This paper, based on the numerical simulation research, has come out with findings, such as the sluggish interregional industrial transformation in China and the factors responsible for that, the need to define the new economic geography from the angle of geographic view, the need to have a theoretical model based on implementing development centre periphery, the use of element resources endowment system reference analysis, and the need for implementation of the numerical simulation of the model, and finally the need to clear the factors that influence the sluggish industrial transfer. The final results show that the factor resource endowment, transportation cost, and labour price are still impediments affecting industrial transfer. Since the development level of the manufacturing industry in eastern China has not reached the critical point of industrial transfer, it is necessary to to find out a pragmatic solution to achieve development.

#### Keywords

- Numerical simulation
- Industrial transformation
- Sluggish
- Factor resource endowment
- Transportation cost
- Labour
- The critical point

#### MSC 2010

- 76U05

According to the analysis of the current stagnating situation of the inter-regional industrial transfer in China, there are many reasons for this phenomenon, such as the increasing liquidity of factors, the changes in the market system and the advantages of market share and labour efficiency. This paper mainly starts with the relationship between industrial agglomeration and transfer, builds a model from the two aspects of labour distribution and manufacturer location, and studies the obstacles caused by industrial agglomeration efficiency on transfer [1].

It is assumed to be an economy composed of two regions

Similarly, the regional factor market has a competitive relationship, so the regional wages of all factors will be affected by marginal productivity, and the externality _{a}

Where, HA and HB represent the number of skilled labour within a region, while LA and LB represent the number of unskilled labour within a region.

Workers have the same preferences. The utility formula for skilled workers living in the region (

Since the above formula does not take into account the externalities of consumption, it is proved that the implicit assumption that the migration of skilled workers in and out of the country does not have much impact on the welfare of local residents is limited by wage differences:

In

Due to the _{a}_{b}

Due to the f′ (0) = ∞ and _{a}_{a}_{a}_{a}_{a}_{b}_{a}_{b}_{a}_{a}_{a}

Among them,

Among them, 0 <

Combined with the above formula analysis, the final migration equation can be obtained as follows:

Once again, we can get:

Combined with the above two formulas obtained by differential analysis, in _{a}^{m}_{a}^{m}_{a}^{m}^{n}_{a}

In this paper, when studying and analysing the location choice of firms, they have price competition with each other and can obtain more benefits from location choice. The specific income distribution is shown in Table 1 below:

The payoff matrix analysis results of vendor layout

A | _{a},π_{a} |
_{s},π_{s} |

B | _{s},π_{s} |
_{b},π_{b} |

In other words, the equilibrium payoff of both vendors can reach

Within the region, the demand function of two different products produced by two manufacturers will be clarified from the perspective of consumers. The specific quadratic utility function is shown as follows:

Where, qi (

The budget constraint conditions for consumers are as follows:

And Max (u–y) can be obtained by combining the above formula, and can be obtained:

Where, _{i}_{j}_{1} = _{i}_{j}_{i}

It is assumed that Enterprise 1 and Enterprise 2, which produce the same products, can play a game, and they are located in the east and the west respectively. In the practical development, it is assumed that both enterprises are rational and have two alternative countermeasures of cooperation and non-cooperation. If there is a potential market for development in the west and its value is _{1} and _{2} before the game, and the cooperation costs are _{1} and _{2}. Assuming that the two enterprises cooperate in the practical development, the income efficiency of Enterprise 1 will increase by Kr-C1, while that of Enterprise 2 will increase by (1-K + S) r-C2, where _{2} _{2}, while the return rate of firm 2 will increase −_{2} _{2}. _{2} represents the lost market share of firm 2. Under this condition, if firm 1 is unwilling to cooperate, but firm 2 is willing to cooperate, then firm 1′s income will increase −_{1}_{1}, and firm 2′s income will increase (_{1} + s) _{1}, where _{1} represents the lost market share of firm 1. But if neither co-operates, the benefits of the partnership will not change [2].

In the development of practice, it is assumed that the premise of cooperation is Kr-c > and (1-K + S) r-c >, and the game results between firm 1 and firm 2 are shown in Table 2.

Game results between firm 1 acting first and firm 2 acting later

Cooperation 1 | Cooperation | 1 | _{1} |
_{1} |
_{2} _{2} |
_{2} _{2} |

2 | (1−_{2} |
(1−_{2} |
− _{2} _{2} |
− _{2} _{2} |
||

Don’t cooperate | 1 | − _{1} _{1} |
0 | − _{1} _{1} |
0 | |

2 | (_{1}+s)_{1} |
0 | (_{1}+s)_{1} |
0 |

Assuming that the game ratio of Enterprise 1 choosing a cooperative strategy is x, then the game ratio of non-cooperative strategy is 1-x. Therefore, benefits and group average expected returns can be obtained by using these two methods respectively as follows:

Combined with the analysis of biological evolution and replication dynamic thought, the differential equation can also be obtained as follows:

And because 0 ≤ _{1} > _{2}_{2} _{1}_{1} Under the condition of, the above differential equation has the following three stagnation points:

Based on the analysis of the above results, the following conclusions can be drawn: in _{1} + _{1}_{1} > 2_{2}_{2} Under the condition of, _{3} = _{2}_{2}/_{1} + _{1}_{1} − _{2}_{2} It is the only policy of the system that remains undetermined.

