How corporate social responsibility auditing interacts with supply chain information transparency

Abstract

The burgeoning digital economy has expanded the information gap in supply chains. Supply chain information transparency has thus attracted increasing attention from both industry and academia. Meanwhile, as consumers pay more attention to corporate social responsibility (CSR), firms have made efforts to audit their suppliers to avoid CSR violations. This paper explores the strategic role of CSR auditing in supply chain information transparency. We examine how CSR auditing interacts with supply chain information transparency by considering a scenario where a firm strategically sells either a single product or a product line through an online retail platform. Our results show that when the product line strategy is uncertain, the firm’s audit commitment strengthens the platform’s incentive to voluntarily disclose information. Our results also show that when the length of the product line is unchangeable, the platform prefers to share the information even if the firm does not make audit commitments. Additionally, when the platform’s information sharing decision and the firm’s product line design are made simultaneously, the platform may choose to privately withhold the information if the product line extension cost is in the moderate range and the demand loss from CSR-concerned consumers is relatively minor.

Appendix: Proof

Proof of Lemma 1

We take the fourth case in Lemma 1 as an example, and the solution process for the other cases is similar. The firm determines both selling quantity q and audit effort e, The Hessian matrix of q and e is obtained by the profit function, that is, $H=\begin{bmatrix} -4(1+\theta )(1-\lambda ) &{} 2 d r \alpha (1 - \lambda ) \\ 0 &{} -1 \end{bmatrix}$. It is straightforward to check that $|H|=4(1-\lambda )(1-\theta -d r \alpha (1 - \lambda ))>0$, so the firm’s profit function is jointly concave in p and e. The equilibrium solutions can be obtained by solving the FOCs of the firm’s profit function. $\square$

Proof of Proposition 1

From Lemma 1, we establish the firm’s and platform’s optimal profits in different cases. Let $T=d r \alpha$ and $\pi _{psw}^{a*}-\pi _{psn}^{a*}=\lambda (\frac{1-2T+T^2}{(2-(1-\lambda )T^2)^2}-\frac{1-2T}{4})$; as $1-2T+T^2\ge 1-2T$ and $(2-(1-\lambda )T^2)^2\le 4$, then $\pi _{psw}^{a*}-\pi _{psn}^{a*} \ge 0$. Similarly, we obtain $\pi _{plw}^{a*}-\pi _{pln}^{a*}\ge 0$. $\square$

Proof of Proposition 2

From the comparison of the firm’s profits, we have $f_n=\frac{(1-\lambda )(1-\theta )}{4(1+\theta )}$ and $f_s=\frac{(1-\lambda )(1-\theta )(1-T)^2}{2(2-(1-\lambda ) T^2)(1+\theta -(1-\lambda )T^2)}$. It is clear that $f_n=f_s$ if $T=0$; then, if $f_s$ decreases with T, we have $f_n\ge f_s$ since $T\in (0,1]$. Let $F_1=\frac{(1-T)^2}{2(2-(1-\lambda )T^2) (1+\theta -(1-\lambda )T^2)}$ and the variation in $F_1$ with T be the same as that of $f_s$, $\frac{\partial F_1}{\partial T} =\frac{(T-1)(2(1-\theta )-(3-\theta )(1-\lambda )T+2(1-\lambda )^2 T^3-(1-\lambda )T^4)}{(2-(1-\lambda )T^2)^2(1+\theta -(1-\lambda )T^2)^2}$. Then, we have to determine only whether $\frac{\partial F_1}{\partial T}$ is positive or negative. Let $F_2(T)=-(2(1-\theta ) -(3-\theta )(1-\lambda )T+2(1-\lambda )^2T^3-(1-\lambda )^2T^4)$; then, $F_3=\frac{\partial F2}{\partial T}=(1-\lambda )(3-\theta +6(1-\lambda )T^2-4(1-\lambda )T^3)$. Obviously, $F_3$ is a constant positive, which means that $F_2(T)$ always increases with T, and because $F_2(T=1)=(\theta -\lambda ) (1+\lambda )\le 0$ and $F_2(T=0)=-2(1-\theta )\le 0$, $\frac{\partial F_1}{\partial T}\le 0$. Thus, $f_s$ is decreasing with T and $f_n\ge f_s$. $\square$

Proof of Proposition 3

Let $M(T)=\pi _{pln}^{a*}-\pi _{psw}^{a*} =\frac{\lambda (1-2T)}{2(1-\theta )} -\frac{\lambda (1-T)^2}{(2-(1-\lambda )T^2)}$, $M(0)=\frac{\lambda (1+\theta )}{4(1-\theta )}>0$, and $M(\frac{1}{2})=\frac{-4\lambda }{(7+\lambda )^2}<0$. As M(T) is continuous, at least point t satisfies $M(t)=0$. Note that $\frac{\partial \pi _{pln}^{a*}}{\partial T} =-\frac{\lambda }{1-\theta }$ and $\frac{\partial \pi _{psw}^{a*}}{\partial T}=\frac{2\lambda (1-T) (-2+2T(1-\lambda )-T^2(1-\lambda ))}{(2-(1-\lambda )T^2)^2}$ are both negative and that $\frac{\partial ^2 \pi _{psw}^{a*}}{\partial T^2} =\frac{2\lambda (8-4\lambda -24T(1-\lambda -(12T^3-3T^4) (1-\lambda )^2+2T^2(13-18\lambda +5\lambda ^2))}{(2-(1-\lambda )T^2)^4}$. Let $M_1(T)=(8-4\lambda -24T(1-\lambda -(12T^3-3T^4)(1-\lambda )^2 +2T^2(13-18\lambda +5\lambda ^2))$, $M_2(T)=\frac{\partial M_1(T)}{\partial T}=4(-6(1-\lambda )-(9T^2-3T^3)(1-\lambda )^2 +T(13-18\lambda +5\lambda ^2))$, and $M_3(T)=\frac{\partial M_2(T)}{\partial T}=4(1-\lambda )(13-5\lambda -18T(1-\lambda ) +9T^2(1-\lambda ))$; as $\frac{\partial M_3(T)}{\partial T} =-72(1-T)(1-\lambda )^2<0$ and $M_3(1)=16(1-\lambda ^2)>0$, $M_3(T)>0$, and $M_2(T)$ always increases with T. Note that $M_2(0)=-24(1-\lambda )$ and $M_2(\frac{1}{2})=-\frac{1}{2} (11+6\lambda +5\lambda ^2)<0$, so $M_1(T)$ decreases with T. Thus, there is threshold t such that $M(T)>0$ when $T<t$, and in this case, the platform is reluctant to share information. $\square$

Proof

The proofs of Propositions 4 and 5 are similar to that of Proposition 3, and the proof of Proposition 6 is similar to that of Proposition 2. $\square$