Week 7  Perfect Competition and Monopoly


 Gyles Michael McDowell
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1 Week 7  Perfect Competition nd Monopoly Our im here is to compre the industrywide response to chnges in demnd nd costs by monopolized industry nd by perfectly competitive one. We distinguish between the short run, when the number if firms in the industry is fixed, nd the long run, where new firms cn enter or exit in the perfect competition cse, nd where loss mking monopolist cn shut down in the monopoly cse. We re prticulrly interested in the consequences of these equilibri for consumer welfre nd producer profits. We will first chrcterize the monopolists pricing behviour with respect to the concepts of elsticity nd mrginl revenue. Let the mount of good x demnded be nd the price of good x be. Suppose tht our mrket demnd function is =D( ) (where the preferences i.e. indifference curve mp  nd income of ech consumer nd the prices of ll other goods re held fixed). Our inverse demnd function will be =D 1 ( ) Suppose tht our firms totl cost function is given by C( ) (where the production technology i.e. isoqunt mp nd the prices of ll inputs re held constnt). Totl revenue will be given by R x = = D 1 ( ) nd mrginl revenue will be given by: MR x = R x / = / x( D 1 ( )) MR x = ( D 1 / )+ D 1 ( ) MR x = (1/( D/ ))+ D 1 ( ) ( using the product rule nd the fct tht D/ =1/( D 1 / ) becuse one function is the inverse of the other inverse function rule ) Averge revenue will be given by AR x =R x / = = D 1 ( ). So, verge revenue is simply the current mrket price. Remember tht the clculus definition of price elsticity of demnd (Vrins definition) is x =( D/ )( / ). This mens tht (from the formuls for MR x nd AR x bove): MR x = / x + D 1 ( ) MR x = AR x (1/ x + 1) MR x = (1/ x + 1) AR x MR x = (1/ x + 1) This is nother wy of estblishing the result tht mrginl revenue cn only be positive (i.e. revenue cn only increse long with the quntity sold) when x < 1 (i.e. long the elstic prt of the demnd curve). When x >1 (but, remember, lwys less thn 0 for norml good on Vrins definition), the (1/ x + 1) prt is lwys negtive nd so revenue decreses s the quntity is incresed (this is long the inelstic prt of the demnd curve). In the cse of liner demnd curve, the price elsticity of demnd is less thn 1 in the top hlf of the demnd curve nd greter thn 1 in the bottom hlf of the demnd curve. By substituting in the formul for price elsticity of demnd long liner demnd curve x =b( / ) we cn find the formul for the mrginl revenue curve long liner demnd curve: MR x = AR x (1/ x + 1) MR x = (1/(b( / )) + 1)
2 MR x = (1/b) ( using the formul for liner demnd curve =b( ) ) MR x =2 From this formul we cn see explicitly tht mrginl revenue will be positive when >/2 nd negtive when </2. So, we now hve enough informtion to sketch wht the mrginl revenue, demnd curve nd elsticity of demnd curves will look like for liner demnd curve: elstic demnd /2 /2 MR x b/2 b inelstic demnd The profit function of monopolist in the mrket for good x will be given by x =R x C x (i.e. profit is totl revenue minus totl cost). The derivtive of the profit function with respect to q is the mrginl increse in profit when quntity sold is incresed. The monopolistic firm will wish to expnd its output until x / =0: x / = R x /  C x / = 0 R x / = C x / MR x = MC x The mrginl cost is lwys positive, so for this condition to be met, the mrginl revenue must lso be positive. This in turn implies tht the elsticity must be less thn 1; i.e. the monopolist will lwys choose to produce n output level on the elstic prt of the demnd curve. Intuitively, if the monopolist is on the inelstic prt of the demnd curve, they cn increse their revenue by reducing the quntity supplied to the mrket. Since this lso sves on production costs, it will never be rtionl for profit mximizing firm to produce on the inelstic prt of the demnd curve. The second order condition for profit mximiztion requires tht: 2 x / 2 = 2 R x / 22 C x / 2 < 0 MC x / > MR x / This condition tells us tht mrginl cost must be climbing fster thn mrginl revenue t the point where they cross if it is to be profit mximum. In the cse of the perfectly competitive firm introduced below, since MR x simply becomes