Dynamics of price cooperating model in commodity market

Ac h i e v i n g t h e g o a l o f carbon and carbon neu-tralization is not only an internal requirement forsustainable and high-quality develop-ment in China, but also the inevitable choice to promote the construction of a community of a shared future for mankind. China-EU carbon pricing became a hot topic at the recent Inter-national Financial Forum (IFF) .Carbon pricing is highly importantAt the two sessions this year, China promised to reach peak carbon emissions by 2030 and carbon neutral-ity by 2060.In this statement, the peak in carbon emissions refers to the level at which carbon emission will start on a steady decline, and carbon neutrality refers to zero carbon dioxide emissions overall.Wang Yi, Deputy Director of the Institute of Science and Technology Strategy Consulting, Chinese Acade-my of Sciences, pointed out that Chi-na is making more stringent policies in carbon pricing and carbon-related areas. Carbon pricing may play a very important role in the carbon peak and carbon neutrality in the future. This is determined by the systematic, leading and practical characteristics of carbon neutrality. In addition, the carbon pricing mechanism itself is not based on the free market, but often intervened by the human-driven mar-ket. Whether it is the setting of a total amount, or the rate and direction of its emission reduction, the cost needs to be determined.Regarding the construction of China’s carbon market in the future, Wang Yi suggested that we should make a better analysis of the currentBy Jo Liquota and the trend of carbon pric-es in the whole trading process; It is necessary to gradually clarify macro policies, including the amount of peak carbon emissions and industrial pol-icies; the coordination mechanism of carbon pricing should be determined. In the future, China’s policies should consider the coordination of each other, including the carbon market, carbon tax, carbon pricing, as well as the coordination with foreign carbon border regulation mechanisms and the domestic investment and financing policies; we should adopt multi-step measures and competition strategies, consider the current situation of Chi-na, seek truth from facts, and not rush to launch a substantial carbon pricing policy. On top of that it is also import-ant to strengthen international coop-eration and dialogue.Domenico Siniscalco, Vice Chair-man of the IFF, Global Vice Chairman of Morgan Stanley and Former Finance Minister of Italy, introduced the ba-sic situation of the European carbonmarket and the carbon pricing mecha-nism. He said that political and social factors should be taken into account when it comes to carbon pricing. The carbon price shall also vary in different regions because of different economic characteristics and industrial struc-tures. However, the price of carbon shall be stable and not too volatile.Domenico Siniscalco also sug-gested that China could learn from the experiences of many other coun-tries and adopt the model of combing carbon pricing and carbon tax in the future.Cyril Cacisa, Senior Energ y Analyst of the Department of Envi-ronment and Climate Change of the International Energy Agency, also expressed his opinion of China’s car-bon trading market. He pointed out, “China has special advantages because many people have rich experiences, which will promote reform and im-provement, and better pilot the carbon trading system to achieve greater prog-ress. China’s carbon trading marketCarbon Pricing Requires MoreInternational Cooperation and Dialogue31will be conducive to China’s achieve-ment of long-term goals. Therefore, we are very glad to see the attempts and efforts in China’s carbon trading market this year, which will certainly promote China’s future development up to 2050 and even further in the fu-ture. We are confident that China will make rapid progress in this respect, and will establish a very significant and effective pricing system for China, and be able to better transform its own industrial system.”Mei Dewen, General Manager of the Beijing Green Exchange, praised such comments. He said, “China has the world’s largest green bond market, which exceeded RMB 12 trillion last year. The carbon market quota to be launched this year is nearly 4 billion tons, which has surpassed that of the European Union. China is also the world’s largest carbon market. There-fore, the Chinese market needs an effective, flexible, stable and inclusive carbon price signal that can ref lect marginal costs and externality costs for emission reduction.”Strengthen international cooperationRegarding specific carbon trad-ing, Wang Yuanfeng, member of the IFF academic committee and Deputy Chairman of the China Develop-ment Strategy Research Association, envisions the personalization of car-bon trading. Wang Yuanfeng said, “with the continuous improvement and maturity of the system, we will have more individuals and small and medium-sized enterprises involved in carbon trading. It is important for all people to engage in carbon trading and pricing, to get consumers deeply involved and have them understand which products feature high carbon or low carbon. In the end consumers will not choose high-carbon products and save energy and reduce emissions through their own choices.”“Carbon prices should not be ei-ther too low or too high. If the price is too low, carbon emitters will not care about the costs for emission; If it is too high, costs will be a great burden for enterprises and consumers,” said Wang Weiquan, Deputy Secretary General of the Renewable Energy ProfessionalCommittee of China Association ofCircular Economy.Mei Dewen stressed the needfor releasing an effective, flexible andstable carbon price signal that canboth reflect the marginal and exter-nality costs for emission reduction. Toachieve this goal, it is imperative tomake nine changes: carbon emissionreduction should be shifted from thecurrent relatively soft constraint tomore stringent emission reduction,or total amount emission reduction;carbon emission accounting shouldbe more direct and rigorous; the mainmarket players of the emission reduc-tion shall extend from emission-con-trolled enterprises only to the focuson emission-controlled enterprises,non-emission controlled enterprises, fi-nancial institutions, intermediaries andindividuals; products should shift fromspot goods to spot, futures and deriv-atives to convert risks and liquidity;the allocation of quotas shall changefrom free allocation to “free + paid al-location” ; the key emission-controlledindustries should shift from eightindustries to emission facilities thatmeet certain emission standards; theservice model shall change from in-termediary service of account openingand settlement to market makers; theintermediary service institutions shallturn from consulting and monitoringservices to other services like businessexploring, sharing and arbitrage; themarket scope shall expand from localmarket to the whole country and thefocus shall shift from the domesticmarket to the international market.“We need to change the socialcost of carbon emissions from a narrowcarbon price to green premium, whichis a more comprehensive governanceconcept.” Peng Wensheng, Chief Econ-omist of CICC, said that the so-calledgreen premium is the difference be-tween the cost of clean energy and thecost of fossil energy. There are threeways to reduce green premium andpromote economic entities to use moreclean energy: first, reduce the cost ofclean energy through technologicalprogress and public policy investment;the second is to increase the cost offossil energy through the carbon emis-The carbon pricingshall be promotedonly when China,the U.S. and the EU,the world’s threelargest economiesand emitters, worktogether.sion price; the third includes means ofsocial governance in terms of culture,value and living habits.Alain Quine, Chairman of theFrench Carbon Pricing Committee,believes that there are two ways toachieve carbon neutrality. One is in-novation, and the other is internationalcooperation. “As for the carbon trad-ing market, it is not only a matter ofprice. I believe we have made a lot ofprogress on the issue of price, mainlyabout the scope. In addition, the coun-tries should use carbon pricing as anincentive to enable enterprises and in-dividuals to achieve these easily-obtainresults,” said Alan Quine.Regarding international coop-eration, Edmond Alphandery, V icePresident of the IFF, Chairman ofthe European Carbon Pricing ActionGroup and former Finance Ministerof France, said, “the carbon pricingshall be promoted only when China,the U.S. and the EU, the world’s threelargest economies and emitters, worktogether. The cooperation among thethree parties will have a significantimpact on the world. At present, bothChina and Europe have issued positivemeasures in terms of carbon market.He hopes that China and Europe canwork together to promote the U.S. toestablish a long-term carbon marketand realize the fundamental change ofenergy transition.” 32。

