# Joint Decisions on Production and Pricing with Strategic Consumers for Green Crowdfunding Products

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## Abstract

**:**

## 1. Introduction

#### Literature Review

## 2. Basic Model

## 3. The Crowdfunding Pricing Strategy Facing Different Types of Consumers

#### 3.1. Facing Strategic Consumers

**1.**${\mathit{v}}_{\mathbf{2}\mathit{A}}\mathbf{\le}{\mathit{v}}_{\mathbf{1}\mathit{B}}$

- (i)
- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, ${\phi}_{1}=\frac{\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}-p}{U}$
- (ii)
- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, ${\phi}_{2}=\frac{\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}-p}{U}$

**2.**${\mathit{v}}_{\mathbf{2}\mathit{A}}\mathbf{>}{\mathit{v}}_{\mathbf{1}\mathit{B}}$

- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, the probability of buying the green product in the second stage is ${\beta}_{3}={\beta}_{4}=\frac{U-\frac{{p}_{2A}-{p}_{1A}}{\delta Q\sigma (1-\lambda )}}{U}$
- (i)
- When $\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}<\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, the probability of participating in the crowdfunding is ${\phi}_{3}=\frac{\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}-p}{U}$
- (ii)
- When $\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}<\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}$ and $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, the probability of participating in the crowdfunding is ${\phi}_{4}=\frac{\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}-p}{U}$

- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, the probability of buying the green product in the second stage is ${\beta}_{5}={\beta}_{6}=\frac{U-\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}}{U}$
- (i)
- When $\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}>\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}$ and $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, the probability of participating in the crowdfunding is ${\phi}_{5}=\frac{\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}-p}{U}$
- (ii)
- When $\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}<\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, the probability of participating in the crowdfunding is ${\phi}_{6}=\frac{\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}-p}{U}$

- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, the probability of buying the green product in the second stage is ${\beta}_{7}=\frac{U-\frac{{p}_{2A}-{p}_{1A}}{\delta Q\sigma (1-\lambda )}}{U}$, and the probability of participating in the crowdfunding is ${\phi}_{7}=\frac{\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}-\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}}{U}$
- When $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}-p}{\sigma \delta Q-1}$, ${\beta}_{8}=\frac{U-\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}}{U}$, ${\phi}_{8}=\frac{\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}-\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}}{U}$

#### 3.2. Facing Myopic Consumers

- When ${v}_{1A}>{v}_{1B}$, $u>\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, the probability of participating in crowdfunding is ${\varphi}_{1}=\frac{U-\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}}{U}$
- When ${v}_{1A}<{v}_{1B}$, $u<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, ${\varphi}_{2}=\frac{\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}-p}{U}$
- When ${v}_{1A}={v}_{1B}$, $u=\frac{U}{2}$, ${\varphi}_{3}=\frac{U-\frac{U}{2}}{U}=\frac{1}{2}$

- When ${v}_{2A}>{v}_{2B}$, $u>\frac{{p}_{2A}+kg-p}{\sigma (\delta Q-1)}$, the probability of buying the green product in the second stage is ${\gamma}_{1}=\frac{U-\frac{{p}_{2A}+kg-p}{\sigma (\delta Q-1)}}{U}$
- When ${v}_{2A}<{v}_{2B}$, $u<\frac{{p}_{2A}+kg-p}{\sigma (\delta Q-1)}$, ${\gamma}_{2}=\frac{\frac{{p}_{2A}+kg-p}{\sigma (\delta Q-1)}-p}{U}$
- When ${v}_{2A}={v}_{2B}$, $u=\frac{U}{2}$, ${\gamma}_{3}=\frac{U-\frac{U}{2}}{U}=\frac{1}{2}$

