# American Institute of Mathematical Sciences

• Previous Article
Producing two substitutable products under a supply chain including two manufacturers and one retailer: A game-theoretic approach
• JIMO Home
• This Issue
• Next Article
Open-loop equilibrium strategy for mean-variance Portfolio selection with investment constraints in a non-Markovian regime-switching jump-diffusion model
doi: 10.3934/jimo.2022049
Online First

Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.

Readers can access Online First articles via the “Online First” tab for the selected journal.

## Study on government subsidy in a two-level supply chain of direct-fired biomass power generation based on contract coordination

 1 School of Economics and Management Beijing Forestry University, Beijing, 100091, China 2 Neusoft Education Technology Group, Dalian Neusoft University of Information, Dalian, 116023, China 3 School of Economics and Management, Zhengzhou University of Light Industry, Zhengzhou, 450001, China

*Corresponding author: Kun Fan

Received  August 2021 Revised  January 2022 Early access April 2022

Fund Project: The research is supported by Ministry of Education Humanities and Social Sciences Foundation of China (No.21YJA630012)and Beijing Municipal Social Science Foundation (No.16GLC059)

Biomass power generation is helpful to build a clean, low-carbon, and green energy system, but the shortage of raw materials supply severely restricts the development of the biomass power generation industry in China. To solve problems of supply chain disharmony and low efficiency of government subsidy caused by stochastic factors in biomass power supply chain, this paper studies the decision-making of government subsidy on biomass power generation supply chain. First, a two-level supply chain model under stochastic supply and stochastic output environment is built. The two-level supply chain consists of farmers and the biomass power plant. Second, to achieve the coordination of the two-level supply chain through the calculation of the model, it sets up the combined contract model based on surplus compensation, shortage penalty, and revenue sharing. Then, the validity of the contract is demonstrated by the data obtained from the field survey. Finally, depending on the model and contract coordination results of the supply chain, the impacts of government subsidies on two members' decision-making are analyzed, and the changes of members' profits and chain's profits are discussed. Therefore, the government subsidy strategy for biomass direct-fired power generation is proposed.