Hedonic Price Models and Indices based on Boosting appliedto the Dutch Housing MarketMartijn Kagie∗Michiel van WezelEconometric Institute,Erasmus School of Economics and Business EconomicsErasmus UniversityP.O.Box1738,3000DR,Rotterdam,The NetherlandsEconometric Institute Report EI2006-17April5,2006AbstractWe create a hedonic price model for house prices for six geographical submarkets in the Netherlands.Our model is based on a recent data mining technique called boosting.Boostingis an ensemble technique that combines multiple models,in our case decision trees,intoa combined prediction.Boosting enables capturing of complex nonlinear relationships andinteraction effects between input variables.We report mean relative errors and mean absolute error for all regions and compare our models with a standard linear regression approach.Our model improves prediction perfor-mance with up to40%compared with Linear Regression.Next,we interpret the boostedmodels:we determine the most influential characteristics and graphically depict the relation-ship between the most important input variables and the house price.Wefind the size ofthe house to be the most important input for all but one region,andfind some interestingnonlinear relationships between inputs and price.Finally,we construct hedonic price indices and compare these to the mean and median index andfind that these indices differ notably in the urban regions of Amsterdam andRotterdam.1IntroductionHedonic pricing theory hypothesizes that the price p of a product is determined by a function p=F∗(x),where x is a bundle of characteristics that define the product.Hedonic pricing theory is generally attributed to Court(1939),Lancaster(1966),Griliches(1971b,1971a)and Rosen (1974).In practice the hedonic function F∗(x)is estimated by a model F(x)which isfitted on a historical dataset{p i,x i}N1.Traditionally,these models are Linear Regression or Box-Cox type models.In the context of housing and real estate hedonic models are useful in three ways.In thefirst place a hedonic model is a very suitable way to predict house prices.House price prediction can be used for bulk appraisal for property tax,but can also help real estate brokers by determining the asking price for a house.However,it is also possible to use a hedonic method for a website ∗We thank Jaap Darwinkel and Dree Op’t Veld for their helpful comments and suggestions.Corresponding author:E-mail:kagie@few.eur.nl.Phone:+31104088940.Fax:+31104089031.feature,where potential costumers can check their house value informally,after which they may decide to sell their house,although they did not intend to do so in advance.The model structure itself can also be interesting,especially when one wants tofind out what the influence is of a characteristic of the house on the price or which characteristics have the highest influence on the price.By interpreting the hedonic model these questions can be answered. Harrison and Rubinfeld(1978)for example use a hedonic model tofind a relationship between air pollution and house prices.The third way in which the hedonic model can be useful,is when it is used to create a hedonic price index.A hedonic price index uses a hedonic model to correct for quality differences over time.Ordinary indices may give a deceptive view,because the average or median product in year t may be a better(or worse)product than in year t−1.An average house in the1930’s for instance can in no way be compared with an average house sold in the year2004(since these have different characteristics),but nonetheless this is what a regular price index does.Hedonic indices for housing are for instance constructed by Wallace(1996)and Clapp(2004).Traditional hedonic models have the advantage they are easy to interpret and estimate,but often suffer from misspecification:The assumptions made on functional form do not allow a good representation of reality,i.e.,the hedonic model does notfit the data well.Several authors,e.g. Anglin and Gen¸c ay(1996),Gen¸c ay and Yang(1996),Pace(1998),Clapp(2004),Boa and Wan (2004),Bin(2004),Martins-Filho and Bin(2005),have used semi-and non-parametric methods to estimate a hedonic price model and compared these models with the traditional parametric hedonic ually these new models outperformed the parametric models in terms of prediction performance.Also artificial neural nets,a popular machine learning technique,are frequently used for the estimation of the hedonic function,e.g.by Daniels and Kamp(1999), Kershaw and Rossini(1999),Lomsombunchai,Gan,and Lee(2004).An artificial neural net is a veryflexible model,which in theory is a universal function approximator.A recent successful machine learning method is boosting.Boosting is a relative new method to combine multiple models into a combined prediction.These individual models are called base learners.Often regression or classification trees(Breiman,Friedman,Olshen,and Stone1983)are used as base learners,but a combination of other models,e.g.,neural nets is also possible(Drucker 1999)(We will describe regression trees and boosting in more detail in Section2.).Van Wezel, Kagie,and Potharst(2005)use boosting for hedonic pricing.Boosted hedonic price models where created for3small and simple datasets available on the internet:one dataset deals with automo-biles,the other two with houses.On two out of the three datasets the boosted models substantially improved out-of-sample performance compared with a stepwise linear regression model.In this paper,boosted regression trees will be used to create hedonic models for6regions in the Netherlands.Real-life data of the year2004,collected by the largest association of real estate brokers in the Netherlands,the NVM,will be used.These hedonic models will be used for prediction,interpretation and the construction of hedonic price indices.The remainder of this paper has the following structure.In the next Section we will discuss regression trees and boosting in more detail.Section3describes the data used in the experiments. Section4describes the performed experiments and their results.In Section5two graphical methods,relative importance plots and partial dependence plots are used to interpret the boosted hedonic price models.A hedonic price index based on our boosted models is discussed in Section 6.Finally Section7gives a discussion,conclusions and directions for further research.2Models&MethodsIn this section we will discuss the Machine Learning techniques used in this paper.Generally, in Machine Learning a model is trained(fit,calibrated)on a dataset D={(x i;y i)}N i=1.An instance(observation,row)(x;y)exists of a vector of J attributes x=(x1,...,x J)and a target y.The x attributes are the explanatory or independent variables and the target is the explained or dependent variable.In Machine Learning a distinction is made between classification and regression models.In the classification case the targets{y i}N1have a categorical or binary value,4875071500173000size < 100type = ’apartment’Figure1:Example of a Regression Tree:The root node divides the houses in the dataset in two parts using the continuous variable size.Instances with a size smaller than100m2go left,all others right.Instances going right get a price of173000euros.The instances who were going right,will be split a second time on the categorical type.When the type is apartment,the instance is going left.in the regression case a continuous value.In both cases the attributes x j can be either continuous, categorical or ordinal.2.1Classification and Regression TreesCART(Classification And Regression Trees)is one of the most frequently used methods for con-structing decision trees and developed by Breiman,Friedman,Olshen,and Stone(1983).In this paper we will use the CART regression tree.A regression tree consists of decision nodes and leaf nodes.Each decision node has two child nodes,which may again be decision nodes or leafs.The root of the tree is on the very top–it is the only node in the tree without an ancestor.Every decision node(also called non-terminal node)contains a split criterion,which divides the data at that point in two parts.This split criterion has the shape of x j<C for continuous variables,where x j is the j th variable and C is some constant.For a categorical variable the split criterion looks like x j (V),V⊂W j.Here is W j collection of all possible levels of variable j.The terminal nodes(leafs)contain aˆy value,an estimate for the target value in that leaf.In practice this value is taken to be the average of all observed y values in that leaf.An example of a regression tree is shown in Figure1.This tree can be used for prediction as follows.We begin at the root and when the split criterion is met we turn left and when it is not met we turn right.We keep on doing this until we reach a terminal node and use theˆy value in that node as our prediction.Decision trees are usually built in two phases.Thefirst phase is a growing phase,the second phase is a pruning phase.In the growing phase,the tree is grown until error reduction on the training set is no longer possible or a predetermined threshold has been reached.The resulting model usually overfits the data,and this is countered in a pruning phase,where the tree is shrunk until the error on a hold-out sample,the pruning set,is minimal.Details on the CART procedure for growing and pruning can be found in,e.g.,(Breiman,Friedman,Olshen,and Stone1983; Ripley1996).Here,we suffice by saying that,given dataset{(x i;y i)}N1,a regression tree B is constructed such that it minimizes the squared error lossB=arg minBE x,y[(B(x)−y)2],where B(x)denotes the prediction of tree B for input vector x.In the context of Boosting,discussed below,the pruning phase of the decision tree algorithm is usually skipped and instead the tree size is limited to a predetermined depth.In the most extreme case the tree depth is1.The tree then consists of a single decision node and two leaves.Such a special tree is called a decision stump.Although a single decision stump has very limited modelling power,an ensemble of such stumps is able to model complex relationships.Regression trees have some advantages over linear regression.In thefirst place regression trees are able to determine themselves which attributes are to be used for modelling the target variable. Another advantage is that regression trees are able to model interactions between attributes and non-linearities,without a required explicit transformation of the inputs.For example,there may be an interaction effect between lot size and location.In the center of a city houses are built more closely to each other so gardens are smaller or absent.A square meter of building site in the city will therefore be far more expensive than in the country,so there is an interaction between the two variables.There are many examples of non-linearities in the context of housing in the Netherlands,of which construction year is probably the most clear one.Where ancient houses from the19th century and before are more expensive than same kind of houses from later periods,because of their monumental character,houses from the1950’s on the other hand are relative cheap.Since many houses where destructed in World War II,a lot of new dwellings had to be built as quick as possible in the late1940’s and1950’s,so that buildings built in this period are of a less quality and also not the most beautiful ones.Finally newly built houses are of course again more expensive, so the average relationship between construction year and price is clearly non-linear.Many other variables show saturation effects,e.g.the utility of a3rd or4th room is much higher than the utility of the8th.Besides the previous advantages there are also two practical ones:In contrast to parametric models regression trees can handle categorical variables and missing values,without transformation of the data.A drawback of decision trees is their instability–The implemented model depends heavily on the dataset used for model creation,and a small change in the data may have large consequences for the model.Ensemble methods,such as bagging(Breiman1996)and boosting,have a stabilizing effect by averaging over a number of decision trees.We consider boosting next.2.2BoostingBoosting is a method to combine multiple models to improve performance.Boosting wasfirst applied to and developed for classification problems(with categorical response)by Freund and Schapire(1996,1997).In a classification context boosting seemed to be able to strongly reduce the error rate on out-of-sample data in many cases(Breiman1998).The idea behind boosting is to create a sequence of models,called base learners,in which each subsequent base learner focusses on the residual error of the previous base learners.Often,these base learners are decision trees or stumps.The original Freund and Schapire boosting algorithm for classification,AdaBoost.M1, tries to do this by increasing the weight of instances that were wrongly classified by the previous base classifier and decreasing the weight of the correctly classified instances.The AdaBoost.M1algorithm was only applicable to binary classification problems.For these problems,the model predicts whether an instance belongs to a class or not.The model thus has a0/1output and the quality of the model is measured with the0−1loss function,which basically counts the number of misclassifications.For modelling house prices this loss function is not suitable.Instead,we need a regression loss function that measures the deviance between two numerical values,as usual in regression.This means that we cannot apply the AdaBoost.M1 algorithm to house price prediction,but we have to use a Boosting algorithm for regression.We will pay more attention to loss functions for regression below.Driven by the success Boosting had in the case of classification various Boosting algorithms were designed for regression(Drucker1997;Zemel and Pitassi2001;Duffy and Helmbold2000; Duffy and Helmbold2002;R¨a tsch,Warmuth,Mika,Onoda,Lemm,and Muller2000;Buhlmann and Yu2003;Friedman2001).Friedman(2001)developed LSBoost,LADBoost and MBoost based on the squared,absolute and Huber loss function respectively.