Effect of green network and emission tax on consumer choice under discrete continuous framework

Abstract

The paper considers a discrete continuous model where consumers choose quality of the product they buy as well as its usage. The product has two quality dimensions, intrinsic quality and environmental quality, that are in conflict with each other. It analyzes a two-stage game in a vertically differentiated duopoly market, where firms choose intrinsic quality in the first stage, and compete in prices in the second stage. It examines the effects of green network, and environmental regulation in the form of an emission tax on equilibrium qualities, market share, and total emissions. It shows that while both green network effect and environmental regulation, individually, improve the overall environmental quality, the effect is stronger when the tax is imposed in the presence of green network effect. Though an increase in green network effect reduces environmental quality of both firms, the market share of the cleaner firm rises at the expense of the other firm, resulting in an overall improvement of the environment. In the presence of green network effect, an emission tax improves environmental quality of both firms with market shares unaltered, thereby resulting in a reduction in total emissions. The green network effect enhances the effect of an emission tax. We also find that the environmental friendly firm benefits from the green network effect. The optimal tax is increasing in the network effect.

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Notes

  1. 1.

    Refer to Matsukawa (2012) for further details.

  2. 2.

    Burtless and Hausman (1978) and Matsukawa (2012)

  3. 3.

    This is the unique solution satisfying the second order conditions.

  4. 4.

    \(Y_i \equiv y - p_i\) or \(y \equiv Y_i + p_i\) and \(Y_i\) is the amount spent on fuel and composite good which is equal to \((\omega + t_e)x_i + p_z z_i\).

  5. 5.

    For \(\alpha > 3\gamma \lambda /b(1+4\lambda \gamma )\), the optimal emission tax is positive. This is consistent with the previous assumptions \(\lambda (2\gamma + \omega ) < 2\) and \(\alpha < (9/16b)\).

References

  1. Amacher GS, Koskela E, Ollikainen M (2004) Environmental quality competition and eco-Labeling. J Environm Econom Manag 47:284–306

    Article  Google Scholar 

  2. Amacher GS, Koskela E, Ollikainen M (2005) Quality competition and social welfare in markets with partial coverage: new results. Bull Econom Res 57(4):391–405

    Article  Google Scholar 

  3. Bansal S, Gangopadhyay S (2003) Tax/Subsidy Policies in the Presence of Environmentally Aware Consumers. J Environm Econom Manag 45:333–355

    Article  Google Scholar 

  4. Bansal S (2008) Choice and dsign of regulatory instruments in the presence of green consumers. Resource Energy Econom 30:345–368

    Article  Google Scholar 

  5. Bansal S, Khanna M, Sydlowski J (2021) Incentives for corporate social responsibility in India: Mandate, peer pressure and crowding-out effects. J Environm Econom Manag 105:102382

    Article  Google Scholar 

  6. Birg L, Voßwinkel JS (2018) Minimum quality standards and compulsory labeling when environmental quality is not observable. Resource Energy Econom 53:62–78

    Article  Google Scholar 

  7. Bottega L, Freitas JS (2013) Imperfect eo-labelling signal in a bertrand duopoly. it DEA Working Papers, Department of applied economics, University of Balearic Islands, 1–21

  8. Brecard D (2013) Environmental quality competition and taxation in the presence of green network effect among consumers. Environm Resource Econom 54:1–19

    Article  Google Scholar 

  9. Burtless G, Hausman JA (1978) The efect of taxation on labor supply: evaluating the gary negative income tax experiment. J Polit Econ 86(6):1103–1130

    Article  Google Scholar 

  10. Carlsson F, Garcia JH, Lofgren A (2010) Conformity and the demand for environmental goods. Environm Resource Econom 47:407–421

    Article  Google Scholar 

  11. Conrad K (2006) Price competition and product differentiation when goods have network effects. German Econom Rev 7(3):339–361

    Article  Google Scholar 

  12. De Jong GC (1990) An indirect utility model of car ownership and car use. Eur Econom Rev 34(5):971–985

    Article  Google Scholar 

  13. Dubin JA, McFadden DL (1984) An econometric analysis of residential electric appliance holdings and consumption. Econometrica 52(3):345–362

  14. Farrell J, Klemperer P (2007) Coordination and Lock-in: Com petition with switching costs and network effects. Handbook Indust Organ 3:1967–2072

    Google Scholar 

  15. Falcone PM (2014) Collusion in a Differentiated Market and Environmental Network Externality. Rev Eur Stud 6(3):102–108