Citation: Kun Fan, Wenjin Mao, Hua Qu, Xinning Li, Meng Wang. Study on government subsidy in a two-level supply chain of direct-fired biomass power generation based on contract coordination. Journal of Industrial and Management Optimization, doi: 10.3934/jimo.2022049
##### References:
 [1] L. Ari, A. Antti, K. Jyrki-Pekko, P. Marjo and S. Lauri, Improving the financial performance of solid forest fuel supply using a simple moisture and dry matter loss simulation and optimization, Biomass and Bioenergy, 116 (2018), 72-79. [2] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [3] R. Fan, L. Dong, E. Policy and and N. France, The dynamic analysis and simulation of government subsidy strategies in low-carbon diffusion considering the behavior of heterogeneous agents, Energy Policy, 117 (2018), 252-262. [4] A. Ghadge, S. Dani, R. Ojha and N. Caldwell, Using risk sharing contracts for supply chain risk mitigation: A buyer-supplier power and dependence perspective, Computers and Industrial Engineering, 103 (2017), 262-270.  doi: 10.1016/j.cie.2016.11.034. [5] B. C. Giri, S. Bardhan and T. Maiti, Coordinating a three-layer supply chain with uncertain demand and random yield, International Journal of Production Research, 54 (2017), 1-20. [6] B. C. Giri, J. K. Majhi, S. Bardhan and K. S. Chaudhuri, Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield, Ann. Oper. Res., 307 (2021), 175-206.  doi: 10.1007/s10479-021-04257-z. [7] A. Hafezalkotob, Competition of two green and regular supply chains under environmental protection and revenue seeking policies of government, Computers and Industrial Engineering, 82 (2015), 103-114. [8] J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11. [9] B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193. [10] C. Jing, Returns with wholesale-price-discount contract in a newsvendor problem, International Journal of Production Economics, 130 (2011), 104-111. [11] J. Li, Y. Li and S. Zhang, Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies, J. Ind. Manag. Optim., 16 (2020), 2065-2086.  doi: 10.3934/jimo.2019043. [12] Y. Li and Y. Wei, Research on green supply chain coordination considering stochastic demand and blockchain doncepts, Systems Engineering, (2021). [13] C. H. Lim and H. L. Lam, Biomass supply chain optimisation via novel biomass element life cycle Analysis (BELCA), Applied Energy, 161 (2016), 733-745. [14] Q. Lin, Q. Zhao and B. Lev, Influenza vaccine supply chain coordination under uncertain supply and demand, European J. Oper. Res., 297 (2022), 930-948.  doi: 10.1016/j.ejor.2021.05.025. [15] F. Morandi and H. Ostergard, Sustainability assessment of two chains of biomass supply from field to bioenergy, Dtu Sustain Conference, (2014). [16] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, (2008). [17] F. Salimi and B. Vandani, Designing a bio-fuel network considering links reliability and risk-pooling effect in bio-refineries, Reliability Engineering and System Safety, 174 (2018), 96-107. [18] J. J. Spengler, Vertical integration and antitrust policy, Journal of Political Economy, 58 (1950), 347-352. [19] C. Wang, W. Wang and R. Huang, Supply chain enterprise operations and government carbon tax decisions considering carbon emissions, Journal of Cleaner Production, 152 (2017), 271-280. [20] G. Xie, Cooperative strategies for sustainability in a decentralized supply chain with competing suppliers, Journal of Cleaner Production, 113 (2016), 807-821. [21] J. Yan and G. H. Zheng, Coordination contracts for supply chain considering supply disruption and loss aversion, Journal of Railway Science and Engineering, 17 (2020), 9. [22] H. Yang and W. Chen, Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing, Omega, 78 (2018), 179-191. [23] H. Yang, Y. Sun and Y. Gong, The agricultural supply chain dontracts under random yield, Systems Engineering, (2021). [24] S. Yang, J. Yang and L. Abdel-Malek, Sourcing with random yields and stochastic demand: A newsvendor approach, Computers & Operations Research, 34 (2007), 3682-3690. [25] F. Ye, Y. Li, Q. Lin and Y. Zhan, Modeling of China's cassava-based bioethanol supply chain operation and coordination, Energy, 120 (2017), 217-228. [26] S. Zhao and Q. Zhu, Remanufacturing supply chain coordination under the stochastic remanufacturability rate and the random demand, Ann. Oper. Res., 257 (2017), 661-695.  doi: 10.1007/s10479-015-2021-3.

