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Externalities a Downriver Externality the Social Optimum First Order

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Externalities a Downriver Externality the Social Optimum First Order Externalities A Downriver Externality • An externality occurs whenever the activities of • Consider the firms on the river example. one economic agent affect the activities of another Both firms use only labor as an input. agent in ways that are not taken into account by the operation of the market. – The upriver firm produces Y with a production •Examples: function of Y = g(LY). – One firm produces down river from another firm. The – The downriver firm produces X. Its production first firm pollutes the river and prevents the second is affected by the upriver firm’s production: from producing. X = f(L ; Y), where: – Doctor works next door to a noisy factory. X ∂X – I care what my daughter eats. < 0 ∂Y First Order Condition at the The Social Optimum Social Optimum • Suppose there is a fixed amount of labor L in the • The first order conditions are: economy. æ ö ∂V ç ∂X ∂X ∂Y ÷ • Suppose prices for X and Y are Px and Py. = P − − λ = 0 ∂L x ç ∂L ∂Y ∂L ÷ æ ∂ ∂ ∂ ö ∂ x è x y ø ç X X Y ÷ Y • The total value of output is PxX + PyY. P − = P x ç ∂ ∂ ∂ ÷ y ∂ ∂V ∂Y è Lx Y Ly ø Ly • At the social optimum, labor is allocated to the two = P − λ = 0 ∂ y ∂ firms such that the total value of output in the Ly Ly economy is maximized: This “extra” term max ()+ () ∂V Px X Lx ;Y PyY Ly = L − L − L = 0 arises because of the Lx , Ly ∂λ x y + = externality. s.t. Lx Ly L The Market Will Not Lead to the Can the Market be Fixed? Social Optimum • In a competitive market, price taking maximize profits: • Pigouvian taxes π π – x = PxX - wLx and y =PyY – wLy – Impose a tax (t) on the production of Y such • The first order conditions in a competitive market are: that it chooses to cut back production to the ∂π ∂ ∂Y ∂X socially optimal level. x X = = P − w = 0 Py Px ∂ x ∂ ∂L ∂L π Lx Lx y x – Y’s profits after the tax are y =(Py-t)Y – wLy ∂π ∂π y ∂Y This is not the same f.o.c. as – Y’s new f.o.c. is: ∂Y = P − w = 0 y = ()P − t − w = 0 ∂ y ∂ the social optimum. Firm Y ∂ y ∂ Ly Ly L L ignores the externality it y y ∂ = − X imposesonXandproduces – For the socially optimal amount: t Px ∂Y too much. 1 Can the Market be Fixed? (II) Does the Market Need Fixing? • The firms can merge. • Suppose that firm X owned the river. Then it – If X and Y merge, the new super firm will maximize could charge the firm Y for the externality it joint profits: π = P Y + P X – w(L + L ) y x x y imposes and the socially efficient outcome would – The first order conditions for the super firm are: result. æ ö æ ∂ ∂ ∂ ö ∂ ∂π ç ∂X ∂X ∂Y ÷ ç X − X Y ÷ = Y • Suppose that firm Y owned the river. The socially = P − − w = 0 Px ç ÷ Py ∂ x ç ∂ ∂ ∂ ÷ ∂L ∂Y ∂L ∂L Lx è Lx Y Ly ø è x y ø y efficient would still occur! ∂π ∂Y This is exactly the f.o.c. for • Why? If it was socially efficient for X to have Y = P − w = 0 ∂L y ∂L the social optimum. By reduce its output, it would pay Y not to produce. y y merging, the externality has been “internalized” The Beneficent Effects of The Coase Theorem Assigning Property Rights • Coase Theorem: In the absence of transaction • The assignment and enforcement of a property costs, the socially efficient outcome will occur, right moves an externality (utility or productivity regardless of the assignment of property rights. interactions not dealt with by the market) into the • Externalities are not caused by one party—they market. are caused by the simultaneous actions of two or • It is the lack of (or poor) assignment of property more parties. rights that causes the externality and leads – For the downriver externality, you need two things: a ultimately to inefficient market outcomes. firm Y that pollutes a river and a firm X that locates – Markets are necessarily incomplete if property rights downriver. are not assigned. Coase Theorem Example M. Welby and W. Wonka • A doctor (M. Welby, MD) operates next door to a • Suppose that Dr. Welby has a right to peace and noisy candy manufacturer (W. Wonka). quiet. – The value of the doctor’s output is $100. – The efficient outcome happens and Mr. Wonka closes shop. (sorry Charlie!). – The value of the candy firm’s output is $50. • Suppose instead that Mr. Wonka convinces the • Dr. Welby cannot operate at all if the candy city council to decree that he has a right to make machines are running. noise. • The socially efficient outcome is that Mr. Wonka – Dr. Welby will pay Mr. Wonka at least $50 to shut shut down. down. – The efficient outcome still happens—no candy is produced. 