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Externalities

Externalities. Chapter 21. Introduction. Driving an automobile is probably a household’s most polluting activity Efforts since 1970 have greatly reduced typical vehicle emissions However, number of miles driven has more than doubled Offset benefits of controlling emissions

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Externalities

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  1. Externalities Chapter 21

  2. Introduction • Driving an automobile is probably a household’s most polluting activity • Efforts since 1970 have greatly reduced typical vehicle emissions • However, number of miles driven has more than doubled • Offset benefits of controlling emissions • Net result is only a small reduction in automobile pollutants • Cause of automobile pollution is a major market failure in presence of an externality (pollution) resulting from missing markets • With missing markets, signals in form of market prices do not exist to reveal consumer preferences for society’s allocation of resources

  3. Introduction • If well-defined property rights exist, markets will generally occur for externalities • Reduces necessity for mechanisms designed to correct externality-generated inefficiencies • One role for government is to provide a legal system to support well-defined property rights for all of society’s resources • We investigate property rights and consequences of externalities resulting from ill-defined property rights • Then broadly classify externalities as either bilateral or multilateral • Discuss inefficiencies associated with bilateral externalities • Address enforceable property rights (given Coase Theorem) as a means for resolving these inefficiencies

  4. Introduction • Coase Theorem states • If a market can be created for an externality, an efficient outcome will result regardless of how well-defined property rights are allocated • We investigate markets where Coase Theorem does not hold • Discuss issue of multilateral externalities • Evaluate government policies involving quotas, taxes, and fostering markets for externalities (eliminating missing markets) as tools for addressing market inefficiencies • Government agencies develop mechanisms that assign property rights and regulate agent behavior • Enforcing policies through penalties for noncompliance and dividends for compliance • However, government mechanisms may not always result in improving social welfare • Such mechanisms can only result in alternative second-best Pareto-efficient allocations

  5. Introduction • Opportunity cost of allocating resources toward establishing and maintaining mechanisms may exceed cost of inefficiency associated with some externalities • Existence of opportunity cost implies that there are still externalities at some allocation where social welfare is maximized • Applied economists are active in estimating costs and benefits of alternative mechanisms for addressing externalities • Aim in chapter is not to determine least-cost allocation for removing an externality • But to understand why ill-defined property rights result in missing markets for commodities and resulting externalities • Can determine optimal level of an externality and minimum cost of achieving a given externality level

  6. Externalities Defined • An externality (z) is present whenever some agent’s (say, A’s) utility or production technology includes commodities whose amounts are determined by other agents • Without particular attention to effect on A’s welfare • Definition rules out any market-price affects on agents’ utility or production, called pecuniary externalities • Arise when external effect is transmitted through price changes • A pecuniary externality does not cause a market failure • For example, suppose a new firm enters a market and drives up rental price of land • Market for land provides a mechanism by which parties can bid for land • Resulting prices will reflect value of land in its various uses

  7. Externalities Defined • Without pecuniary externalities price signals would fail to sustain an efficient allocation • Consumers relying on firms for supply of commodities are not externalities • Deliberately affecting welfare of others is not an externality • For example, deliberate criminal actions against agents are not externalities • However, waiting for someone who is not particularly concerned about your welfare is an externality

  8. Property Rights • A bundle of entitlements defining an owner’s rights, privileges, and limitations for use of a resource • For example, in many cities owning a plot of land may give you entitlement to build a house but not drill a well • Entitlements vary considerably • From being very restrictive in a planned community to essentially no restrictions in some rural areas • A well-defined structure of property rights will provide incentives for efficient allocation of resources

  9. Property Rights • Following list is one set of well-defined private-property rights that results in a Pareto-efficient allocation • Universality • All resources are privately owned and all entitlements completely specified • Exclusivity • All benefits and costs from owning and employing resources accrue to owner • Transferability • All property rights are transferable from one owner to another in a voluntary exchange • Enforceability • Property rights are secure from involuntary seizure or encroachment by others

