Can the Market be Fixed? (II) Does the Market Need Fixing? The Beneficent Effects of Assigning Property Rights. The Coase Theorem

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1 Eternaltes An eternalt occurs whenever the actvtes of one economc agent affect the actvtes of another agent n was that are not taken nto account b the operaton of the market. Eamples: One frm produces down rver from another frm. The frst frm pollutes the rver and prevents the second from producng. Doctor works net door to a nos factor. I care what m daughter eats. A Downrver Eternalt Consder the frms on the rver eample. Both frms use onl labor as an nput. The uprver frm produces Y wth a producton functon of Y = g(l Y ). The downrver frm produces X. Its producton s affected b the uprver frm s producton: X = f(l X ; Y), where: < 0 The Socal Optmum Suppose there s a fed amount of labor L n the econom. Suppose prces for X and Y are and. The total value of output s X + Y. At the socal optmum, labor s allocated to the two frms such that the total value of output n the econom s mamzed: ma L L X ( L Y ) Y ( L ), ; + s. t. L + L = L Frst Order Condton at the Socal Optmum The frst order condtons are: = λ = 0 = λ = 0 = L L L = 0 λ X X Y Y = L Y L Ths etra term arses because of the eternalt. The Market Wll Not Lead to the Socal Optmum In a compettve market, prce takng mamze profts: π = X - wl and π = Y wl The frst order condtons n a compettve market are: π = π = = Ths s not the same f.o.c. as the socal optmum. Frm Y gnores the eternalt t mposesonxandproduces too much. Can the Market be Fed? ouvan taes Impose a ta (t) on the producton of Y such that t chooses to cut back producton to the socall optmal level. Y s profts after the ta are π =( -t)y wl Y s new f.o.c. s: π = ( t) For the socall optmal amount: t =

2 Can the Market be Fed? (II) The frms can merge. If X and Y merge, the new super frm wll mamze jont profts: π = Y + X w(l + L ) The frst order condtons for the super frm are: π = π = X X Y Y = L Y L Ths s eactl the f.o.c. for the socal optmum. B mergng, the eternalt has been nternalzed Does the Market Need Fng? Suppose that frm X owned the rver. Then t could charge the frm Y for the eternalt t mposes and the socall effcent outcome would result. Suppose that frm Y owned the rver. The socall effcent would stll occur! Wh? If t was socall effcent for X to have Y reduce ts output, t would pa Y not to produce. The Coase Theorem Coase Theorem: In the absence of transacton costs, the socall effcent outcome wll occur, regardless of the assgnment of propert rghts. Eternaltes are not caused b one part the are caused b the smultaneous actons of two or more partes. For the downrver eternalt, ou need two thngs: a frm Y that pollutes a rver and a frm X that locates downrver. The Benefcent Effects of Assgnng ropert Rghts The assgnment and enforcement of a propert rght moves an eternalt (utlt or productvt nteractons not dealt wth b the market) nto the market. It s the lack of (or poor) assgnment of propert rghts that causes the eternalt and leads ultmatel to neffcent market outcomes. Markets are necessarl ncomplete f propert rghts are not assgned. Coase Theorem Eample A doctor (M. Welb, MD) operates net door to a nos cand manufacturer (W. Wonka). The value of the doctor s output s $00. The value of the cand frm s output s $50. Dr. Welb cannot operate at all f the cand machnes are runnng. The socall effcent outcome s that Mr. Wonka shut down. M. Welb and W. Wonka Suppose that Dr. Welb has a rght to peace and quet. The effcent outcome happens and Mr. Wonka closes shop. (sorr Charle!). Suppose nstead that Mr. Wonka convnces the ct councl to decree that he has a rght to make nose. Dr. Welb wll pa Mr. Wonka at least $50 to shut down. The effcent outcome stll happens no cand s produced. 2