show all references

##### References:
 [1] L. Ari, A. Antti, K. Jyrki-Pekko, P. Marjo and S. Lauri, Improving the financial performance of solid forest fuel supply using a simple moisture and dry matter loss simulation and optimization, Biomass and Bioenergy, 116 (2018), 72-79. [2] G. P. Cachon, Supply chain coordination with contracts, Handbooks in Operations Research and Management Science, 11 (2003), 227-339.  doi: 10.1016/S0927-0507(03)11006-7. [3] R. Fan, L. Dong, E. Policy and and N. France, The dynamic analysis and simulation of government subsidy strategies in low-carbon diffusion considering the behavior of heterogeneous agents, Energy Policy, 117 (2018), 252-262. [4] A. Ghadge, S. Dani, R. Ojha and N. Caldwell, Using risk sharing contracts for supply chain risk mitigation: A buyer-supplier power and dependence perspective, Computers and Industrial Engineering, 103 (2017), 262-270.  doi: 10.1016/j.cie.2016.11.034. [5] B. C. Giri, S. Bardhan and T. Maiti, Coordinating a three-layer supply chain with uncertain demand and random yield, International Journal of Production Research, 54 (2017), 1-20. [6] B. C. Giri, J. K. Majhi, S. Bardhan and K. S. Chaudhuri, Coordinating a three-level supply chain with effort and price dependent stochastic demand under random yield, Ann. Oper. Res., 307 (2021), 175-206.  doi: 10.1007/s10479-021-04257-z. [7] A. Hafezalkotob, Competition of two green and regular supply chains under environmental protection and revenue seeking policies of government, Computers and Industrial Engineering, 82 (2015), 103-114. [8] J. Heydari, K. Govindan and R. Sadeghi, Reverse supply chain coordination under stochastic remanufacturing capacity, International Journal of Production Economics, 202 (2018), 1-11. [9] B. Hu and Y. Feng, Optimization and coordination of supply chain with revenue sharing contracts and service requirement under supply and demand uncertainty, International Journal of Production Economics, 183 (2017), 185-193. [10] C. Jing, Returns with wholesale-price-discount contract in a newsvendor problem, International Journal of Production Economics, 130 (2011), 104-111. [11] J. Li, Y. Li and S. Zhang, Optimal expansion timing decisions in multi-stage PPP projects involving dedicated asset and government subsidies, J. Ind. Manag. Optim., 16 (2020), 2065-2086.  doi: 10.3934/jimo.2019043. [12] Y. Li and Y. Wei, Research on green supply chain coordination considering stochastic demand and blockchain doncepts, Systems Engineering, (2021). [13] C. H. Lim and H. L. Lam, Biomass supply chain optimisation via novel biomass element life cycle Analysis (BELCA), Applied Energy, 161 (2016), 733-745. [14] Q. Lin, Q. Zhao and B. Lev, Influenza vaccine supply chain coordination under uncertain supply and demand, European J. Oper. Res., 297 (2022), 930-948.  doi: 10.1016/j.ejor.2021.05.025. [15] F. Morandi and H. Ostergard, Sustainability assessment of two chains of biomass supply from field to bioenergy, Dtu Sustain Conference, (2014). [16] B. A. Pasternack, Optimal pricing and return policies for perishable commodities, Marketing Science, (2008). [17] F. Salimi and B. Vandani, Designing a bio-fuel network considering links reliability and risk-pooling effect in bio-refineries, Reliability Engineering and System Safety, 174 (2018), 96-107. [18] J. J. Spengler, Vertical integration and antitrust policy, Journal of Political Economy, 58 (1950), 347-352. [19] C. Wang, W. Wang and R. Huang, Supply chain enterprise operations and government carbon tax decisions considering carbon emissions, Journal of Cleaner Production, 152 (2017), 271-280. [20] G. Xie, Cooperative strategies for sustainability in a decentralized supply chain with competing suppliers, Journal of