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doi: 10.3934/jimo.2019110

## Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy

 1 Department of Information Management and Decision Sciences, School of Business Administration, Northeastern University, Shenyang 110169, China 2 State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110819, China

* Corresponding author: ZHI-PING FAN

Received  November 2018 Revised  March 2019 Published  September 2019

Fund Project: The study is supported in part by the National Natural Science Foundation of China (Project No. 71871049, 71772034) and the 111 Project (B16009).

To stimulate the capital-constrained manufacturer to produce green products, the government often adopts two incentive mechanisms: green credit (i.e., subsidy offered directly to bank) and subsidy (i.e., subsidy offered directly to manufacturer). This paper examines the optimal interest rate of the bank, and the optimal product green degree and sales price of the manufacturer under the two mechanisms, respectively. Furthermore, we investigate the effects of these mechanisms on the optimal decisions, the profits of players, the social welfare and the environmental benefits. Several important results are obtained. First, when the total government subsidy is low, the green credit mechanism can bring the higher green degree, product sales price and demand, as well as higher profits for the bank and manufacturer, rather than the subsidy mechanism. Otherwise, the result is opposite. Second, the government should adopt the green credit mechanism to support the manufacturer to develop green products when the budget is limited and relatively low. If the government budget is sufficient, the subsidy mechanism is the best choice, which can bring higher economic and environmental benefits.

Citation: Shuai Huang, Zhi-Ping Fan, Xiaohuan Wang. Optimal financing and operational decisions of capital-constrained manufacturer under green credit and subsidy. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019110
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show all references

##### References:
The green credit mechanism
The subsidy mechanism
The interest rate, product's green degree, sales price and market demand
The profits of the bank and the manufacturer
The social welfare and the environmental benefits
The profits of the bank and manufacturer under three scenarios
 ${\Pi ^B}$ ${\Pi ^M}$ Non-subsidy $\Pi _0^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2}} \right)}}$ $\Pi _0^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2}} \right)}}{{8\left( {2k - {\theta ^2}} \right)}}$ Green credit $\Pi _1^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}}$ $\Pi _1^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2} - 4k{\tau _1}} \right)}}{{8\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}}$ Subsidy $\Pi _2^{B*} = \frac{{{a^2}{\theta ^2}{{\left( {1 + {\tau _2}} \right)}^2}}}{{16\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}}$ $\Pi _2^{M*} = \frac{{{a^2}\left[ {4k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]\left( {1 + {\tau _2}} \right)}}{{8\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}}$
 ${\Pi ^B}$ ${\Pi ^M}$ Non-subsidy $\Pi _0^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2}} \right)}}$ $\Pi _0^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2}} \right)}}{{8\left( {2k - {\theta ^2}} \right)}}$ Green credit $\Pi _1^{B*} = \frac{{{a^2}{\theta ^2}}}{{16\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}}$ $\Pi _1^{M*} = \frac{{{a^2}\left( {4k - {\theta ^2} - 4k{\tau _1}} \right)}}{{8\left( {2k - {\theta ^2} - 2k{\tau _1}} \right)}}$ Subsidy $\Pi _2^{B*} = \frac{{{a^2}{\theta ^2}{{\left( {1 + {\tau _2}} \right)}^2}}}{{16\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}}$ $\Pi _2^{M*} = \frac{{{a^2}\left[ {4k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]\left( {1 + {\tau _2}} \right)}}{{8\left[ {2k - {\theta ^2}\left( {1 + {\tau _2}} \right)} \right]}}$
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