Perfect competition model (PCM)


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1 18/9/21 Consumers: Benefits, WT, nd Demnd roducers: Costs nd Supply Aggregting individul curves erfect competition model (CM) Key ehviourl ssumption Economic gents, whether they e consumers or producers, pursue their selfinterest when mking choices individuls mke choices rtionlly y weighing enefit nd cost of ech possile ction nd choosing ction which mximizes difference, tht is, their privte net enefit. Consumers mke choices (consumption, work, leisure, etc.) to mximize their utility or enefit suject to udget constrint while producers mke decisions (production, investment, dvertising, etc.) to mximize their profits (revenue less costs). Key technicl ssumptions Complete set of mrkets fully ssigned property rights ll goods nd services re privte goods no externlities lrge numer of prticipnts perfect informtion zero trnsction costs well ehved production nd utility functions In the CM, lrge numers of utilitymximizing consumers nd profitmximizing producers meet in the mrket. Consumers nd producers ct s price tkers when mking consumption nd production decisions ecuse the numer of mrket prticipnts is sufficiently lrge so tht no individul prticipnt s ction ffects prices. Thus, prices re treted s exogenous y prticipnts when mking privte decisions. The interction of consumers nd producers in the mrketplce results in the determintion of prices or mrket vlutions of goods nd services. Thus, mrket prices re determined endogenously. The equilirium mrket price (the level t which the price settles down) is the price which clers the mrket (equtes supply nd demnd). The mrket price, in turn, determines the lloction of the good, tht is, how much of the good will e consumed y individul consumers nd produced y individul producers. Let s review how mrkets work, tht is, how consumers nd producers mke their respective choices nd how these choices re ggregted in the mrket, ultimtely determining the mrket vlution or price of good nd hence the lloction of the good. We cn then ssess the mrket s n lloction mechnism. 2 1
2 18/9/21 Consumers: Benefits, WT nd Demnd How do economists mesure the enefits tht ccrue to n individul from consuming good? Economists elieve tht wht people wnt k individul REFERENCES should e the sis of BENEFIT MEASUREMENT How cn we identify n individul s preferences or tstes? One wy is to sk n individul to revel their preferences y sking out their willingness to py (WT) for good. If someone is WT for good, then we cn conclude tht they hve positive preference for tht something. WT concept gives us monetry indictor of preferences Willingness to py WT MWT i or MB i Individul s mrginl willingness to py curve (MWT i ) is locus of individul s MWT!Q pirs. It tells us how much n individul is WT for incrementl units of Q consumption. Individul i is WT 6 for 1 unit, for 2 units, 2 for units nd for units. MWT i is thus flling with consumption level MWT i downwrdsloping. MWT i is lso known s the mrginl enefit of consumption curve (MB i ) MWT i idiosyncrtic Suppose there re I individuls indexed y i so tht MWT i for i = 1,,I. Whenever individuls re heterogeneous (for instnce, if they hve different tstes, vlues or income), then the MWT i for ny two individuls j,k will not e equl MWT j MWT k. MWT i TWT i An individul s totl willingness to py for consumption level (TWT i ( )) is monetry mesure of the enefit (B i ( )) ccruing to the individul from consuming. TWT i is the re under MWT i to the left of the consumption level. TWT i is the sum of the individul s consumer surplus (CS i ), re, nd consumer expenditures (CE i ), re. Individul i s TWT i for one unit of the good cn e derived s follows: CS i (1) = = 1 CE i (1) = = 6 TWT i (1) = B i (1) = CS i (1) + CE i (1) = + = 7 Using the sme methodology, one cn clculte TWT i (2) = + 8 = 12 nd so on. Note tht TWT i is incresing with consumption level. 2