    Article  Google Scholar 

  16. Glerum A, Frejinger E, Karlstrom A, Hugosson M.B, Bierlaire M (2014) A dynamic discrete-continuous choice model for car ownership and usage: estimation procedure. Proceedings of the 14th Swiss Transport Research Conference, Switzerland, 1–18

  17. Griva K, Vettas N (2011) Price competition in a differentiated products duopoly under network effects. Inform Econom Policy 23(1):85–97

    Article  Google Scholar 

  18. Greaker M, Midttomme K (2014) Optimal environmental policy with network effects: Will Pigovian taxation lead to excess inertia? CESifo Working Paper No. 4759: 1–38

  19. Grover C, Bansal S (2019) Imperfect certification and eco-labelling of products. Indian Growth Develop Rev 12(3):288–314

    Article  Google Scholar 

  20. Grover C, Bansal S, Martinez Cruz AL (2019) May a regulatory incentive increase WTP for Cars with a fuel efficiency label?. Estimating regulatory costs through a split-sample DCE in New Delhi, India, SSRN Discussion Paper, pp 1–30

  21. Hanemann WM (1984) Discrete/continuous models of consumer demand. Econometrica 52(3):541–562

    Article  Google Scholar 

  22. Hauck D, Ansink E, Bouma J, Soest D.V (2014). Social network effects and green consumerism. Tinbergen Institute Discussion Paper, TI - 150/VIII, 23: 1–27

  23. Hensher DA, Milthorpe FW, Smith NC (1990) The demand for vehicle use in the Urban household sector. J Transport Econom Policy 24(2):119–137

    Google Scholar 

  24. Katz ML, Shapiro C (1985) Network externalities, competition, and compatibility. Am Econom Rev 73(3):424–440

    Google Scholar 

  25. Lambertini L, Orsini R (2005) The eexistence of equilibrium in a differentiated duopoly with network externalities. Japanese Econom Rev 56(1):55–56

    Article  Google Scholar 

  26. Leibenstein H (1950) Bandwagon, snob and veblen effects in the theory of consumers’ demand. Quart J Econom 64(2):183–207

    Article  Google Scholar 

  27. Lombardini-Riipinen C (2005) Optimal tax policy under environmental quality competition. Environm Resource Econom 32:317–336

    Article  Google Scholar 

  28. Mantovani A, Tarola O, Vergari C (2016) Hedonic and environmental quality: a hybrid model of product differentiation. Resource Energy Econom 45:99–123

    Article  Google Scholar 

  29. Marette S, Crespi JM, Schiavina A (1999) The role of common labelling in a context of asymmetric information. Eur Rev Agricul Econom 26(2):167–178

    Article  Google Scholar 

  30. Matsukawa I (2012) The welfare effects of environmental taxation on a green market where consumers emit a pollutant. Environm Resource Econom 52:87–107

    Article  Google Scholar 

  31. Rasouli S, Timmermans H (2016) Influence of social networks on latent choice of electric cars: a mixed logit specification using experimental design data. Netw Spat Econ 16:99–130

    Article  Google Scholar 

  32. Roychowdhury (2019) Peer effects in consumption in Inda: An instrumental variables approach using negative idiosyncratic shocks. World Develop 114:122–137

    Article  Google Scholar 

  33. Zago AM, Pick D (2004) Labeling policies in food markets: private incentives, public intervention, and welfare effects. J Agricul Resource Econom 29(1):150–165

    Google Scholar 

Download references

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Appendices

Appendix

Properties of indirect utility function

The conditional indirect utility function is non-increasing in price of the fuel (\(\omega \)), price of the composite good (\(p_z\)) and non-decreasing in income (y) -

$$\begin{aligned} \frac{\partial U_i}{\partial \omega } = -\frac{\lambda s_i + \delta }{p_z} + \frac{\beta (\omega + t_e)}{p_z^2} = -\frac{x_i}{p_z}< 0 \\ \frac{\partial U_i}{\partial p_z} = -\frac{-p_z Y_i + p_z(\lambda s_i + \delta )(\omega + t_e) - \beta (\omega + t_e)^2}{p_z^3} = -\frac{z_i}{p_z} < 0 \\ \frac{\partial U_i}{\partial y} = \frac{1}{p_z} > 0 \end{aligned}$$

