3.1. The equilibrium configuration in the absence of consumption home bias

Consider as a baseline scenario a framework of two open economies with firms competing in an international duopoly and serving both the domestic market and, through export, the foreign one. We assume that consumers are immobile; each buys at most one unit of the good, either green or brown. Moreover, markets are segmented, and firms price discriminate between countries. Depending on their location, the indirect utility function $U_{i}\left ( \theta \right )$ of a consumer residing in country $i,$ $i=h,\,l,$ is written as

(1)\begin{equation} \begin{array}{@{}c} U_{i}\left( \theta \right) =\left\{ \begin{array}{@{}ll@{}} \theta u_{g}-p_{ig} & \text{if she buys }g \\ \theta u_{d}-p_{id} & \text{if she buys }d \end{array} \right.,\quad i=h,l, \end{array} \end{equation}

where $p_{ig}$ and $p_{id},$ $i=h,\,l,$ are the country-specific prices for the green and the brown good, respectively. In line with the traditional model of vertical product differentiation à la Mussa and Rosen (Reference Mussa and Rosen1978), the indifferent consumer $\theta _{i}\left ( p_{ig},\,p_{id}\right ) ,$ between buying the environmentally high quality variant or the low one in country $i=h,\,l,$ derives from the indifference condition

\[ \theta _{h}u_{g}-p_{hg}=\theta _{h}u_{d}-p_{hd}\text{ and }\theta_{l}u_{g}-p_{lg}=\theta _{l}u_{d}-p_{ld}. \]

Therefore, the expressions for the two marginal consumers in each country are

\[ \theta _{h}(p_{hg},p_{hd})=\dfrac{p_{hg}-p_{hd}}{u_{g}-u_{d}}\text{ and } \theta _{l}\left( p_{hd},p_{ld}\right) =\dfrac{p_{lg}-p_{ld}}{u_{g}-u_{d}}. \]

Then, the demand functions for the two goods $x_{g}(p_{hg},\,p_{hd})$ and $x_{d}(p_{hd},\,p_{ld})$ can be written as follows:

\begin{align*} x_{g}(p_{hg},p_{hd})& =b-\theta _{h}(p_{hg},p_{hd})+b-\theta _{l}\left( p_{hg},p_{hd}\right),\\ x_{d}(p_{hd},p_{ld})& =\theta _{l}\left( p_{hd},p_{ld}\right) -a+\theta _{h}\left( p_{hd},p_{ld}\right) -a. \end{align*}

As mentioned previously, goods can be shipped across countries at a constant unit trade cost $t$, borne by firms and independent of the direction of trade. The firms’ profits are written as:

\begin{align*} \Pi _{g}\left( p_{hg},p_{lg}\right) & =\left( b-\dfrac{p_{hg}-p_{hd}}{ u_{g}-u_{d}}\right) p_{hg}+\left( b-\dfrac{p_{lg}-p_{ld}}{u_{g}-u_{d}} \right) (p_{lg}-t), \\ \Pi _{d}\left( p_{ld},p_{hd}\right) & =\left( \dfrac{p_{lg}-p_{ld}}{ u_{g}-u_{d}}-a\right) p_{ld}+\left( \dfrac{p_{hg}-p_{hd}}{u_{g}-u_{d}} -a\right) \left( p_{hd}-t\right) . \end{align*}

Maximizing the above profits yields the equilibrium prices:

(2)\begin{align} p_{hg}^{{\ast} }& =\frac{t}{3}+\frac{\left( 2b-a\right) \left( u_{g}-u_{d}\right) }{3} \; \text{and} \; p_{lg}^{{\ast} }=\frac{2t}{3}+\frac{ \left( 2b-a\right) \left( u_{g}-u_{d}\right) }{3}, \end{align}

(3)\begin{align} p_{ld}^{{\ast} }& =\frac{t}{3}+\frac{\left( b-2a\right) \left( u_{g}-u_{d}\right) }{3}\;\text{and}\;p_{hd}^{{\ast} }=\frac{2t}{3}+\frac{ \left( b-2a\right) \left( u_{g}-u_{d}\right) }{3}. \end{align}

All optimal prices are positively signed due to condition $b>2a.$ Notice that the equilibrium prices of domestically traded and exported goods depend on trade costs due to strategic price complementarity.

At these equilibrium prices, the indifferent consumers $\theta _{h}^{\ast }$ and $\theta _{l}^{\ast }$ in each country at equilibrium are:

\[ \theta _{h}^{{\ast} }=\frac{a+b}{3}-\frac{t}{3\left( u_{g}-u_{d}\right) }\text{ and }\theta _{l}^{{\ast} }=\frac{a+b}{3}+\frac{t}{3\left( u_{g}-u_{d}\right) }, \]

and both expressions lie within the admissible interval $\left [ a,\,b\right ]$ if, and only if, $t< t^{\prime }\equiv \left ( u_{g}-u_{d}\right ) \left ( b-2a\right ) ,$ which we assume hereafter. If $t>t^{\prime },$ then trade costs are so high that international trade stops.

The corresponding total quantities $x_{g}^{\ast }$ and $x_{d}^{\ast }$ produced at equilibrium for both markets are written as

\[ x_{g}^{{\ast} }=\frac{2\left( 2b-a\right) }{3}\text{ and }x_{d}^{{\ast} }= \frac{2\left( b-2a\right) }{3}, \]

with $x_{g}^{\ast }>x_{d}^{\ast },$ and where $x_{g}^{\ast }$ and $x_{d}^{\ast }$ include both the domestic and foreign consumption of variants $g$ and $d$, respectively.

