Minimum Quality Standards in Hedonic Markets with Environmental Externalities

Abstract

We investigate the introduction of a minimum quality standard (MQS) in a vertically differentiated duopoly with an environmental externality. We establish that the MQS bites only if the hedonic component of consumer preferences is sufficiently strong. Then, we illustrate an underlying trade-off between the beneficial effects of quality enhancement on prices and the associated undesirable increase in the environmental externality.

Appendix

Proof of Proposition 1

For all ΘQ ∈ (2b, 6b),

$$ \begin{array}{rll} &&{\kern-6pt}\pi _{H}^{\textrm{MQS}}+\pi _{L}^{\textrm{MQS}}-\pi _{H}^{\textrm{N}}+\pi _{L}^{\textrm{N}}\equiv \Delta \Pi \\ &&{\kern12pt} = \frac{\left( \Theta Q-2b\right) \left( 2b-3\Theta Q\right) }{Q}<0 \end{array} $$

(22)

$$ \textrm{CS}^{\textrm{MQS}}\!-\!\textrm{CS}^{\textrm{N}}\equiv \Delta \textrm{CS}=\frac{3\left( \Theta Q\!-\!2b\right) \left( 7\Theta Q\!-\!2b\right) }{64Q}>0 $$

(23)

$$ s^{\textrm{MQS}}-s^{\textrm{N}}\equiv \Delta s=\frac{3b\left( \Theta Q-2b\right) }{16Q}>0. $$

(24)

As a consequence, the fact that in the same range $W^{\textrm{MQS}}>W^{\textrm{N}}$, or equivalently

$$ \Delta \Pi +\Delta \textrm{CS}-\Delta s>0, $$

(25)

is due to the price effect enhancing consumer surplus largely enough to more than offset the reduction in industry profits and the increase in the environmental externality. Moreover, firms now compete over a product that now consumers value more. That is to say, the introduction of a binding MQS causes an increase in the average quality available to consumers as compared to the unregulated setting.□

Proof of Proposition 3

The result in Eq. (21) can be obtained by decomposing the effect of a variation of q _L on each component of social welfare when $\partial \pi _{L}/\partial q_{L}=0$. Differentiating π _H , s, and CS with respect to q _L yields

$$ \frac{\partial \pi _{H}}{\partial q_{L}}=-\frac{4\Theta ^{2}q_{H}^{2}\left( 2q_{H}-q_{L}\right) }{\left( 4q_{H}-q_{L}\right) ^{3}}<0, $$

(26)

$$ \frac{\partial s}{\partial q_{L}}=\frac{3b\Theta q_{H}}{\left( 4q_{H}-q_{L}\right) ^{2}}>0, $$

(27)

$$ \frac{\partial \textrm{CS}}{\partial q_{L}}=\frac{4\Theta ^{2}\left( q_{H}\right) ^{2}\left( 28q_{H}+5q_{L}\right) }{2\left( 4q_{H}-q_{L}\right) ^{3}}>0 $$

(28)

By adding Eq. (26) to Eq. (28) and subtracting Eq. (27), we obtain Eq. (21). Therefore, as in Proposition 1, the fact that W ^MQS > W ^N is due to an increase in consumer surplus large enough to more than compensate the reduction in industry profits and the increase in the environmental externality.□