Chapter 4: Negative Externalities

1. Chapter 4: Negative Externalities • General Overview • Production Externalities • Policy 1: Externality Tax • Policy 2: Output-reduction Subsidy • Policy 3: Standards • Elasticity Effects on Magnitude of Externalities • Imperfect Competition and Externality Policy • Consumption Externalities • Externalities from Cigarette Smoking • The Economics of Illicit Drugs

2. General Overview • Externalities are a type of market failure -prices in a market do not reflect the true marginal costs and/or marginal benefits associated with the goods and services traded in the market. • Externalities may be related to production activities, consumption activities, or both. -Production externalities: production activities of one individual imposes costs/benefits on other individuals that are not transmitted accurately through a market. -Consumption externalities: consumption of an individual imposes costs or benefits on other individuals that are not accurately transmitted through a market.

3. Examples of production externalities • Air pollution from burning coal • Ground water pollution from fertilizer use • Food contamination and farm worker exposure to toxic chemicals from pesticide use • Irrigation water and consequential decline of waterfowl population in nearby wildlife refuge • Production of refrigerators using CFC’s • Health issues resulting from gold mining

4. Production Externalities MSC $ A MPC E B MEC G P* C PC H PP F D Q* QC

5. Mathematical Representation of production externalities The Social Welfare Maximization Problem is: Max{W(Q)=B(Q)-C(Q)-E(Q)} Q where: Q = Output B(Q) = Total Social Benefit of Producing Q. C(Q) = Total Private Cost of Producing Q. E(Q) = Total External Cost of Producing Q. W(Q) =Social Welfare Function (Total Surplus From producing Q) • Social Welfare is maximized where Q satisfies the First-Order Condition (FOC): WQ=BQ (Q)-CQ (Q)-EQ (Q), which can be rearranged as BQ(Q) = CQ(Q) + EQ(Q) Where: BQ(Q) =the partial derivative of B(Q) with respect to Q=MB CQ(Q) = the partial derivative of C(Q) with respect to Q=MPC EQ(Q) = the partial derivative of C(Q) with respect to Q=MEC • Socially optimum output, Q*, occurs when MB = MPC + MEC.

6. Unregulated competition with externalities • Under unregulated competition, firms maximize profits, resulting in the FOC:BQ(Q) = CQ(Q), or MB = MPC. When this FOC is solved for Q, call it QC, we find that QC< Q* whenever MEC > 0. Because QCQ*, QC is inefficient.

7. Policies to achieve social optimum Q* • Three possible policies: -Tax -Subsidy -Restriction, Standard, or Quota • Choice of policy affects the distribution of economic benefits among producers, consumers and government. • Targeting: Process of deciding which economic variable to control to reduce externality. Ex. Outputs, inputs, or the externality-generating activity itself (i.e., the pollutant).

8. MSC $ A MPC E B MEC G P* C PC H PP F D Q* QC Policy 1: Tax-1 • Externality Tax: t* = P* - PP=MEC (Q*), where t* is the required market correction to achieve Q* units of production. • Firms treat the tax rate as an additional component of their marginal private cost; that is, a unit tax of t* shifts the MPC curve upwards in a parallel fashion by the distance t*.

9. Mathematical expression • t* = EQ(Q*) = MEC(Q*). • Private optimization problem: Max {(Q)=PQ-C(Q)-t*Q} Q • FOC: Q(Q)-P-C Q(Q)-t*=0or, P = CQ(Q) + t*. Since P = MB at all points along the demand curve, and t* = EQ(Q*), we can express the private condition (which is identical to the condition for a social optimum) under the tax as: • BQ(Q*) = CQ(Q*) + EQ(Q*)

10. MSC $ A MPC E B MEC G P* C PC H PP F D QC Q* Welfare implications of externality tax • Consumer surplus= ABP* • Producer surplus= OFPP • Government revenue= P*BFPP

11. Policy 1: Tax-2 • Production tax: If the government knows how much pollution is produced per unit of production output, then it can set a tax on production output that achieves the same results as an externality tax. However, the relationship between pollution and production output is often very difficult to estimate with any degree of precision.

12. Policy 1: Tax-3 • Consumption Tax:Sales tax on polluting goods. Demand curve for firms in the market shifts downward to represent the net price of each unit sold. The net price, or Net Marginal Benefit (NMB), is the Marginal Benefit of consumers less the level of the sales tax (NMB = D - t*). Q*=Social Optimum output Pc*=Optimal Consumer price Ps*=Pc*-t=net producer price t=consumption tax

13. Policy 2: Output-reduction Subsidy • Subsidy = P* - PP for each unit of output that is not produced. • If = the current level of output, firms in a competitive industry have the following objective: , and FOC= • Optimal subsidy level: (i.e., the unit subsidy that equates the optimal social and private outcomes) S* = t* = MEC(Q*).

14. MSC $ A MPC E B MEC G P* C PC H PP F D Q* QC Welfare implications of subsidy • Consumer surplus = ABP*. • Producer surplus = OFBP* + BGHF,where BGHF = (P* - PP)·(Qc - Q*)]. • Government expenditure = BGHF.