P x (becuse the firm is pricetker) then MR x / becomes 0 nd we simply hve the condition tht MC must be incresing t the crossing point. In the following nlysis, we will ssume tht the monopolist, or ech individul firm in the cse of the perfectly competitive industry, hs production technology which exhibits decresing returns to scle (i.e. incresing mrginl cost) t ll output levels nd hs fixed cost F, so tht totl cost C x =V x +F where V x is the vrible cost so tht V x / = MC x (becuse the derivtive of F with respect to is 0). This ssumption ensures tht there is point of minimum verge cost, where ll economies of scle hve been exhusted nd diseconomies ε x 1
3 of scle re beginning to set in. We lso ssume liner demnd curve so tht we cn be precise bout the shpe of the mrginl revenue curve. A profit mximizing firm will lwys mximize its profits by setting mrginl revenue equl to mrginl cost. The mrginl revenue curve for monopolist hs been discussed bove. The re bove the mrginl cost curve nd below the mrket price is in fct simply the producers surplus; it is the difference between the price the firm gets for ech dditionl unit nd the minimum mount (ssuming it hs pid its fixed cost F) tht the firm is willing to supply ech dditionl unit for. To find the firms profits, we must tke the producers surplus nd subtrct the fixed cost F. The digrm below illustrtes the cse of monopolistic firm. Since the monopolist fces the entire mrket demnd curve nd cn freely choose ny point on it (this is not the cse with perfectly competitive firm, s we shll shortly see) they will mximize their profits by choosing quntity q x where mrginl revenue equls mrginl cost. The producers surplus is the horizontlly hshed roughly trpezoid re. The monopolists profit is equl to the producers surplus minus the fixed cost. It cn be shown on the grph s the verticlly hshed rectngle becuse since is the verge revenue, then the height of the rectngle is verge revenue minus verge cost nd the width of the rectngle is the mount produced, so the re of the rectngle is totl revenue minus totl cost. The re of the rectngle is sometimes referred to s the monopolists economic profit. This is becuse we ssume tht the mrginl cost curve includes ll of the fctors of production, including mngeril nd entrepreneuril bility. So, the ide is tht there is norml wge for entrepreneurs nd mngers, which could be quite high if these skills re in short supply. The economic profit is the extr income (received by the owner of the firm, which could be the entrepreneur, or the shreholders, which will probbly include mong their number the mngers) which derives from the monopolists monopoly power or mrket power, which refers to the monopolists bility to set the price level to whtever it chooses without fer of other firms competing with it by setting prices lower. The price nd output quntity which would mximize totl surplus (i.e. would be socilly optiml) is (q x, p x ). This mrket power, s well s leding to positive economic profits for the monopolist, leds to loss in consumer welfre (since the monopolists price p x is higher thn the socilly optiml output quntity p x the consumers surplus must be lower) nd dedweight loss, due to the distortion of the mrket below the socilly optiml quntity This is shown s the digonlly hshed re in the grph below. MC x AC x MR x
4 The digrm below illustrtes the effect on the monopolists economic profits nd on consumers surplus when the demnd curve shifts outwrds. The outwrds shift in the demnd curve shifts the mrginl revenue curve s well (so tht it still touches the x xis hlf wy between the origin nd the point where the demnd curve touches the xxis). There is therefore n increse in the quntity sold but lso the mrket price. This mens tht the monopolist is ble to trnslte some of the incresed demnd into higher price for its goods (s we shll shortly see, this cnnot occur in the long run equilibrium of perfectly competitive industry). The monopolists profits clerly increse from the verticlly hshed rectngle to the verticlly nd horizontlly hshed rectngle (including the smll double hshed prt). The effect on consumers surplus is mbiguous becuse lthough the consumers gin the northestsouthwest digonlly hshed prt on the right, they lose the verticlly nd