3.2. Environmental damage

From the firm side, we contemplate two sources of environmental pollution: production and transportation. In particular, we assume that when producing a good, firms generate emissions. Firms generate emissions when transporting goods from one country to another. To the best of our knowledge, our analysis is the first to disentangle the effect of different sources of pollution on the environment using a vertically-differentiated goods model. To this aim, we do not distinguish between local and transboundary pollution, as this distinction refers to where emissions occur. Instead, our crucial reference is the source of pollution, namely the level of emissions generated by a good when it is produced, traded and consumed.

Formally, the environmental damage generated by the brown firm at equilibrium, $E_{d}^{\ast },$ is written as

\[ E_{d}^{{\ast} }=\phi _{p}x_{d}^{{\ast} }+\phi _{t}(\theta _{h}^{{\ast} }-a). \]

The first component, $\phi _{p}x_{d}^{\ast }$, captures pollution from production. This component is more prominent, the larger is the amount of the goods targeted to the domestic market $\left ( \theta _{l}^{\ast }-a\right )$ and the foreign market $\left ( \theta _{h}^{\ast }-a\right )$, and the higher is the emissions coefficient of the production activity $\phi _{p}$. This coefficient captures the environmental impact of the production activity, i.e., the per-unit emissions generated by the brown firm when producing its variant. The second component, $\phi _{t}(\theta _{h}^{\ast }-a),$ captures pollution from the transportation of the exported quantity of good $d$. It increases with the amount of transported goods and the emissions coefficient of transportation, $\phi _{t}$. This coefficient summarizes the environmental characteristics of the transportation undertaken by the brown firm, i.e., it measures the per-unit emissions of the transported goods.Footnote ¹¹ For the sake of simplicity, and to better highlight the possible differences between the green and the brown goods, we normalize $\phi _{p}=\phi _{t}=1.$

The equilibrium environmental damage associated with the green firm $E_{g}^{\ast }$ is given by:

(4)\begin{equation} E_{g}^{{\ast} }=\mu _{p}x_{g}^{{\ast} }+\mu _{t}\left( b-\theta _{l}^{{\ast}}\right),\end{equation}

where the parameter $\mu _{p}\gtreqqless 1$ is the production emissions coefficient of green good $g$. The production process of variant $g$ can be highly polluting even if the per-unit consumption-based emissions of this variant are very low (e.g., the production of batteries for electric bicycles is a very polluting activity, irrespective of the fact that using a bicycle is more environmentally friendly than a car). Whenever $\mu _{p}<1,$ then the green good has a lower environmental footprint in terms of consumption and unit production. The parameter $\mu _{t}$ measures the transportation emissions coefficient. Since the environmental impact of transportation is not a by-product of cleaner quality, the transportation of the high quality good can be more, less, or equally polluting compared to the transportation of the brown good. Formally, $\mu _{t}\gtreqqless 1$. Given $\left ( b-\theta _{l}^{\ast }\right ) ,$ a high value of $\mu _{t}$ (e.g., $\mu _{t}>1$) magnifies pollution generated by exporting the green good, whereas a low value of the parameter (e.g., $\mu _{t}<1$) diminishes the environmental impact of transportation. Hence, in the range where both $\mu _{p}<1$ and $\mu _{t}<1,$ the green good has a smaller environmental footprint in unit production, transportation and consumption ($u_{g}>u_{d}$ ). Nevertheless, it must be noted that this does not imply that the total level of emissions from the green good is necessarily smaller than the total level of emissions from the brown. When the effects of trade are taken into account, it is possible that, in the setting of a closed economy, the emissions generated by the green good will increase, while those flowing from the brown one will decrease. Whenever the former rise overcompensates the latter reduction, total emissions increase. This is known as the product mix effect.Footnote ¹²

Then, the level of environmental damages generated by the green and the brown firm at the market solution in the absence of home bias is obtained as

(5)\begin{equation} E_{g}^{{\ast} }=\frac{2b-a}{3}\left( 2\mu _{p}+\mu _{t}\right) -\frac{t}{ 3\left( u_{g}-u_{d}\right) }\mu _{t}\text{ and }E_{d}^{{\ast} }=\left( b-2a\right) -\frac{t}{3\left( u_{g}-u_{d}\right) }. \end{equation}

The consumption-based damage from consumers buying variant $j,$ $j=g,\,d$, is written as

\[ E_{j,c}=\beta _{j}x_{j}, \]

where $\beta _{j}$ is the consumption emissions coefficient when consumers choose variant $j,$ i.e., it measures the per-unit emissions of good $j$ when it is consumed. Since $u_{g}>u_{d},$ we assume that $\beta _{g}<\beta _{d}.$ At the equilibrium, we obtain:

\[ E_{g,c}^{{\ast} }=\frac{2\beta _{g}\left( 2b-a\right) }{3}\text{ and } E_{d,c}^{{\ast} }=\frac{2\beta _{d}\left( b-2a\right) }{3}. \]

Although the green good has a higher environmental quality than the dirty variant, whenever the emissions coefficient of consumption $\beta _{g}$ is not sufficiently low, the more considerable demand the green variant faces generates more significant emissions than the competing good.