  10. Property Rights • Previously we implicitly assumed well-defined property rights existed • We demonstrated that perfectly competitive markets yield an efficient price system for resource allocation • Such a system is where producers maximize their profits and households maximize their utility • Given their respective resource constraints and current state of technology • Presence of externalities violates assumption of well-defined property rights • For example, building a cabin that blocks neighbor’s view of lake results in a cost that accrues to neighbor • With externalities, household preferences for commodities are not defined solely over bundle of commodities that it has ability to choose

  11. Property Rights • Assumption of firms freely choosing inputs is also violated with presence of production externalities • Generally, consumption or production externalities exist when agents (households and firms) are directly affected by actions (external effects) of other agents • Examples are • Presence of other vehicles on a congested highway (negative externality) • Sight of a neighbor’s flower garden (positive externality)

  12. Property Rights • When externalities exist, perfectly competitive equilibrium does not correspond with a Pareto-optimal allocation • A common property exists when no individual agent has property entitlements • Agent cannot employ resource for individual gain • In a communist economy, all society’s resources are considered common property • In a centrally planned socialist economy, state (government) has property entitlements and controls property (resource) allocation for common good of society • In a free-market economy, property entitlements are vested privately with individual agents • Leading to private property as dominant form of property rights

  13. Bilateral Externalities • Where one agent’s utility or profit is affected by another agent’s actions • Agents could be two firms with their production technologies linked • Firms could be producing either same or different outputs • For example, firms could be a chemical plant and a kayak rental company located on the same river • Alternatively, agents could be two households or one firm and a household • For example, two households living in a duplex where one household enjoys loud music

  14. Bilateral Externalities • For expository purposes, we will assume agents are firms • With one firm experiencing a negative externality from the other • Rather than well-defined property rights, assume Firm 1’s short-run total cost function is a function of marketable output q1 and a nonmarket output (externality) z, STC1(q1, z) • For example, q1 could be production of steel and z the associated river water pollution • Assuming Stage II of production for q1, associated marginal cost curve, ∂STC1/∂q1 = SMC1 > 0 • Has a positive slope, ∂SMC1/∂q1 > 0 • For externality z, ∂STC1/∂z < 0 • Increasing z will decrease cost of production • Represents a marginal benefit to firm

  15. Bilateral Externalities • Define marginal benefit as marginal benefit of the externality (MBE) • MBE = -∂STC1/∂Z > 0 • Associated MBE curve is illustrated in Figure 21.1, given Law of Diminishing Marginal Returns • As z increases, MBE declines • Given a missing market for z, there is no positive market price for z • A profit-maximizing firm would produce where ∂STC1/∂z = 0

  16. Figure 21.1 Negative externality

  17. Bilateral Externalities • An increase in costs with no associated change in revenue will decrease profit • Level of z that minimizes costs is ∂STC1/∂z = 0 • Assume firm 2’s short-run total cost function is directly affected by firm 1’s nonmarket output z, STC2(q2, z) • q2 denotes Firm 2’s marketable output, kayak rentals • Firm 2’s cost of producing q2 is directly affected by amount of z firm 1 produces • A negative externality implies ∂STC2/∂z > 0 • An increase in z increases STC2 and depresses profit • Partial ∂STC2/∂z > 0 is called marginal social cost (MSC) of externality • Illustrated in Figure 21.1 • Positive slope associated with MSC indicates • As z increases, marginal social cost increases • ∂MSC/∂z > 0 and ∂2MSC/∂z2 > 0 • Firm 2’s costs are increased by an increase in z at an increasing rate • For example, the river may be able to assimilate initial increases in water pollution, so MSC of water pollution for kayaking is low • However, as water pollution increases, capacity of river for assimilating pollution may be exceeded, resulting in marginal cost for the kayak firm increasing at an increasing rate

  18. Bilateral Externalities • Positive slope associated with MSC indicates • As z increases, marginal social cost increases • ∂MSC/∂z > 0 and ∂2MSC/∂z2 > 0 • Firm 2’s costs are increased by an increase in z at an increasing rate • For example, river may be able to assimilate initial increases in water pollution • MSC of water pollution for kayaking is low • However, as water pollution increases, capacity of river for assimilating pollution may be exceeded • Resulting in marginal cost for kayak firm increasing at an increasing rate