(All these loss functions apply to regression problems.)Duffy and Helmbold(2000,2002),R¨a tsch,Warmuth,Mika,Onoda,Lemm, and Muller(2000)and Buhlmann and Yu(2003)developed similar algorithms but with other lossfunctions.Friedman(2002)also created stochastic variants of his boosting algorithms,where a base learner is repeatedly trained on a sample drawn without replacement from the dataset.In this paper we will use the non-stochastic versions of Friedman’s LSBoost and LADBoost algorithms.These algorithms are chosen because,contrary to many other Boosting algorithms, they have a solid mathematical foundation:they are instantiations of a general Boosting algorithm for general loss functions named GradientBoost.We now give a brief,imprecise description of GradientBoost,LSBoost and LADBoost.More detailed descriptions of these algorithms can be found in(Friedman2001)and in Appendix A.We will pay more attention to loss functions shortly, in Subsection2.3.Contrary tofitting a single model,like the decision tree B above,boosting starts of with an initial guess F0and thenfits a sequence of M models B1,...,B M(the base learners)which are subsequently combined in a weighted manner.Thefinal model is thusF M(x)=F0(x)+Mm=1νρm B m(x).Here,ρm denotes the weight for model m and is determined by the algorithm.M,the number of iterations,is to be set by the user.ν∈(0;1]denotes a regularization parameter parameter called the learning rate.Small values ofνwill help prevent the algorithm overfitting the training data.Note that in the m th iteration,B m()is added to F m−1:F m(x)=F m−1(x)+νρm B m(x).It makes sense to choose B m()such that is minimizes the residual error of F m−1.Roughly speaking, given a general loss function L(y,F),B m attempts to minimize the expected value of this loss function over the dataset:B m=arg minBNi=1L(y i,[F m−1(x i)+B(x i)]).In practice this is done byfitting pseudo responses˜y i in each iterationB m=arg minBNi=1{˜y i−B(x i)}2.Three remarks must be made about this equation.Thefirst remark is that the˜y values depend upon the loss function in question.See the appendix for details on how these pseudo-responses are derived.Here,we suffice by stating that the pseudo-responses for the•squared error loss function L(y,F)=(y−F)2/2are given by˜y i|m=y i−F m−1(x i),and •for the absolute deviation loss function L(y,F)=|y−F|are given by˜y i|m=sign(y i−F m−1(x i)).The squared error loss function and the absolute deviation loss function are used in the LSBoost and LADBoost algorithms respectively.The second remark is that the minimization over B is done by minimizing over B’s parameter space.If B is a tree,these parameters are the split variables and split points in the decision nodes, and B M is the tree that gives the bestfit of the˜y values in iteration m.If B is a neural network, these parameters are the weights and biases of the neural network.The third remark is that no matter what loss function boosting attempts to minimize,a least squares regression is performed in each step of the Boosting algorithm.So,even if the Boosting algorithm as a whole does not minimize squared error loss but another loss function,the individual base models arefit by least squares regression.v o l u m e lotsize0 10000 20000 30000 40000 50000 0 1000 2000 3000 4000 5000l o t s i z evolume 0 1002003004005000 100 200 300 400 500no.volume lotsize price 1450045270431091224253234200003400310329000431036027500053802552325006360180210000736015619500083001541835009225901670001022570137500Table 1:Dataset used in the example.Left:scatter plot with outlier,middle:scatter plot without outlier,right:dataset.2.3Loss Functions &Boosting ExampleIn this subsection we give an illustrative example of the first iterations of the Boosting process for a small dataset.This subsection also serves to illustrate the consequences of using the squared error-or absolute deviation loss function.The first loss function is the most common in regression settings.However,a drawback of this loss function is its sensitivity to outliers,since squaring the errors blows up the large errors caused by the outliers.This drawback can be relieved by using the absolute deviation loss function.For the example,we use the data in Table 1.These data come from the Apeldoorn dataset (see below)and represent 10houses in the Apeldoorn region.Both volume,lot size and price are approximately 10times as high for house 1as for the 2nd most expensive house,number 2.Clearly,house 1is an outlier.In the example below,we use both LSBoost,which attempts to minimize the squared loss function,and LADBoost,based on the absolute deviation.We will see how both these methods cope with the outlier.As base learners,we will use decision stumps –trees with only one decision node and two leaves.The learningrate is set to 1.2.3.1LSBoost exampleFirst we start with the LSBoost algorithm.First the initial guess F 0is computed.This is the mean price of the datapoints:F 0=¯y =646041.20The outlier is responsible for the fact that the first guess F 0is in between the highest and the second highest price.With the use of F 0the residuals ˜y are computed and on these residuals the first tree is trained.The first stump splits on lotsize <22815,which means that outlier datapoint 1is excluded from the other points.After this step there are thus two groups:the outlier and the rest.Since our interest is mainly in the normal houses,we actually know nothing at all after this step,which is graphically shown in plot F 1of Figure 2.In the second iteration again a stump is trained on the residuals.Outlier datapoint 1has a residual of 0,because it is correctly predicted by the first base learner.Further datapoints 2and 3have a positive residual and the rest a negative one.It is the task of the second stump to find a split that separates the high (positive)from the low (negative)residuals.In fact the second stump uses lotsize <282.5to separate the 5less expensive (who had negative residuals)from the 3expensive houses (who had non-negative residuals).In plot F 2this division is shown.Datapoint 1is not shown in the plot,so that the focus is on the “normal”houses.Remarkable is that the prediction of datapoint 1is not perfect any more after the second iteration,since this second stump adds €76875to the (correct)price of F 1.In the third iteration again datapoint 1has the highest residual in absolute terms.Although the prediction of F 2has only made a mistake of 1.8%on this point,datapoint 1will again has a high influence on the third stump.Also points 4and 8were highly overestimated up to now,where datapoint 5is highly underestimated.It is obvious that there is no way to separate these3overestimated point from the underestimated one.But when datapoint1was excluded from the dataset,we could use the criterion volume<335to split the overestimated points from the underestimated ones.But the third stump chooses to separate point1and4from the rest using lotsize≥341.5.This means that this stump in fact gives a penalty on these high lot sizes,i.e.it modelled a negative effect between lot size and price.When we look at plot F3we see that due to this penalty,houses with a lotsize≥341.5(and lotsize<22815)have a lower predicted price than houses with a lotsize<341.5.Finally in the fourth iteration the four cheapest houses are separated form the6expensive ones again on the variable lotsize.The spit criterion is lotsize<155.After4iterations LSBoost has produced a model that divides the space of possible houses into5parts all based on lotsize.A higher lotsize leads to a higher price,except for the area341.5≤lotsize<22815.Only datapoint4is in this area.This house has indeed the second largest lotsize of the10houses,but in terms of volume it comes only on a seventh place.This typical split(of the third iteration)was influenced by the outlier,despite the prediction of this house was relative good.And also thefirst iteration was negative influenced by the outlier,because we had preferred an extra split between the normal houses,which is far more useful for out-of-sample prediction.Of course these effects will be smaller in the real experiments,because of the larger sizes of the datasets and the use ofa smaller value for the learningrate parameter.2.3.2LADBoost exampleLADBoost tries to minimize an absolute loss function.To do this,it uses the sign(-1,0or1)of the residual instead of the residual themselves as pseudo responses and medians instead of means.In theory these adaptations should make LADBoost more resistant to outliers.Also with LADBoost we start with an initial guess,in this case the median of the prices of the dwellings in the dataset:F0=median(y)=221250Since it is the median,it is obvious5datapoints are overestimated and5underestimated.Thefive more expensive houses get a˜y=1and thefive cheaper ones get a˜y=−1.Thefirst stump can split these to groups perfect using the split criterion lotsize<217.5.The medians of the residuals of the datapoints in a node arefinally used as the prediction.For the left side this is the residual of datapoint8,-37750,and for the right side this is the residual of datapoint3,107750.So after thefirst iteration datapoints3and8are correctly classified and the outlier has had no influence in the process.Graphically thefirst step of LADBoost is shown in plot F1of Figure3.In the second iteration,shown in plot F2,it is impossible for a decision stump to separate the positive signed targets from the negative signed ones.The stump splits the data on volume<335. This is the split we wanted LSBoost to make in its third iteration,but that it did not make,caused by the outlier.In the LADBoost algorithm the residual of the outlier has the same influence on the training process as the other residuals due to the fact that the signs of the residuals are taken. This is the reason the split on volume is performed here.In the third iteration the outlier has for thefirst time influence on the process.There are five datapoint with positive signs,the2most expensive houses and houses6,8and9,which are situated relatively in the middle of the data.Since it is impossible to separate datapoints6,8and 9in some way from the other points,it is obvious that the split is made on volume<412.5,so that point1and2are separated from the rest.House1and2are thus together one node with residuals of3962912and72000.According to the algorithm these houses are predicted by the base learner by taking the median of the residuals in the node.The median of two points is the mean: 2017456.Obviously this has a terrible influence on the prediction of the second house,which was predicted72000euros too low by F2,but is predicted nearly2million too high by F3.The outlier has in this case a high influence,but in large datasets this situation is unlikely to occur.Finally in the fourth iteration the same split is made as in thefirst iteration,only signs are switched:lot≥217.5.In fact the influence of thefirst base learner is reduced.When we compare these steps of LADBoost with LSBoost,we see that the influence of the outlier is less than in the LSBoost algorithm.Only in the third iteration the outlier has an+−−−−1000200030004000020********F1Volume L o t S i z e 238833.34310912+++−−−−−−01002003004005000100300500F2VolumeL o t S i z e187583.3315708.3++−+++−−−01002003004005000100300500F3VolumeL o t S i z e 202281.3330406.3256916.7+−+++−−−−01002003004005000100300500F4VolumeL o t S i z e 162666.7219258.9347383.9273894.3Figure 2:LSBoost process++++−−−−−01002003004005000100300500F1Volume L o t S i z e183500329000+o −−++o −−01002003004005000100300500F2Volume L o t S i z e141125297750202500348000+−−−+−++−01002003004005000100300500F3VolumeL o t S i z e 1522502866251913753368752365456−−−−++++−01002003004005000100300500F4VolumeL o t S i z e 1597502750002100003252502353831Figure 3:LADBoost processinfluence,but this is a rather large one.However,the small size of the dataset is mostly responsible for this inflDBoost has the advantage that it is less sensitive to outliers,but this means also that is expected to be worse in the appraisal of expensive houses.Therefore we will use both algorithms in this paper.2.3.3Loss Functions for Model EvaluationWe mentioned above that we use either absolute or squared error in the boosting (model fitting,training)procedure.However,for the purpose of interpretation the squared error loss function is not very suitable,as the mean (or sum of)squared error(s)may largely be determined by an outlier.Figure4:The situation of the6NVM Regions.Thus,for model evaluation we use either the Mean Absolute Error or the Mean Relative Error:MAE=1NNi=1|F M(x i)−y i|,(1)MRE=1NNi=1F M(x i)−y iy i.(2)where F M(x i)denotes the prediction as before.These loss functions have the advantage of better interpretability,and they are used to report model performance even when a model isfit using the squared loss function.3DataThe datasets used in this paper are derived from the database of the Nederlandse Vereniging van Makelaars(NVM,Dutch Association of Real Estate Brokers).The NVM is the largest Dutch association of real estate brokers with3751members.80%of the sworn brokers in The Netherlands is a member of the NVM.The NVM has divided The Netherlands in80living regions or housing markets.Most people move inside such a region and therefore these regions can be seen as distinct markets.For the experiments6living regions are used:City of Groningen and environs,Apeldoorn and environs,Eindhoven and environs,Amsterdam,Rotterdam and Zeeland.In the next section the6regions will be briefly described and in Section3.2an overview of the used variables will be given.。

