SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY


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1 1 SIMULATION OF THE PERFECT COMPETITION AND MONOPOLY MARKET STRUCTURE IN THE COMPANY THEORY ALEXA Vasil ABSTRACT Th prsnt papr has as targt to crat a programm in th Matlab ara, in ordr to solv, didactically but not only, hav problms concrning company thory xtrm cass prfctd comptition and monopoly markt structur. This programm is capabl, for a known function of total costs of 3 CTS = a0 + a1q a Q + a3q, to giv data rgarding: lvl of balanc production, total costs, to b mad wholly and on th limit, on th lvl of balanc production. KEY WORDS: programm, matlab ara, comptition, monopoly markt, costs, didactically matrial, simulation 1. GENERAL OUTLOOK Th bhavior of a company with rspct to thir main dcisions can only b undrstood within th framwork of th markt structur which it carris out its activity in. Any company has to fac th issu of making two basic dcisions: how much to produc and what pric to sll thir products at? Markt structur dfins th lvl of comptition for a crtain product offrd by th company. Th markt consists in all th companis and individuals that ar willing, availabl and capabl of buying or slling a crtain product. Th most important charactristics of th markts ar th numbr and siz of sllrs and buyrs, as wll as th xtnt of product diffrntiation. Traditionally, four markt structurs ar mntiond with rspct to ths charactristics: prfct comptition markt; monopoly; monopolistic comptition; oligopoly.
2 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3. PERFECT COMPETITION In a prfct comptition markt structur th company will dcid only upon th quantity to b producd and offrd on th markt, but not upon th pric or product divrsification (implicitly upon th advrtising) as thy would infring th hypothss of th prfct comptition modl. Th graph of th short trm ovrall incom in a prfct comptition a straight lin that crosss th origin having as a slop th markt balanc pric. VTS = p Q (1) Th short trm marginal incom has th form: VMS = p () Th curv of short trm ovrall costs has th form: 3 CTS = a + a Q a Q + a (3) 0 1 3Q Dpnding on th position of th short trm ovrall cost curv CTS with rspct to th lin of ovrall incoms VTS, w can distinguish four situations, namly: a) th company that maks ovr profit; b) th company that maks normal profit; c) th company that dos not mak th ntir normal profit; d) th company that has actual losss. a) Th company maks ovr profit In this cas th diffrnc btwn th ovrall incoms and th ovrall costs is maximal for balanc output Q. Mathmatically: Π TS = VTS CTS (4) Th marginalistic principl of profit maximization implis quality btwn th marginal cost and th marginal incom: CMS = VMS = pq (5) Th hatchd ara in figur 1 rprsnts an ovr profit that is qual to th product btwn Q and th diffrnc btwn p and CUTS at th lvl of output Q namly: [ovr profit] = [ p CUTS( Q )] Q (6) b) Th company maks a normal profit CMS = VMS = p (7) Th company will mak a normal profit by functioning at minimal point Q of curv CUTS (s figur ), as: CUTS = CMS = VMS = (8) c) Th company dos no mak th ntir normal profit For crtain output lvls, th company is abl to covr at last th total variabl costs and partially th total fixd costs, so that th profit xists, but it is infrior to th normal on (s figur 3). Q CUTS Q p (9) [xploitation loss] = [ ( ) ] p 198
3 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 Fig.1. Prfct comptition th company maks ovr profit Fig.. Prfct comptition th company maks a normal profit Fig. 3. Prfct comptition th company dos no mak th ntir normal profit Fig. 4. Prfct comptition th company has actual losss d) Th company has actual losss At th lvl of balanc output Q, th ovrall incoms cannot covr vn th ovrall variabl costs, th total loss bing OR, mor than th loss that would b rgistrd at lvl 0 of output, qual to th amount of ovrall fixd costs (s figur 4). 199
4 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 3. THE MONOPOLISTIC TYPE OF MARKET Monopoly is th nam givn to th xtrm cas of markt in which thr is just on sllr of a product. Th monopolistic structur involvs mainly th xistnc of just on sllr for a crtain product, so it cannot ntr comptition with any othr companis, which lads to two rsults: th markt dmand curv is in th sam tim th dmand curv for that vry product; othr companis ar dnid th ntranc on th markt; A monopolistic company will bhav on th markt by taking corrlatd dcisions upon paramtrs: th quantity offrd on th markt; th pric at which this quantity is bing offrd. On short trm, it dos not imply th knowldg of th dmand curv for a product offrd by th monopolistic company, as xprssd by th rlation: Q = b0 b1p (10) or, p = a 4 a5q (11) Th company aiming at maximizing th profit will hav to dcid upon th volum of output for which th maximal profit condition is mt, namly: VMS = CMS (1) From costs thory w know that for a linar dmand curv, th curv of marginal incom VMS, crosss th ara prpndicular to th pric axis at its mdian point, starting from th sam point as th dmand curv. Thus, th ovrall incom on short trm in a monopolistictyp comptition has th form: VTS = p Q = a Q a (13) 4 5Q which rprsnts a parabl admitting an apx. According to th position of th ovrall cost curv on short trm, CTS with rspct to th parabl of th ovrall incoms on short trm, VTS four diffrnt situations can b distinguishd, namly: a) th monopolistic company maks ovr profit; b) th monopolistic company maks normal profit; c) th monopolistic company has losss in xploitation; d) th monopolistic company has to tmporarily clos down ; a) Th monopolistic company maks ovr profit Th ovr profit will b maximal at th lvl of balanc output whn th vrtical distanc btwn curv VTS and curv CTS is maximal (th tangnts to th two curvs bcom paralll). Th ovr profit is th cas givn in th figur (s figur 5) as a hatchd ara, its analytical xprssion bing: CUTS [ovr profit] = Q p (14) Q Q 00