Assuming that the two groups of western enterprises choose the cooperation plan, and the ratio of players is _{2} > (_{1} + _{1} Under the condition, the above equation has three stagnation points:

The following conclusions can also be drawn from this: in (1 + _{2} > (_{1} + _{1} Under the condition of, _{3} = _{2}_{2}/[(1 + _{2} + _{2}_{2} − (_{1} + _{1}] is the only evolutionarily stable strategy of the system.

By integrating the operation stability and related strategies of the above systems, it can be seen that if the cooperative strategy ratio of Enterprise 1 is X, then the non-cooperative strategy ratio is 1-X, while the cooperative strategy ratio of western Enterprise 2 is Y, then the non-cooperative strategy ratio is 1-Y. Eastern Enterprise 1 selects two strategies for the expected revenue of the players and the average expected revenue of the group, respectively [3]:

The corresponding western Enterprise 2 is as follows:

Combining the above formulas, the following equations can be obtained:

This conclusion can be drawn from it. Based on the above equations meeting the following two conditions, it is proved that both eastern and western enterprises finally choose the cooperation strategy. The specific conditions are: on the one hand, _{1} > _{2}_{2} − _{1}_{1}; On the other hand, (1 + _{2} > (_{1} + _{1}.

It can be seen from the analysis of the above overview that, because the equations are nonlinear, it is difficult to achieve the final goal by using only a single analytical method. In this case, computer simulation software is needed for analysis, and data simulation and digital examples are combined. In the research exploration, this paper uses MA TLAB7.0 to carry out data simulation for the model, and thus obtains the relationship between the real wage difference, factor resource endowment, transportation cost and other factors in the two regions. At the same time, considering the common assumptions of NEC, the parameter

To more intuitively grasp the impact of resource endowments of different factors on the composition of industrial distribution, we can make assumptions at this time and make reference therefrom. It is assumed that the factor resource endowments of the enterprises in the two regions are similar, and the actual wage levels of the two regions are the same, thus proving that the manufacturing industries of the two regions are balanced and meet the expected requirements. According to the analysis of Figure 2, it can be found that the capital advantage of the eastern region is significantly higher than that of the enterprises in the western region. In other words, the research results as shown in Figure 2 can be obtained under the condition of the first analysis at this time. The comparative analysis between the two shows that, under the condition of difference in factor resource endowment, if the manufacturing industry appears in the area with

In the case of large differences in resource endowments between the two places, for example, the following results can be obtained by combining the analysis in Figure 3 below: First, based on the deviation of resource endowment between the east and the west, a large number of industries will be concentrated in the eastern region. According to the analysis of different proportions, under the same wage level, the industries will move to the west, but they cannot get more advantages in labour cost. Second, based on the advantages of resources, the manufacturing industry in the eastern region will be more and more concentrated, and the corresponding quantity transferred to the western region will continue to decline., therefore, in the face of this development trend, the local governments should be based on the integration of previous development experience, according to the location of the enterprise development trend, a large number of valuable countermeasures to promote the development of the differences in different areas to control things, at the same time, the western region should also be based on its own development advantage, strengthen its infrastructure level, optimise the industrial undertaking ability, To lay the foundation for industrial transfer and development.

When transportation cost impact on the industrial transfer form, to facilitate the observation analysis, need to clear this condition, and then will transport costs

In conclusion, according to the analysis of the model constructed in this study and the analysis of the lag of China’s inter-regional industrial transformation and various influencing factors in the numerical simulation, it can be found that, firstly, the manufacturing industry in the eastern region of China does not reach the critical value of the industrial transfer, and the control of the actual transportation cost does not meet the requirements at all. Secondly, based on optimising the regional factor resource endowment, it is necessary to strengthen the industry carrying level and supporting capacity of local enterprises, which is also an important task of industrial transformation and development nowadays. Finally, the local district government should initiate to provide more powerful resources, such as transportation, finance and access to information, communication and cooperation, actively promote the regional industry and provide more supporting facilities for the transfer of industry and the environment, such that it not only supports the industrial chain of the market but also promotes industrial transfer at the same time, which will improve local economic development. Therefore, in the future construction and development, it is necessary to start from China’s inter-regional industrial transformation, combined with the accumulated experience and values of previous development to conduct a comprehensive exploration.

#### Game results between firm 1 acting first and firm 2 acting later

Cooperation 1 | Cooperation | 1 | _{1} |
_{1} |
_{2} _{2} |
_{2} _{2} |

2 | (1−_{2} |
(1−_{2} |
− _{2} _{2} |
− _{2} _{2} |
||

Don’t cooperate | 1 | − _{1} _{1} |
0 | − _{1} _{1} |
0 | |

2 | (_{1}+s)_{1} |
0 | (_{1}+s)_{1} |
0 |

#### The payoff matrix analysis results of vendor layout

A | _{a},π_{a} |
_{s},π_{s} |

B | _{s},π_{s} |
_{b},π_{b} |

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