Production,Manufacturing and LogisticsCoordination of cooperative advertising in a two-levelsupply chain when manufacturer offers discount qJinfeng Yue a ,Jill Austin a ,Min-Chiang Wang b ,Zhimin Huangc,*a Department of Management and Marketing,Jennings A.Jones College of Business,Middle Tennessee State University,Murfreesboro,TN 37132,USAb Department of Management and Decision Sciences,College of Business and Economics,Washington State University,Pullman,WA 99164-4736,USAc School of Business,Adelphi University,Hagedorn Hall of Enterprise,Garden City,NY 11530,USAReceived 14October 2003;accepted 14May 2004Available online 2September 2004AbstractWe studied the coordination of cooperative advertisement in a manufacturer–retailer supply chain when the manufac-turer offers price deductions to customers.With a price sensitive market,the expected demand with cooperative advertising and price deduction is demonstrated.When the manufacturer is a leader,we obtained the optimal national brand name investment,local advertisement and associated manufacturer Õs allowance with any given price deduction.When the man-ufacturer offers more price deduction to customers,the retailer will increase local advertisement if the manufacturer pro-vides the same portion of the local advertising allowance.We obtained the necessary and sufficient condition for the price deduction to ensure an increase of manufacturer Õs profit,and a search procedure for determining such an optimal price deduction is provided as well.When the manufacturer and retailer are partners,we obtained the optimal national brand name investment and local advertisement.For any given price deduction,the total profit for the supply chain with coop-erative scheme is always higher than that with the non-cooperative scheme.When price elasticity of demand is larger than one,the resulting closed form optimal price deduction with partnership is also obtained.To increase profits for both parties in a supply chain,we recommend that coordination in local and national cooperative advertising with a partnership rela-tionship between manufacturer and retailer is the best solution.The bargaining results show how to share the profit gain between the manufacturer and the retailer,and determine the associated pricing and advertising policies for both parties.Ó2004Elsevier B.V.All rights reserved.Keywords:Supply chain;Co-op advertising;Price discount;Game theory0377-2217/$-see front matter Ó2004Elsevier B.V.All rights reserved.doi:10.1016/j.ejor.2004.05.005qThis research is supported in part by MTSU FRCAC grant.*Corresponding author.Tel.:+15168774633;fax:+15168774607.E-mail addresses:jyue@ (J.Yue),jaustin@ (J.Austin),mcwang@ (M.-C.Wang),huang@ (Z.Huang).European Journal of Operational Research 168(2006)65–85/locate/ejor66J.Yue et al./European Journal of Operational Research168(2006)65–851.Introduction1.1.Non-cooperative vs.cooperative supply chainTwo-level supply chains have been extensively studied in recent operations management literature.In a two-level supply chain,the manufacturer and retailer make interactive actions to benefit themselves or the whole chain.These relationships may be non-cooperative or cooperative.In non-cooperative situations, the party with the manipulative power in the chain controls the other party who becomes the follower in the relationship.The leader of the chain estimates the reactions of the follower and decides thefirst move and then prescribes the behavior of the follower(Gaski,1984;Munson and Rosenblatt,2001).In manufacturer and retailer two-level supply chains,traditionally manufacturers hold manipulative powers,act as leaders,and are followed by retailers.For example,automobile makers may coerce their small,family run dealership networks by using slow delivery or by removing business from poorer perform-ing dealers(Lambet al.,1996).McDonalds typically imposes strong control over its franchisees(Love, 1986).In recent years,more leading powers have shifted from manufacturers to retailers(Huang et al., 2002).For example,Wal-Mart effectively uses its power to get reduced prices from its suppliers(manufac-turers)(Lucas,1995).When both parties in the supply chain have negotiation power,they mayfinally agree to cooperate rather than not cooperate with each other.In a cooperative environment,the manufacturer and retailer work together advantageously in determin-ing price,order quantity,advertising,etc.,to achieve maximum savings and/or to enhance profit for the whole chain.For example,Procter&Gamble(P&G),a former leader in the supply chain(Walton and Huey,1992),now partners with Wal-Mart,through demand monitoring,JIT delivery,and information sharing(Foley and Mahmood,1996;Coyle et al.,1996).This new partnership approach for P&G and Wal-Mart has changed the relationship from a win–lose situation into a win–win situation for cost saving and revenue increases for both parties(Huang et al.,2002).1.2.Co-op advertising and price discount in the supply chainThere are many possible interactive actions in a manufacturer and retailer supply chain.In this research, we focus on cooperative(co-op)advertising between the two parties and price discount.In several supply chain management studies(Monahan,1984;Lee and Rosenblatt,1986;Drezner and Wesolowsky,1989; Chiang et al.,1994),price discounts were discussed as part of the lot sizing decisions.In these studies, the total market demand was assumed to be unaffected by price discounts when the manufacturer provided the discount price to the retailer to compensate for the increase of inventory costs for ordering at a large lot size.Abad(1994)and Li et al.(1996),however,discussed pricing and lot sizing when demand was price sensitive.In fact,for price sensitive demand,the manufacturer and/or retailer could give deeper discounts to customers to increase the market share and profit in the chain.It is becoming commonplace for manufacturers to offer price deductions directly to customers instead of through retailers.These direct price deductions may be in the form of direct price discounts,sales coupons, mail-in rebates,on-site rebates,etc.The manufacturerÕs price deduction is a reflection of the competitive pressures;furthermore,price deduction produces more competitiveness and stimulates the market for the brand name,especially when demand for the product is price sensitive(Lambet al.,1996).In the auto-mobile industry,for example,at the end of2002,General Motors(GM)provided rebates of$3000or no interest forfive years for12car models andfive truck models.During the same time,Ford rebates of$3000 were available for only three models of Ford vehicles and three models of Mercury vehicles.Chrysler pro-vided$3000rebates forfive vehicles models(Teahen,2003).In2003,GM is not only providing a$500re-bate toward the purchase of a new truck,but also waiving lease payments for some customers as an incentive to purchase.GM launched a credit card loyalty program in Canada in the early1990s as wayJ.Yue et al./European Journal of Operational Research168(2006)65–8567 to provide customer rebates.Rebate dollars can be earned by making purchases on the credit card(5%on all credit card purchases made)and these credits can be applied toward the purchase of a GM vehicle.Orig-inally,a maximum of$3500could be accumulated over7years,but new rules reduce the rebate to3%and the$3500allowance is only applicable toward the purchase of a Cadillac(Menzes,2002).Some analysts are concerned that American automakersÕpractice of providing incentives for consumers may create an expec-tation among consumers that these incentives are permanent and this will create profitability problems for automakers over the long W Marketing Research estimated that the average rebate expected by consumers when they purchase a new vehicle is$3700(Grant,2003).Although the retailer selling the brand name product does not receive a price discount from the manufacturer,the retailer will benefit from an enhancement of the brand name and an increase in sales.Co-op advertising is typically defined as a cost sharing and promotion mechanism used by manufactur-ers and retailers.It allows them to focus on building image by national brand name investment and to focus on short-term sales incentives by local advertisement.Cooperative advertising has been in use in the United States since the early1900s.Warner Brothers,a maker of corsets,issued thefirst co-op agreement in1903. The use of co-op advertising spread to grocery stores and then to fashion and hard good stores.The auto-mobile industry is the most common user of cooperative advertising.It was not until after World War II that co-op advertising became commonplace in the United States(Wirebach,1983).In recent studies,Dant and Berger(1996)used game theory to obtain the Stackelberg equilibrium in advertising cost sharing where allowance from the manufacturer promotes the retailerÕs advertising expense and increases the profit for the whole chain.Huang et al.(2002)observed that manufacturers not only paid brand name investments,but also paid part of local advertisement costs incurred by retailers.They used a game theory approach to dis-cuss both leader–follower and co-op partnership advertising models,and provided optimal brand name investments,local advertisement with manufacturerÕs allowance in both cases.In this research,we consider cooperative advertising in a two-level manufacturer retailer supply chain when demand is price sensitive.Game theory is used to analyze both leader–follower and partnership co-op cases.When the manufacturer provides a price deduction directly to customers,the optimal brand name investments and local advertisement with the manufacturerÕs local advertising allowance are ob-tained.The optimal price deductions are also determined for both cooperative and non-cooperative cases.The rest of the paper is organized as follows:Section2gives the demand function with brand name investments and local advertising effects when demand is price sensitive.The profit functions for both the manufacturer and retailer when the manufacturer offers a price deduction directly to customers are also obtained.Section3provides the Stackelberg equilibrium when the manufacturer is the leader and retailer is the follower.The condition that a manufacturerÕs profit will increase when providing a price deduction is obtained.A search procedure is also provided to obtain the best price deduction to customers by the man-ufacturer.Section4discusses the manufacturer and retailer partnership co-op advertising decision.A closed form optimal price deduction is also obtained.Section5discusses the bargaining results to deter-mine the shares of profits between the manufacturer and the retailer.Conclusion remarks are given in Sec-tion6.2.Demand function and profit function determinationIn this section,we will determine the demand function with local advertisement,brand name investment, and price deduction efforts.When demand is not price sensitive,Huang et al.(2002)suggest that the one period expected demand(sale volume)S,influenced by local advertising effects and brand name invest-ments,is determined bySða;qÞ¼aÀaÀc qÀd;where a,c and d are positive constants,a and q represent local advertisement and brand name investments, respectively.Furthermore,c and d are called the quasi-advertising elasticity and the quasi-investment elas-ticity,respectively,and S(a,q)is a non-decreasing function with respect to a and q.When either or both local advertisement and brand name investments tend to infinity,the demand S tends to the constant a.If demand is price sensitive with constant price elasticity(Abad,1994;Li et al.,1996),we can express the demand function asSðPÞ¼x PÀe;ð1Þwhere P is the price charged to customers,x is a scaling parameter,and e is the price elasticity,which is always positive.Integrating the local advertisement,brand name investments and price sensitivity effects together,we suggest that the one period expected demand(sale volume)is determined bySða;q;PÞ¼½aÀb aÀc qÀdPP0Àe;ð2Þwhere b is a scaling parameter,P0is the full price for customers and other parameters are defined the same as before.In many situations,P0can be considered as the manufacturer suggested retail price(MSRP). Scaling parameter b is multiplied to the factor aÀc qÀd so that it has the same dimensionality as a.The value of b will also determine the impact of brand name investment and local advertisement to the expected mar-ket demand.Note that S(a,q,P)in(2)is an increasing function for local advertisement a and brand name investments q,but a decreasing function for price P.Furthermore,a and q in(2)must be no less than some positive values(a P a0and q P q0)since otherwise S(a,q,P)there will be negative.Therefore,the above function (2)is valid only when brand name investment and local advertisement are no less than some appropriate levels.A number of remarks can be made regarding the demand function(2).Observe that the local advertise-ment a and brand name investment q determine the potential customer base for the brand name.Price determines the demand elasticity to the brand name with the determined customer base.When either or both a and q increase,the potential customer base increases as well.Furthermore,price deduction makes the customers more willing to buy the brand name with the customer base determined by a and q.Therefore the multiplicative rule is applied to integrate the effects of a and q with the effect of P.If price is the full price (P=P0),(2)has exactly the same form as Huang et al.