We denote by $\breve {\mu }_{t}$ and $\breve {\beta }_{g}$ the values of the transportation and of the consumption coefficients such that $E_{g}^{\ast }=E_{d}^{\ast }$ and $E_{g,c}^{\ast }=E_{d,c}^{\ast },$ respectively. Then, comparing the environmental damage associated with each variant, we find the following:

Proof. Comparing $E_{g}^{\ast }$ and $E_{d}^{\ast },$ we find

\[ E_{g}^{{\ast} }-E_{d}^{{\ast} }\gtreqqless 0\text{ }\Leftrightarrow \mu_{t}\gtreqqless \breve{\mu}_{t}\equiv \frac{3\left( b-2a\right) \left(u_{g}-u_{d}\right) -t}{\left( 2b-a\right) \left( u_{g}-u_{d}\right) -t}-\mu_{p}\frac{2\left( 2b-a\right) \left( u_{g}-u_{d}\right) }{\left( 2b-a\right)\left( u_{g}-u_{d}\right)-t}, \]

whereas, considering the consumption-based damages $E_{g,c}^{\ast }$ and $E_{d,c}^{\ast }$, we obtain

\[ E_{g,c}^{{\ast} }-E_{d,c}^{{\ast} }\gtreqqless 0\Leftrightarrow \beta _{g}\gtreqqless \breve{\beta}_{g}\equiv \frac{(b-2a)\beta _{d}}{2b-a} \]

that concludes the proof.

Notice that the threshold $\breve {\mu }_{t}\gtreqqless 1$ and recall that $x_{g}^{\ast }>x_{d}^{\ast }.$ Accordingly, emissions generated by the green firm may exceed those generated by the brown rival firm due to a quantity driver and an emissions intensity driver playing a role in production and transportation. When $\mu _{p}<1$ and $\mu _{t}<1,$ the green good undoubtedly has a greener per-unit footprint than the brown variant. The green good has an emissions-intensity driver that is environmentally friendly not only in terms of consumption ($u_{g}>u_{d}),$ but also in terms of production (since $\mu _{p}<1)$, and transportation ($\mu _{t}<1$). Nonetheless, the quantity driver hurts the environment due to the larger market share of the green firm in both the domestic and foreign markets. Whenever $\mu _{t}\in \left [ \breve {\mu }_{t},\,1\right ] ,$ the environment-enhancing force due to the emissions intensity driver in transportation is so weak that the green good turns out to be environmentally detrimental. This finding holds a fortiori when $\mu _{t}>\breve {\mu }_{t}>1$ because both the quantity driver and the emissions intensity driver in transportation reinforce each other, thereby magnifying the component of pollution from transportation. This effect on quantity is reminiscent of the composition effect, which considers how trade liberalization encourages some sectors at the expense of others. Here, the values of these coefficients may magnify the environmental impact of a variant, whereas it reduces that of the other (see Aller and Herrerias, Reference Aller, Ductor and Herrerias2015, inter alia).

If both coefficients $\mu _{t}$ and $\mu _{p}$ are set at one, it holds that $E_{g}^{\ast }=2b-a- {t}/{3\left ( u_{g}-u_{d}\right )}>E_{d}^{\ast }.$ At equal emissions intensity in production and transportation between the green and the brown variants, the green good is still produced in larger quantities than the brown one. Due to the production-based emissions, the damage generated by the green firm is more relevant than the damage generated by the rival brown good.

As a final point, we want to draw attention to a simplifying assumption of our research: the absence of production costs. One can wonder whether this assumption has a strong impact on our main findings. Assume that the cleaner firm has higher costs due to, for instance, abatement costs. Then, the equilibrium price of the high quality variant would be higher than the one we have in the absence of costs, and this is true for both the equilibrium price set in the home market and for the one set abroad. We can guess that, if the price of the green good dramatically increases, the demand met at equilibrium by the cleaner firm may decrease. This will certainly mitigate the product mix effect highlighted in the paper. However, the demand faced by the more polluting firm increases as well, and this would have a negative impact on the environment. In fact, two drivers are the basis of the link between costs and emissions. On the one hand, costs will increase both prices (with different intensity). This will reshuffle the demands at equilibrium and a priori this could be in favor of the dirtier good, whose price could increase less than that of the dirtier variant. On the other hand, home bias will sustain the demand for the local good in each country, with unpredictable effects on the different components of damage. Overall, it seems that introducing productions costs will not necessarily change all our main conclusions.

3.3. The equilibrium configuration in the presence of consumption home bias

Consider now a setting where each good is evaluated not only based on its intrinsic environmental quality. In this setting, consumers are green persuaded to display consumption home bias. Green persuasion changes a green behavior into a socially desirable decision. A green persuaded consumer is not just environmentally aware but has “a nonpecuniary feeling of being a good person” when contributing to abating emissions, whereas the consumer suffers “a nonpecuniary feeling of shame” otherwise (Glaeser, Reference Glaeser2014: 209). Local consumption abates the component of emissions from transportation. This abatement is obtained whatever the environmental quality of a good. Thus, when buying a local variant, consumers have a utility benefit because they contribute to curbing emissions. In contrast, they incur a utility loss when consuming the goods produced in a foreign country, whose transportation causes pollution. In this circumstance, whatever the quality of the foreign good, their choice is environmentally detrimental because of the emissions generated by the transportation of the product.

