| According to the difference of market organizations ,production market can be devided into four types : perfect competition, monopolistic-competition, oligopoly, monopoly. The latter three marketable organizations are called imperfect competitive markets .After a period, economic equilibrium can be destroyed duo to its , inner conflict in marketable economy . And this situation can lead to break out a serious economic crisis about more productions . In the crisis , productive resources go through enormous ruin , so the economic equilibrium is recovered coercively, and the crisis becomes the adjusting system of equilibrium. Up to 1930s, western countries begin to put policy tools into the adjusting system , and perform macro-adjusting policies to make the economic equilibrium about whole demands and supplies. As a result , they gain the equivalent increasing of economics .The government has all kinds of policies about macroeconomics. This paper will discuss how to adjust macroeconomics by economic policies including financial and monetary policies , and to realize the macroeconomic object which government is in search of.If government wants to get its expecting results , and to avoid that "one has policies , the other has antidotes" , it must possess both accomplished macro-adjusting system and corresponding micro-basis . The relationbetween macroeconomic policies and micro-basis shows a both-side encouragement-response system : on the one hand , macro-adjusting body enact a series of economic policies to influence micro-economic body, and to realize macroeconomic object via some economic parameters ; on the other hand , due to the motive of chasing the maximal profit, micro-economic bodies make corresponding reaction via the market, which can aiso influence the macroeconomic object which government is in search of . According to the influence , government can educe whether it realize the macroeconomic object , otherwise , government begins to adjust macroeconomic policies , and the next both-side encouragement-response adjusting system is beginning in order to realize the macroeconomic object . This paper tries to discuss the relation between government's macro-adjusting policies and microeconomic basises.In the marketable mechanism, and in different market economic organizations , there exist three kinds of economic behaviour bodies: Producer Consumers and Government .the relations can be expressed by the following graph :Producers t^ ConsumersGovernmentThere also exist many relations among three kinds of economic behaviour bodies . The authors in articles [2]-[4], [6], [7], [57],etc., have studied behaviour relations between producters and government; the authors in article [58],etc. have studied behaviour relations between consumers and government in perfect competitive markets.In a word , why we will discuss macroeconomic optimal models inimperfect competitive markets is : first, the need of economic theory; secondly , the need of practice in the studies of combining government's macro-adjusting policies with microeconomic basises. So this paper tries to discuss the relation between government and. enterprises in imperfect markets (monopoly, oligopoly , monopolistic competition ). The following is concrete contents :Chapter one in this paper introduces the definations and characters of imperfect competitive markets □ the economic signification of macro-adjusting policies n optimal methods in this paper D the main problems discussed in this paper .Chapter two and chapter three discuss macroeconomic optimal model that government is in search of optimality of the whole output .The microeconomic basis is the profit's optimality that monopoly enterprises chase .We have the following assumptions on monopolistic market : there are n monopoly firms , and every monopoly firm products only one monopoly product, so there are n different monopoly products in all. Firstly we consider the optimal model of the ith firms on basis of [8]-[14] , and we use methods of [2]-[4] . The profit's optimal model of the ith monopoly firm ismaxpi(ci-kipi)-rdixi x, < 1\aixi =ci-kipi (2.2.1) SM . -Pi^ Pix,>0,Pi >0,where pj denotes the price of the ith product; capital rate r is a given parameter, and it is also one of government's macro-agjusting method ; pi denotes the government's constrained price for monopolyfirmst8J"[13]; x, denotes effective time that the ith firm products the ith product in one year; a, denotes the one-year whole output that the ith firm products in one year. And we also assume that the demandingfunction of the ith producter is linear, c, - klpl about price p,.Convex quadratic optimal model that government chases the optimality of social whole output is given in chapter two:max1=1(2.3.1) s.t.xt<\ i = l,2,---,wpt0,Pi>0 i = l,2,-,nAt last , we show that monopoly firms, government can reach their optimization by government's macro-adjusting policies and monopoly firm's chasing its profit at the same time.In chapter three , bilevel programmings are used to reflect the relation between government and its microeconomic basisesFrom [ 1 ],i.e. lemmal .3.1, we know that equivalent form- of bilevel programming (3.2.3) is (3.2.6) that its uplevel programming has only uplevel's variable and it has no relation with downlevel's variable , so (3.2.6) can be divided into programming (3.2.7) and a programs' group LP(x, p\ n) with n programmings ,we haveTheorem3.3.1 Given the , optimal solution (3c,p) to (3.2.7) , if (p,u,v,7) is the corresponding optimal solution to (3.3.2), there exist w^{wx,w2,---,wn) and p = (px,p1,---:pn) so that (u,v,?,w,p) is the solution to programs group LP(x,p;n) at the parameter (x, p), and the optimal value of every subprogramming is CiPj-lkiP,, / = 1,2, ??