Cleaner Production, 113 (2016), 807-821. [21] J. Yan and G. H. Zheng, Coordination contracts for supply chain considering supply disruption and loss aversion, Journal of Railway Science and Engineering, 17 (2020), 9. [22] H. Yang and W. Chen, Retailer-driven carbon emission abatement with consumer environmental awareness and carbon tax: Revenue-sharing versus Cost-sharing, Omega, 78 (2018), 179-191. [23] H. Yang, Y. Sun and Y. Gong, The agricultural supply chain dontracts under random yield, Systems Engineering, (2021). [24] S. Yang, J. Yang and L. Abdel-Malek, Sourcing with random yields and stochastic demand: A newsvendor approach, Computers & Operations Research, 34 (2007), 3682-3690. [25] F. Ye, Y. Li, Q. Lin and Y. Zhan, Modeling of China's cassava-based bioethanol supply chain operation and coordination, Energy, 120 (2017), 217-228. [26] S. Zhao and Q. Zhu, Remanufacturing supply chain coordination under the stochastic remanufacturability rate and the random demand, Ann. Oper. Res., 257 (2017), 661-695.  doi: 10.1007/s10479-015-2021-3.
The expected profit of whole supply chain under centralized decision-making
Expected profit of farmers and foresters and the biomass power plant respectly
Profit of the supply chain under different subsidy distribution policies
Situation under different subsidy distribution policies when total subsidy value = 350
 $r_A$ $r_B$ r b $\lambda$ x q 0 7/18 259 55 $13.64\%$ 161135 173087 10 17/45 265 47 $11.63\%$ 164141 173020 20 11/30 271 38 $9.52\%$ 167091 172956 30 16/45 278 29 $7.32\%$ 169989 172895 40 31/90 285 20 $5.00\%$ 172838 172838 50 1/3 292 10 $2.56\%$ 175639 172783
 $r_A$ $r_B$ r b $\lambda$ x q 0 7/18 259 55 $13.64\%$ 161135 173087 10 17/45 265 47 $11.63\%$ 164141 173020 20 11/30 271 38 $9.52\%$ 167091 172956 30 16/45 278 29 $7.32\%$ 169989 172895 40 31/90 285 20 $5.00\%$ 172838 172838 50 1/3 292 10 $2.56\%$ 175639 172783
Situation under different subsidy distributions when total subsidy value = 200
 $r_A$ $r_B$ $E(\pi_A)$ $E(\pi_B)$ $E(\pi_C)$ x q 0 2/9 2999732 18998304 21998036 155921 167486 10 19/90 2455410 18661118 21116528 158725 167310 20 1/5 1928749 18323116 20251865 161468 167135 30 17/90 1419743 17983412 19403156 164153 166959 40 8/45 928479 17641108 18569587 166783 166783 50 1/6 455139 17295277 17750416 169359 166605
 $r_A$ $r_B$ $E(\pi_A)$ $E(\pi_B)$ $E(\pi_C)$ x q 0 2/9 2999732 18998304 21998036 155921 167486 10 19/90 2455410 18661118 21116528 158725 167310 20 1/5 1928749 18323116 20251865 161468 167135 30 17/90 1419743 17983412 19403156 164153 166959 40 8/45 928479 17641108 18569587 166783 166783 50 1/6 455139 17295277 17750416 169359 166605
Situation under different subsidy distribution policies
 $r_A$ $r_B$ $E(\pi_A)$ $E(\pi_B)$ $E(\pi_C)$ x q 0 0 -1407826 -8916234 -10324060 144216 154913 10 0 -1116079 -8482206 -9598285 147293 155260 20 0 -843398 -8012288 -8855686 150340 155617 30 0 -592460 -7504496 -8096956 153361 155983 40 0 -366136 -6956586 -7322722 156358 156358 50 0 -167527 -6366028 -6533555 159334 156743 0 0.057 -310685 -1967673 -2278359 148015 158994 10 0.057 -178318 -1355214 -1533532 151145 159321 20 0.057 -73484 -698095 -771579 154244 159658 30 0.057 496 6284 6780 157314 160003 40 0.057 40045 760846 800891 160357 160357 50 0.057 41286 1568873 1610159 163376 160719 0 0.157 1675358 10610602 12285960 153230 164596 10 0.157 1518248 11538685 13056933 156431 164893 20 0.157 1318612 12526818 13845431 159597 165198 30 0.157 1072002 13578691 14650692 162729 165511 40 0.157 773601 14698425 15472027 165831 165831 50 0.157 418174 15890630 16308805 168905 166159 0 0.257 3712806 23514436 27227242 157182 168841 10 0.257 3257909 24760109 28018018 160434 169112 20 0.257 2745391 26081216 28826607 163647 169390 30 0.257 2169674 27482542 29652217 166824 169675 40 0.257 1524706 28969420 30494127 169967 169967 50 0.257 803889 30547792 31351681 173080 170266 0 0.357 5783661 36629858 42413519 160282 172171 10 0.357 5025561 38194268 43219829 163572 172420 20 0.357 4194682 39849485 44044167 166820 172676 30 0.357 3284320 41601399 44885719 170031 172937 40 0.357 2287187 43456554 45743741 173205 173205 50 0.357 1195321 45422232 46617553 176346 173479
