Positive ExternalitiesFigure 5.2The Benefits of Pollution TradingStandards Are Less Efficient than Taxes, But Result in Higher OutputConclusionsSo which Specification Is Best?Technology DiffusionChapter #5: Issues in Externality Control Contents: Positive Externalities Polluter Heterogeneity The Benefits of Pollution Trading Problems Associated with Pollution Permit Markets Choice of Pollution Taxes or Standards Specification of Pollution in Productive Activities Components of Externality Policy Technology Diffusion Positive Externalities A positive externality exists if the activities of one individual (or group) lead to increases in the utility or productive ability of some other individual (or group), when the benefits are not transmitted through a market. For example, an apple farmer might receive unpaid benefits from a neighboring honey producer if the honey producer’s bees pollinate the apple trees. Because the benefits associated with positive externalities are not paid for in market transactions, the activities producing these benefits are carried out at an inefficiently low level. In the first example above, unless the apple farmer pays the bee keeper for the marginal value of pollinating services, the bee keeper will not recognize this value in her objective function and thus keep an inefficiently low number of bees. An Economic Model of Positive Externalities: Consider a fertilizer manufacturers who uses animal waste as an input and generates a positive externality by removing the waste from the environment. Let: X = the amount of animal waste used by fertilizer manufacturers. D(P) = the fertilizer manufacturers’ demand for X PB(X) = the fertilizer manufacturers’ private benefit from output X (i.e., the area under the demand curve). EB(X) = environmental benefit of removed waste X. SB(X) = social benefit of X = PB(X) + EB(X). C(X) = cost of obtaining X. SW(X) = social welfare of using X = PB(X) + EB(X) - C(X)Now Consider the Market for Animal Waste Social optimization problem: {}Max SW X PB X EB X C XX.() () ()()=+− First-Order Condition: PBx +EBx - Cx = 0, or, MPB + MEB = MC. Hence, the socially optimal solution is to use X* animal waste, such that: MSB(X*) = MC(X*) Positive Externalities Figure 5.1 Q* = optimal output P*c = optimal consumer price = (P*c + S*) = optimal producer price Pp* Qc = competitive output Pc = competitive price S* = P*p - P*c = MEB = optimal subsidy [note that S* = MEB(Q*)] -2-In Figure 5.1, the socially optimal solution, where MSB = MC, occurs at point A. In contrast, the competitive solution is to use fertilizer until MPB = MC, which occurs at point B. At point B, the quantity of fertilizer used is lower than under the socially optimal solution ( Qc < Q*), which means that the competitive solution results in an insufficient utilization of X. A subsidy S* = MEB(X*) will achieve the optimal solution. With subsidy S*, the following welfare implications arise: consumer gain = Pc BC Pc* producers gain = AB Pc P p* environmental gain = MBCA subsidy cost = CA P Pc*p* net social gain = BAM. Note the asymmetry between optimal policies for positive and negative externalities: The likely policy to address positive externalities is a subsidy. The likely policy to address negative externality is direct controls or taxes. Polluter Heterogeneity and Markets for Pollution When firms are heterogeneous and differ in their ability to abate, or cut back, their pollution, it is necessary to determine both the efficient amount of total emissions and the efficient mix of pollution among alternative sources. The efficient mix of pollution is simply the combination of controls that generates the efficient amount of total pollution at the lowest cost. This may require that all polluting firms in a given location abate pollution to the same level, or perhaps that only one of many firms should abate. The market approach, or transferable permit system to correct negative externalities attempts to establish markets for pollution. The approach utilizes economic incentives found in conventional markets to allocate pollution abatement between firms in the most cost-effective manner. -3-Assume there are I groups of polluters (different industries, firms, etc.) emitting pollution into a common medium, for example, an airshed or a lake. We will also assume that the medium is “well mixed”, in the sense that pollution emitted by any one polluter does not cause local damage outside the common medium; that is, all pollution is the same in the model and cannot be decomposed by location. Let: Xi = pollution generated by polluter i. Bi(Xi) = the monetary benefit of polluter i derived from pollution (we can think of pollution benefits in terms of foregone abatement costs). Total pollution = X = X1 + X2 + X3, . . ., XI = Xii=1I∑ SC(X) = social cost of pollution (depends on total pollution). The social optimization problem is: max. B(I∑ subject to . X) SC( )ii1i=−Χ Χ=∑=Xii1IUsing Lagrange multiplier techniques, this problem becomes max L B (X ) SC( ) Xii1Iiii1I=∑−+−∑==ΧΧλ where, λ, the shadow price of pollution = marginal cost to society from an added unit of pollution. FOC: LXi=∂L∂Xi=∂Bi∂Xi−λ= 0 for i = 1,I LLSC0ΧΧΧ==− +=∂∂∂∂λ where: ∂Bi∂Xi= BXii= MBi= marginal benefit of polluter i from polluting and ∂∂SCSCΧΧ= = MSC = marginal social cost of pollution. -4-At the optimal solution, MBi = MSC = λ for all i. Marginal benefit of pollution is equal across producers and equal to marginal cost of pollution. The optimal solution can be attained by a unit tax, t*=MSC(X *), which could be charged for each unit of pollution. The optimal solution can also be attained by trading pollution permits, where total pollution is restricted to the optimal pollution level, X*. At the optimal solution, assuming competitive trading, the price of a pollution permit will be λ. Heterogeneity: The Case of Two Polluters (I = 2) Figure 5.2 where: ABC = horizontal sum of MB1 and MB2 = aggregate demand for pollution ∂SC∂X= SCX= MSC = marginal social cost of pollution , X* = optimal levels of pollution X1*,X2* = initial unregulated levels of pollution