(2002)(here a parameter b is multiplied to the aÀc qÀd in HuangÕs form with the reason given before).If price is reduced(P<P0),S(a,q,P)can be rewritten as {a(P/P0)ÀeÀ[b(P/P0)Àe]aÀc qÀd},which still has the same form as of Huang et al.(2002)but with different parameter values.In this case,the demand is consistently higher than that with full price({a(P/P0)ÀeÀ[b(P/ P0)Àe]aÀc qÀd}>[aÀb aÀc qÀd]),and it has a higher upper limit(a(P/P0)Àe>a)when either or both a and q tend to infinity.This multiplication really makes sense for a demand sensitive market.Furthermore,forfixed a and q,define[aÀb aÀc qÀd]P0e as x in(1),then(2)has the same form of(1), which shows the price effect for a sensitive demand with constant elasticity.Since[aÀb aÀc qÀd]P0e is an increasing function of a and q with a given deductive price,the higher the value of either or both a and q,the more the market demand.We discuss a two-level supply chain with one manufacturer and one retailer.Similar supply chain structure is seen in other literatures;for example,Monahan(1984),Lee and Rosenblatt(1986),Abad (1994),Chiang et al.(1994),Li et al.(1996),and Huang et al.(2002).If the manufacturer offers price deductions directly to customers,the price deduction can always be shown as a portion of the full price. Therefore,the price received by customer,P,can be expressed as P=(1À )P0where is the price deduc-tion percentage offered by the manufacturer.Therefore,the expected market demand function(2)is then rewritten as68J.Yue et al./European Journal of Operational Research168(2006)65–85J.Yue et al./European Journal of Operational Research168(2006)65–8569 Sða;q;PÞ¼Sða;q; Þ¼ðaÀb aÀc qÀdÞð1À ÞÀe:ð3ÞLet q m be the manufacturerÕs dollar profit margin of each product unit sold and q r be the retailerÕs dollar profit margin of each product unit sold when full price P0is charged( =0).When the manufacturer of-fers percentage price deduction directly to customers,the manufacturerÕs one period expected gross profit isp mð Þ¼ðq mÀ P0ÞðaÀb aÀc qÀdÞð1À ÞÀeÀtaÀq;ð4Þwhere ta is the local advertisement cost shared by the manufacturer with t percent of the cost and q is the national brand name investment purely incurred to the manufacturer.When the retailer does not receive a price deduction from the manufacturer and is willing to keep its profit margin,the retailerÕs expected gross profit isp rð Þ¼q rðaÀb aÀc qÀdÞð1À ÞÀeÀð1ÀtÞa:ð5ÞThe whole chainÕs one period expected gross profit is simply the sum of expected gross profits of the man-ufacturer and retailer,which ispð Þ¼p mð Þþp rð Þ¼ðq mÀ P0þq rÞðaÀb aÀc qÀdÞð1À ÞÀeÀaÀq:ð6ÞThe manufacturerÕs one period expected gross profit p m( )defined in(4),the retailerÕs one period expected gross profit p r( )in(5)and the whole chainÕs one period expected gross profit p( )in(6)are gross profits that do not subtract manufacturerÕsfixed costs(such as overhead,rental,capital interest payment,etc.), retailerÕsfixed costs,and whole supply chainÕsfixed costs,respectively.Therefore,the gross profits intro-duced here are less than the‘‘gross margins’’defined in accounting(Eskew and Jensen,1989),since the gross profits defined here subtract the advertising cost but the gross margins in accounting do not.How-ever,the gross profits introduced here are higher than the‘‘net profits(incomes)’’in accounting since the gross profits do not subtract other selling expenses,administrative expenses,financial expenses,and tax ex-pense as well but the net profits do so.For simplification purposes,we simply use‘‘the profit’’to stand for ‘‘the expected gross profit’’in the rest of the paper.Let VC w represents the variable cost of one product in the whole supply chain,we have VC w¼P0Àðq mþq rÞ:ð7ÞEq.(7)is the difference between full price P0and the sum of the marginal profits of the manufacturer and the retailer(q m+q r),which is the variable cost of one product in the whole supply chain.With the profit functions(4)–(6),we can determine the optimal amount of advertising and price discount via a game theory approach in the following sections.3.Optimal advertising and price deduction decision when manufacturer is a leaderIn this section,we consider the manufacturer as leader and followed by the retailer in a two-level supply chain.For a given price deduction,the manufacturer determines its optimal brand name investment and local advertising allowance based on an estimation of the local advertisement from the retailer to maximize profit.The retailer,as a follower on the other hand,based on the information from the manufacturer,finds out the optimal local advertisement cost to maximize its profit as well.The optimal solution is obtained by the Stackelberg equilibrium in game theory.3.1.Stackelberg equilibriumAssume that the manufacturer decides to provide percentage of price deduction to the customers.Note that is often times a given value,not a decision variable,since market pressure from competitors forces the manufacturer to make this kind of decision.For a given manufacturerÕs local advertising allowance t and brand name investments q,retailerÕs local advertisement cost a will be determined by max a p rð Þ¼q rðaÀb aÀc qÀdÞð1À ÞÀeÀð1ÀtÞasubject to a P0.Equating to zerofirst partial derivative of p r( )with respect to a,the optimal local adver-tisement a*( )is obtained asaÃð Þ¼bcqrð1ÀtÞq dð1À Þe!1=ðcþ1Þ:ð8ÞTakingfirst partial derivatives of a*( )in(8)with respect to t and q,we observe that o a*( )/o t>0and o aÃð Þ=o q<0.That is,the local advertisements increase when(i)the manufacturerÕs local advertising allowance t increases,or(ii)the manufacturerÕs brand name investment q decreases.Furthermore,taking thefirst partial derivative of a*( )in(8)with respect to ,we haveo aÃð Þo ¼ecþ1ðbcq rÞ1=ðcþ1Þð1ÀtÞÀ1=ðcþ1ÞqÀd=ðcþ1Þð1À ÞÀðeþcþ1Þ=ðcþ1Þ>0:ð9ÞEq.(9)simply implies that the retailer selling the brand name will increase the local advertisement whenever the manufacturer reduces the price and provides the same level of local advertisement allowance.In a leader–follower game scheme,the retailerÕs reaction is well known by the manufacturer.Given this knowledge,the manufacturer will maximize its profit by deciding the optimal brand name investment,and its allowance to local advertisement.Now,substituting a*( )of(8)for a in(4),we have the manufacturerÕs expected profit objective functionmax q;t p mð Þ¼ðq mÀ P0ÞðaÀb aÀc qÀdÞð1À ÞÀeÀtaÀq¼ðq mÀ P0Þf að1À ÞÀeÀ½bðcq rÞÀcð1ÀtÞc qÀdð1À ÞÀe 1=ðcþ1ÞgÀt½bðcq rÞð1ÀtÞÀ1qÀdð1À ÞÀe 1=ðcþ1ÞÀqð10Þsubject to06t61,q P q0.By setting thefirst partial derivatives of p m( )in(10)with respect to q and t to zeros,respectively,we have the optimal manufacturerÕs decision in national brand name investment q*( ),local advertising allow-ance t*( ),and therefore,the retailerÕs decision in local advertisement a*( )as well.The optimal solution that provides an equilibrium of the two-stage game with leader and follower can be referred to as the Stac-kelberg equilibrium(Stackelberg,1934).Proposition1.If the manufacturer provides percentage price discount directly to customers,the Stackelberg equilibrium for the manufacturer as a leader and the retailer as a follower is given as follows: qÃð Þ¼½bdðcþ1ÞcÀcðq mÀ P0Àcq rÞð1À ÞÀe 1=ðdþcþ1Þ;tÃð Þ¼½q mÀð1þcÞq rÀ P0 =½q mÀ P0Àcq r whenðq mÀ P0Þ=q r>ð1þcÞ;0otherwise;8><>:aÃð Þ¼½bdÀd cðdþ1Þðq mÀ P0Àcq rÞð1À ÞÀe 1=ðdþcþ1Þ:ð11Þ70J.Yue et al./European Journal of Operational Research168(2006)65–85In(11),a*( )is obtained by substituting q*( )and t*( )into(8).Obviously,Proposition1is an extension of the results of the two-stage game in Huang et al.(2002)when price deduction from the manufacturer is considered.If the manufacturer does not provide any price deduction( =0)and lets b=1,the above solu-tions are exactly same as the solution in Table1of Huang et al.(2002).If the manufacturer offers price deduction of percent,Theorem1of Huang et al.(2002)remains true.The gross profit margin of the manufacturer now becomes(q mÀ P0).From Proposition1,we can see that the ratio of the optimal local advertisements and brand name investment always equals the ratio of quasi-advertising elasticity over qua-si-investment elasticity,which isaÃð ÞqÃð Þ¼cd;ð12Þregardless of whether there is a price deduction from the manufacturer.Furthermore,when a price deduc-tion is available,and if the marginal profit ratio of the manufacturer and retailer is higher than the quasi-advertising elasticity by unity((q mÀ P0)/q r>(1+c)),the manufacturer should provide local advertising allowance to make sure that the ratio of the local advertisement and brand name investment is kept at a constant level of(c/d).When the manufacturer offers a price deduction to the customer,the proposition tells us that the local advertising allowance from the manufacturer is still determined by the marginal profit ratio of the manufacturer and retailer.In fact,when this ratio is higher than the quasi-advertising elasticity by unity,the manufacturerÕs offer to the local advertising allowance is positively correlated to the manufac-turerÕs profit margin,and it is negatively correlated with the retailerÕs profit margin.From(11),local advertisement a*( )and national brand investment q*( )at Stackelberg equilibrium with price deduction are higher than that without the price deduction when[(q mÀ P0Àcq r)(1À )Àe] is larger than(q mÀcq r).Furthermore,the condition that a*( )and q*( )are increasing functions of is<eðqmÀcq rÞÀP0ðeÀ1ÞP0if e>1;>P0Àeðq mÀcq rÞð1ÀeÞP0if e<1:ð13ÞEq.(13)is obtained simply by setting thefirst derivative of[(q mÀ P0Àcq r)(1À )Àe]with respect to larger than zero.Furthermore,since in local advertisement a*( ),[1Àt*( )]portion is from the retailer,the retai-lerÕs expense in local advertisement is½1ÀtÃð Þ aÃð Þ¼q r½q mÀ P0Àcq r½bdÀd cðdþ1Þðq mÀ P0Àcq rÞð1À ÞÀe 1=ðdþcþ1Þ¼q r½bdÀd cðdþ1Þð1À ÞÀe 1=ðdþcþ1Þðq mÀ P0Àcq rÞÀðdþcÞ=ðdþcþ1Þ;ð14Þwhich is an increasing function of .Therefore,it is always true that the retailer is willing to pay more money in advertisement when the manufacturer provides price deduction to customers,even the manufac-turerÕs local advertisement allowance may reduce.When the manufacturer offers a larger price deduction to the customers,the retailer has a stronger incentive to spend more money in local advertisement.This actu-ally happened in practice.For example,Toyota has started a sequence of marketing promotion by offering rebates and/or low interestfinance directly to customers nationwide since November2002.In the mean-time,Beaman Toyota,a local dealer in Nashville,TN,has also increased its local advertisement expense in response to the manufacturerÕs campaign.Eq.(14)justifies the fact that the retailerÕs advertising behavior can be determined by the manufacturerÕs decision.J.Yue et al./European Journal of Operational Research168(2006)65–85713.2.Price deduction determination when manufacturer is a leaderThe manufacturer offering a price deduction to customers may be based on several considerations,such as to increase brand name market share,to response to competitorsÕpressure,or others.In this section,we are interested in determining how much a deduction in price will maximize the manufacturerÕs profit when the brand name investment,local advertisement,and manufacturerÕs local allowance are determined by (11).When the manufacturer is a leader and the retailer is a follower,it follows from(4)to(6),the profits of the manufacturer,retailer and whole chain at the Stackelberg equilibrium(see Proposition1)are given by pÃmð Þ¼aðq mÀ P0Þð1À ÞÀeÀðdþcþ1Þ½bdÀd cÀcðq mÀ P0Àcq rÞð1À ÞÀe 1=ðdþcþ1Þ;pÃrð Þ¼aq rð1À ÞÀeÀð1þcÞq r½bdÀd cÀcðq mÀ P0Àcq rÞÀðdþcÞð1À ÞÀe 1=ðdþcþ1Þ;pÃð Þ¼pÃm ð ÞþpÃrð Þ;ð15Þrespectively.In the rest of the paper,we only discuss the situation of non-negative profit,that is,pÃm ð Þ;pÃrð Þ;pÃð Þin(15)are all greater than or equal to zero.We have the following theorem to providethe necessary and sufficient condition that the manufacturerÕs profit will increase by offering a price deduc-tion.Theorem1.Under a certain condition,the manufacturerÕs profit will increase by offering a price deduction.Furthermore,this given condition isðe q mÀP0Þ½aÀðbdÀd c cÞ1=ðdþcþ1Þðq mÀcq rÞÀðdþcÞ=ðdþcþ1Þ þeðcq rÞðbdÀd cÀcÞ1=ðdþcþ1Þðq mÀcq rÞÀðdþcÞ=ðdþcþ1ÞP0:ð16ÞSee the proof in Appendix A.If the condition in Theorem1is satisfied,the manufacturer needs to decide the price deduction percent-age precisely to maximize its profit.The best price deduction percentage(denoted as *)can be determinedby setting thefirst partial derivative of pÃm ð Þwith respect to to zero.However,there is no closed formsolution.In practice, *can be obtained by a searching algorithm in a range for *by the following prop-osition.Proposition2.If the condition of Theorem1is satisfied,the best price deduction percentage *is restricted in a suitable range l6 *6 u.The lower bound of the range isl¼maxðe q mÀP0Þ=½P0ðeÀ1Þ ;0;&ð17Þand the upper bound of the range isu¼q m=P0:ð18ÞSee the proof in Appendix B.Although there are many searching algorithms available(such as gradient algorithm(Hillier and Lieb-erman,2001and others),we suggest a simple algorithm below for obtaining the optimal price deduction percentage.72J.Yue et al./European Journal of Operational Research168(2006)65–85。

