Consumer misperception of eco-labels, green market structure and welfare

Abstract

Eco-labels are essential for informing consumers about products’ environmental characteristics. However, the many different labels consumers encounter can be confusing, which makes assessing environmental quality associated with each label difficult. How does consumer misperception of competing eco-labels affect market structure and welfare? This article provides theoretical insight into this issue by using a double-differentiation model in which three products compete: an unlabeled product and two distinctly eco-labeled products, one with a medium and one with a high level of environmental quality. The study investigates the effects of consumers’ imperfect information when they perceive all eco-labels as a sign of the same high environmental quality and consider each label as a unique product. This misperception can weaken the firm that provides the greenest product, though paradoxically this situation is not always detrimental to social welfare. However, depending on the certifying organizations, consumer misperception can induce firms to use a greenwashing strategy and encourage nongovernmental organizations and regulators to introduce less stringent standards.

Appendices

Appendix 1: Price equilibrium

1.1 Case of perfect eco-labels

From Eqs. (11) to (13) and definitions of demand functions, the following market shares of the three firms are deduced:

$$\begin{aligned} d_{LM}^*= & {} \frac{c\left( {\underline{q}} \right) -\theta \underline{q}}{3\theta q_{LM} }+\frac{c\left( {q_{LH} } \right) q_{LM} +\left( {2\theta q_{LM} -c\left( {q_{LM} } \right) } \right) \left( {2q_{LH} +3q_{LM} } \right) }{6\theta q_{LM} \left( {q_{LH} +q_{LM} } \right) }\qquad \quad \end{aligned}$$

(17)

$$\begin{aligned} d_{LH}^*= & {} \frac{c\left( {\underline{q}} \right) -\theta \underline{q}}{3\theta q_{LH} }+\frac{c\left( {q_{LM} } \right) q_{LH} +\left( {2\theta q_{LH} -c\left( {q_{LH} } \right) } \right) \left( {3q_{LH} +2q_{LM} } \right) }{6\theta q_{LH} \left( {q_{LM} +q_{LH} } \right) },\qquad \quad \end{aligned}$$

(18)

and $d_{NL}^*=1-d_{LM}^*-d_{LH}^*$. Profits are $\uppi _{NL}^*=\frac{\theta q_{LM} q_{LH} }{q_{LM} +q_{LH} }d_{NL}^{*\,{2}}$, $\uppi _{LM}^*=\theta q_{LM} d_{LM}^{*\,{2}}-k_{LM}$ and $\uppi _{LH}^*=\theta q_{LH} d_{LH}^{*\,{2}}-k_{LH}$.

The three conditions for triopoly, $d_{NL}^*\ge 0$, $d_{LM}^*\ge 0$ and $d_{LH}^*\ge 0$, can be translated into the conditions $\theta \le \theta _{NL}$, $\theta \ge \theta _{LM}$ and $\theta \ge \theta _{LH}$, where the thresholds are defined as follows:

$$\begin{aligned} \theta _{NL}\equiv & {} \frac{c\left( {q_{LH} } \right) q_{LM} +c\left( {q_{LM} } \right) q_{LH} -\left( {q_{LM} +q_{LH} } \right) c\left( {\underline{q}} \right) }{2q_{LM} q_{LH} -\left( {q_{LM} +q_{LH} } \right) \underline{q}} \end{aligned}$$

(19)

$$\begin{aligned} \theta _{LM}\equiv & {} \frac{-c\left( {q_{LH} } \right) q_{LM} +c\left( {q_{LM} } \right) \left( {2q_{LH} +3q_{LM} } \right) -2\left( {q_{LM} +q_{LH} } \right) c\left( {\underline{q}} \right) }{6q_{LM}^2 +4q_{LM} q_{LH} -2\left( {q_{LM} +q_{LH} } \right) \underline{q}} \qquad \qquad \end{aligned}$$

(20)

$$\begin{aligned} \theta _{LH}\equiv & {} \frac{c\left( {q_{LH} } \right) \left( {3q_{LH} +2q_{LM} } \right) -c\left( {q_{LM} } \right) q_{LH} -2\left( {q_{LM} +q_{LH} } \right) c\left( {\underline{q}} \right) }{6q_{LH}^2 +4q_{LM} q_{LH} -2\left( {q_{LM} +q_{LH} } \right) \underline{q}}.\qquad \qquad \end{aligned}$$

(21)

1.2 Case of imperfect eco-labels

From Eqs. (14) to (16) and definitions of demand functions, the following market shares of the three firms can be deduced:

$$\begin{aligned} \tilde{d}_{NL}^*= & {} \frac{c\left( {q_{LM} } \right) +c\left( {q_{LH} } \right) -2c\left( {\underline{q}} \right) -2\theta \left( {q_L -\underline{q}} \right) }{12\theta q_L } \end{aligned}$$

(22)

$$\begin{aligned} \tilde{d}_{LM}^*= & {} \frac{4c\left( {\underline{q}} \right) -5c\left( {q_{LM} } \right) +c\left( {q_{LH} } \right) +2\theta \left( {5q_L -4\underline{q}} \right) }{12\theta q_L } \end{aligned}$$