  19. Independent Decision Making • In its profit maximization, firm 1 has control over both q1 and z • p1 is per-unit price firm 1 receives for its output, q1 • Since z is a nonmarket output, there is no associated market price • F.O.C.s are • ∂1/∂q1 = p1 – SMB1(q1, z) = 0 • Discussed in Chapter 9 and illustrated in Figure 21.1 • ∂1/∂z = -∂STC1(q1, z)/∂z = 0 • Establishes cost-minimizing level of z as a necessary condition for profit maximization

  20. Independent Decision Making • Level of externality z should be adjusted to point where additional reduction in cost of generating an additional unit of z is zero • Solving F.O.C.s simultaneously for z and q1 results in their optimal levels zP and qP1 • Figure 21.1 illustrates this optimal solution • zP is associated with -∂STC1/∂z = MBE = 0 and qP1 with SMC1 = p1 • For its profit maximization, firm 2 only has control over its output, q2, but production of q2 is influenced by externality z, so • p2 is per-unit price of q2 • F.O.C. is • ∂2/∂q2 = p2 – SMC2(q2, z) = 0 • Establishes price equaling marginal cost as a condition for profit maximization

  21. Independent Decision Making • Externality results from firm 2 having no control over z, which affects its production • Firm 1 controls level of z and has no incentive to consider effect z has on firm 2’s production • When firm 2’s additional social cost, MSC, associated with firm 1’s pollution, z, is not considered by firm 1, an inefficient high level of pollution may result • At zP in Figure 21.1, MSC > MBE • Decreasing z will subtract more from cost than from benefits • Not considering additional social costs or benefits from an externality generally results in an inefficient allocation of resources

  22. Dependent (Joint) Decision Making • Internalizing social costs of a negative externality into agent’s decisions • Results in a Pareto-efficient allocation of resources • Internalization of social costs results in firm 1 taking into consideration impact its production decisions have on firm 2’s production possibilities • With this consideration, output z is no longer an externality • All effects of z are now internalized into firm 1’s production decisions • Accomplished by maximizing joint profit of the two firms ( = 1 + 2) • Equivalent to two firms merging to form one firm that produces marketable outputs q1 and q2, with associated prices p1 and p2, along with nonmarket output z • With joint action, there is no longer an externality • Additional social costs are now internalized within this one firm

  23. Dependent (Joint) Decision Making • Mathematically, joint profit maximization is • F.O.C.s are • ∂/∂q1 = p1 – SMCJ1(q1, z) = 0 • ∂/q2 = p2 – SMCJ2(q2, z) = 0 • ∂/∂z = -∂STC1(q1,z)/∂z - ∂STC2(q2, z)/ ∂z = 0 • SMCJj is short-run marginal joint cost of producing qj, j = 1, 2 • First two F.O.C.s are same as when firms act privately • A perfectly competitive firm equates price to marginal cost • Under joint action, optimal levels of q1 and q2, (qJ1 and qJ2) are where price is equated with marginal cost • For a negative externality, qJ1 < qP1, given z increases costs for producing q2

  24. Dependent (Joint) Decision Making • Last F.O.C. differs from independent conditions where firms act privately • Now optimal levels of q1, q2, and z depend on effect z has on firm 2’s costs • Figure 21.1 illustrates optimal levels of z and q1 • Instead of setting ∂STC1/∂z equal to zero, joint production sets -STC1/∂z equal to marginal social cost • -∂STC1(q1, z)/∂z = ∂STC2(q2, z)/ ∂z • MBEJ = MSC • MBEJ is marginal joint benefit of externality from joint production of q1 and q2 • Joint action will result in firm 1 decreasing level of z below point where MBE = 0 • Marginal social cost derived from firm 2 is now internalized into decision process

  25. Dependent (Joint) Decision Making • Difference between private and joint optimal solution is illustrated in Figure 21.1 • Optimal level of z decreases, from zP to zJ, along with a decrease in the optimal level of output, from qP1 to qJ1 • Firm 1’s short-run marginal cost of producing q1 shifts to the left, from SMC1 to SMCJ1 • Given increased cost of internalizing production of z • Similarly, firm 1’s marginal benefit of externality shifts to left, to MBEJ, given decrease in q1 • Through internalization, firm 1 pays a cost for producing z • At Pareto-efficient level of z, zJ, amount firm 1 is willing to pay for producing an additional unit of z is equal to firm 2’s additional costs associated with this additional unit of z • Note that if firm 2’s cost of producing q2 is independent of z, no externality exists • Firm 2’s cost associated with z is zero • Firm 1 will again equate additional cost of producing an additional unit of z to zero