horizontlly hshed prt, which is trnsferred to the monopolists economic profits. The size of these res would depend on the shpe of the demnd curve, so we cnnot drw ny firm conclusions just from this digrm. There is lso n mbiguous effect on the size of the dedweight loss. The stndrd model of perfect competition firm differs from tht of monopolist in the following wys: I. There re lrge number of firms. This mens tht the output of ech firm is tiny reltive to the output of the industry s whole. This is very importnt s justifiction of the simplifying ssumptions mde. For simplicity, we ssume tht ll firms hve identicl production functions (nd therefore cost curves), nd so ech mke up n equl prt of totl industry output, due to the symmetry of the model. II. There is distinction between the profit mximiztion decision of ech individul firm nd the mrket equilibrium in the industry s whole. Ech firm is modelled s hving perfectly elstic demnd curve t the current industry mrket price. The ide is tht if perfectly competitive firm tries to chrge price bove the current industry mrket price its demnd immeditely goes to 0 becuse consumers will be ble to buy from other firms t the industry mrket price, nd so will ll bndon the firm which rised its price. Similrly, if the individul firm chrges price lower thn the current industry mrket price, customers will flood
5 to it from ll the other firms, nd becuse the individul firm is so smll reltive to industry output, to ll intents nd purposes demnd is perfectly elstic. III. There is distinction between the short run nd long run responses to chnges in demnd or supply conditions. In the short run, individul firms lter their behviour, nd this is reflected in new equilibrium for the industry s whole. The number of firms, however, is considered fixed in the short run. In the long run, on the other hnd, we ssume tht new firms cn enter the mrket. They will do this whenever the firms currently in the mrket re mking positive economic profits. This is becuse the positive economic profits enble firms to mke higher rte of profit thn the stndrd requirements built into the mrginl cost function (i.e. if entrepreneurs move into this industry, they will get higher return on their skills thn the verge elsewhere in the economy). By the sme token, firms will leve n industry where they re mking negtive economic profits. This mens tht the industry cn only be in long run equilibrium where ll firms re mking 0 economic profits. Since the demnd curve fced by ech individul firm is perfectly elstic, it must lwys be the cse tht AR x = =MC x. Since 0 economic profits cn only occur when AR x =AC x this in turn implies tht t the long run industry equilibrium =MC x =AC x. So, the long run equilibrium price is where the mrginl cost nd verge cost curves cross, i.e. the point of minimum verge cost. Intuitively, new firms will enter the industry, or existing firms leve the industry, until ech firm is producing t its minimum verge cost. This is the only sitution where there re no profitble opportunities for new firms to enter the mrket nd undercut the prices of the existing firms. The digrm below illustrtes the effect of n outwrd shift in the demnd curve for perfectly competitive industry. Suppose tht the industry is initilly in long run equilibrium so tht ech firm is producing units nd there re N firms so tht overll industry supply is N units, which is the mount demnded by consumers long demnd curve t price. Ech firm is initilly mking 0 economic profits. Suppose the demnd curve then shifts to. Since the number of firms is fixed in the short run, the short run supply curve SS x must be upwrd sloping becuse ech firm experiences decresing returns to scle. It must lso go through the initil long run equilibrium becuse the number of firms is fixed t the level comptible with long run equilibrium t the intersection of the LS curve with the initil demnd curve. So, the new short run industry price will be. Ech individul firm will hve incresed output to nd will be mking economic profits in the short run equl to the shded rectngle. In the long run, the number of firms will increse to N nd ech firm will gin be producing units so tht there is once gin long run industry equilibrium with 0 economic profits for ech firm.