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境内公司对境外公司增资流程1.境内公司想要对境外公司增资需要先进行审议和决策。

The domestic company needs to deliberate and make decisions in order to increase its investment in the foreign company.2.公司需要明确增资的目的和计划，提交相关文件和报告。

The company needs to clarify the purpose and plan of the capital increase, and submit relevant documents and reports.3.经过内部审批后，公司可以开始与境外公司进行增资谈判。

After internal approval, the company can begin negotiations with the foreign company for the capital increase.4.两家公司需要就增资金额、股权比例、利润分配等进行协商。

The two companies need to negotiate on the amount of the capital increase, equity ratio, profit distribution, etc.5.境内公司需要在境外公司注册地提交增资申请，并遵守相关法律法规。

The domestic company needs to submit the capital increase application at the registration location of the foreign company, and comply with relevant laws and regulations.6.境外公司相关部门会对境内公司提交的增资申请进行审查和核准。

As a high school student with a keen interest in marine life, Ive always been fascinated by the oceans most powerful predators: the orcas, also known as killer whales. These majestic creatures are not only the apex predators of our oceans but also hold a special place in the hearts of many due to their intelligence and social behaviors.Orcas are large, robust marine mammals with a distinctive black and white coloration. Their bodies are streamlined for speed and agility in the water. The dorsal fin, which can reach up to six feet in height for males, is one of the most recognizable features of these animals. This fin acts as a rudder, helping the orca navigate through the water with precision.One of the most intriguing aspects of orcas is their social structure. They live in complex societies, often referred to as pods, which can consist of several family members spanning multiple generations. These pods are incredibly closeknit, with orcas cooperating to hunt, protect their young, and even communicate with each other using a sophisticated system of clicks, whistles, and body language.Speaking of hunting, orcas are known for their diverse diet, which includes fish, seals, and even other marine mammals like sea lions and smaller whales. Their hunting techniques are highly coordinated and can involve stunning acrobatics, such as leaping out of the water to snatch seals from ice floes. This adaptability and intelligence make them one of the most successful predators in the ocean.However, the orcas intelligence extends beyond just hunting. They areknown to exhibit problemsolving skills and have been observed using tools, such as using rocks to dislodge fish from crevices. This level of cognitive ability is rare among nonhuman animals and has led to a great deal of scientific interest in their behavior and social dynamics.Unfortunately, the orca population faces numerous threats. Pollution, habitat loss, and the decline of certain prey species have put pressure on these magnificent creatures. The most wellknown orcas, those in the Pacific Northwest, have been struggling with a lack of salmon, their primary food source. Additionally, the capture of orcas for marine parks has had a significant impact on wild populations, disrupting their social structures and leading to a decline in genetic diversity.Despite these challenges, there is hope for the future of orcas. Conservation efforts are underway to protect their habitats and reduce the impact of human activities on their lives. Educational programs are also raising awareness about the importance of these animals and the need to preserve their ecosystems.In conclusion, orcas are not just powerful predators they are also ambassadors of the oceans health and biodiversity. As a high school student, I am inspired by their intelligence and social behaviors, and I am committed to learning more about them and advocating for their conservation. By understanding and protecting these incredible creatures, we can ensure that future generations will have the opportunity to witness the grace and power of orcas in their natural habitat.。