  26. Resolving Externality Inefficiency • In February 2002, Oakland County International Airport in Waterford, Michigan, helped 650 residents to sound insulate and vibration reinforce their homes against airplane takeoffs and landings • Such solutions to externality inefficiencies are possible when conditions allow agents to negotiate an optimal solution • Providing favorable negotiating conditions is one approach to mitigating inefficiencies associated with externalities • Based on these negotiations, a market for externality is then established • For example, suppose for a negative externality z, enforceable property rights are established where firm 2 is assigned rights to production level of z (noise) • Firm 1 is unable to produce z without firm 2’s approval

  27. Resolving Externality Inefficiency • Denote total price (fee) for z units that firm 2 charges firm 1 as Fee • For profit maximization, firm 2 will determine level of Fee • Where firm 1 is indifferent between paying Fee to produce z units of externality or not producing any of the externality • If firm 2 charges a price below Fee, firm 1 will still produce z units • An increase in Fee will enhance firm 2’s profits without changing level of z • Increasing Fee transfers some of firm 1’s producer surplus in production of z to firm 2 • Firm 2 will increase Fee to point where all producer surplus from producing z units is absorbed by Fee • At this point, firm 1 is indifferent between paying Fee to produce z units or not producing any z

  28. Resolving Externality Inefficiency • Mathematically, this occurs where • 1(q1, z) – Fee = 1(q01, 0) • p1q1 – STC1(q1, z) – Fee = p1,q01 – STC1(q01, 0) • q01 represents optimal level of output given z = 0 • Firm 2 will then maximize profits subject to level of Fee where firm 1 is indifferent • Solving for Fee in the constraint and substituting into objective function yields

  29. Resolving Externality Inefficiency • F.O.C.s are • ∂2/∂q2 = p2 – SMCJ2 = 0 • ∂2/∂z = -∂STC2(q2, z)/∂z - ∂STC1(q1, z)/∂z = 0 = -MSC + MBEJ = 0 • Optimal levels for q2 and z are same solutions for joint production, zJ and qJ2 • Given this charge, Fee, for producing zJ units of a negative externality, firm 1’s profit-maximizing problem is • F.O.C. is • ∂1/∂q1 = p1 – SMCJ1 = 0 • F.O.C.s are identical to F.O.C.s for joint profit maximization • By assigning a property right to z, a market is created for z • Allows a firm to charge a price for its production of z • Resulting solution is the same optimal solution obtained under joint action, zJ

  30. Resolving Externality Inefficiency • Coase Theorem • If trade of an externality can occur (a market exists) • Bargaining will lead to an efficient outcome no matter how property rights are allocated • Assumes there are no transaction costs associated with bargaining • Any asymmetry in information between buyer and seller can cause transaction costs • Will not result in an efficient outcome no matter how property rights are allocated • Specifically, suppose firm 1 now has property rights to produce as much of the externality z as it desires • In absence of any trading, firm 1 will select private level of z, zP • Firm 2 will offer to pay firm 1 to move from firm 1’s private solution zP to joint-optimal solution zJ

  31. Resolving Externality Inefficiency • Firm 1 will be indifferent between producing an alternative level of z and receiving S as payment from firm 2 or producing zP and receiving no payment • 1(q1, z) + S = 1(qP1, zP) • p1q1 – STC1(q1, z) + S = p1qP1 – STC1(qP1, zP) • Firm 2 will then maximize profits, subject to levels of S, where firm 1 is indifferent

  32. Resolving Externality Inefficiency • Solving for S in the constraint and substituting into objective function yields • F.O.C.s are • ∂2/∂q2 = p2 – SMCJ2 = 0 • ∂2/∂z = -∂STC2(q2, z)/∂z - ∂STC1(q1, z)/∂z = 0 • Again, optimal levels for q2 and z are the same as in joint production, zJ and qJ2