To formalize these ideas, we use the classical vertical differentiation model presented in Section 3.1, where standard preferences are now nested with a consumption home bias component. Formally, the utility function $U_{h}\left ( \theta \right )$ of a consumer in country $h$ is given by

(6)\begin{equation} U_{h}\left( \theta \right) =\left\{ \begin{array}{@{}ll} \theta u_{g}-p_{hg}+(\gamma _{h}u_{g}-u_{d}) & \text{if she buys }g, \\ \theta u_{d}-p_{hd}-(\gamma _{h}u_{g}-u_{d}) & \text{if she buys }d. \end{array} \right. \end{equation}

Symmetrically, the utility function $U_{l}\left ( \theta \right )$ of a consumer in $l$ is written as

(7)\begin{equation} U_{l}\left( \theta \right) =\left\{ \begin{array}{@{}ll} \theta u_{g}-p_{lg}-(\gamma _{l}u_{d}-u_{g}) & \text{if she buys }g, \\ \theta u_{d}-p_{ld}+(\gamma _{l}u_{d}-u_{g}) & \text{if she buys }d. \end{array} \right. \end{equation}

The term $\theta u_{j}-p_{ij},$ $i=h,\,l$ and $j=g,\,d$ follows from the traditional approach in vertical differentiation: ceteris paribus, the satisfaction of consuming a variant $j$ increases with its quality $u_{j},$ $j=g,\,d$ and decreases with its price $p_{ij},\,i=h,\,l$.

The component $(\gamma _{i}u_{j}-u_{-j}),$ $i=h,\,l$ and $j=g,\,d$ is the by-product of the green persuasion of consumers. More specifically, this part of the utility function is the effect of environmental campaigns, actions, or policies that aim at raising green persuasion in consumers. Consumers know that a variant generates some per unit emissions whose level unambiguously defines its environmental quality. Nonetheless, if they prefer their local variant over the foreign one, they may curb some emissions generated during the transportation of that variant from the foreign country to their home country. Preferring local variants belongs to the set of green behaviors; for green persuaded consumers, it is a worthy consumption choice. The parameter $\gamma _{i}$ $i=h,\,l$ measures the intensity of consumption home bias and, thus, of nonpecuniary feelings of being a good person when consuming domestic items. Symmetrically, it measures the intensity of nonpecuniary feelings of shame in consuming imported goods. For a consumer living in country $i$, consuming the domestic variant means higher abatement of emissions, ceteris paribus. This abatement translates into the higher perceived environmental quality of the local good, i.e., $\gamma _{h}u_{g}>u_{d}$ and $\gamma _{l}u_{d}>u_{g}$. Ultimately, in the spirit of the analysis, green persuasion gives an additional utility benefit to a consumer living in $i,$ $i=h,\,l,$ when buying local and, on the contrary, a penalty when buying foreign.Footnote ¹³ Ceteris paribus, the higher the environmental quality of a variant, the higher the satisfaction that a consumer obtains when purchasing that variant, due to the higher contribution they are making to the environment. Following the same rationale, their contribution to decarbonizing the world is by far more relevant, the lower the environmental quality of the alternative variant.Footnote ¹⁴

We assume that $a>\max \left \{ \gamma _{h} {u_{g}}/{u_{d}}-1,\,{2\left ( \gamma _{l}u_{d}-u_{g}\right )}/{\left ( u_{g}-u_{d}\right ) }\right \}$ and $\gamma _{h}$ $>1$ and $\gamma _{l}>1,$ to guarantee that the utility level of a native $h$ consumer buying good $d$ is a priori positive and the utility of a native $l$ consumer when buying $g$ is also positive. The condition on the parameter $a$ also guarantees that consuming the high quality good gives a higher level of utility than consuming the lower quality good (i.e., $\theta u_{d}+(\gamma _{l}u_{d}-u_{g})<\theta u_{g}-(\gamma _{l}u_{d}-u_{g}),$ for $\theta \in \left [ a,\,b\right ]$). This condition avoids the fact that our model deviates from the standard vertical product differentiation setting (Gabszewicz and Thisse, Reference Gabszewicz and Thisse1979) and becomes horizontal differentiation: consumers in country $l$ receive a higher utility from the dirty good. In this new scenario, the home bias would be so strong that it would dramatically alter the modes of competition and a high-quality variant would no longer exist. Thus, to be consistent with a standard vertically-differentiated approach, we restrict the analysis to the range of parameters such that $a>{2\left ( \gamma _{l}u_{d}-u_{g}\right )}/{\left ( u_{g}-u_{d}\right )}.$Footnote ¹⁵

The marginal consumer in each country $\theta _{h}\left ( p_{h},\,p_{l}\right )$ and $\theta _{l}\left ( p_{h},\,p_{l}\right ) ,$ respectively, is written as

(8)\begin{align} \theta _{h}(p_{hg},p_{hd})=\frac{p_{hg}-p_{hd}-2\left( \gamma _{h}u_{g}-u_{d}\right) }{u_{g}-u_{d}}\text{ and }\theta _{l}(p_{lg},p_{ld})=\frac{p_{lg}-p_{ld}+2\left( \gamma _{l}u_{d}-u_{g}\right) }{u_{g}-u_{d}}. \end{align}

The smaller the price gap $\left ( p_{hg}-p_{hd}\right )$ or the more prominent the green persuasion $\left ( \gamma _{h}u_{g}-u_{d}\right )$, the larger the market share of the green good in country $h$. Similarly, the smaller the price gap $p_{lg}-p_{ld}$ or the more significant the green persuasion $\left ( \gamma _{l}u_{d}-u_{g}\right )$, the larger the market share of the brown good in country $l$.

