From boycott to buycott: is activism from the North good for the South?

Abstract

This article provides an original theoretical exploration of the potential effects of northern activism on labor conditions and welfare in the South using a duopoly model with endogenous prices, wages and qualities. We assume that all consumers derive the same utility from one (“northern") good but are heterogeneous with respect to the other (“southern") good. This asymmetry captures in a stylized fashion the consensus among northern consumers on the labor conditions prevailing in the North and their ambivalence concerning labor practices in the South. A greater consumer’s social consciousness can be seen as a punishment (boycott) for harmful practices or a reward (buycott) for more virtuous practices. If both forms of activism seem to have the same objectives, one should prefer an activism based on positive information. In an in-depth analysis of a boycott and a buycott campaign, we show that the less socially conscious a firm, the higher the likelihood to be targeted by a boycott or a buycott campaign. A higher quality may reduce this likelihood to be targeted. Northern firm should prefer boycott to buycott whereas southern one always prefer buycott. We also show that consumer surplus may decrease with the both form of activism.

A Appendix

1.1 A.1 Wage equilibria

Setting to zero the derivatives $\dfrac{ \partial {G_i}}{\partial {w_i}}$ of the $G_i$’s in Eq. (7) yields the system of equations

$$\dfrac{\partial G_1}{\partial w_1}=G_1 \left( \dfrac{2-\alpha _1}{\Delta c-\Delta q+q_2 (\delta _m-2 \delta _M)+w_1-w_2}+\frac{\alpha _1}{w_1}\right) =0$$

(27a)

$$\dfrac{\partial G_2}{\partial w_2}=G_2 \left( \dfrac{2-\alpha _2}{\Delta c-\Delta q+q_2 (\delta _M-2 \delta _m)+w_1-w_2}-\frac{\alpha _2}{w_2}\right) =0.$$

(27b)

For $G_i>0$, solutions $w_1^w$ and $w_2^w$ are given in Eq. (8) below. Second order conditions are easily checked.

$$\begin{aligned}&\begin{pmatrix} w_1^w(q_1,q_2)\\ w_2^w(q_1,q_2) \end{pmatrix}\nonumber \\&\quad =\dfrac{1}{4-\alpha _1 \alpha _2}\begin{pmatrix} \alpha _1 ((\Delta q-\Delta c)(2-\alpha _2)+q_2 (\delta _M(4+\alpha _2)-2\delta _m (1+\alpha _2)) \\ -\alpha _2 ((\Delta q-\Delta c)(2-\alpha _1)+q_2(\delta _m(4+\alpha _1)-2\delta _M (1+\alpha _1)) \end{pmatrix}. \end{aligned}$$

(28)

1.2 A.2 Quality equilibria

$$\begin{aligned} \Pi _i^w= & {} q_i \left( \delta _M-\delta _m\right) \left( D_i^w\right) ^2 \end{aligned}$$

(29)

$$\begin{aligned} \frac{\partial \Pi _i^w}{\partial q_i}= & {} \left( D_i^w\right) ^2 \left( \delta _M-\delta _m\right) +2q_i\delta _M-\delta _m\frac{\partial D_i^w}{\partial q_i}D_i^w \end{aligned}$$

(30)

If we assume that both demands are positive at wage equilibria then the first order condition can be written as follows:

$$\begin{aligned} \frac{\partial \Pi _i^w}{\partial q_i}=0\Leftrightarrow \frac{\frac{\partial D_i^w}{\partial q_i}}{D_i^w}=-\frac{1}{2 q_i}. \end{aligned}$$

(31)

The only positive equilibria are then:

$$\begin{aligned} \begin{pmatrix} q_1^q\\ q_2^q \end{pmatrix} = \begin{pmatrix} \dfrac{1}{2c_1} \\ \dfrac{ \left( 1-\dfrac{\delta _m(4+\alpha _1)-2\delta _M (1+\alpha _1)}{2-\alpha _1}\right) +\sqrt{ \left( 1-\dfrac{\delta _m\left( 4+\alpha _1\right) -2\delta _M \left( 1+\alpha _1\right) }{2-\alpha _1}\right) ^2 +3\dfrac{c_1}{c_2} }}{6c_2} \end{pmatrix}. \end{aligned}$$

(32)