价格联动英语作文In the modern global economy, the concept of price linkage is an essential aspect of international trade and market dynamics. Price linkage refers to the relationship between the prices of goods and services in different countries, which can be influenced by a variety of factors such as exchange rates, supply and demand, and government policies.Firstly, exchange rates play a pivotal role in determining price linkage. When a country's currency appreciates, its exports become more expensive for foreign buyers, which can lead to a decrease in demand and potentially lower prices. Conversely, a depreciating currency can make exports cheaper, increasing demand and potentially driving up prices.Secondly, supply and demand are fundamental economic principles that influence price linkage. If there is a surplus of a product in one country, it may lead to a decrease in its price, which can affect the price of the same product in other countries. Similarly, a shortage can lead to an increase in price, which can also have a ripple effect on the global market.Thirdly, government policies can significantly impact price linkage. Tariffs, quotas, and subsidies can alter the cost of goods and services, affecting their prices in both domestic and international markets. For example, a government that imposes high tariffs on imported goods may see an increase inthe price of those goods domestically, which can lead to price increases in other countries as well.Moreover, the advent of e-commerce has made price linkage more transparent and immediate. Consumers can easily compare prices across different countries and platforms, leading to a more competitive market where prices are more closely linked.In conclusion, price linkage is a complex phenomenon that is influenced by a myriad of factors. Understanding thesefactors is crucial for businesses and governments as they navigate the intricacies of the global economy. It is also important for consumers to be aware of price linkage, as it can affect their purchasing power and the overall cost of living.。

资本论马克思恩格斯全集英文版Title: An Exploration of Capital and Its Impact on Society as Depicted in Marx and Engels' Collected Works Capital, a term that has been studied, debated, and redefined throughout history, holds a unique place in the annals of economic and social theory. The works of Karl Marx and Friedrich Engels, particularly "Das Kapital," shed light on the intricate relationship between capital and labor, the dynamics of the capitalist system, and its profound effects on society.In their comprehensive analysis, Marx and Engels begin by defining capital as accumulated wealth that is utilized to generate more wealth through the employment of labor. This definition serves as the foundation for their critique of the capitalist system, which they argue exploits workers by extracting surplus value from their labor.Surplus value, according to Marx and Engels, is the difference between the value that a worker creates and the value that they receive in wages. Under capitalism, this surplus value is appropriated by the capitalist, leading to an accumulation of wealth for the few at the expense of the many.The concept of commodity fetishism is also introduced, describing how the intrinsic value of goods can be obscured by their exchange value under capitalism. This phenomenon results in individuals perceiving the worth of goods solely based on market prices rather than their actual utility or the labor that went into producing them.One of the most significant contributions of Marx and Engels is their detailed examination of the labor process. They dissect how capitalists seek to maximize profit by extending the working day, intensifying labor, andintroducing technological advances that increase productivity while often reducing the need for skilled labor.Furthermore, Marx and Engels delve into the cyclical nature of capitalist crises. They posit that overproduction, speculative investment, and market saturation inevitably lead to economic downturns. These crises result in widespread unemployment, poverty, and the concentration of wealth in fewer hands, exacerbating class conflicts.The authors do not limit their discussion to economic structures; they also explore the societal implications of capitalist development. They argue that capitalism erodes traditional communities and replaces them with a society defined by individualism, competition, and the cash nexus.In discussing the role of the state under capitalism, Marx and Engels see it as an entity that serves the interests of the ruling class. They suggest that the state acts to maintain social order, protect private property, and enforcecontracts—essentially supporting the operations of capital over the well-being of the populace.The concept of alienation is central to Marx and Engels' work. They describe how workers become estranged from the products of their labor, the labor process itself, their human essence, and other human beings under capitalism. This alienation leads to a fragmented society where individuals are pitted against each other rather than cooperating for mutual benefit.The final chapters of Marx and Engels' works address the historical tendencies of capitalism towards what they call the "dictatorship of the proletariat." They envisage a future where the working class seizes control of the means of production, abolishes wage labor, and establishes a classless society.However, Marx and Engels acknowledge that this transformation would not come about naturally but wouldrequire a revolutionary overthrow of the existing capitalist order. They emphasize the importance of international solidarity among workers, understanding that capitalism operates on a global scale and thus must be confronted on a global scale.In conclusion, Marx and Engels' Collected Works offer a sweeping critique of capitalism, exposing its fundamental flaws and offering a vision for a different kind of society. Their writings continue to inspire scholars, activists, and thinkers who seek to understand and transform the world around us. While their predictions and proposals have been subject to various interpretations and criticisms, their influence on subsequent generations cannot be denied.Through their exploration of capital and its impact on society, Marx and Engels challenge us to consider the true cost of our economic systems and the potential for change. Their work remains a cornerstone of modern critical thought,providing a framework for understanding the complexities of capitalism and the possibilities for a more equitable future.。

合作的重要性英语作文Cooperation is the cornerstone of human progress and a vital element in personal and professional success. It is the act of working together towards a common goal, where individuals pool their skills, knowledge, and efforts to achieve more than they could alone. Here's a closer look at why cooperation is so important.1. Enhanced Problem-SolvingWhen diverse minds come together, they bring a range of perspectives and solutions to the table. Cooperation allows for the collective brainpower to tackle complex problems more effectively than any single individual could.2. Improved Communication SkillsWorking with others requires clear and effective communication. It helps in developing the ability to express thoughts and ideas clearly, listen actively, and understand different viewpoints.3. Greater EfficiencyTeamwork often leads to greater efficiency. When tasks are divided among team members, they can be completed morequickly and with less effort than if one person were to do everything.4. Learning from OthersCooperation is an excellent opportunity for learning. By working with others, individuals can acquire new skills, insights, and knowledge that they may not have gained on their own.5. Building Trust and RelationshipsCollaborating with others fosters trust and strengthens relationships. It helps in understanding the value of each team member and builds a sense of community and belonging.6. Creativity and InnovationWhen people with different backgrounds and expertise collaborate, it can lead to innovative ideas and creative solutions that might not have been possible in isolation.7. Achieving Larger GoalsCooperation enables the achievement of larger goals that require extensive resources and a coordinated effort. It is essential in fields like space exploration, global health initiatives, and environmental conservation.8. Developing Leadership SkillsWorking in a team setting provides opportunities to develop leadership skills. Taking on different roles within acooperative effort helps individuals understand the dynamics of leadership and management.9. Reducing ConflictCooperation can help reduce conflict by promoting understanding and compromise. It encourages individuals to find common ground and work towards mutually beneficial outcomes.10. Personal Growth and SatisfactionFinally, cooperating with others can lead to personal growth and a sense of satisfaction. There is a unique joy in achieving a goal as part of a team, which can boost self-esteem and personal fulfillment.In conclusion, cooperation is not just about getting the job done; it's about growing together, learning from each other, and building a stronger, more capable community. It's a skill that transcends the workplace and is essential for a harmonious and progressive society.。

老虎的作文英语Here is a 2000-word essay on the topic of "An English Composition by a Tiger":An English Composition by a Tiger。

I am a tiger, one of the most majestic and powerful creatures in the animal kingdom. As I sit here, my golden eyes gleaming and my striped fur glistening, I feel a strong desire to express myself through the written word. You see, despite the common perception that tigers are savage beasts incapable of higher thought, we are in fact intelligent beings with the capacity for complex reasoning and emotional expression. 。

