Research On Bertrand Game Of Rare Earth Products With Spatial Location Difference

Rare earth industry is a pillar industry established by the Inner Mongolia Autonomous Region Government.The state has given the rare earth industry protection and support in policy.However,due to the escalating trade frictions between China and the United States,United States,Japan and Europe jointly promote China's export of rare earth products,resulting in a series of problems such as over-exploitation of resources,serious damage to the ecological environment,long-term unreasonable pricing of rare earth products and so on,which has brought serious negative impact on China's national economy.Therefore,how to make good use of the differential advantages of rare earth products in China to help rare earth enterprises to improve their profits has become the key.Bertrand model,which was proposed by Bertrand in the 1980 s,is a model with price as the decision variable under the static game of complete information.The purpose is to enable participants to make the best price strategy in a certain situation,in order to ensure interests.However its theory infers that the result that competitive price equals marginal cost is too extreme,which leads to the so-called Bertrand paradox.Hotelling is another static game model with complete information considering spatial location differences,which was proposed by Hotelling in the 1920 s.At present,these two models have been successfully applied to the study of market competition among different types of enterprises.Inspired by the Hotelling model,this paper introduces the spatial differences of rare earth products to avoid the Bertrand paradox and studies the Bertrand game of rare earth products with spatial differences.There are three oligarchs and three demanders in this model.The products have both horizontal and vertical differences,which makes it very difficult to solve the analytical solution of the model.Therefore,this paper will give the equilibrium numerical solution of the model through numerical simulation experiments.In the model,the difference of product spatial location is reflected by the difference of transportation cost from each manufacturer to each demander.According to the unit transportation cost of one oligarch and three oligarchs to one demander and three demanders as variables,1296 sets of examples are designed.Lingo software is used to iterate the numerical solutions of 1296 cases.In each case,nine equilibrium prices,nine equilibrium outputs and three oligarchs' equilibrium profits will be iterated out,totaling 27216 values.Origin software was used to draw price and profit contours of oligarchs under different conditions.Spss software was used to regression the relationship between price and profit and transportation cost,and the results were analyzed.Finally,the above results are verified by the real data of three rare earth products manufacturers,Chengdu Galaxy Magnets,Beijing Zhong Kesanhuan and Ning Boyunsheng,and two demand sides of Korea and Switzerland.The study found that when there are only spatial differences in products and the buyer pays for the freight,the reduction of transport costs from the enterprise to a certain demander unit is more significant than the increase of transport costs from the rival enterprise to the demander unit.Moreover,the change of transport costs from the enterprise to the dominant demander unit has the greatest impact on the profits of the enterprise.Note that the advantage of the demand side is compared with other enterprises reflects the spatial position of a transportation cost advantage level range,spatial location advantage rather than their own to between the demand side compared to the cost of transportation.Rare earth enterprises can be reasonably adjusted to different spatial distance class demand side between the cost of transportation,as far as possible to reduce the enterprise and has a spatial location advantage of the demand side of the transportation cost,the profits of the enterprise can be improved.