#### 3.3. Facing Strategic and Myopic Consumers

**Lemma**

**1.**

## 4. Equilibrium Analysis

**1.**${\mathit{v}}_{\mathbf{2}\mathit{A}}\mathbf{\le}{\mathit{v}}_{\mathbf{1}\mathit{B}}$

**Proposition**

**1.**

- (i)
- if $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}\le \frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$,when given $\delta =\frac{1}{2}$, as shown in Figure 1:
- (a)
- volume strategy (L), if ${\xi}_{LD}(\alpha )\le \xi \le 1$ and ${\xi}_{LH}(\alpha )\le \xi \le 1$
- (b)
- intertemporal strategy (D), if ${\xi}_{DH}(\alpha )\le \xi \le {\xi}_{LD}(\alpha )$
- (c)
- margin strategy (H), if $0\le \xi \le {\xi}_{DH}(\alpha )$ and $0\le \xi \le {\xi}_{LH}(\alpha )$

when given $\delta =1$, as shown in Figure 2:- (a)
- volume strategy (L), if ${\xi}_{LD}(\alpha )\le \xi <1$
- (b)
- margin strategy (D), if $0<\xi <{\xi}_{LD}(\alpha )$

- (ii)
- If $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, as show in Figure 3,
- (a)
- volume strategy (L), if ${\xi}_{LD}(\alpha )\le \xi <1$
- (b)
- intertemporal strategy (D), if $0<\xi <{\xi}_{LD}(\alpha )$

**2.**${\mathit{v}}_{\mathbf{2}\mathit{A}}\mathbf{>}{\mathit{v}}_{\mathbf{1}\mathit{B}}$

**Proposition**

**2.**

- (i)
- when $\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}\le \frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$, as shown in Figure 4,
- (a)
- volume strategy (L), if ${\xi}_{LM}(\alpha )\le \xi <1$;
- (b)
- menu strategy (M), if $0\le \xi <{\xi}_{LM}(\alpha )$.

- (ii)
- when $\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}\le \frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, as shown in Figure 5,
- (a)
- volume strategy (L), if ${\xi}_{LD}(\alpha )\le \xi <1$, and ${\xi}_{LH}(\alpha )\le \xi <1$;
- (b)
- intertemporal strategy (D), if ${\xi}_{DH}(\alpha )\le \xi <{\xi}_{LD}(\alpha )$;
- (c)
- margin strategy (H), if $0<\xi <{\xi}_{LH}(\alpha )$ and $0<\xi <{\xi}_{DH}(\alpha )$;

**Proposition**

**3.**

- (i)
- when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, as shown in Figure 6,
- (a)
- volume strategy (L), if ${\xi}_{LM}(\alpha )\le \xi <1$ and ${\xi}_{LH}(\alpha )\le \xi <1$;
- (b)
- menu strategy (M), if ${\xi}_{MH}(\alpha )\le \xi <{\xi}_{LM}(\alpha )$
- (c)
- margin strategy (H), if $0<\xi <{\xi}_{LH}(\alpha )$ and $0<\xi <{\xi}_{MH}(\alpha )$;

- (ii)
- when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$, as shown in Figure 7,
- (a)
- volume strategy (L), if ${\xi}_{LM}(\alpha )\le \xi <1$;
- (b)
- menu strategy (M), if $0\le \xi <{\xi}_{LM}(\alpha )$.