  33. Resolving Externality Inefficiency • Firm 1’s profit-maximizing problem is • F.O.C. is • ∂1/∂q1 = p1 – SMCJ1 = 0 • Exactly the same optimal result as when property rights are controlled by firm 2 or with joint production • Given well-defined property rights and that agents can bargain with essentially zero transaction costs, resulting solution will be Pareto efficient • In practice, it is rare to find externalities with these characteristics • Normally, a profit incentive exists to either internalize the externality by merging or establish a market for the externality • Thus, market forces tend to remove any possible existence of a bilateral externality

  34. Resolving Externality Inefficiency • There are distributional effects that depend on assignment of property rights • Property rights are a form of initial endowments, which do have market value • For example, even though Coase Theorem states that optimal levels of z, q1, and q2 remain unaffected by property rights assignment • Resulting profit levels of firms are affected • When an agent is bestowed property right, its benefits will not decrease • Potential exists for enhancing benefits • Greater control over property rights improves bargaining power of an agent and, hence, potential rewards • Distribution of benefits can change with assignment of property rights • A market with well-defined property rights and essentially zero transaction costs will provide a Pareto-optimal allocation • Any improvement in social welfare is dependent on equity impacts of resulting allocation

  35. Multilateral Externalities • Decreasing automobile emissions can have a major impact on air quality and on asthma in children • This example illustrates multilateral externalities • Far more common than bilateral externalities • Numerous agents create transaction costs associated with ill-defined property rights • Obstruct market from internalizing externalities • Coase Theorem no longer holds under these transaction costs • Efforts to internalize these externalities may require some type of government intervention into markets

  36. Government Policies • Government actions to mitigate inefficient exploitation of resources have taken a number of forms • One policy is to instill some form of private-property rights on a common-property resource • For example, in western U.S., common- property problem of livestock overgrazing was addressed by issuing grazing permits • Ranchers who own grazing permits are allowed to use public rangeland for a set fee • Original grazing permits issued by state and federal agencies were freely given to ranchers • Common property of public lands was transferred to private ownership • Without a permit, one could not use public land for its major usegrazing • Permits acquired a market value through their incorporation into land value of ranch holding permits • Policy of granting private-property rights to common property may result in improving economic efficiency • However, it raises equity issues in terms of enhancing ranchers’ endowments at expense of other agents

  37. Permit System • Trading of emission permits represents a government management tool for a common property • Government controls resource and establishes barriers to prevent agents from exacting resource unless licensed by the government • For example, government may issue a permit to extract a certain quantity and/or size of a resource • Fishing and hunting licenses are examples

  38. Permit System • A permit system can also be employed for reducing a firm’s undesirable emissions that adversely affect air and water quality • Prior to generating a negative externality firm would be required to obtain a permit • Number of permits can be limited to achieve some target level • Allocation of permits transfers certain property rights to permit holder • In the case of a hunting permit, hunter pays for this transfer of property right • In terms of firms generating some negative externality, they may be issued permits at or below their historical emissions level • Given they possess a history of quasi-property rights to emission releases

  39. Permit System • Permits that can be traded (called marketable permits), create a market for permits with an associated equilibrium price • If a firm’s marginal cost of reducing emissions is greater than market price for a permit to release emissions • It would minimize cost by purchasing permit and releasing emissions • If its marginal cost is less than market price, it would minimize cost by selling permits and reducing its emissions • In equilibrium, each firm’s marginal cost of reducing emissions would be equal to market price for permits

  40. Permit System • Specifically, let’s consider two firms engaged in generating a negative externality • Let z1 and z2 represent emission levels of firm 1 and firm 2, respectively, with associated short-run total cost functions STC1(q1, z1) and STC2(q2, z2) • Assume target level of total emissions (zJ) is established, so zJ = z1 + z2 • Determine minimum cost of achieving emissions level zJ by • TC is total cost of reduced emissions

  41. Permit System • Lagrangian is • F.O.C.s are

  42. Permit System • Minimum-cost condition of achieving a zJ level of emissions is MBEJ1 = MBEJ2 = J • Firms’ short-run marginal benefits of emissions are set equal to J • In this case, Lagrange multiplier is marginal social cost of combined emissions by two firms, J = ∂TC/∂z • Setting this equal to each firm’s MBEJ yields minimum cost of establishing a zJ level of emissions • Illustrated in Figure 21.2 • Target level zJ is obtained at minimum cost with firm 1 and firm 2 generating zJ1 and zJ2 emissions, respectively