3 Transacton Costs The concluson of the Coase Theorem depends crucall on low cost barganng. Suppose Dr. Welb had to pa a $50 for a lawer to help negotate wth the ntractable Mr. Wonka. In that case, the assgnment of propert rghts would determne whether the socall optmal outcome happened. Wh Do Frms Est? Recall that one soluton the the eternalt problem s merger. B mergng, the combned Welb-Wonka operaton s optmal prvate choces would also be socall optmal. The advantage of mergng to form a frm s reduced transactons costs of barganng. There s less need for Mr. Welb to hre a lawer f Wonka and Welb work for the same compan. In a sense, frms est to nternalze hgh transactons cost nteractons. ublc Goods ublc goods are goods for whch t s nherentl dffcult to assgn propert rghts. The classc eample s natonal defense. The defnng characterstcs of publc goods are noneclusvt and nonrvalr. Noneclusvt: It s ver costl or mpossble to eclude those who have not pad from enjong the good. Nonrvalr: The consumpton of addtonal unts nvolves zero socal margnal costs of producton. Eamples of ublc Goods Rval Non- Rval Eclusve Cand, BMW s, Houses Scrambled satellte dsh sgnals, Brdges Noneclusve Fshng ponds, ublc parks Natonal defense, Justce, Internet broadcasts, Lghthouses Queston to ponder: Is educaton a publc good? Is t eclusve? Is t rval? Market rovson of ublc Goods In prvate goods markets, we have seen that an effcent outcome requres that the F must be tangent to the socet s utlt curve ( socal MRS = RT). Suppose there are two goods n the econom a prvate good (G) and a publc good (). The margnal rate of substtuton for an ndvdual s: dg MU MRS ( for G) = = d MU G Market rovson of ublc Goods (II) The socal MRS s the total amount everone would gve up of G to get an etra unt of. The socal MRS s the sum of the ndvdual MRS: n n dg = SMRS ( for G) = MRS = d = The socal optmum (areto effcenc) requres that the SMRS be equal to the rate of product transformaton (RT). 3

4 Market rovson of ublc Goods (III) If a market provded, however, each person would pck and G to equate ther own MRS to the RT of for G. MU RT ( for G) = MRS ( for G) = < SMRS MU The amount of publc good purchased would be less than optmal. Each ndvdual n the market gnores the postve eternalt caused b the purchase of more of the the publc good ( free rder problem). G Government rovson of ublc Goods ublc goods are often (though not alwas) provded b the government. A famous countereample s lghthouses n Brtan. Another s the 9 Freewa In a sense, the government nternalzes the eternalt b forcng everone to contrbute to fundng the publc good. Whether or not a good s publc often depends on the estence of ecluson technologes. e.g. wthout the development of the transponder bo, prvate road provson s cumbersome (toll booths). Lndahl Taes for ublc Goods How much should the government ta each person to fund the publc good? In a Lndahl prcng equlbrum, the government mposes taes on each ndvdual n proporton to the beneft the derve from the publc good. Ths nformaton s hard to collect. Everone has an ncentve to underreport how much beneft the derve from the publc good. If wllngness to pa nformaton can be collected, the sum of all taes collected eactl equals the optmal amount of spendng on the publc good. Lndahl Taes An Eample Two people n an econom. Two goods: A prvate good (G) prce = p g A publc good () prce = p p The government charges taes: g * a to the frst person, sa Welb g * a 2 to the second person, sa Wonka Wherea + a 2 = Choosng The Rght Taes Lndahl Taes and rvate Choces a Welb Wonka s demand for Welb s demand for Wonka a 2 Welb chooses and G such that hs MRS equals the prce rato he faces: ap = MRSWelb ( for G) Wonka chooses and G such that hs MRS equals the prce rato he faces: a2p = MRSWonka( for G) roducers mamze profts b settng RT equal to the prce rato: p = RT ( for G) g 4

5 Lndahl Taes and the Socal Optmum At the Lndahl ta equlbrum, the socall optmal levels of the publc and prvate goods wll be produced. Add Welb and Wonka s MRS s: ap a2p p MRS Welb ( for G) + MRSWonka( for G) = + = Compare wth the frm s proft mamzng condton: p MRSWelb ( for G) + MRSWonka ( for G) = = RT ( for G) But ths s eactl the condton for the socal optmum But Wll the Government Get t Rght? Wth ouvan taes and the assgnment of propert rghts, the government has tools to nternalze eternaltes Wth Lndahl taes, the government has a tool to allow the market to provde effcentl for publc goods. If fng these problems s so eas, then wh s t rare for the government to get t rght? Collectng nformaton about what s optmal ma be dffcult or mpossble. When there are fundamental dsagreements about what s a publc good, then under democratc government, there ma be no rght answer. 5