6 MC x AC x SS x S LS x L N N Once we hve reched the new long run equilibrium, consumers surplus will hve unmbiguously incresed, nd industry economic profit will remin unchnged t 0. An increse in workers wges is represented by n upwrd shift in the mrginl nd verge cost curves. This will clerly led to n increse in price nd reduction in output quntity in the cse of monopolist becuse the intersection of MC with MR must now be t lower quntity. Consumers surplus therefore clerly decreses. The effect of the monopolists profit will lso be unmbiguously negtive becuse the totl cost of production t ny quntity will increse, nd so the monopolists profits will be reduced whtever output they choose. In the digrm below, the monopolists economic profits go from the digonlly hshed re to the smller drk solid rectngle. N Q x In the cse of perfectly competitive industry, the increse in workers wges shifts the long run industry supply curve upwrds becuse the minimum verge cost of production increses from 1 to 2. The short run supply curve is upwrds sloping becuse ech firm hs decresing returns to scle nd goes through the point on the new long run supply curve which corresponds to the initil N firms producing output ech nd selling t price 2. Since the number of firms is fixed in the short run, the short run equilibrium requires tht ech firm reduce its output from to nd tht the price increse to (resulting in reduced consumer surplus). Ech individul firm is now mking negtive economic profits equl to the re of the drk rectngle. The long run equilibrium involves firms leving the industry until N firms re producing units of output ech nd selling for price 2. Consumers surplus
7 hs clerly been reduced. Overll industry economic profits hve returned to their long run equilibrium level of L 2 S L 1 SS x 2 LS x 2 LS x 1 N N N Q x If the proportionl tx on profits flls only on economic profits, this will hve no effect on the behviour of either monopolistic or competitive industry in turns of the bove nlysis. Regrdless of whether the firm is monopolist or competitive one, its ftertx economic profits re given by x T =(1t) x =(1t)(R x C x ) where t is the tx rte nd x is pretx economic profits. A profitmximizing form sets: x T / =(1t)( R x /  C x / ) = 0 (1t) R x / = (1t) C x / MR x = MC x So, the proportionl tx on economic profits hs no effect on the profit mximiztion condition of mrginl revenue equls mrginl cost. The proportionl tx will reduce the firms economic profits by certin proportion but will hve no effect on its price or output setting behviour. In the cse of the perfectly competitive industry, the long run equilibrium requires 0 economic profits, so proportionl tx on economic profits will clerly hve no effect on the long run equilibrium. Supposing s n lterntive tht the proportionl tx flls not just on economic profits but on the wge pid to entrepreneurs or the norml rte of return on the cpitl owned by the firm. (This would likely occur in the rel world becuse ccounting profits include entrepreneuril wges nd the entire erning from the firms cpitl stock.) This would hve similr effect on mrginl, verge nd totl costs s the increse in workers wges, nd so the sme digrms would pply. We sw erlier tht the existence of monopoly power cretes dedweight loss of totl socil welfre becuse the monopolist sets MR x =MC x insted of =MC x which would be required if the mrginl utility (strictly speking, ssuming tht we hve qusiliner utility) of the consumer from consuming the finl unit is to be equted with the mrginl cost of producing the finl unit. Clerly, on the nlysis so fr, monopoly is bd thing for society, not only becuse of the totl loss of welfre, but becuse the economic profits generted by monopoly power will tend to be trnsferred from consumers to smll group (e.g. shreholders) nd thus lso increse the inequlity of the utility generted by the economy s well s reducing the totl mount of it. There is n re of controversy in economics bout the true extent of monopoly power, how dmging it relly is, nd how much the government cn or
8 should intervene to prevent it. We will shortly see ltertions to the model which my led to the conclusion tht monopoly is not s bd s the simple model would suggest. Firstly, however, we should consider the resons why monopoly power my exist: 1) Technologicl If we look t the digrm for firm with economies of scle t high output levels below, we cn see tht if there were to be two firms in the mrket insted of 1, there would simply not be enough mrket demnd for both firms to produce t their minimum verge cost. If both firms tried to produce (1/2) ech so tht the overll quntity produced is the optiml mount for the single monopolist to produce, the verge cost for ech firm would be bove the price, nd so both would mke loss. This is becuse both firms re now pying the fixed cost F, wheres only one ws before. It would lso not be optiml from societys point of view for both firms to py F. The best thing from the point of view of mximizing totl surplus would be for single firm to produce, nd for tht firm to be forced to produce so tht price equls mrginl cost. This is roughly wht hppens with regulted privte monopolies such s wter compnies in the UK. MC x AC x (1/2) MR x 2) Brriers to entry  The monopolist my be the only firm ble to produce its prticulr product, either becuse it hs legl protection such s ptent or government contrct, or, for exmple, becuse it hs closely gurded secret product design. Firms my lso use strtegic ploys such s building up excess cpcity so tht if ny other firm tries to chllenge them they will flood the mrket nd thus drive the chllenger out of business. 