## 5. Exploring the Influence of the Fraction of Strategic Consumers ($\mathit{\theta}$) on the Total Profits

## 6. Further Research

## 7. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

- Buysere, K.D. A Framework for European Crowdfunding; Report della Commissione Europea; European Crowdfunding Network: Brussels, Belgium, 2012. [Google Scholar]
- Kuppuswamy, V.; Bayus, B.L. Does my contribution to your crowdfunding project matter? J. Bus. Ventur.
**2017**, 32, 72–89. [Google Scholar] [CrossRef] - Qiu, C. Issues in crowdfunding: Theoretical and empirical investigation on kickstarter. SSRN Electr. J.
**2013**. [Google Scholar] [CrossRef] - Mollick, E. The dynamics of crowdfunding: An exploratory study. J. Bus. Ventur.
**2014**, 29, 1–16. [Google Scholar] [CrossRef] - Cumming, D.J.; Leboeuf, G.; Schwienbacher, A. Crowdfunding cleantech. Energy Econ.
**2017**, 65, 292–303. [Google Scholar] [CrossRef] - Lam, P.T.I.; Law, A.O.K. Crowdfunding for renewable and sustainable energy projects: An exploratory case study approach. Renew. Sustain. Energy Rev.
**2016**, 60, 11–20. [Google Scholar] [CrossRef] - Lao, K. Research on mechanism of consumer innovativeness influencing green consumption behavior. Nankai Bus. Rev.
**2013**, 5, 211–224. [Google Scholar] [CrossRef] - Tian, H.; Yuan, H. The contingent effect of corporate social responsibility fit on consumer brand attitude. Nankai Bus. Rev.
**2013**, 4, 349–364. [Google Scholar] [CrossRef] - Chen, Y.; Ge, C. An Analysis of the Long—Tail Effect of China’s Environmental Protection. Res. Prod.
**2016**, 10, 28–30. [Google Scholar] - Zhao, Q.; Chen, C.D.; Wang, J.L.; Chen, P.C. Determinants of backers’ funding intention in crowdfunding: Social exchange theory and regulatory focus. Telemat. Inform.
**2017**, 34, 370–384. [Google Scholar] [CrossRef] - Weng, Z.; Ge, C.; Chen, Y. Research on the Development of China’s Environmental Protection Public Welfare. Environ. Sustain. Dev.
**2015**, 40, 39–43. [Google Scholar] - Fan, J. Research on crowd-funding bussiness model. Enterp. Econ.
**2013**, 8, 72–75. [Google Scholar] - Davis, B.C.; Hmieleski, K.M.; Webb, J.W.; Coombs, J.E. Funders’ positive affective reactions to entrepreneurs’ crowdfunding pitches: The influence of perceived product creativity and entrepreneurial passion. J. Bus. Ventur.
**2017**, 32, 90–106. [Google Scholar] [CrossRef] - Cachon, G.P.; Swinney, R. Purchasing, pricing, and quick response in the presence of strategic consumers. Manag. Sci.
**2009**, 55, 497–511. [Google Scholar] [CrossRef] - Besanko, D.; Winston, W.L. Optimal Price Skimming by a Monopolist Facing Rational Consumers; INFORMS: Catonsville, MD, USA, 1990. [Google Scholar]
- Aydin, G.; Porteus, E.L. Joint inventory and pricing decisions for an assortment. Oper. Res.
**2008**, 56, 1247–1255. [Google Scholar] [CrossRef] - Agrawal, A.; Catalini, C.; Goldfarb, A. Some simple economics of crowdfunding. Innov. Policy Econ.
**2014**, 14, 63–97. [Google Scholar] [CrossRef] - Hu, M.; Li, X.; Shi, M. Product and pricing decisions in crowdfunding. Mark. Sci.
**2015**, 34, 331–345. [Google Scholar] [CrossRef] - Su, X. Intertemporal pricing with strategic customer behavior. Manag. Sci.
**2007**, 53, 726–741. [Google Scholar] [CrossRef] - Su, X.; Zhang, F. On the value of commitment and availability guarantees when selling to strategic consumers. Manag. Sci.
**2009**, 55, 713–726. [Google Scholar] [CrossRef] - Li, H.; Zhang, Y.; Zhong, W. Dynamic Prricing Strategies in the presence of strategic consumer behavior risks. J. Manag. Sci. China
**2012**, 15, 11–25. [Google Scholar] - Parlakturk, A.K. The Value of Product Variety When Selling to Strategic Consumers; INFORMS: Catonsville, MD, USA, 2012. [Google Scholar]
- Bi, G.; Wang, Y.; Ding, J. Dynamic pricing basedonsubstitutes and strategic consumers. J. Syst. Eng.
**2013**, 28, 47–54. [Google Scholar] - Zeng, H.; Zhang, Y. Intertemporal Pricing of Substitutes under the Coexistence of Myopic and Strategic Consumers. Syst. Eng.
**2015**, 65, 33–39. [Google Scholar] - Mussa, M.; Rosen, S. Monopoly and product quality. J. Econ. Theory
**1978**, 18, 301–317. [Google Scholar] [CrossRef] - Moorthy, K.S. Market Segmentation, Self-Selection, and Product Line Design; INFORMS: Catonsville, MD, USA, 1984. [Google Scholar]
- Desai, P.; Kekre, S.; Radhakrishnan, S.; Srinivasan, K. Product differentiation and commonality in design: Balancing revenue and cost drivers. Manag. Sci.
**2001**, 47, 37–51. [Google Scholar] [CrossRef] - Guo, L.; Zhang, J. Consumer Deliberation and Product Line Design; INFORMS: Catonsville, MD, USA, 2012. [Google Scholar]
- Mostafa, M.M. Egyptian consumers’ willingness to pay for carbon-labeled products: A contingent valuation analysis of socio-economic factors. J. Clean. Prod.
**2016**, 135, 821–828. [Google Scholar] [CrossRef] - Li, X.; Li, Y. Chain-to-chain competition on product sustainability. J. Clean. Prod.
**2016**, 112, 2058–2065. [Google Scholar] [CrossRef] - Liu, P. Pricing policies of green supply chain considering targeted advertising and product green degree in the big data environment. J. Clean. Prod.
**2017**. [Google Scholar] [CrossRef] - Jiang, S.-Y.; Li, S.-C. Green Supply Chain Game Models and Revenue Sharing Contract with Product Green Degree. Chin. J. Manag. Sci.
**2015**, 23, 169–176. [Google Scholar] - Aviv, Y.; Pazgal, A. Optimal Pricing of Seasonal Products in the Presence of Forward-Looking Consumers; INFORMS: Catonsville, MD, USA, 2008. [Google Scholar]