In this framework, demand functions faced by the green firm and the brown one are written, respectively, as

\begin{align*} x_{g}(p_{h},p_{l})& =b-\theta _{h}(p_{hg},p_{hd})+b-\theta _{l}(p_{lg},p_{ld}) \text{ and }x_{d}(p_{h},p_{l})\\& =\theta _{h}(p_{hg},p_{hd})-a+\theta _{l}(p_{lg},p_{ld})-a. \end{align*}

Maximizing the profit function of each firm, we get the optimal price $\hat {p }_{ij}^{\ast },$ $i=h,\,l$ and $j=g,\,d:$

(9)\begin{align} \hat{p}_{hg}^{{\ast} } & =p_{hg}^{{\ast} }+\frac{2\left( \gamma _{h}u_{g}-u_{d}\right) }{3} \; \text{and}\;\hat{p}_{lg}^{{\ast} }=p_{lg}^{{\ast} }- \frac{2\left( \gamma _{l}u_{d}-u_{g}\right) }{3}, \end{align}

(10)\begin{align} \hat{p}_{ld}^{{\ast} } & =p_{ld}^{{\ast} }+\frac{2\left( \gamma _{l}u_{d}-u_{g}\right) }{3} \; \text{and}\; \hat{p}_{hd}^{{\ast} }=p_{hd}^{{\ast} }- \frac{2\left( \gamma _{h}u_{g}-u_{d}\right) }{3}. \end{align}

Notice that the optimal price of the domestic good always increases with the intensity of the domestic consumption home bias: $\partial \hat {p} _{hg}^{\ast }/\partial \gamma _{h}>0$ and $\partial \hat {p}_{ld}^{\ast }/\partial \gamma _{l}>0.$ In contrast, the optimal price of the foreign good always decreases with the domestic consumption home bias: $\partial \hat {p}_{lg}^{\ast }/\partial \gamma _{l}<0$ and $\partial \hat {p} _{hd}^{\ast }/\partial \gamma _{h}<0.$ Clearly, the stronger the home bias in country $h,$ the more significant the benefits consumers in country $h$ obtain when buying the domestic variant and, thus, the higher the equilibrium price that the green firm sets to maximize profits. Symmetrically, an increase in $\gamma _{l}$ magnifies the utility benefit of buying the domestic variant $d$ for consumers living in country $l,$ with an immediate raise of $\hat {p}_{ld}^{\ast }.$ However, a rise in $\gamma _{l}$ increases the penalty of buying the foreign good $g$ in country $l$. This generates a downward pressure on $\hat {p}_{lg}^{\ast }.$ Mutatis mutandis, a rise in $\gamma _{h}$ reduces $\hat {p}_{hd}^{\ast }.$

Using the optimal prices, we obtain the optimal marginal consumer in each market $\hat {\theta }_{h}$ and $\hat {\theta }_{l},$

\[ \hat{\theta}_{h}^{{\ast} }=\theta _{h}^{{\ast} }-\frac{2\left( \gamma _{h}u_{g}-u_{d}\right) }{3\left( u_{g}-u_{d}\right) } \; \text{and} \; \hat{ \theta}_{l}^{{\ast} }=\theta _{l}^{{\ast} }+\frac{2\left( \gamma _{l}u_{d}-u_{g}\right) }{3\left( u_{g}-u_{d}\right) }, \]

where both expressions lie within the admissible interval $\left [ a,\,b\right ]$ if, and only if, $t^{\prime \prime }< t< t^{\prime }$ (see online appendix A) $,$ which we assume hereafter. If $t^{\prime \prime }< t< t^{\prime }$ there is bilateral trade; if $t< t^{\prime \prime }< t^{\prime }$ only the green good is traded; and if $t^{\prime \prime }< t^{\prime }< t$ there is no trade. This condition on $t$ also guarantees that all optimal prices are non-negative.

It follows that

\[ \hat{\theta}_{h}^{{\ast} }-\theta _{h}^{{\ast} }<0\text{ and }\hat{\theta} _{l}^{{\ast} }-\theta _{l}^{{\ast} }>0. \]

Home bias increases the domestic quantities in both countries $h$ and $l,$ whereas it reduces the demand for the exported goods. This happens although the utility benefit from consuming local products is coupled with the high price for these goods. Ultimately, domestic goods are consumed more, whereas imported goods are consumed less.

The corresponding quantities $\hat {x}_{g}^{\ast }$ and $\hat {x}_{d}^{\ast }$ at equilibrium are

\begin{align*} \hat{x}_{g}^{{\ast} }& =x_{g}^{{\ast} }+\frac{2\left( \left( \gamma _{h}u_{g}-u_{d}\right) -\left( \gamma _{l}u_{d}-u_{g}\right) \right) }{ 3\left( u_{g}-u_{d}\right)}, \\ \hat{x}_{d}^{{\ast} }& =x_{d}^{{\ast} }-\frac{2\left( \left( \gamma _{h}u_{g}-u_{d}\right) -\left( \gamma _{l}u_{d}-u_{g}\right) \right) }{ 3\left( u_{g}-u_{d}\right) }. \end{align*}

Comparative statics show that

\[ \frac{\partial \hat{x}_{g}^{{\ast} }}{\partial \gamma _{h}}>0\text{ and } \frac{\partial \hat{x}_{g}^{{\ast} }}{\partial \gamma _{l}}<0;\frac{\partial \hat{x}_{d}^{{\ast} }}{\partial \gamma _{h}}<0\text{ and }\frac{\partial \hat{x}_{d}^{{\ast} }}{\partial \gamma _{l}}>0. \]

In line with the rationale evoked above for optimal prices, the equilibrium demand for the domestic green good $\hat {x}_{g}^{\ast }$ increases unambiguously with $\gamma _{h},$ implying that a consumption home bias in country $h$ has a positive effect on the firm producing the green good: it increases the price and the quantity. Similarly, home bias in country $l$ favors the dirty rival: the price of its variant and the corresponding price is increasing in $\gamma _{l}.$ We now compare the market solution in the presence and absence of home bias. Direct comparison of optimal prices yields:

This price effect is the direct consequence of the green persuasion of consumers that exercises a downward pressure on the willingness to pay for the exported good, and it boosts the willingness to pay for the domestic good. As expected, this finding also implies that home bias increases the price gap between the domestic and exported goods for the green and brown variants.

