There are two principles which are fundamental to economic analysis: a) the optimisation principle b) the equilibrium principle

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1 Microeconomic I. Antonio Zabalza. Univerity of Valencia 1 Leon 9: Market Euilibrium 9.1 Market euilibrium There are two rincile which are funamental to economic analyi: a) the otimiation rincile b) the euilibrium rincile So far, in the erivation of the main reult of conumer theory, we have alie the otimiation rincile. Now we want to conier the euilibrium rincile. In articular, we combine the behaviour of conumer an firm to tuy how they interact in the market, how they reach euilibrium outcome, an what roertie thi euilibrium oition have. For that we will nee to conier market uly, eite not having eveloe the microeconomic analyi of the behaviour of the firm (you will o that next emeter). Here we will conier uly intrumentally, in orer to concentrate on how agent reach euilibrium oition in a market. The uly curve give information on how much outut roucer are willing to uly at each oible market rice. More rigorouly it tell the maximum uantity of a given goo that eller will ut in the market at each oible rice.

2 Microeconomic I. Antonio Zabalza. Univerity of Valencia 2 We will aume that both iniviual emaner an ulier take rice a given (out of their control) an imly etermine their bet reone (in orer to maximize utility or rofit) given thoe market rice. That i, we will aume that the market i cometitive. Now, it i imortant to unertan that although the market rice i ineenent of any one agent action in a cometitive market, it i the collective action of thee agent that etermine the market rice. The euilibrium rice of a goo i that rice where the uly of thi goo eual the eman for it. In the grah below, thi rice i. Suly Deman

3 Microeconomic I. Antonio Zabalza. Univerity of Valencia 3 Why houl thi be an euilibrium rice? An economic euilibrium i a ituation where: a) all agent are chooing the bet oible action for themelve; an b) each agent behaviour i conitent with that of the other. The eman an uly curve rereent the otimal choice of conumer an firm reectively. So conition a) i fulfille. The fact that at both eman an uly coincie, mean that at that rice the behaviour of thee two et of agent are conitent an therefore that conition b) i alo atifie. At any other rice, thee two conition woul not be atifie. At >, uly i greater than eman. Thi mean that at thi rice ome ulier cannot ell the outut they exect to ell. If they want to ell more outut they have to lower the rice. Exce uly exert a ownwar reure on the market rice. At <, eman excee uly. There are iaointe buyer an ulier will realie that

4 Microeconomic I. Antonio Zabalza. Univerity of Valencia 4 they can ell at a higher rice than to thee iaointe buyer. Exce eman exert an uwar reure on the market rice. The only rice at which thee reure iaear i the euilibrium rice. Two ecial cae A. Fixe uly. The amount ulie i given an ineenent of rice. The uly curve i vertical. In thi cae the uantity of euilibrium i entirely etermine by uly an the rice i etermine by eman (given the available uly of the goo). B. Fixe rice. Sulier cannot offer the goo below a given rice, but will offer any uantity at a contant given rice. The uly curve i horizontal. Then the rice i entirely etermine by uly. Deman will etermine the amount of the goo that will be bought at thi rice. S S D D

5 Microeconomic I. Antonio Zabalza. Univerity of Valencia 5 Math Suoe the eman an uly function of the market for x are = a b = c+ The euilibrium conition i = Thi i a ytem of three euation with three unknown:, an. The olution i (Derive it!) = = a c + b a + bc + b 9.2 Comarative tatic The aumtion economit make about uly an eman allow them to itinguih factor that will influence eman but not uly an vice vera. For intance, change income will affect the eman curve, but leave the uly curve unchange. Change in the rice of wage reect the rice of caital, will affect the uly curve an leave eman unchange. Change in the rice of a ubtitute goo will affect eman but not uly.

6 Microeconomic I. Antonio Zabalza. Univerity of Valencia 6 Change in the cot of a raw material will affect uly but not eman. Of coure in the real worl everything affect everything. A change in the relative rice of labour might alo affect eman through it imact on income. A change in technology might make one ector of emaner feel oorer, an may alo affect eman. So, the aumtion ue by economit to aortion thee effect neatly to either eman or uly houl be unertoo a a imlification, but a imlification that make ene from an emirical oint of view an that enable economit to convert the eman uly moel into a owerful tool of analyi. The imlification make ene becaue, although it i true that everything affect everything, emirically we know that ome effect are negligible while other are very ignificant. What thi aumtion oe i to concentrate only on the ignificant effect. Thi aumtion convert the moel of uly an eman into a owerful tool becaue it allow economit to make reiction (otentially refutable by emirical ata) much harer than it otherwie woul be. A an illutration of all thi, think, for intance, on the examle on the effect of everal olicy change