The conditional indirect utility function is quasi-convex in prices. We use expenditure function to calculate diagonal elements of Slutsky matrix. Rearranging terms in equation (8) and using \(Y_i \equiv y - p_i\), we get expenditure function as

$$\begin{aligned} e(p_z, \omega , \overline{U})= y = \overline{U} p_z - \theta s_i p_z - \gamma (e_j - e_i) p_z - \alpha q_L p_z + (\lambda s_i + \delta )(\omega + t_e) -\frac{\beta }{2} \frac{(\omega + t_e)^2}{p_z} + p_i \end{aligned}$$

The diagonal elements of Slutsky equation, \(s_{11}\) and \(s_{22}\) are given by

$$\begin{aligned} s_{11} = \frac{\partial ^2 e(p_z,\omega ,\overline{U})}{\partial \omega ^2} = -\frac{\beta }{p_z}< 0 s_{22} = \frac{\partial ^2 e(p_z,\omega ,\overline{U})}{\partial p_z^2} = -\frac{\beta (\omega + t_e)}{p_z^3} < 0 \end{aligned}$$

Thus all the properties of an indirect utility function are satisfied.

Conditions for fully covered market

For the market to be fully covered, all consumers including the consumer with the lowest preference parameter \(\theta = 0\) should derive a positive utility from buying a unit of the product in equilibrium. Plugging \(\theta = 0\) in equation (8), the utility is

$$\begin{aligned} U = \gamma (e_j - e_i) + \alpha q_L - (\lambda s_i + \delta ) (\omega + t_e) + \frac{\beta (\omega + t_e)^2}{2} + y - p_i \end{aligned}$$
(24)

Substituting the equilibrium values from equation (14),(15) in equation (24), we get the utility which consumer with \(\theta =0\) obtains from buying from firm L under the benchmark case (in the absence of regulation and green network effect) -

$$\begin{aligned} U = \frac{2\gamma \lambda (2 - \lambda (2\gamma + \omega ))}{3b} + \frac{\beta \omega ^2}{2} - \delta \omega + y \end{aligned}$$

Assuming \(\delta \) is sufficiently small, the condition \(\lambda (2\gamma + \omega ) < 2\) ensures that market is fully covered.

Similarly, we can derive a condition for the market to be fully covered under environmental regulation in the presence of green network effect. Substituting the equilibrium values from equation (16), (17) in equation (24), we get utility function as

$$\begin{aligned} U = \frac{3\gamma \lambda }{2b} + \frac{\alpha (9 - 8b\alpha )}{6(3 - 4b\alpha )} + \frac{\lambda ^2(2\gamma + \omega + t_e) (\omega + t_e)}{b} + \frac{\beta (\omega + t_e)^2}{2} - \frac{\lambda (\omega + t_e)(8b\alpha - 3)}{4b(3-4b\alpha )} - \delta (\omega + t_e) \end{aligned}$$

The equation (25) ensures that market is fully covered, i.e., for sufficiently small values of \(\delta \) and \(\lambda (\omega + t_e)\).

$$\begin{aligned} \frac{\lambda (\omega + t_e)(8b\alpha - 3)}{4b(3-4b\alpha )} + \delta (\omega + t_e) < \frac{3\gamma \lambda }{2b} + \frac{\alpha (9 - 8b\alpha )}{6(3 - 4b\alpha )} + \frac{\lambda ^2(2\gamma + \omega + t_e) (\omega + t_e)}{b} + \frac{\beta (\omega + t_e)^2}{2} \end{aligned}$$
(25)

Second order conditions for profit maximization

Absence of green network effect and no regulation

The second order conditions at the market equilibrium are given by (using equation (13), (14) and \(\alpha = t_e = 0\))

$$\begin{aligned} \frac{\partial ^2 \pi _H}{\partial s_{H}^{2}}= & {} -\frac{b(4 - 2\lambda (2\gamma + \omega ))}{27}<0 \\ \frac{\partial ^2 \pi _L}{\partial s_{L}^2}= & {} - \frac{b(8 + 5\lambda (2\gamma + \omega ))}{27} < 0 \end{aligned}$$

The second order conditions holds under A2.

Green network effect with environmental regulation

Using equation (13), (16) we get second order conditions at the market equilibrium as

$$\begin{aligned} \frac{\partial ^2 \pi _H}{\partial s_{H}^{2}}= & {} - \frac{b (9 - 16b\alpha ) (32 (b\alpha )^2 - 56b\alpha + 27)}{36 (3 - 4b\alpha )^2 (3 - 2b\alpha )}< 0 \\ \frac{\partial ^2 \pi _L}{\partial s_{L}^2}= & {} - \frac{b (9 - 8b\alpha ) (32 (b\alpha )^2 - 32b\alpha + 15)}{36 (3 - 4b\alpha )^2 (3 - 2b\alpha )} < 0 \end{aligned}$$

The above condition for high quality firm holds for \(\alpha < 9/16b\). The second order conditions is same for green network with no regulation.