Turning to the total quantities exchanged at the market equilibrium, denote by $\bar {\gamma }_{h}\equiv \frac {u_{d}+\gamma _{l}u_{d}-u_{g}}{u_{g}}$ the threshold value such that $\hat {x}_{g}^{\ast }=x_{g}^{\ast }$ and $\hat {x} _{d}^{\ast }=x_{d}^{\ast }.$

Although home bias is present in both countries, the total produced quantity of either good may decrease at the equilibrium. When home bias about the green good is strong, the demand increases despite the high price since the utility consumers obtain from that product in country $h$ is exceptionally high. In that case, the domestic consumption component is large enough to raise $\hat {x}_{g}^{\ast }.$ This is no longer true when home bias $\gamma _{h}$ is weak. In this circumstance, although the domestic component of consumption of the green good increases, the demand for that good observed in the other country $l$ decreases, and this reduction is so relevant that the demand $\hat {x}_{g}^{\ast }$ turns out to be lower than the one occurring in the absence of home bias, i.e., $x_{g}^{\ast }$. The above findings open the door to new results about the effect of policies pushing for home bias in consumption.

Before moving to the emission analysis, we treat the impact of home bias on equilibrium profits. Online appendix B provides the technical details of the proof that the presence of home bias in countries $h$ and $l$ may increase or reduce profits. In particular, we find that equilibrium profits are higher in the presence of home bias than in the absence of home bias for high transportation costs. In order to capture the economic reason for this surprising result, one has to keep in mind the impact that home bias has on the equilibrium prices and quantity. We know that home bias raises the price of the domestic good. For example, $\gamma _{h}$ raises $\hat {p}_{hg}^{\ast }$. Nonetheless, it decreases $\hat {p}_{hd}^{\ast }$, the price of the imported good. The same argument holds for the impact that home bias in country l exerts on prices. Of course, these effects are weakened or magnified by transportation costs. The higher the level of these costs, the more distant the markets and, thus, the higher the equilibrium prices that firms can set in the domestic and foreign markets—a similar economic rationale applies to the analysis of equilibrium quantities. Indeed, the demands in each country depend on $t$. In particular, as transportation costs rise, the equilibrium domestic demand gets larger and larger. Since, due to home bias, the price set by firms in their domestic market is extremely high, the transportation costs benefit firms through a two-fold mechanism: they enable firms to set very high prices in their domestic market, and jointly they sustain the demand for firms in these markets. As a result, equilibrium profits are higher in the presence of home bias than in the absence of home bias for sufficiently high transportation costs. Finally, it is worth noting that a rise in home bias in country $h$ (resp. $l$) always benefits firm $g$ (resp $d$):

\begin{align*} \frac{\partial \hat{\Pi}_{g}^{{\ast} }}{\partial \gamma _{h}} & =\frac{ 4u_{g}\left( t+\left( 2b-a\right) \left( u_{g}-u_{d}\right) +2(u_{g}\gamma _{h}-u_{d})\right) }{9\left( u_{g}-u_{d}\right) }>0,\\ \frac{\partial \hat{\Pi}_{d}^{{\ast} }}{\partial \gamma _{l}} & =\frac{4\left( t+\left( b-2a\right) \left( u_{g}-u_{d}\right) +2(u_{d}\gamma _{l}-u_{g})\right) u_{d}}{9\left( u_{g}-u_{d}\right) }>0, \end{align*}

while the cross-effect of home bias,

\begin{align*} \frac{\partial \hat{\Pi}_{g}^{{\ast} }}{\partial \gamma _{l}} & =\frac{4\left( t-\left( 2b-a\right) \left( u_{g}-u_{d}\right) +2(u_{d}\gamma _{l}-u_{g})\right) }{9\left( u_{g}-u_{d}\right) }u_{d}\gtrless 0, \\ \frac{\partial \hat{\Pi}_{d}^{{\ast} }}{\partial \gamma _{h}} & =\frac{4\left( t-\left( b-2a\right) \left( u_{g}-u_{d}\right) +2(u_{g}\gamma _{h}-u_{d})\right) }{9\left( u_{g}-u_{d}\right) }u_{g}\gtrless 0, \end{align*}

changes with the transportation costs.

Once more we observe that home bias in country $i=h,\,f$ pushes the price of the domestic good upward, with a direct and positive effect on the corresponding equilibrium profits. Nonetheless, it affects the rival country too. In particular, when focusing on the equilibrium prices, home bias in country $i$ reduces the price of the imported goods in that country, negatively affecting profits. The intensity of these conflicting effects depends on transportation costs. Since the transportation costs magnify the positive effect of the domestic price on the equilibrium profits, the higher these costs, the larger the set of parameters such that the cross-effect is positive.

As a natural step, having elucidated the effects of home bias on the market configuration, we now turn to the focal question: how does home bias impact the environment?