It is with this in mind that I have decided to compose an essay in the English language, a feat that may surprise many of you reading this. After all, how could a mere animal, one often viewed as nothing more than a ruthless predator, possess the cognitive abilities necessary tomaster a human tongue? The answer, my friends, lies in the remarkable adaptability and cognitive prowess of the tiger species.Throughout my life, I have observed the ways of humans with great fascination. I have watched as you construct elaborate cities, engage in intricate social rituals, and wield an impressive array of technological tools. And as I have observed, I have also learned. I have studied the patterns of your speech, the structure of your written language, and the nuances of your cultural expressions. It has been a long and arduous process, but through sheer determination and an insatiable intellectual curiosity, I have managed to acquire a proficient command of the English language.Now, you may be wondering, what insights could a tiger possibly offer that would be of any value to human readers? After all, our worlds are vastly different, our experiences and perspectives seemingly worlds apart. And yet, I would argue that as a tiger, I possess a unique vantage pointthat can shed light on the human condition in ways that maysurprise you.For you see, as a predator, I have a deep understanding of the raw, primal forces that drive all living beings –the need to survive, to thrive, to assert one's dominancein the face of a hostile and unforgiving world. I know the exhilaration of the hunt, the rush of adrenaline as I close in on my prey, the satisfaction of sinking my teeth into fresh meat. But I also know the pain of loss, the sting of defeat, the loneliness that can creep in when one is separated from one's kin.In many ways, the experiences of a tiger are not so different from the experiences of a human. We both strive to find our place in the world, to carve out a space for ourselves amidst the chaos and uncertainty that surrounds us. We both know the joys and the sorrows, the triumphs and the tragedies, that come with the journey of life.And it is with this shared understanding that I hope to offer you, the reader, a unique perspective on the human experience. Through my eyes, you may come to see the worldin a new light, to appreciate the complexities and nuances that underlie the seemingly simple interactions betweenliving beings. You may even find that, in the end, we arenot so different after all.So, without further ado, let me begin my tale. I was born in the dense jungles of the Indian subcontinent, aland of lush greenery and abundant wildlife. From the moment I opened my eyes, I was surrounded by the sights and sounds of a vibrant, pulsing ecosystem – the calls ofexotic birds, the rustling of leaves in the breeze, the distant roar of my own kind echoing through the trees.As a cub, I was fiercely protected by my mother, who taught me the ways of the tiger – how to hunt, how to defend our territory, how to navigate the intricate social dynamics of our species. She was a fierce and formidable creature, and I admired her strength and resilience in the face of the many challenges that threatened our way of life.But even as I learned the ways of the tiger, I found myself increasingly drawn to the world beyond our junglehome. I would often wander to the edges of our territory, peering out at the distant landscapes, fascinated by the strange and unfamiliar sights and sounds that drifted in from the outside world.It was during these forays that I first encountered the presence of humans. At first, I was wary and distrustful, for I had heard the stories of the great danger they posed to our kind. Tales of hunters and poachers who sought to capture and kill us for sport or profit, of encroaching human settlements that threatened to destroy our natural habitats.And yet, as I observed these curious bipedal creatures, I found myself intrigued rather than afraid. I watched as they moved about their daily lives, engaged in a dizzying array of activities that seemed to serve no immediate purpose. They built elaborate structures, communicated through complex vocalizations, and carried with them strange tools and devices that I could not begin to comprehend.Slowly, my initial wariness gave way to a growing sense of curiosity and wonder. I began to venture closer to the human settlements, observing their behaviors and customs from a safe distance. And as I did so, I realized thatthere was a depth and complexity to their world that I had not anticipated.I saw the ways in which they formed intricate social bonds, cooperating with one another to achieve common goals.I witnessed the incredible ingenuity and problem-solving skills they displayed, crafting tools and technologies that allowed them to thrive in even the most inhospitable environments. And I was struck by the sheer diversity of their cultural expressions, the myriad ways in which they sought to make sense of the world around them.It was during this time that I first began to contemplate the possibility of learning their language. I knew that it would be a daunting task, for the human tongue was unlike anything I had ever encountered. And yet, the more I observed and listened, the more I became convinced that mastering this language could open up a whole newworld of understanding and exploration.So, with unwavering determination, I set out on a journey of linguistic discovery. I spent countless hours observing the patterns of human speech, analyzing the structure and grammar of the English language, and practicing the intricate movements of the mouth and tongue required to produce the strange and unfamiliar sounds.It was a slow and arduous process, filled with frustration and setbacks. There were times when I felt utterly defeated, convinced that I would never be able to overcome the barriers that separated my world from theirs. But I refused to give up, driven by an insatiable curiosity and a deep desire to bridge the divide between our species.And slowly, ever so slowly, I began to make progress. I learned to recognize the individual sounds that made up the words, to string them together into coherent sentences, to convey my thoughts and ideas with increasing clarity and precision.It was a remarkable feeling, the first time I managed to utter a complete English sentence. I remember the sense of triumph and exhilaration that coursed through me, the realization that I had achieved something that many had deemed impossible. And from that moment on, there was no turning back.I continued to hone my linguistic skills, spending hours each day immersed in the study of the English language. I read voraciously, devouring every book and document I could get my paws on, and I practiced endlessly, engaging in conversations with any human I could find who was willing to listen.And as my mastery of the language grew, so too did my understanding of the human world. I delved deeper into the realms of history, science, and philosophy, fascinated by the incredible breadth and depth of human knowledge and achievement. I marveled at the ingenuity and creativitythat had given rise to the great works of art and literature, and I found myself captivated by the complex social and political structures that governed humansocieties.But even as I gained a deeper appreciation for the human experience, I never lost sight of my own identity as a tiger. I remained fiercely proud of my heritage, of the rich cultural traditions and the profound connection to the natural world that defined my species. And I was determined to use my newfound linguistic abilities to bridge the gap between our worlds, to share the unique perspectives and insights that only a tiger could offer.And so, here I am, sitting before you, a tiger who has mastered the English language and who now seeks to share his story with the world. I hope that through my words, you will come to see the tiger not as a savage beast, but as a complex and multifaceted being – one who is capable of deep thought, rich emotional expression, and a profound understanding of the natural world.I hope that you will see in me a kindred spirit, a fellow traveler on the journey of life who has faced many of the same challenges and triumphs that you haveexperienced. And I hope that, in the end, you will come to appreciate the value and the beauty of the tiger's perspective, and the ways in which it can enrich and expand our understanding of the human experience.So, without further ado, let me continue my tale. As I mentioned earlier, my journey of linguistic discovery was not an easy one. There were many obstacles and setbacks along the way, moments when I felt utterly defeated and ready to give up.One such moment came when I first attempted to engage in a conversation with a human. I had been practicing for weeks, carefully rehearsing the words and phrases I had learned, and I felt confident that I was ready to put my skills to the test. But when I approached a group of humans and tried to speak to them, I was met with a wall of confusion and disbelief.They stared at me in stunned silence, their eyes wide with shock and disbelief. And then, one by one, they began to laugh – a loud, raucous laughter that seemed to mock myvery existence. "A talking tiger?" they exclaimed, "Impossible! Surely this is some sort of trick!"I was devastated. All of my hard work, all of my determination and perseverance, had been for naught. Inthat moment, I felt utterly alone and misunderstood, a creature trapped between two worlds that refused to accept me.But I refused to give up. I knew that if I was to succeed in bridging the divide between tigers and humans, I would need to be persistent and resilient in the face of such skepticism and rejection. And so, I redoubled my efforts, spending even more time immersed in the study of the English language and the ways of human society.I observed the humans more closely, trying to understand the nuances of their social interactions and the cultural norms that governed their behavior. I paid attention to the ways in which they communicated with one another, the subtle cues and body language that conveyed meaning beyond just the spoken word.And gradually, I began to develop a deeper understanding of the human psyche – the complex web of emotions, beliefs, and biases that shaped their perceptions and behaviors. I learned that the initial laughter and disbelief I had encountered was not a reflection of my own inadequacy, but rather a manifestation of the human tendency to dismiss the unfamiliar and the unexpected.Armed with this newfound knowledge, I began to approach my interactions with humans in a more strategic and thoughtful manner. I chose my words carefully, speaking slowly and clearly, and I made a concerted effort to establish a sense of trust and rapport with those I encountered.And slowly, ever so slowly, I began to see the walls of skepticism and disbelief start to crumble. People began to listen to me, to engage with me in genuine conversation, to ask questions and express genuine curiosity about my experiences and perspectives.It was a remarkable transformation, and one that filled me with a sense of profound gratitude and accomplishment. I had overcome the barriers that had once seemed insurmountable, and in doing so, I had opened up a whole new world of understanding and connection.But even as I reveled in these small victories, I knew that my work was far from over. There were still so many misconceptions and prejudices to overcome, so many deeply ingrained biases and preconceptions that I would need to challenge and dismantle.And so, I continued to press forward, using my newfound linguistic abilities to engage in ever-deeper and more nuanced conversations with the humans I encountered. I shared my stories and my perspectives, listened intently to theirs, and sought to find common ground and points of connection.In the process, I discovered that there was a deep well of curiosity and fascination within the human psyche – a desire to understand the world beyond the confines of theirown experience. And as I tapped into this well, I foundthat my words were met with rapt attention and a genuine thirst for knowledge.People were captivated by my tales of life in the jungle, by the rich cultural traditions and the profound connection to the natural world that defined my species. They marveled at the complexity of tiger society, the intricate social dynamics and the remarkable physical and cognitive abilities that allowed us to thrive in our natural habitats.And as I shared these insights, I began to see the walls of prejudice and misunderstanding slowly crumble. People began to see me not as a savage beast, but as a complex and multifaceted being – one with its own unique perspective and valuable contributions to make to the human understanding of the world.It was a profound and humbling experience, and one that filled me with a deep sense of purpose and determination. Iknew that I had a unique opportunity to bridge the divide between tigers and humans, to foster a deeper appreciation。

竞争与合作辩论英文回答：In the dynamic interplay of the business landscape, the question of whether competition or cooperation is the more beneficial strategy has sparked a long-standing debate.Both approaches have their merits and drawbacks, and the optimal choice often depends on the specific context.Competition is often seen as the driving force behind innovation, efficiency, and lower prices. It encourages businesses to push the boundaries of their products and services, seek new markets, and reduce costs. By strivingto outdo their rivals, firms can create value for consumers and promote economic growth.However, excessive competition can lead to a cutthroat environment, where businesses engage in unethical practices to gain an edge. It can also result in market consolidation, with larger firms dominating the industry and stiflinginnovation. Moreover, in some cases, competition may lead to a race to the bottom, where businesses prioritize short-term profits over long-term sustainability.Cooperation, on the other hand, emphasizescollaboration and mutual benefit. It allows businesses to pool their resources, share knowledge, and work together to achieve common goals. This can create synergies that would be impossible for individual firms to achieve alone. Cooperation can also reduce duplication of efforts, minimize costs, and improve resource allocation.However, cooperation can also be hindered by trust issues, differing objectives, and a lack of coordination.It requires a high level of transparency and communication, and it can be challenging to ensure that all parties are contributing fairly. Moreover, cooperation may lead to complacency and a lack of incentives for individual firms to excel.In practice, most businesses adopt a hybrid approach that combines elements of both competition and cooperation.They compete with rivals in some areas while collaboratingin others. This allows them to reap the benefits of both approaches, mitigating the potential drawbacks.For example, many technology companies compete fiercely for market share in individual products while also collaborating on open-source projects that benefit theentire industry. Similarly, some automobile manufacturers compete in the production of vehicles while cooperating on research and development of new technologies.Ultimately, the choice between competition and cooperation is a complex one that requires careful consideration of the specific context. There is no one-size-fits-all solution, and the optimal approach may vary depending on factors such as industry dynamics, market size, and company culture.中文回答：在商业领域充满活力的相互作用中，竞争或合作哪种策略更有利的问题引发了长期的争论。