15. Problem with subsidy In the long run, subsidies for pollution reduction may actually increase pollution because the subsidy may attract more firms into the market.

16. Policy 3: Standards on Pollution/Output • Command-and-control approach through production quotas to restrict output to Q*.

17. MSC $ A MPC E B MEC G P* C PC H PP F D QC Q* Welfare implications of quotas • Consumer surplus= ABP* • Producer surplus= OFBP* (larger than it is for Externality Tax) • Government revenue= zero (smaller than it is for Externality Tax)

18. Tradable permit • Government allocates Q* Units of pollution permits to industry • Producers can trade • The price of a permit will be P* • The government will not need to pay subsidies and producers will not need to pay taxes. • It may be desirable from the political economy perspective

19. Production Externalities:Example • Inverse demand (D) = Marginal Benefit (MB)= a - bQ • Marginal private cost (MPC)=C(Q) = c + dQ • Marginal externality cost (MEC) = e + fQ • Marginal social cost (MSC) = MPC + MEC = c + dQ + e + fQ = c + e + (d + f)Q

20. Social optimum • The Social Optimum is where MB = MSC • Marginal Benefit (MB)= a - bQ • Marginal social cost (MSC) = MPC + MEC = c + dQ + e + fQ = c + e + (d + f)Q

22. Unregulated vs. Regulated Competition: • Unregulated competition:B Q(Q) = C Q(Q), MB = MPC • Marginal Benefit (MB)= a - bQ • Marginal Private Cost (MPC)=C(Q) = c + dQ • Regulated competition: B Q(Q*) = C Q(Q*) + t* Impose tax t* = MEC(Q*) for regulated competition. • MarginalExternality Cost (MEC)= e + fQ • Q* at social optimal = t* = MEC(Q*) = =

23. Quotas v. externality taxes • Producers prefer quotas to externality taxes because they gain a larger share of social surplus. • If quota is transferable, producers will bid against each other for the quota rights until the quota price equals P*- PP. -Whoever initially had the legal rights to the transferable quota will earn quota rents equal to P*BFPP by selling the quota rights. -Buyer of the rights will be have surplus= PPFO. *Note: producer surplus is the same as it is under an externality tax. The quota rents is the same as government revenue under the externality tax.

24. Elasticity Effects on the Magnitude of Externalities MSC Q MPC D Inelastic PC, QC=Competitive price & quantity PI, QI=Socially optimal price & quantity, when D is inelastic PE, QE=Socially optimal price & quantity, when D is elastic Pl PE PC D elastic P Ql QC QE

25. Elasticity and regulation • When demand is inelastic, the socially optimal level of production, Qi, is not too far from the competitive level of production, Qc. Therefore, the inefficiency associated with a production externality may be small, and it may not be worth regulating the externality. • When demand is elastic, the socially optimal level of production, Qe, is farther away from the competitive level, Qc. In this case, the inefficiency associated with the production externality may be relatively large, and regulation may be desirable.

26. Unexpected result of regulation?! • If demand is inelastic, pollution regulation may increase producer profit. -regulations that decrease production, such as a quota, will move producers towards the monopoly level of output. This decrease in turn will raise the market price of the final product and increase producers revenues. • The more inelastic the demand, the higher the producer revenues under regulation!

27. Imperfect Competition and Externality Policy High MSC Low MSC=small MEC High MSC=large MEC Unregulated competition=Qc Monopoly=Qm $ A MR Low MSC MPC B D Qc Q* High Qm Q*low Q

28. High MSC $ A MR Low MSC MPC B D Qc Q* High Qm Q*low Q Low MSC • Optimal output, Q*low, is larger than the monopoly output, Qm. • In monopolistic market with low MSC, the optimal policy may be to subsidize the polluting monopolist to produce more of the polluting good.

29. High MSC Low MSC $ A MR B MPC D Qc Q* High Qm Q*low Q High MSC • Optimal output, Q*high, is smaller than the monopoly output, Qm. • In monopolistic market with high MSC, the optimal policy may be to impose tax, T*=the distance AB. If this tax is imposed, MPC+t* will intersect MR at Point B, which produces the optimal amount. tax

30. Unregulated Monopoly • Monopolist sets MPC=MR, where MR (marginal revenue) is the derivative of R (total revenue), R= P(Q)Q • Demand = P(Q)=a – bQ • Marginal private cost (MPC)=C(Q) = c + dQ    • Setting MPC = MR: ( ) 2 R = a - bQ Q R = aQ - bQ

31. Unregulated Middleman • Unregulated middleman sets MR = MO, where MO (marginal outlay) is the derivative of Outlay • MR=a-2bQ • Marginal private cost (MPC)=C(Q) = c + dQ • Outlay =MPC(Q)Q=(c + dQ)Q  MO = c + 2dQ • Setting MR = MO: a-2bQ=c+dQ  • Price that middleman pays producers -substitute QD into the equation for MPC:  • Price that middleman charges consumers- substitute QD into the equation for inverse demand: P = + P c dQ C = -  P a bQ