3.4. Environmental damage of home bias

The impact of home bias on the environment is the disparity between total environmental damage under the two market scenarios: one with home bias and one without. Given preferences, we define the total environmental damage in the economy as the sum of pollution emitted by green firm $E_{g}$, brown firm $E_{d}$ and by consumers in both countries when consuming variants $g$ and $d,$ i.e., $E_{g,c}$ and $E_{d,c}.$ Then, to assess the effects of home bias, we conduct an analysis that compares total emissions with home bias, $\hat {E}$ , and those without home bias, $E^{\ast }$. Formally, the impact of the home bias, $\hat {E}-E^{\ast },$ is written as follows:

\[ \hat{E}-E^{{\ast} }=(\hat{E}_{g}-E_{g}^{{\ast} })+(\hat{E}_{d}-E_{d}^{{\ast} })+( \hat{E}_{g,c}^{{\ast} }-E_{g,c}^{{\ast} })+(\hat{E}_{d,c}^{{\ast} }-E_{d,c}^{{\ast}}). \]

In this equation, the first two terms represent the environmental damage caused by the production and transportation of green and brown goods by firms. The last two terms relate to emissions resulting from the consumption of these goods.

In this section, our analysis begins by assessing the environmental damage caused by each individual firm. We then explore the damage arising from consumption patterns. Finally, we examine the total environmental damage caused by home bias.

Emissions from the green firm

The environmental damage caused by the green firm $\hat {E}_{g}^{\ast }$ is

\[ \hat{E}_{g}^{{\ast} }=\mu _{p}\left( (b-\hat{\theta}_{h}^{{\ast} })+(b-\hat{ \theta}_{l}^{{\ast} })\right) +\mu _{t}\left( b-\hat{\theta}_{l}^{{\ast} }\right) . \]

By symmetry, with environmental damage in the absence of home bias $E_{g}^{\ast }$ in (5), the former component $\mu _{p}((b-\hat {\theta }_{h}^{\ast })+(b-\hat {\theta }_{l}^{\ast }))$ captures the emissions generated by production to serve both the domestic and the foreign market, whereas the second component $\mu _{t}(b-\hat {\theta } _{l}^{\ast })$ represents emissions during transportation.

Directly comparing $\hat {E}_{g}^{\ast }$ and $E_{g}^{\ast }$, the impact of home bias on environmental damage coming from the green firm yields the following proposition:

Proposition 2 The presence of home bias leads to an increase in emissions from the green firm when the ratio of the production and transportation emissions coefficient is relatively high (i.e., $\mu _{p}/\mu _{t}>\bar {\mu }$). Conversely, when this ratio is low (i.e., $\mu _{p}/\mu _{t}<\bar {\mu }$), home bias results in a decrease in emissions from the green firm.

Proof. Comparing $\hat {E}_{g}^{\ast }$ and $E_{g}^{\ast }$:

(11)\begin{equation} \hat{E}_{g}^{{\ast} }\ -E_{g}^{{\ast} }=\frac{2}{3}\frac{\left( u_{g}-\gamma _{l}u_{d}+\gamma _{h}u_{g}-u_{d}\right) \mu _{p}+\left( u_{g}-\gamma _{l}u_{d}\right) \mu _{t}}{\left( u_{g}-u_{d}\right) }\gtreqqless 0 \end{equation}

if, and only if,

\[ \frac{\mu _{p}}{\mu _{t}}\gtreqqless \bar{\mu}\equiv \frac{\gamma _{l}u_{d}-u_{g}}{\gamma _{h}u_{g}-u_{d}-\gamma _{l}u_{d}+u_{g}}, \]

which concludes the proof.

It follows that in the presence of a large ratio between the emissions intensity of production and that of transportation ($\mu _{p}/\mu _{t}>\bar { \mu }$), home bias certainly increases the pollution generated by the green firm. This effect is generated by a more significant consumption of the more environmentally friendly good in the domestic country, which expands pollution from production while reducing pollution from transport. Suppose the ratio is low (i.e., $\mu _{p}/\mu _{t}<\bar {\mu }$), then home bias reduces emissions because of the efficiency in production and the lower pollution from transportation. Instead, if the green producer is not very efficient in production (i.e., $\mu _{p}/\mu _{t}>\bar {\mu }$), then the greater demand in the domestic market due to home bias generates higher emissions. In this circumstance, with a high $\mu _{p}/\mu _{t}$ ratio, the negative environmental effect of production dominates the pollution reduction generated by the lower amount of traded goods.

In addition, it is interesting to consider the interplay between market integration and consumption home bias. Threshold $\bar {\mu }$ depends on both coefficients of home bias, $\gamma _{h}$ and $\gamma _{l}.$ In fact, there is a spillover effect of $\gamma _{l}$ on the emissions produced by the green good because of the export-import relations between the two economies. In particular,

\[ \frac{\partial \bar{\mu}}{\partial \gamma _{h}}<0\text{ and }\frac{\partial \bar{\mu}}{\partial \gamma _{l}}>0. \]

Stated in words, buying local is increasingly bad news for the emissions produced by the green firm as the green home bias increases. Furthermore, rising home bias in the country producing the brown variant has positive spillover effects. A rise in $\gamma _{l}$ unambiguously increases the threshold value $\bar {\mu },$ thereby shrinking the range of parameters where home bias increases total emissions generated by the green product ($\frac { \mu _{p}}{\mu _{t}}>\bar {\mu }$). The rationale is that $\gamma _{l}$ decreases emissions from the production of variant $g.$ If this reduction is relevant, it can overcompensate for the higher emissions from transportation of the green variant generated by a higher $\gamma _{l}$. These are unexpected and largely neglected effects of buying local campaigns.