(23)

$$\begin{aligned} \tilde{d}_{LH}^*= & {} \frac{4c\left( {\underline{q}} \right) +c\left( {q_{LM} } \right) -5c\left( {q_{LH} } \right) +2\theta \left( {5q_L -4\underline{q}} \right) }{12\theta q_L }. \end{aligned}$$

(24)

The existence conditions for triopoly are characterized by marginal WTP $\tilde{\theta }_{NL}$, $\tilde{\theta }_{LM}$ and $\tilde{\theta }_{LH}$ such as $\tilde{d}_{NL}^*\ge 0$ when $\theta \le \tilde{\theta }_{NL}$, $\tilde{d}_{LM}^*\ge 0$ when $\theta \ge \tilde{\theta }_{LM}$ and $\tilde{d}_{LH}^*\ge 0$ when $\theta \ge \tilde{\theta }_{LH}$:

$$\begin{aligned} \tilde{\theta }_{NL}\equiv & {} \frac{c\left( {q_{LH} } \right) +c\left( {q_{LM} } \right) -2c\left( {\underline{q}} \right) }{2\left( {q_L -\underline{q}} \right) } \end{aligned}$$

(25)

$$\begin{aligned} \tilde{\theta }_{LM}\equiv & {} \frac{-c\left( {q_{LH} } \right) +5c\left( {q_{LM} } \right) -4c\left( {\underline{q}} \right) }{10q_L -4\underline{q}} \end{aligned}$$

(26)

$$\begin{aligned} \tilde{\theta }_{LH}\equiv & {} \frac{5c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) -4c\left( {\underline{q}} \right) }{10q_L -4\underline{q}}. \end{aligned}$$

(27)

Appendix 2: Effects of consumer misperception on market equilibrium

1.1 The green product

From Eq. (16), it is evident that price $\tilde{p}_{LH}^*$ is an increasing function of $q_{L}$. Thus, to prove that $p_{LH}^*\ge \tilde{p}_{LH}^*$, it is sufficient to demonstrate that this inequality is true for $q_L =q_{LH}$. Because $\left. {p_{LH}^*-\tilde{p}_{LH}^*} \right| _{q_L =q_{LH} } =\frac{\left( {q_{LH} -q_{LM} } \right) \left( {2\theta q_{LH} -c\left( {q_{LH} } \right) +c\left( {q_{LM} } \right) } \right) }{12\left( {q_{LM} +q_{LH} } \right) }$ and $c\left( {q_{LH} } \right) \le 2\theta q_{LH}$, $p_{LH}^*\ge \tilde{p}_{LH}^*$ is always fulfilled.

Similarly, it is evident that $\tilde{d}_{LH}^*$ is an increasing function of $q_{L}$ and that $d_{LH}^*\ge \tilde{d}_{LH}^*$ for $q_L =q_{LH}$, as $d_{LH}^*-\left. {\tilde{d}_{LH}^*} \right| _{q_L =q_{LH} } =\frac{\left( {q_{LH} -q_{LM} } \right) \left( {2\theta q_{LH} -c\left( {q_{LH} } \right) +c\left( {q_{LM} } \right) } \right) }{12\theta q_{LH} \left( {q_{LH} +q_{LM} } \right) }\ge 0$, and thus for all $q_L \le q_{LH}$. Finally, because consumer misperception decreases both the price and the market share of the green product, it also lowers the profit of the green firm.

1.2 The blue product

From Eq. (15), it follows that $\tilde{p}_{LM}^*$ declines with $q_{L}$. Moreover $p_{LM}^*\le \tilde{p}_{LM}^*$ when $q_L =q_{LM}$ because $\left. {p_{LM}^*-\tilde{p}_{LM}^*} \right| _{q_L =q_{LM} } =\frac{-\left( {q_{LH} -q_{LM} } \right) \left( {c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) +2\theta q_{LM} } \right) }{12\left( {q_{LM} +q_{LH} } \right) }\le 0$. Consequently, $p_{LM}^*\le \tilde{p}_{LM}^*$ for all $q_L \ge q_{LM}$.

From Eq. (23), $\frac{\partial \tilde{d}_{LM}^*}{\partial q_L }=\frac{5}{6q_L }-\frac{\tilde{d}_{LM} }{q_L }$, which is positive when the blue product captures less than five sixths of the market. Furthermore, $d_{LM}^*\le \tilde{d}_{LM}^*$ for $q_L =q_{LM}$, as $d_{LM}^*-\left. {\tilde{d}_{LM}^*} \right| _{q_L =q_{LM} } =\frac{-\left( {q_{LH} -q_{LM} } \right) \left( {2\theta q_{LM} +c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) } \right) }{12\theta q_{LM} \left( {q_{LH} +q_{LM} } \right) }\le 0$, and thus for all $q_L \ge q_{LM}$. In summary, the profit of the firm producing the blue product is increased by consumer misperception about the perfect information case.