**Figure 1.**Comparison of the four strategies given $\delta =\frac{1}{2}$ when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}\le \frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$.

**Figure 2.**Comparison of the four strategies given $\delta =1$ when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}\le \frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$.

**Figure 3.**Comparison of the four strategies given $\delta =\frac{1}{2}$ when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}$.

**Figure 4.**Comparison of the four strategies given $\delta =2$ when $\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}\le \frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}.$

**Figure 5.**Comparison of the four strategies given $\delta =2$ when $\frac{{p}_{1A}+kg-p}{\lambda \sigma \delta Q-1}\le \frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$.

**Figure 6.**Comparison of the four strategies given $\delta =3$ when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}>\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$.

**Figure 7.**Comparison of the four strategies given $\delta =3$ when $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}<\frac{{p}_{2A}+kg-p}{\sigma \delta Q-1}$.

**Figure 8.**Comparison of the four strategies when ${v}_{2A}<{v}_{1B}$ and $\frac{{p}_{2A}-{p}_{1A}}{\sigma \delta Q(1-\lambda )}\le \frac{{p}_{1A}-p}{\lambda \sigma \delta Q-1}$.

**Figure 10.**Comparison of the profits of the margin strategy and the intertemporal strategy as a function of $\theta $ (intercepted from Figure 9).

Symbol | Mean |
---|---|

${p}_{1A}$ | The price of A in the first stage (decision variable) |

${p}_{2A}$ | The price of A in the second stage (decision variable) |

p | The price of B in the first and second stage |

${s}_{ij}$ | The consumer surplus of j (j = A, B) in the i (i = 1, 2) stage |

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## Share and Cite

**MDPI and ACS Style**

Chen, Y.; Zhang, R.; Liu, B.
Joint Decisions on Production and Pricing with Strategic Consumers for Green Crowdfunding Products. *Int. J. Environ. Res. Public Health* **2017**, *14*, 1090.
https://doi.org/10.3390/ijerph14091090

**AMA Style**

Chen Y, Zhang R, Liu B.
Joint Decisions on Production and Pricing with Strategic Consumers for Green Crowdfunding Products. *International Journal of Environmental Research and Public Health*. 2017; 14(9):1090.
https://doi.org/10.3390/ijerph14091090

**Chicago/Turabian Style**

Chen, Yuting, Rong Zhang, and Bin Liu.
2017. "Joint Decisions on Production and Pricing with Strategic Consumers for Green Crowdfunding Products" *International Journal of Environmental Research and Public Health* 14, no. 9: 1090.
https://doi.org/10.3390/ijerph14091090