  43. Figure 21.2 Minimum cost of achieving a given emission level

  44. Permit System • Establishing a marketable permit system achieves this minimum social cost of emissions • Let pz represent per-unit equilibrium price of a permit and z01 and z02 initial level of permits for firms 1 and 2, respectively • zJ = z01 + z02 • With j = 1, 2, representing either of the firms, each firm will maximize profits as follows • When z0j - zj < 0, firm is using more permits than it was allocated • It will acquire additional permits in amount of (zj - z0j) at per-unit price of pz • If z0j – zj > 0, firm is not using all of its permit allocation • Will sell (z0j - zj) at per-unit price of pz

  45. Permit System • F.O.C.s are • ∂j/∂qj = pj – SMCJj(qj, zj) = 0 • Discussed in Chapter 9 • ∂j/∂zj = -∂STCj(qj, zj)/ ∂zj – pz = 0 = MBEJj – pz = 0, j = 1, 2 • Each firm equates their marginal benefit of emissions to pz • A major limitation of this marketable permit system exists when spatial distribution of externality generated by all firms is not uniform • If agents who are being affected by externalities are not uniformly affected by each firm • Permit system will result in some agents receiving even more of the externality • For example, assume households of type A are only affected by firm 1’s emissions and households of type B only by firm 2’s emissions • As illustrated in Figure 21.3, firm 1 sells permits to firm 2 • Thus, from initial emission levels (z01,z02) emissions for type A households are reduced at expense of type B households, who receive a higher emissions level • Although emissions level is now generated at a minimum cost, distribution of resulting emissions are not optimal

  46. Figure 21.3 Minimum cost of achieving a given emission level with marketable permits

  47. Taxes and Standards (Quotas) • If general knowledge exists about which firms can efficiently reduce a negative externality relative to other firms • Direct taxes or standards may be employed • Direct taxes on negative externalities have the theoretical foundation of the agent receiving an inefficient price for negative externality it is generating • With ill-defined property rights firms would receive a zero price for generation of emissions • An efficient price would be a tax equivalent to marginal social cost of negative externality • Profit-maximizing problem for firm j is • j is a per-unit tax for firm j on negative externality, z

  48. Taxes and Standards (Quotas) • Potentially, firms with differing production capabilities for efficiently reducing negative externality would face different tax levels • On a practical level, tax would generally be the same for firms with like production technologies within same industry and causing similar harm to other agents • Assuming a constant tax level across two firms, , F.O.C.s are • ∂j/∂qj = pj – SMCJj(qj, zj) = 0 • Discussed in Chapter 9 • ∂j/∂zj = -∂STCj(qj, zj)/∂zj -  = 0 = MBEJj -  = 0, j = 1, 2 • Firm j equates its marginal benefit of emission to  • Equating tax  to MSCj will yield an efficient level of emissions generation by each firm, zJj • Illustrated in Figure 21.4

  49. Figure 21.4 Pigouvian tax on emissions

  50. Taxes and Standards (Quotas) • As illustrated in Figure 21.1, if there is only one agent being affected by firm j’s emissions, then  = ∂STC2/∂zj • Given well-defined property rights, Coase Theorem would apply • No government-established price for market would be required for efficiency • However, as number of agents increase, even with well-defined property rights • Transaction costs of determining who are being affected by a negative externality increases • A government mechanism design in form of an emissions tax may be socially desirable • Such a tax, equivalent to MSC, is called a Pigouvian tax, after Arthur Pigou • Assuming general knowledge exists of which firms can efficiently reduce a negative externality relative to other firms • Pigouvian taxes directly associated possible spatial MSC would not have spatial distribution limitation associated with a permit system • Aside from the problem of acquiring this general knowledge for implementation • Pigouvian taxes are a Lindahl taxface same limitations • Agents facing a higher tax rate relative to others may not respond well to tax-discriminating nature of Pigouvian taxes

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