Proof of proposition 1

Impact of green network effect with emission tax

  1. (i)

    From equation (16), we have \(\frac{ds_i^{**}}{d\alpha } = \frac{3}{(3 - 4 b \alpha )^2} > 0\)

  2. (ii)

    From equation (17),we have

    $$\begin{aligned} \frac{dp_H^{**}}{d\alpha }= & {} -\frac{2}{3} + \frac{3(9 - 8b\alpha )}{4(3 - 4b\alpha )^3} - \frac{3\lambda (2\gamma + \omega + t_e)}{(3 - 4b\alpha )^2}> 0 \\ \frac{dp_L^{**}}{d\alpha }= & {} -\frac{1}{3} + \frac{9}{4(3 - 4b\alpha )^3} - \frac{3\lambda (2\gamma + \omega + t_e)}{(3 - 4b\alpha )^2}> 0 \end{aligned}$$
  3. (iii)

    From equation (17),we have

    $$\begin{aligned} \frac{dq_H^{**}}{d\alpha }= & {} -\frac{2b}{(3 - 4b\alpha )^2} < 0 \\ \frac{dq_L^{**}}{d\alpha }= & {} \frac{2b}{(3 - 4b\alpha )^2} > 0 \end{aligned}$$
  4. (iv)

    From equation (17),we have

    $$\begin{aligned} \frac{d\pi _H^{**}}{d\alpha }= & {} -\frac{(9 - 16b\alpha ) (63 - 108b\alpha + 64 (b\alpha )^2)}{36(3 - 4b\alpha )^3} < 0 \\ \frac{d\pi _L^{**}}{d\alpha }= & {} \frac{(9 -8b\alpha )( 9 + 36b\alpha - 32(b\alpha )^2)}{36(3 - 4b\alpha )^3} > 0 \end{aligned}$$
  5. (v)

    From equation (16), we have \(\Delta s^{**} = s_H^{**} - s_L^{**} = 3/2b\)

  6. (vi)

    By substituting \(t_e = 0\) in equation (16) and (17), it can be seen that above results hold for green network effect without environmental regulation.

Proof of proposition 2

Impact of emission tax in the absence of green network effect

The values \(\hat{s_i}\), \(\hat{p_i}\), \(\hat{q_i}\) and \(\hat{\pi _i}\) denote qualities, prices, quantity and profits under absence of green network without environmental regulation. It is calculated by replacing \(\omega \) with \((\omega + t_e)\) in equations (14) and (15).

  1. (i)

    From equation (14), we have \(\frac{d\hat{s_H}}{dt_e} = -\frac{2\lambda }{3b} < 0\) and \(\frac{d\hat{s_L}}{dt_e} = 0.\)

  2. (ii)

    From equation (15), we have \(\frac{d\hat{p_H}}{dt_e} = -\frac{20\lambda (2 - \lambda (2\gamma + \omega + t_e))}{27b} < 0\) and \(\frac{d\hat{p_L}}{dt_e} = -\frac{2\lambda (1 + 4\lambda (2\gamma + \omega + t_e))}{27b} < 0\).

  3. (iii)

    From equation (15), we have \(\frac{d\hat{q_H}}{dt_e} = -\frac{2\lambda }{9} < 0\) and \(\frac{d\hat{q_L}}{dt_e} = \frac{2\lambda }{9} > 0\).

  4. (iv)

    From equation (15), we have \(\frac{d\hat{\pi _H}}{dt_e} = -\frac{6\lambda (2 - \lambda (2\gamma + \omega + t_e))^2}{2187b} < 0\) and \(\frac{d\hat{\pi _L}}{dt_e} = \frac{\lambda (1 - 2\lambda (2\gamma + \omega + t_e))(5 + 2\lambda (2\gamma + \omega + t_e))}{1458b} \gtrless 0\) for \(\lambda (2\gamma + \omega + t_e) \lessgtr 1/2\)

  5. (v)

    From equation (14), \(\Delta {\hat{s}} \equiv (\hat{s_H} - \hat{s_L}) = \frac{4 - 2\lambda (2\gamma + \omega + t_e)}{3b}\) and \(\frac{\Delta {\hat{s}}}{dt_e} = -\frac{2\lambda }{3b} < 0\)

Proof of proposition 3

Impact of emission tax under green network

  1. (i)

    From equation (16),we have \(\frac{ds_H^{**}}{dt_e} = \frac{ds_L^{**}}{dt_e} = -\frac{\lambda }{b} < 0\).