7 Microeconomic I. Antonio Zabalza. Univerity of Valencia 7 in the market of butter an margarine icue at the beginning of the coure. There we aw that a change in the tate of conumer in favour of margarine i bet analye by initially hifting the eman curve for margarine an then tracing the ubeuent effect in both market. An imrovement in the technology of margarine rouction by initially hifting only the uly curve of margarine, etc. Change of tate in favour of margerine Price butter S Price margarine S D D D Quantity butter Quantity margarine

8 Microeconomic I. Antonio Zabalza. Univerity of Valencia 8 Better technology in the rouction of margarine Price butter S Price margarine S S D D Quantity butter Quantity margarine Be careful. The movement eicte in the above figure are only the initial movement. The initial rice iturbance in one market get then tranmitte to the other market trough the change in rice an it effect on the correoning ceteri aribu of the curve. For intance, if ue to an imrovement in technology the rice of margarine fall, the eman for butter will alo fall (will hift to the left) on account of both goo being ubtitute. Thi will caue alo a fall in the rice of butter, which in turn will reuce omewhat the eman for margarine (hift to the left) with a further ecreae in the rice of thi goo.

9 Microeconomic I. Antonio Zabalza. Univerity of Valencia 9 The roce will continue for a time with the effect being graually maller an maller until they ie out an the two market reach a new euilibrium oition. If the two market are table (that i, if given the reective loe of eman an uly, they are caable of reaching euilibrium oition), we know for certain that thi new euilibrium will be achieve. Thi way of analying the effect of olicy change or iturbance in market i known a comarative tatic. It concentrate on the comarion of the two oition of euilibrium (initial an final) ignoring the ajutment ath from one to the other. If thi ath wa the interet of the analyi, then we woul have to ue ynamic tool of analyi, which are beyon the coe of thi coure. Deite it imlicity, the comarative tatic aroach i very owerful. For intance, even without knowing the uantitative arameter of the eman an uly function in the above roblem, we woul be able to conclue that a a reult of the imrovement in technology, the rice of both margarine an butter woul fall, the uantity conume of margarine woul increae an the uantity conume of butter woul ecreae.

10 Microeconomic I. Antonio Zabalza. Univerity of Valencia Taxe. The eaweight lo of taxation Thi i an illutration of the comarative tatic aroach. It alo bring in imortant ubtantive inight into the way taxe affect economic activity an how taxe are tranlate between economic agent. Main iue to unertan. When taxe are reent in a market, intea of only one, there are two rice of interet: the rice the buyer ay an the rice the eller receive. The ifference between thee two rice i reciely the amount of the tax. To imlify the exoition let u uoe that the tax i a er unit tax (uantity tax). A given fixe tax i levie er unit of the goo bought or ol. [There are other tye of taxe. Namely, the a valorem taxe. The argument woul be the ame]. If the tax on a litre of gaoline i 50 cent, an it i ol at 1, then we have that the eman rice (the rice ai by the buyer),, i 1, an the uly rice (the rice receive by the eller),, i In general, if t i the amount of the er unit tax, then = + t

11 Microeconomic I. Antonio Zabalza. Univerity of Valencia 11 Suoe that the tax i imoe on the eller. What will be the effect of thi tax on the euilibrium of the market? The ulier, in orer to ecie how much to uly to the market, look at the rice he actually get into hi ocket. Thi i not the market rice (the rice ai by the buyer) but the market rice le the amount of the tax. The emaner, on the other han, in orer to ecie how much it will buy, look at the marker rice becaue thi i the rice he will really have to ay. In grahical term what thi mean i that the uly curve hift u by the amount of the tax. To uly the ame uantity a before the tax, I now nee the rice I wa getting before lu the amount of the tax, becaue I know that from the market rice I will have to euct the tax. So, how will the euilibrium of the market be affecte? Euilibrium, a uual, will be at that oint where eman eual uly. ( ) = ( ) x x

12 Microeconomic I. Antonio Zabalza. Univerity of Valencia 12 We have written the uantitie a function of the correoning rice, to remin ourelve that now the behaviour of emaner an ulier reon to two ifferent rice. Alo we know that the eman an uly rice are relate through the tax a follow = t Subtituting thi euation into the reviou one we have that the conition of euilibrium i ( ) = ( + ) x x t Now, ifferently from the reviou euilibrium conition, thi i one euation with only one unknown,, (in the reviou conition there were two unknown, an ). So, the new euilibrium rice can be foun an from it, the new euilibrium uantity. How oe thi new euilibrium comare with the ol (without tax) one? The bet way to ee thi i through a iagram.