-,?.The economic meaning is :at the first , government gives every firm's output so that government gains the optimal social whole output by solving model (3.2.7) ,but firms will propose demands of capital rate and others in order to chase the optimal profit. Taking the optimal solution(x, p) to (3.2.7) as parameters , we can find capital rate and other demands by solving programming (3.3.2) which satisfy firms' and government's demands . Under this capital rate and other demands , every firm's output so that government gains the optimal social whole output is that they gain the optimal profits .In chapter four.the converse problem of a parametric programming and its economic application is discussed further on the basis of article [1] . First, we consider the following convex quadratic programming :min ±txTQx + (cT +uTDx)x(4.1.1) (Ax>b-D2uSJA\x>0Due to the dual theory of convex quadratic programming^, we can get the dual programming :From lemma 4.1.1[5], taking the maximum of - txTQx + (b - D2uf X - uTDxxas the objective function , we can get the following parametric programming with x as parameter:max - txTQx + (b - D2u)Tk - uTD{x -tQx + A1" X-D\uO,t>OLemma4.1.2 Given parameter x > 0, objective function value for any feasible solution (X,t ,u) of quadratic parametric programming (4.1.5) is smaller than or equal to ex *Theorem 4.1.1 Givenx > 0,(t,u)is the solution to the converse problem of convex quadratic parametric programming (4.1.1) at parameter 3c if and only if there exists X so that {X,t,u) is the optimal solution to parametric programming (4.1.5) at parameter 3c and the optimal value of parametric programming (4.1.5) is c3c <,Parametric programming ( 4.1.5 ) is called the converse programming of convex quadratic parametric programming (4.1.1 )oTheorem 4.1.2 Consider the following more general quadratic parametric programmingmin \xTQTx + (cT + uTD^x (4.1.6) Ux>b-D4vSj\x > 0given x >0,(/,-,/ = 1,2,??-,?,,u,v) is the solution to the converseproblem of convex quadratic parametric programming (4.1.6) at parameter 3c if and only if tthere exists A so that (AjjJ = 1,2,??-,?,,?,v) is the optimal solution to parametric programmingmax -xTQTx + (b-DAv)TZ-uTD3x (4.1.7)si.-- DAv < -b + Axat parameter x and the optimal value of parametric programming (4.1.7) is c3ccThe bilevel programming model that government chases the maximum of social whole output and monopoly firms are in search of the maximum of profit with taxes ismax-\Q,pi>Q,i = l,2,---,n,where x,, pt are solutions to subprogram min gsmax piaixi(1 -/,■)- rc/,x;(4.2.2) s.t.aixl =ci-kjpisi-Pi ￡ Pii = \2.-,n.From [l],i.e. lemmal.3.1, we also know that equivalent form of bilevel programming (4.2.2) is (4.2.8) that its uplevel programming has only uplevel's variable and it has no relations with downlevel's variable , so (4.2.8) can be translated into a single-level programming (4.2.9) and a programs' group LP(x,p;n) with n programmings ,The economic meaning of equivalent form is : first government gives every firm's output so that government gains the maximum of the social whole output by solving model (4.2.9) , but firms will propose demands of capital rate and others in order to chase the optimal profit . Taking the optimal solution (5c, p) to (4.2.9) as parameters , we can find capital rate and other demands by solving a programs group LP(x,p;n) which satisfy firms'and government's demands. And so far, every firm's output that government gains the optimal social whole output is that they gain the optimal profits .From the definitions of oligopoly and monopoly competition, usually we think that oligopoly market has less firms and the monopolistic competitive market has more firms , but according to economic theory , we don't try to distinguish this two markets from firms' numbers . The main difference between them is their relations . In oligopolistic markets , every corporation must decides its own price and output on basis of assuming its rivals' behaviours .In chapter five , we establish the model of oligopolitic marketThe economic meaning of model (5.2.2) : due to [6] , there exist equivalent solutions to n interactive programmings of the downlevel under some conditions , so government can choose equivalent solutions via marco-adjusting methods-capital rate and tax etc.in order to make the maximal social whole output.In the following , we discuss marco-adjusting methods'influence to equivalent solutions to two oligopolistic markets . The authors in [4] have discussed marco-adjusting model in perfect competitive market; Three authors in [16] have proposed oligopolistic markets' model with mathematic programmings . On basis of [2]-[4], we will discuss further oligopolistic markets' equivalent models about output and price with taxes and the taxes' influence to equivalene .In chapter six , we try to discuss monopolistic competitive markets : many corporations product and sell homogeneous products with some difference .From the difference , every corporation is the monopolist of his own products ; from the homogeneous products,they can take place of one another , so there exist competitions among them . there are four assumptions from Chamberlin,E.H.: a lot of firms product homogeneous products with some difference :the ratio they possess in market is very small so that they can ignore their opponents' behaviours ; every firm has the same demanding and cost curves ; it is easy to come in and go out of the market for firms in a long period.In short period ,due to that every corporation is the monopolist of his own products and it has similar behaviour with monopolist ,so we will treat monopolistic competitive markets as monopoly markets , the model is following (6.2.2).In a long period ; due to that it is difficult to change their prices, and they have similar behaviours with perfect competitive firms ,so we try to treat monopolistic competitive markets as competitivemarkets .From perfect competitive theory and [l]-[4], [62]-[64] etc., the macroeconomic optimal model is (6.2.3).Similarly , we can get that monopolistic competitive firms and government can reach the optimization at the same time under some rational policies. |
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