Emissions from the brown firm

Consider now the damage generated by the brown firm in production and transportation of the brown good, $\hat {E}_{d}^{\ast }.$ The level of pollution caused by the brown firm $\hat {E}_{d}^{\ast }$ is written as:

\begin{align*} \hat{E}_{d}^{{\ast} }& =\frac{2\left( u_{d}-u_{g}+2au_{d}-bu_{d}-2au_{g}+bu_{g}-u_{g}\gamma _{h}+u_{d}\gamma _{l}\right) }{3\left( u_{g}-u_{d}\right)}\\& \quad +\frac{\left( b-2a\right) \left( u_{g}-u_{d}\right) -2(u_{g}\gamma _{h}-u_{d})-t}{3\left( u_{g}-u_{d}\right) }. \end{align*}

Thus, using the expression for $E_{d}^{\ast }$ in (5)$,\,$ and taking the difference of the two levels of emissions, we can state:

Proposition 3 Strong (resp. weak) home bias in country $h$ unequivocally reduces (resp. increases) emissions generated by the brown firm.

Proof. Comparing $\hat {E}_{d}^{\ast }$ and $E_{d}^{\ast }$, we find $\hat {E} _{d}^{\ast }-E_{d}^{\ast }=2\frac {\left ( u_{d}\gamma _{l}-u_{g}\right ) -2(u_{g}\gamma _{h}-u_{d})}{3\left ( u_{g}-u_{d}\right ) }\gtrless 0\Leftrightarrow$ $\gamma \lessgtr \ddot {\gamma }_{h}\equiv \frac { 2u_{d}-u_{g}+u_{d}\gamma _{l}}{2u_{g}}.$

We observe that home bias in country $h$ may reduce emissions generated by the brown producer. The reason is that a higher $\gamma _{h}$ increases the demand for the green good in country $h$ at the expense of the dirty variant. Although the demand for the dirty variant increases in country $l$, for a high value of $\gamma _{h}$, this rise does not suffice to sustain the demand for the dirty good worldwide. As a result, the contribution to pollution from the brown producer decreases in terms of production and transportation. Of course, the reverse occurs when $\gamma _{h}$ is low.

Total environmental damage

We can now evaluate the impact of home bias on total emissions, combining the role of firms and consumers. Formally, we can rewrite the total damage as follows:

\[ \hat{E}-E^{{\ast} }=\frac{2}{3}\frac{\left( \mu _{p}-\Delta \beta -2\right) \hat{\gamma}_{h}+\left( 1+\Delta \beta -\left( \mu _{t}+\mu _{p}\right) \right) \hat{\gamma}_{l}}{\left( u_{g}-u_{d}\right) }, \]

where for readability $\hat {\gamma }_{h}=(\gamma _{h}u_{g}-u_{d});$ $\hat { \gamma }_{l}=(\gamma _{l}u_{d}-u_{g}),$ and $\Delta \beta =\beta _{d}-\beta _{g}.$ Recall that $\hat {\gamma }_{h}$ and $\hat {\gamma }_{l}$ capture green persuasion. The first component of the numerator encompasses the gains and losses due to home bias in country $h$. Pollution will increase due to the larger production of the green good ($\mu _{p}$), but it will decrease due to larger consumption of the green $(\Delta \beta )$ and due to the lower production and transportation of the dirty good, ($\phi _{p}+\phi _{t}=2$). The second terms represents the gains and losses due to home bias in country $l.$ Pollution increases due to the higher production of the brown ($\phi _{p}=1)$ and due to higher consumption of the dirty good, $\Delta \beta.$ But it will decrease thanks to lower production and transportation of the green towards country $l,$ $\left ( \mu _{t}+\mu _{p}\right )$.

Solving the equality $\hat {E}-E^{\ast }=0$ gives the threshold level of utility benefit in country $h,$ denoted by $\vec {\gamma }\equiv {\left ( \mu _{t}+\mu _{p}\right ) -1-\Delta \beta }/{\mu _{p}-\Delta \beta -2}\hat { \gamma }_{l}$ (see online appendix C for details)$.$ We can then express the following result:

Proposition 4 When the green firm has high environmental efficiency in production ($\mu _{p}<1+\Delta \beta -\mu _{t})$, strong green persuasion in $h$ (i.e., $\hat { \gamma }_{h}>\vec {\gamma })$ is globally beneficial. By contrast, when the green firm has low environmental efficiency ($\mu _{p}>2+\Delta \beta )$, strong green persuasion $h$ is globally detrimental. Finally, when the green firm has moderate environmental efficiency ($\mu _{p}\in \lbrack 1+\Delta \beta -\mu _{t},\,2+\Delta \beta ]$), any level of green persuasion is always detrimental.

Proof. See appendix C for details.

Our findings suggest that promoting a product with high environmental quality in terms of consumption-based emissions and eco-friendly transportation does not necessarily guarantee a positive impact on the environment. This finding brings some good news for the environment, as long as the marketing of such green products does not become excessively persuasive or, if it does, then the green good must be very green in production. When a product enters the market, it becomes a source of three types of pollution: emissions arising from its consumption, production and transportation. Therefore, even if a product is labeled as “green,” it is crucial to consider the overall emissions associated with it. In some cases, a green product may actually have a detrimental effect on the environment if it is highly polluting during the production process and/or consumption.

The increased production and consumption of such a green product can result in a significant negative impact on the environment when we take into account the total emissions it generates. Therefore, it is essential to assess the entire life cycle of a product, including its production, consumption and transportation, in order to fully understand its environmental implications.