13 Microeconomic I. Antonio Zabalza. Univerity of Valencia 13 Suly with tax B Suly without tax t 0 A B Deman t 0 The initial euilibrium i at A. The introuction of the tax ha two effect: a) The uantity tranacte fall from 0 t to. b) The tax i itribute between both emaner an ulier. Thi i o eite that legally the tax wa imoe on eller. Examle with linear eman an uly Suoe the eman an uly function are x = a b x = c+

14 Microeconomic I. Antonio Zabalza. Univerity of Valencia 14 We imoe a er unit tax t o that the relation between eman an uly rice i = + t The conition of euilibrium i a b + t = c+ ( ) From where we can erive the euilibrium uly rice a c bt = + b Aing t to thi we have the euilibrium eman rice a c bt a c t = + t = + + b + b Comare with the rice without taxe 0 a c = + b we ee that the rice ai by buyer increae, wherea the rice receive by eller ecreae. The ame reult woul be obtaine if the tax wa legally imoe on emaner (check that thi i o). The tax houl not be regare a imoe on conumer or ulier, but on tranaction between firm an conumer. The final itribution of the tax between buyer an eller oe not een on the legal roviion but on the elaticitie of eman an uly. In general, the higher i the elaticity of the curve, the le of the tax buren will the agent

15 Microeconomic I. Antonio Zabalza. Univerity of Valencia 15 rereente by thi curve have to bear. Contrariwie, if the curve i very inelatic the higher the buren for the grou in uetion. Elatic uly S with tax 0 S without tax Deman Inelatic uly S with tax S without tax 0 Deman

16 Microeconomic I. Antonio Zabalza. Univerity of Valencia 16 If the uly curve i relatively elatic, eller are able to a along mot of the tax to buyer. We ay that the buren of the tax fall mainly on buyer. If the uly curve i inelatic, eller are only able to a along a mall art of the tax. We ay then that the buren of the tax fall mainly on eller. Two extreme cae are when uly i comletely elatic an when uly i comletely inelatic. In the firt cae eller a along the whole tax to buyer. In the econ, eller bear the whole buren of the tax. 0 0 Taxe imoe an efficiency cot (eaweight lo of taxation) ue to the fact that the reence of taxe revent ome tranaction to take lace. Thi reuce the amount of market urlu. Thi reuction in the market urlu i the efficiency cot of the tax.

17 Microeconomic I. Antonio Zabalza. Univerity of Valencia 17 c t a b t Buyer looe area a+c. Seller looe area b+. The government gain area a+b (tax revenue). Therefore the net lo i area c+. Thi i the efficiency cot (eaweight lo) of taxation. 9.4 Pareto efficiency An economic ituation i Pareto efficient if there i no way to make any eron better off without hurting anyboy ele.

18 Microeconomic I. Antonio Zabalza. Univerity of Valencia 18 A cometitive market achieve Pareto efficiency. Conier the following figure. 1 At what buyer are willing to ay what eller want to receive. There i no room for further imrovement of the ituation of buyer an eller. At any other uantity, ay at, buyer are willing to ay a much larger rice for an extra unit than what eller woul nee in orer to rouce thi extra unit. Therefore, here we are in an inefficient ituation. By roucing one more unit, what eller woul be willing to ay i greater then the cot of

19 Microeconomic I. Antonio Zabalza. Univerity of Valencia 19 thi extra unit for eller. There i a net gain. While there i a net gain to be realize, we are not in a Pareto oition. If you reeat the above argument, you will ee that thee net gain exit until we reach. Thi oition, the euilibrium of a cometitive market, i therefore a oition which ilay the roerty of being Pareto efficient. Pareto efficiency oe not ay anything about the itribution of welfare. Recall the Prouction Poibility Frontier icue lat year. All oint on the frontier are Pareto efficient (you cannot imrove the welfare of one agent without hurting the other). An yet, oint A ha very ifferent itributional imlication from oint B. In A the itribution of welfare i very eual, while in B i very uneual. But both a Pareto efficient oint. Utility of agent 1 B A Utility of agent 2