  2. (ii)

    Change in the prices can be written as

    $$\begin{aligned} \frac{dp_i^{**}}{dt_e}= & {} \frac{\partial p_i^{**}}{\partial s_H^{**}} \frac{ds_H^{**}}{dt_e} + \frac{\partial p_i^{**}}{\partial s_L^{**}} \frac{ds_L^{**}}{dt_e} + \frac{\partial p_i^{**}}{\partial t_e}, i = H,L \end{aligned}$$

    Using equation (10) and \(\frac{ds_H^{**}}{dt_e} = \frac{ds_L^{**}}{dt_e} = -\frac{\lambda }{b}\), we have

    $$\begin{aligned} \frac{dp_H^{**}}{dt_e}= & {} \frac{b(2s_H^{**} + s_L^{**})\frac{ds_H^{**}}{dt_e}}{3} - \frac{\lambda \Delta s^{**}}{3} = -\lambda s_H^{**}< 0 \\ \frac{dp_L^{**}}{dt_e}= & {} \frac{b(s_H^{**} + 2s_L^{**})\frac{ds_H^{**}}{dt_e}}{3} + \frac{\lambda \Delta s^{**}}{3} = -\lambda s_L^{**} < 0 \end{aligned}$$
  3. (iii)

    Change in the quantity can be written as

    $$\begin{aligned} \frac{dq_i^{**}}{dt_e}= & {} \frac{\partial q_i^{**}}{\partial s_H^{**}} \frac{ds_H^{**}}{dt_e} + \frac{\partial q_i^{**}}{\partial s_L^{**}} \frac{ds_L^{**}}{dt_e} + \frac{\partial q_i^{**}}{\partial t_e}, i = H,L \end{aligned}$$

    Using equation (11) and \(\frac{ds_H^{**}}{dt_e} = \frac{ds_L^{**}}{dt_e} = -\frac{\lambda }{b}\), we have

    $$\begin{aligned} \frac{dq_H^{**}}{dt_e}= & {} -\frac{b\Delta s^{**}\frac{ds_H^{**}}{dt_e}}{3(\Delta s^{**} - \alpha )} - \frac{\lambda \Delta s^{**}}{3(\Delta s^{**} - \alpha )} = 0 \\ \frac{dq_L^{**}}{dt_e}= & {} \frac{b\Delta s^{**}\frac{ds_H^{**}}{dt_e}}{3(\Delta s^{**} - \alpha )} + \frac{\lambda \Delta s^{**}}{3(\Delta s^{**} - \alpha )} = 0 \end{aligned}$$
  4. (iv)

    Change in the profits can be written as

    $$\begin{aligned} \frac{d\pi _i^{**}}{dt_e}= & {} \frac{\partial \pi _i^{**}}{\partial s_H^{**}} \frac{ds_H^{**}}{dt_e} + \frac{\partial \pi _i^{**}}{\partial s_L^{**}} \frac{ds_L^{**}}{dt_e} + \frac{\partial \pi _i^{**}}{\partial t_e}, i = H,L \end{aligned}$$

    Using equation (12) and \(\frac{ds_H^{**}}{dt_e} = \frac{ds_L^{**}}{dt_e} = -\frac{\lambda }{b}\), we have

    $$\begin{aligned} \frac{d\pi _H^{**}}{dt_e}= & {} \frac{d\pi _L^{**}}{dt_e} = 0 \end{aligned}$$
  5. (v)

    Using equation (16), \(\Delta {s}^{**} \equiv ({s_H}^{**} - {s_L}^{**}) = \frac{3}{2b}\)

Proof of proposition 4

The total emissions are given by \(E = e_Hq_H + e_Lq_L\). Using \(p_z = 1\) and \(e_i = x_i = \lambda s_i - \beta (\omega + t_e) + \delta \), we get \(E = \lambda (s_H q_H + s_L q_L) - \beta (\omega + t_e) + \delta \). We calculate total emissions by substituting the values of \(s_H\), \(s_L\), \(q_H\) and \(q_L\) for each case discussed below.