2 Transaction Costs Why Do Firms Exist? • Recall that one solution the the externality • The conclusion of the Coase Theorem problem is merger. depends crucially on low cost bargaining. • By merging, the combined Welby-Wonka – Suppose Dr. Welby had to pay a $50 for a operation’s optimal private choices would also be lawyer to help negotiate with the intractable socially optimal. Mr. Wonka. • The advantage of merging to form a firm is reduced transactions costs of bargaining. – In that case, the assignment of property rights – There is less need for Mr. Welby to hire a lawyer if would determine whether the socially optimal Wonka and Welby work for the same company. outcome happened. • In a sense, firms exist to “internalize” high transactions cost interactions. Public Goods Examples of Public Goods • Public goods are goods for which it is inherently Exclusive Nonexclusive difficult to assign property rights. Candy, BMW’s, Fishing ponds, – The classic example is national defense. Rival Houses Public parks • The defining characteristics of public goods are nonexclusivity and nonrivalry. Scrambled satellite National defense, – Nonexclusivity: It is very costly or impossible to Non- dish signals, Justice, Internet exclude those who have not paid from enjoying the good. Rival Bridges broadcasts, – Nonrivalry: The consumption of additional units Lighthouses involves zero social marginal costs of production. Question to ponder: Is education a public good? Is it exclusive? Is it rival? Market Provision of Public Goods Market Provision of Public Goods (II) • In private goods markets, we have seen that an • The social MRS is the total amount everyone efficient outcome requires that the PPF must be would give up of G to get an extra unit of P. tangent to the “society’s” utility curve (“social” – The social MRS is the sum of the individual MRS: MRS = RPT). n æ dG öi n SMRS (P for G) = åç− ÷ = å MRS i • Suppose there are two goods in the economy—a i=1 è dP ø i=1 private good (G) and a public good (P). • The social optimum (Pareto efficiency) requires • The marginal rate of substitution for any that the SMRS be equal to the rate of product individual i is: æ dG öi MU i transformation (RPT). i = ç− ÷ = P MRS (P for G) i è dP ø MUG 3 Market Provision of Public Goods (III) Government Provision of Public Goods • Public goods are often (though not always) • If a market provided P, however, each person provided by the government. would pick P and G to equate their own MRS to – A famous counterexample is lighthouses in Britain. the RPT of P for G. – Another is the 91 Freeway MU i RPT (P for G) = MRS i (P for G) = P < SMRS • In a sense, the government “internalizes” the MU i G externality by forcing everyone to contribute to • The amount of public good purchased would be funding the public good. less than optimal. • Whether or not a good is public often depends on • Each individual in the market ignores the positive the existence of exclusion technologies. externality caused by the purchase of more of the – e.g. without the development of the transponder box, the public good (“free rider” problem). private road provision is cumbersome (toll booths). Lindahl Taxes for Public Goods Lindahl Taxes—An Example • How much should the government tax each person to fund the public good? • Two people in an economy. Two goods: • In a Lindahl pricing equilibrium, the government – A private good (G)—price = pg imposes taxes on each individual in proportion to – A public good (P)—price = pp the benefit they derive from the public good. • The government charges taxes: – This information is hard to collect. – Everyone has an incentive to underreport how much –Pg * a1 to the first person, say Welby benefit they derive from the public good. –Pg * a2 to the second person, say Wonka • If willingness to pay information can be collected, –Wherea + a =1 the sum of all taxes collected exactly equals the 1 2 optimal amount of spending on the public good. Choosing The Right Taxes Lindahl Taxes and Private Choices Wonka’s demand for P Wonka • Welby chooses P and G such that his MRS equals the price 1 ratio he faces: a P 1 p = MRSWelby (P for G) Pg • Wonka chooses P and G such that his MRS equals the a1 a2 price ratio he faces: a P 2 p = MRSWonka (P for G) Pg • Producers maximize profits by setting RPT equal to the price ratio: 1 P Welby p = Welby’s demand for P RPT (P for G) Pg 4 Lindahl Taxes and the Social Optimum But Will the Government Get it Right? • At the Lindahl tax equilibrium, the socially • With Pigouvian taxes and the assignment of property optimal levels of the public and private goods will rights, the government has tools to internalize externalities be produced.
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