1.2.1 The brown product

From Eq. (14), it appears that $\tilde{p}_{NL}^*$ is a decreasing function of $q_{L}$. In addition,

$$\begin{aligned}&p_{NL}^*-\left. {\tilde{p}_{NL}^*} \right| _{q_L =q_{LM} } =\frac{-\left( {q_{LH} -q_{LM} } \right) \left( {2\theta q_{LM} +c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) } \right) }{6\left( {q_{LH} +q_{LM} } \right) }\le 0,\\&p_{NL}^*-\left. {\tilde{p}_{NL}^*} \right| _{q_L =q_{LH} } =\frac{\left( {q_{LH} -q_{LM} } \right) \left( {2\theta q_{LH} -c\left( {q_{LH} } \right) +c\left( {q_{LM} } \right) } \right) }{6\left( {q_{LH} +q_{LM} } \right) }\ge 0. \end{aligned}$$

Therefore, there is a threshold $\hat{{q}}_L$ such that $\tilde{p}_{NL} >p_{NL}$ when $q_L \le \hat{{q}}_L$, and $\tilde{p}_{NL} <p_{NL}$ otherwise. This threshold is defined as $\hat{{q}}_L =\frac{2\theta q_{LM} q_{LH} +\left( {q_{LH} -q_{LM} } \right) \left( {c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) } \right) }{2\theta \left( {q_{LM} +q_{LH} } \right) }$.

From Eq. (22), it follows that $\frac{\partial \tilde{d}_{NL}^*}{\partial q_L }=\frac{-c\left( {q_{LH} } \right) -c\left( {q_{LM} } \right) +2c\left( {\underline{q}} \right) -2\theta \underline{q}}{3\theta q_L^2 }\le 0$. Moreover,

$$\begin{aligned} \left. {d_{NL}^*-\tilde{d}_{NL}^*} \right| _{q_L =q_{LM} }= & {} \frac{-\left( {q_{LH} -q_{LM} } \right) \left( {c\left( {q_{LH} } \right) -c\left( {\underline{q}} \right) +\theta \underline{q}} \right) }{3\theta q_{LM} q_{LH} }\le 0\\ \left. {d_{NL}^*-\tilde{d}_{NL}^*} \right| _{q_L =q_{LH} }= & {} \frac{\left( {q_{LH} -q_{LM} } \right) \left( {c\left( {q_{LM} } \right) -c\left( {\underline{q}} \right) +\theta \underline{q}} \right) }{3\theta q_{LM} q_{LH} }\ge 0. \end{aligned}$$

Consequently, there is a threshold $\hat{{\hat{{q}}}}_L$ such that $\tilde{d}_{NL} >d_{NL}$ when $q_L \le \hat{{\hat{{q}}}}_L$, and $\tilde{d}_{NL} <d_{NL}$ otherwise. The profit of the brown firm follows the same development, which translates to better performance when $q_{L}$ is close to $q_{LM}$ and worse performance when $q_{L}$ is close to $q_{LH}$.

Appendix 3: Effects of consumer misperception on the quality of the environment

The derivative of global environmental quality in the imperfect information case is characterized by

$$\begin{aligned} \frac{\partial \tilde{Q}}{\partial q_L }=\frac{\left( {5q_{LH} -q_{LM} -4\underline{q}} \right) c\left( {q_{LH} } \right) -\left( {q_{LH} -5q_{LM} -4\underline{q}} \right) c\left( {q_{LM} } \right) +4\left( {q_{LH} +q_{LM} -2\underline{q}} \right) \left( {\theta q_{NL} -c\left( {\underline{q}} \right) } \right) }{12\theta q_L^2 } \end{aligned}$$

Because the second term of the numerator is necessarily lower than the first term and the third term is positive, the global environmental quality rises with perceived quality $q_{L}$. Furthermore, using the fully coverage property, it is possible to characterize $Q^{*}-\tilde{Q}^{*}$ in two ways:

$$\begin{aligned} Q^{*}-\tilde{Q}^{*}= & {} \left( {q_{LM} -q_{LH} } \right) \left( {d_{LM}^*-\tilde{d}_{LM}^*} \right) \nonumber \\&+\,\left( {\underline{q}-q_{LH} } \right) \left( {d_{NL}^*-\tilde{d}_{NL}^*} \right) \ge 0\quad \hbox { if }\quad q_L \le \hat{{\hat{{q}}}}_L ,\hbox { and}\\ Q^{*}-\tilde{Q}^{*}= & {} \left( {q_{LH} -q_{LM} } \right) \left( {d_{LH}^*-\tilde{d}_{LH}^*} \right) \nonumber \\&+\,\left( {\underline{q}-q_{LM} } \right) \left( {d_{NL}^*-\tilde{d}_{NL}^*} \right) \le 0\quad \hbox { if }\quad q_L \ge \hat{{\hat{{q}}}}_L . \end{aligned}$$

Therefore, when the perceived quality is low (high), the global environmental quality is lower (greater) than that occurring in the perfect information case.