3 18/9/21 Individul consumption decision nd demnd curve An individul pursues his/her selfinterest when mking consumption decisions. Tking price s given, the individul chooses the level of consumption which mximizes their net enefits from consumption: 18 Individul A : = : = Implicitly defines individul A s demnd curve 18 2 = MB A / MWT A 12 Q A = 2 18 = 12 2 Individul A s demnd curve Convention in economics is to plce economic vlue of on verticl xis nd quntity or Q on horizontl xis. When we grph demnd curve in (,Q A ) we re grphing inverse demnd curve. Inverting the demnd curve yields the inverse demnd curve : = = 12 = 2 12 = 18 2 Simplifying, the inverse demnd curve is or or. = 18. Note tht the curve cn lso e leled s Aggregte Demnd Aggregte or mrket demnd for commodity, Q D (), is constructed y ggregting or horizontlly summing the demnd curves of ll consuming individuls in the economy. = = 18 = 18 = 18 = 18 = 12 2 = 6 1 =18 To horizontlly sum individul demnd curves, invert the inverse demnd curves to find the demnd curves nd then dd together. Aggregtion entils summing individul quntities ( ) t ll possile price levels (), tht is, = +. Fix, Vry Q 6
4 18/9/21 Aggregte Demnd = = = TWT, B, CE, CS Aggregte or totl willingness to py, TWT, is the re under the ggregte demnd curve to the left of the quntity demnded. Suppose tht = 12 so tht Q = 6 units re demnded. TWT for 6 units of the good is the sum of ggregte consumer surplus (CS), re, nd ggregte consumer expenditures (CE), re. TWT for Q units of the good cn e derived s follows: CS(6) = = 18 CE(6) = = 72 TWT(6) = + = = 9 Individul A Individul B Aggregte Demnd (Q A ) 6 6 (Q B ) Q A Q B Q B 7 roducers: Costs nd Supply roduction costs include ll costs incurred to produce good cpitl equipment costs, lour costs, cost of mteril inputs, etc. roduction costs re privte costs incurred y n individul producer. MC i = /2 C i Firm i MC i c 2 The locus of incrementl production costq pirs is the firm s mrginl cost of production curve, MC i. It is mrginl cost function ecuse it descries the firm s cost of producing incrementl units of the good. Individul firm s MC i idiosyncrtic MC i sed on firm s production processes nd technologies so will generlly e different eg., cost differences cn derive from different vintges of cpitl equipment. Firm i s cost of producing the 1 th unit is 2. Height of verticl line t 1 units is C pi (1 th unit), tht is, the incrementl or mrginl cost of producing the 1 th unit. The incrementl cost of producing the 2 th unit is. MC i is upwrdsloping ecuse the incrementl cost of producing is incresing. Firm i s cost of producing units is the re under MC i to the left of. The firm s cost of producing 1 units is C pi (1) = 1 (re ) nd the cost of producing units is 6 (res + + c). Note tht C pi is incresing t n incresing rte. 8
5 18/9/21 roduction decision nd supply curve An individul firm pursues its selfinterest when mking production decisions. Tking price s given, the firm chooses level of output to mximize profit, where profit is the difference etween totl revenue, R i, or lterntively production enefit, B i, nd production cost, C pi. =rg = Firm i MC i p or S() : = Implicitly defines firm i s supply curve : = Revenue, Costs nd roducer Surplus R i ( ) = * = + C i ( ) = = 2 = 2 Firm i s inverse supply curve Firm i s supply curve = = + = is lso known s producer surplus 9 Aggregte or Mrket Supply The ggregte or mrket supply of commodity is constructed y ggregting or horizontlly summing the supply curves of ll the producing firms in the economy. = 2 2 = = 2 = 1 1 = = 1 1 = 2 = 1 2 Inverse ggregte supply curve Aggregte supply curve Aggregtion of production entils summing individul producers quntities ( ) t ll possile price levels (), tht is, = + 1
6 18/9/21 Aggregte or Mrket Supply R, C, S When = 12, 6 units re supplied. Industry revenue, R, is re A + B. Industry production cost, C, is re B. Industry surplus is re A, the difference etween industry revenue nd production cost. We cn compute the vlues for our exmple s follows: R(6) = A + B = 72 C (6) = B = 6 S(6) = B(6) = A B = 6 Firm 1 Firm 2 Aggregte Supply 18 MC 1 18 MC 2 18 Q S () or MC A B Q Q 2 Q 11 6
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