3) Product differentition There my be big difference between the products produced by different compnies in the sme industry (e.g. cr firms). This will men tht whilst the different firms products re substitutes, they re not perfect substitutes (which is the ssumption required for the perfect competition model) nd so ech firm hs some monopoly power. If monopolist were ble to discriminte perfectly between consumers, it would be ble to chrge highest price ech consumer would be willing to py for ech mrginl unit. This mens tht the monopolists producers surplus would be the entire re between the demnd curve nd the mrginl cost curve. The monopolist would be ble to gin the whole of wht would hve been the consumers surplus becuse s you go long the demnd curve it chrges ech mrginl consumer exctly
9 wht they would hve been willing to py. This lso mens tht by expnding production beyond the optiml nonpricediscriminting quntity, the monopolist is ble to gin wht would hve been the dedweight loss in the nonpricediscriminting cse. So, monopolist ble to perfectly price discriminte produces t the socilly optiml output level, nd there is therefore no dedweight loss, i.e. totl surplus is mximized. Consumers re, however, mde worse off s they lose the turquoise digonlly hshed tringle which ws their consumers surplus in the nonprice discriminting cse. This suggests tht lthough perfect price discrimintion is good from the point of view of mximizing totl welfre, it will cuse even more inequlity thn nonpricediscriminting monopoly power becuse the smll groups who own the monopolistic firm will be ble to tke ll of the welfre which would hve gone to the consumers if we hd hd single mrket price equl to mrginl cost (s suggested the government should do in the question bove). So even if perfect price discrimintion were possible, government regultion of monopoly pricing would probbly still be preferble. It is very unlikely tht perfect price discrimintion could be prcticl in relity nywy becuse it would involve the monopolist knowing exctly how much ech consumer would be willing to py. Other forms of price discrimintion re more likely to be chievble in prctice, but with these dedweight loss from monopoly power will remin. MC x MR x We hve so fr looked t the lloctive inefficiency cused by monopoly power, which refers to the socilly suboptiml mount of output produced by monopolist. Another common result of monopoly power is productive inefficiency. This refers to filure of monopolist to minimize cost of production. This is similr in effect to the nlysis erlier on where we sw tht higher prices for inputs will reduce the economic profit of monopolist. The problem rises when the group receiving wges s prt of the mrginl cost curve is the sme s the group which receives the economic profits. It my then be desirble for tht group to push up the mrginl cost curve becuse it will give them extr income in excess of the loss of economic profit. This cnnot occur in the long run equilibrium in competitive industry becuse ny firm which does not produce t the minimum verge cost vilble with the existing technology will be undercut by new competitors. It is generlly ccepted tht the government should try to remove s mny brriers to entry s possible; it should not grnt ny specil licenses unless bsolutely necessry (e.g. for consumer sfety, s with the medicl industry). However, it is
10 sometimes rgued tht monopoly in high tech sectors is good thing becuse it gives firms greter incentive to invest in reserch nd development, becuse they will rep the benefits s monopolist. However, there re better wys for the government to encourge reserch nd development thn by tolerting or delibertely fostering monopoly. The exception to this rgument is tht of ptents for new ides. Although R&D cn be encourged by directly trgeted government subsidies, the more specific new ide, production technique or product is, the more it is likely to be necessry to llow the developer to enjoy the exclusive use of it for certin finite period so tht they cn recoup their initil expenses nd be given n incentive to direct the investment in the first plce. The government is not likely to succeed in the business of picking which specific ides to fund becuse it hs less informtion thn the sum of ll gents in the mrket. However, there will lwys be finite time period for n optiml ptent becuse sooner or lter the rents ccruing to the firm with the ptent re sufficient to provide the required incentive nd the sttic welfre losses from monopoly power become pure dedweight loss even from this dynmic efficiency perspective. The technologicl cuses of monopoly power (high fixed costs) often men tht it would be either undesirble or impossible for the government to delibertely put more firms in the industry thn is socilly optiml. We hve lredy seen tht there re other wys to llevite the negtive effects of monopoly power. These include regulting the monopolists price nd ensuring tht if there is smll number of firms tht these re prevented from colluding to keep prices high (this is the role of competition policy). It my be possible through well designed competition policy to mke even smll number of firms behve competitively, s would be predicted by the Bertrnd model of duopoly with homogenous goods nd identicl costs.
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