Benchmark case- absence of green network effect and no regulation

Using equation (14) and (15) we get total emissions as

$$\begin{aligned} E^{*} = \frac{4\lambda (2 - \lambda (2\gamma + \omega ))^2}{27b} - \beta \omega + \delta \end{aligned}$$

Environmental regulation in absence of green network effect

Replacing \(\omega \) with (\(\omega + t_e)\) in benchmark case, we get total emissions as

$$\begin{aligned} \hat{E} = \frac{4\lambda (2 - \lambda (2\gamma + \omega + t_e))^2}{27b} - \beta (\omega + t_e) + \delta \end{aligned}$$

Green network effect without environmental regulation

Using equations (16), (17) and \(t_e = 0\) we get total emissions as

$$\begin{aligned} \widetilde{E} = \frac{\lambda (9 - 24b\alpha + 16(b\alpha )^2)}{2b(3 - 4b\alpha )^2} - \frac{\lambda ^2 (2\gamma + \omega )}{b} - \beta \omega + \delta \end{aligned}$$

Green network effect with environmental regulation

Using equations (16) and (17) we get total emissions as

$$\begin{aligned} E^{**} = \frac{\lambda (9 - 24b\alpha + 16(b\alpha )^2)}{2b(3 - 4b\alpha )^2} - \frac{\lambda ^2 (2\gamma + \omega + t_e)}{b} - \beta (\omega + t_e) + \delta \end{aligned}$$

It can be clearly seen that \(E^{*} > \hat{E}\) and \(\widetilde{E} > E^{**}\). For sufficiently small values of \(\beta \) and \(3/8b< \alpha < 9/16b\) we observe that \(\hat{E} > \widetilde{E}\). Thus, \(E^{*}> \hat{E}> \widetilde{E} > E^{**}.\)

Proof of proposition 6

Optimal tax rate under green network effect with environmental regulation

Using equation (22) and substituting the equilibrium values of \(s_H\), \(s_L\) and \(\theta _2 = q_L\) from equation (16, 17) we get -

$$\begin{aligned} \frac{dW}{dt_e} = \frac{3\lambda }{2b(3 - 4b\alpha )} - \frac{\lambda (1 + 4\lambda \gamma )}{2b} -\frac{(\lambda ^2 + \beta b)t_e}{b} \end{aligned}$$

The optimal tax rate is obtained by setting \(\frac{dW}{dt_e} = 0\), is given by

$$\begin{aligned} t_e^{**} = \frac{2\lambda (b\alpha - \lambda \gamma (3 -4b\alpha ))}{(3-4b\alpha )(\beta b + \lambda ^2)} \end{aligned}$$

For \(\alpha > \frac{3\lambda \gamma }{b(1 + 4\lambda \gamma )}\), optimal tax rate is positive, \(t_e^{**} > 0\).

The effect \(\alpha \) and \(\gamma \) on opitmal tax rate is given by

$$\begin{aligned} \begin{aligned} \frac{dt_e^{**}}{d\alpha } =&\frac{6\lambda b}{ (\beta b + \lambda ^2)(3 - 4b\alpha )^2} > 0\\ \frac{dt_e^{**}}{d\gamma } =&\frac{-2\lambda ^2}{ (\beta b + \lambda ^2)} < 0 \\ \end{aligned} \end{aligned}$$

Optimal tax rate under absence of green network effect with environmental Regulation

Using equation (22) and substituting the equilibrium values of \(s_H\), \(s_L\) and \(\theta _2 = q_L\) from equation (14, 15) we get -

$$\begin{aligned} \frac{dW}{dt_e}|t_e = 0 = \frac{\lambda }{243b} (328\lambda ^2(2\gamma + \omega )^2 + 524\lambda (2\gamma + \omega ) - 209) - \frac{2\lambda ^2 \gamma }{3b} \end{aligned}$$

The optimum is achieved with a small positive emission tax - \(t_e > 0\) if \(328\lambda ^2(2\gamma + \omega )^2 + 524\lambda (2\gamma + \omega ) > 162\lambda \gamma + 209\) which holds for \(\lambda (2\gamma +\omega )>0.33\).

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Grover, C., Bansal, S. Effect of green network and emission tax on consumer choice under discrete continuous framework. Environ Econ Policy Stud (2021). https://doi.org/10.1007/s10018-021-00312-y

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Keywords

  • Conflicting quality dimensions
  • Discrete-continuous
  • Emission tax
  • Green network effect
  • Vertical differentiation