5 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 On can notic that th balanc lvl of output output lvl Qm for which CUTS is minimal. Q, is infrior to Fig.5. Th monopolistic company maks ovr profit Fig.6. Th monopolistic company maks normal profit b) Th monopolistic company maks a normal profit Th monopolistic company maks only a normal profit whn it offrs on th markt th quantity of products Q, as at this lvl, curv VTS bcoms tangnt to CTS (s figur 6), th ovr profit bing null as ΠTSis tangnt to th horizontal axis at th lvl of output Q. At point C curv CUTS is tangnt to lin VUS, dtrmining th lvl of balanc pricp. c) Th monopolistic company has xploitation losss In this cas, thr ar lvls of output for which th company manags to covr th total fixd costs and partially th total variabl costs, but it dos not vn mak a normal profit (s figur 7). Th monopolistic company will tnd to obtain th balanc output Q, for which curv VTS approachs most CTS, th loss bing minor. Th loss is rprsntd graphically by sgmnt OR and th hatchd ara, analytically: [xploitation loss] = Q [ CUTS( Q ) p ] (15) d) Th monopolistic company has to tmporarily clos down For any output lvl, th company cannot covr vn th fixd costs (s figur 8). Th total loss is largr than th loss that would com from output lvl 0, i.. qual to th total amount to fixd costs. 01
6 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 Fig.7. Th monopolistic company has losss in xploitation Fig.8. Th monopolistic company has to tmporarily clos down 3. MATLAB WORK SOFTWARE Th packag of programs MATLAB (MATrix LABoratory) offrs advancd softwar aiming at simplifying th mans of numrical procssing of data. Matlab allows th usr to xprss th solutions of scintific applications in a simpl languag, clos to th analytical (mathmatical) xprssion of th problm undr considration. In this way, th usr can focus mainly on th solving mthod, without having to fac major difficultis in translating th solution into th MATLAB languag. MATLAB krnl includs a larg numbr of prdfinit functions mant for all purpos mathmatical oprations (arithmtic in floating point, polynomial calculations, trigonomtric, xponntial, logarithmic, spcial functions, tc.), tabl and matrix handling, solving numric analysis problms, D and 3D graphic rprsntations, dvloping programs in MATLAB languag and thir intrfacing with th host opration systm. To th prdfind functions availabl in th basic krnl w can add a sris of toolboxs covring spcific filds (signal procssing, th thory of control, statistics, nural ntworks, symbolic calculations, imag procssing, optimizing, tc.). Ths toolboxs, as wll as th usr programs ar sourc fils writtn in a simpl programming languag, charactristic to MATLAB. MATLAB krnl can oprat both as command lin, th command givn by th usr bing xcutd immdiatly, and also as intrprtr, xcuting a program xisting as sourc fil. This charactristic nhancd th xtnsiv charactr of th languag, allowing th usrs to add thir own functions to th alrady xistnt st (prdfind or in th firmwar toolboxs). Th flxibility of th languag is also advantagd by th xistnc of on typ of basic data, th matrix on, having as lmnts ral or 0
7 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 imaginary valus. Unlik in othr languags, th variabld do not hav to b dclard or dimnsiond. Th actual vrsion of MATLAB krnl is ntirly writtn in C and can run on svral computing systms (IBM PC, VAX, SUN, Macintosh). It offrs th facilitis of a compltly intgratd systm, basd on its own languag and on an fficint intrprtr. This allows th xprssion of a rlativly intricat algorithm in a compact form, xcutd in an accptabl tim span, in a highly accurat way, th solution bing displayd in a convnint form, alphanumrically, vntually accompanid by a graph. Th Matlab programm for prfct comptition markt it is 3 prsntd down, for numrical xmpl: CTS = Q 6Q + 0,Q and th pic p = 60 Runing th programm w obtind th nxt windows: Fig.9. Th Matlab programm for numrical xmpl: 3 = Q 6Q 0,Q, p = 60 CTS + Fig.10. Th graphical xprssion of cost, incom, profit, marginal costs,marginal incoms and th pric 03
8 ANNALS OF THE FACULTY OF ENGINEERING HUNEDOARA 004 TOME II. Fascicol 3 4. CONCLUSIONS Th papr introducs a program capabl to solv all th problms rlatd to th thory of th company th xtrm cass (th prfct comptition markt and th monopolistic on) dtrmining th balanc output, th maximal incom, th maximal costs and maximal profit, as wll as th graphical xprssion of costs, incoms, incom and profit, with rspct to th output. BIBLIOGRAFIE [1.] Smarandach Ion Ena, ş.a., Microconomi, Editura Univrsitaria Craiova, 1999; [.] Gogonaţă Ctin, ş.a., Microconomi, vol. I, Editura Economică Bucurşti, 1999; [3.] Firţanu Virgiliu, ş.a., Matlab  calcul numric, grafică, aplicaţii, Editura Tora, 1999; [4.] Băbăiţă Ili, Microconomi aplicaţii, Editura Mirton Timişoara 000; [5.] Şarp Danila Ancuţa, ş.a., Microconomi Tori şi aplicaţii, Editura Economică Bucurşti,
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