 $r_A$ $r_B$ $E(\pi_A)$ $E(\pi_B)$ $E(\pi_C)$ x q 0 0 -1407826 -8916234 -10324060 144216 154913 10 0 -1116079 -8482206 -9598285 147293 155260 20 0 -843398 -8012288 -8855686 150340 155617 30 0 -592460 -7504496 -8096956 153361 155983 40 0 -366136 -6956586 -7322722 156358 156358 50 0 -167527 -6366028 -6533555 159334 156743 0 0.057 -310685 -1967673 -2278359 148015 158994 10 0.057 -178318 -1355214 -1533532 151145 159321 20 0.057 -73484 -698095 -771579 154244 159658 30 0.057 496 6284 6780 157314 160003 40 0.057 40045 760846 800891 160357 160357 50 0.057 41286 1568873 1610159 163376 160719 0 0.157 1675358 10610602 12285960 153230 164596 10 0.157 1518248 11538685 13056933 156431 164893 20 0.157 1318612 12526818 13845431 159597 165198 30 0.157 1072002 13578691 14650692 162729 165511 40 0.157 773601 14698425 15472027 165831 165831 50 0.157 418174 15890630 16308805 168905 166159 0 0.257 3712806 23514436 27227242 157182 168841 10 0.257 3257909 24760109 28018018 160434 169112 20 0.257 2745391 26081216 28826607 163647 169390 30 0.257 2169674 27482542 29652217 166824 169675 40 0.257 1524706 28969420 30494127 169967 169967 50 0.257 803889 30547792 31351681 173080 170266 0 0.357 5783661 36629858 42413519 160282 172171 10 0.357 5025561 38194268 43219829 163572 172420 20 0.357 4194682 39849485 44044167 166820 172676 30 0.357 3284320 41601399 44885719 170031 172937 40 0.357 2287187 43456554 45743741 173205 173205 50 0.357 1195321 45422232 46617553 176346 173479
Profit statement of biomass power plant under different subsidies when $r_A$ = 20
 $r_B$ $r_B+p_B$ x Q $R(\pi_B)$ $C(\pi_B)$ $E(\pi_B)$ p 0 0.393 150340 155617 57988171 66000459 -8012288 -13.82% 0.007 0.4 150862 156157 59200760 66326206 -7125446 -12.04% 0.057 0.45 154244 159658 67808514 68506609 -698095 -1.03% 0.107 0.5 157120 162635 76338929 70475997 5862932 7.68% 0.157 0.55 159596 165198 84805198 72278380 12526818 14.77% 0.207 0.6 161753 167430 93218692 73947086 19271606 20.67% 0.257 0.65 163647 169390 101586998 75505782 26081216 25.67% 0.307 0.7 165324 171127 109917862 76974277 32943585 29.97%
 $r_B$ $r_B+p_B$ x Q $R(\pi_B)$ $C(\pi_B)$ $E(\pi_B)$ p 0 0.393 150340 155617 57988171 66000459 -8012288 -13.82% 0.007 0.4 150862 156157 59200760 66326206 -7125446 -12.04% 0.057 0.45 154244 159658 67808514 68506609 -698095 -1.03% 0.107 0.5 157120 162635 76338929 70475997 5862932 7.68% 0.157 0.55 159596 165198 84805198 72278380 12526818 14.77% 0.207 0.6 161753 167430 93218692 73947086 19271606 20.67% 0.257 0.65 163647 169390 101586998 75505782 26081216 25.67% 0.307 0.7 165324 171127 109917862 76974277 32943585 29.97%
 [1] Xiaohong Chen, Kui Li, Fuqiang Wang, Xihua Li. Optimal production, pricing and government subsidy policies for a closed loop supply chain with uncertain returns. Journal of Industrial and Management Optimization, 2020, 16 (3) : 1389-1414. doi: 10.3934/jimo.2019008 [2] Xue-Yan Wu, Zhi-Ping Fan, Bing-Bing Cao. Cost-sharing strategy for carbon emission reduction and sales effort: A nash game with government subsidy. Journal of Industrial and Management Optimization, 2020, 16 (4) : 1999-2027. doi: 10.3934/jimo.2019040 [3] Sushil Kumar Dey, Bibhas C. Giri. Coordination of a sustainable reverse supply chain with revenue sharing contract. Journal of Industrial and Management Optimization, 2022, 18 (1) : 487-510. doi: 10.3934/jimo.2020165 [4] Chuong Van Nguyen, Phuong Huu Hoang, Hyo-Sung Ahn. Distributed optimization algorithms for game of power generation in smart grid. Numerical Algebra, Control and Optimization, 2019, 9 (3) : 327-348. doi: 10.3934/naco.2019022 [5] Han Zhao, Bangdong Sun, Hui Wang, Shiji Song, Yuli Zhang, Liejun Wang. Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk. Discrete and Continuous Dynamical Systems - S, 2022  doi: 10.3934/dcdss.2022021 [6] Xiaojiao Tong, Felix F. Wu, Jifeng Su. Quadratic approximation and visualization of online contract-based available transfer capability region of power systems. Journal of Industrial and Management Optimization, 2008, 4 (3) : 553-563. doi: 10.3934/jimo.2008.4.553 [7] Yuan-Hang Su, Wan-Tong Li, Fei-Ying Yang. Effects of nonlocal dispersal and spatial heterogeneity on total biomass. Discrete and Continuous Dynamical Systems - B, 2019, 24 (9) : 4929-4936. doi: 10.3934/dcdsb.2019038 [8] Enrique R. Casares, Lucia A. Ruiz-Galindo, María Guadalupe García-Salazar. Transitional dynamics, externalities, optimal subsidy, and growth. Journal of Dynamics and Games, 2018, 5 (1) : 41-59. doi: 10.3934/jdg.2018005 [9] Xiaoxue Gong, Ying Xu, Vinay Mahadeo, Tulin Kaman, Johan Larsson, James Glimm. Mesh convergence for turbulent combustion. Discrete and Continuous Dynamical Systems, 2016, 36 (8) : 4383-4402. doi: 10.3934/dcds.2016.36.4383 [10] H. Thomas Banks, V. A. Bokil, Shuhua Hu, A. K. Dhar, R. A. Bullis, C. L. Browdy, F.C.T. Allnutt. Modeling shrimp biomass and viral infection for production of biological countermeasures. Mathematical Biosciences & Engineering, 2006, 3 (4) : 635-660. doi: 10.3934/mbe.2006.3.635 [11] Tone Arnold, Myrna Wooders. Dynamic club formation with coordination. Journal of Dynamics and Games, 2015, 2 (3&4) : 341-361. doi: 10.3934/jdg.2015010 [12] Zhisong Chen, Shong-Iee Ivan Su. Assembly system with omnichannel coordination. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1863-1889. doi: 10.3934/jimo.2021047 [13] Jun Wu, Shouyang Wang, Wuyi Yue. Supply contract model with service level constraint. Journal of Industrial and Management Optimization, 2005, 1 (3) : 275-287. doi: 10.3934/jimo.2005.1.275 [14] Nikolaz Gourmelon. Generation of homoclinic tangencies by $C^1$-perturbations. Discrete and Continuous Dynamical Systems, 2010, 26 (1) : 1-42. doi: 10.3934/dcds.2010.26.1 [15] Michael Baur, Marco Gaertler, Robert Görke, Marcus Krug, Dorothea Wagner. Augmenting $k$-core generation with preferential attachment. Networks and Heterogeneous Media, 2008, 3 (2) : 277-294. doi: 10.3934/nhm.2008.3.277 [16] Johannes Giannoulis. Transport and generation of macroscopically modulated waves in diatomic chains. Conference Publications, 2011, 2011 (Special) : 485-494. doi: 10.3934/proc.2011.2011.485 [17] Wenxiong Chen, Shijie Qi. Direct methods on fractional equations. Discrete and Continuous Dynamical Systems, 2019, 39 (3) : 1269-1310. doi: 10.3934/dcds.2019055 [18] John Leventides, Iraklis Kollias. Optimal control indicators for the assessment of the influence of government policy to business cycle shocks. Journal of Dynamics and Games, 2014, 1 (1) : 79-104. doi: 10.3934/jdg.2014.1.79 [19] Alejandro Cataldo, Juan-Carlos Ferrer, Pablo A. Rey, Antoine Sauré. Design of a single window system for e-government services: the chilean case. Journal of Industrial and Management Optimization, 2018, 14 (2) : 561-582. doi: 10.3934/jimo.2017060 [20] Elvio Accinelli, Filipe Martins, Humberto Muñiz, Bruno M. P. M. Oliveira, Alberto A. Pinto. Firms, technology, training and government fiscal policies: An evolutionary approach. Discrete and Continuous Dynamical Systems - B, 2021, 26 (11) : 5723-5754. doi: 10.3934/dcdsb.2021180

2021 Impact Factor: 1.411