1.3 A.3 Modeling the activist’s behavior

To solve this program we calculate the highest activist’s request ($\alpha _{2d}(\delta _{mh})$) for which $\pi _{2f} = \pi _{2h}$.

$$\begin{aligned} \Pi _2^w&= \frac{(M_{2f}^w)^2}{q_2(\delta _{Mf}-\delta _m)} =q_2(\delta _{Mf}-\delta _m)(D_{2f}^w)^2 \end{aligned}$$

(33)

$$\begin{aligned} \Pi _{2h}^w&= \frac{(M_{2h}^w)^2}{q_2(\delta _M-\delta _ {mh})} =q_2(\delta _M-\delta _{mh})(D_{2h}^w)^2 \end{aligned}$$

(34)

$$\begin{aligned} \Pi _{2f}^w&= \Pi _{2h}^w \Leftrightarrow \dfrac{D_{2f}^w}{D_{2h}^w}= \left( \dfrac{\delta _M-\delta _{mh}}{\delta _{Mf}-\delta _m}\right) ^{1/2} \end{aligned}$$

(35)

With $c_1=1/2$, $\alpha _1=1$, $q_1=1$ we obtain the following demands at the wage stage:

$$\begin{aligned} D_{2f}^w=\frac{(\alpha _{2f}-2) (2 c_2 q_2^2+2 q_2 (5 \delta _m-4 \delta _{Mf}-1)+1)}{6 q_2 (\alpha _{2f}-4) (\delta _m-\delta _{Mf})} \end{aligned}$$

(36)

where $\alpha _{2}=\alpha _{2f}$ and $\delta _{M}= \delta _{Mf}$.

$$\begin{aligned} D_{2h}^w=-\frac{(\alpha _2-2)(2 c_2 q_2^2-2 q_2 (4 \delta _M-5 \delta _{mh}+1)+1)}{6 q_2 (\alpha _2-4) (\delta _M-\delta _{mh})} \end{aligned}$$

(37)

where $\alpha _{2}=\alpha _{2d}$ and $\delta _{m}= \delta _{mh}$. To solve the programs we calculate $\forall z=f,h$ the highest activist’s request ($\alpha _{2z}$) for which $\pi _2 = \pi _{2z}$.

$$\begin{aligned} \dfrac{D_{2f}^w}{D_{2h}^w}=\dfrac{\delta _M-\delta _{mh}}{\delta _{Mf}-\delta _m}\dfrac{B_h(B_f-2)A_f}{B_f(B_h-2)A_h} \end{aligned}$$

(38)

where $A_f\overset{\text {def.}}{=}1+ 2 c_2 q_2^2-2 q_2 (1+ 4\delta _{Mf}-5 \delta _m)$, $A_h\overset{\text {def.}}{=}1+ 2 c_2 q_2^2-2 q_2 (1+ 4\delta _M-5 \delta _{mh})$, $B_f\overset{\text {def.}}{=}4-\alpha _{2d}$, $B_h\overset{\text {def.}}{=}4-\alpha _{2}$.

$$\begin{aligned} \alpha _{2z}=4-\dfrac{2A_f B_h}{A_f B_h-\Delta A_h(B_h-2)} \end{aligned}$$

(39)

where $\Delta \overset{\text {def.}}{=}\dfrac{\delta _{Mf}-\delta _m}{\delta _{mh}-\delta _m}$. In the boycott case ($z=h$) $\delta _{Mf}=\delta _M$ whereas in the buycott case ($z=f$) $\delta _{mh}=\delta _m$.

1.4 A.4 Sensitivity tests of the activist’s utility function

See Fig. 9.

Fig. 9

Activist’s utilities. The upper graph represents the optimal boycott and the optimal buycott with $q_2=0.4$. Utility functions reach a maximum in the shaded areas. The lower bound of the areas corresponds to $\alpha _2=1$ and the higher bound represents the poorest working condition ($\alpha _2=0$). The other parameters are the same as in Fig. 7. Similarly, the lower graph represents the two optimal private policies for average working conditions ($\alpha 2=0.4$). The hatched area is bounded at the bottom by the maximum quality ($q2=1$) and at the top by the minimum quality (which ensures equilibrium). Optimal boycott and optimal buycott are increasing functions of $\alpha _2$ and $q_2$