strategies. Our findings illustrate that both the publisher and the bookstore can benefit from the agency model if they agree on a moderate proportion of e-books’ profit sharing. Moreover, we find that both the publisher and the bookstore can benefit from the delaying launch strategy when the product substitutability between electronic books and physical books is low and the cannibalization effect of delaying launch is significant. This finding is different from former study, which ignored the cannibalization rate caused by delaying launch strategy and showed that the delaying launch strategy always hurts the profits of publishers and bookstores.

Appendix

1.1 Proof of Proposition 1

• (1) $w_p^{AS} - w_p^{WS} = \dfrac{\alpha (1-\gamma )}{2(\alpha - 1)} <0$, so we can get $w_p^{AS} < w_p^{WS}$.

• (2) $w_p^{AD} - w_p^{WD} = \dfrac{\alpha (2\gamma -1)(4\gamma (1-\lambda )+\alpha (C_p+(4\gamma -1)(1+\lambda )))}{2(8 \gamma -\alpha ^2)}$, we can get Proposition 1(2) by solving this function.

1.2 Proof of Proposition 2

• (1) $w_e^{WD} - w_e^{WS} = \dfrac{\alpha ^2+\lambda (\alpha -1)^2}{2(\alpha - 1)} <0$, so we can get $w_e^{WD} < w_e^{WS}$.

• (2) $w_p^{WD} - w_p^{WS} = \dfrac{\alpha +2\lambda }{2(\alpha -1)}$, we can get Proposition 2(2) and (3) by solving this function.

1.3 Proof of Proposition 3

• (1) $p_p^{AS} - p_p^{WS} = \dfrac{\alpha }{4(\alpha - 1)} <0$, $p_e^{AS} - p_e^{WS} = \dfrac{1}{4(\alpha - 1)} <0$, so we can get $p_p^{AS} < p_p^{WS}$ and $p_e^{AS} < p_e^{WS}$.

• (2) $p_p^{AD} - p_p^{WD} = \dfrac{\alpha ^2 (2\gamma -1)(-2+2C_p+\alpha +\alpha ^2+(\alpha -2)(1+\alpha )\lambda )}{2(\alpha ^2-4)(\alpha ^2-8\gamma )}$, we can get Proposition 3(2) and (3) by solving this function.

1.4 Proof of Proposition 4

• (1) $p_e^{WD} - p_e^{WS} = \dfrac{3}{4(\alpha - 1)} + \dfrac{6(\lambda -1)-\alpha ^2(\lambda -1)+\alpha ^3(1+\lambda )-\alpha (5+C_p+5\lambda )}{2(\alpha ^2 - 4)} <0$, so we can get $p_e^{WD} < p_e^{WS}$.

• (2) $p_p^{WD} - p_p^{WS} = \dfrac{-\alpha (10+\alpha -C_p \alpha +\alpha ^2(C_p-2))+2\lambda (6-7\alpha +\alpha ^3)}{4(\alpha ^2-4)(\alpha -1)}$, we can get Proposition 4(2) and (3) by solving this function.

The following Propositions’ demonstrations are simple, so we omit them.