Externalities and the Environment

This is Unit Eleven of Principles of Microeconomics: externalities, the market failure that competition cannot fix, and the three remedies for it. Unit ten closed on what the law does about market power. This unit takes up a failure that survives even perfect competition: a cost that falls on someone who neither bought nor sold, so it never enters the price. The remedies are a rule, a charge and a cap. By the end you will be able to define an externality and find the overproduction in a market. To state the flaws of command-and-control and compute abatement under a charge. To predict who trades under a cap. To state the Coase theorem and say why zero pollution is rarely efficient. And to run one market under three remedies, and work Coase's field and railroad both ways.

Five entries on the failure: what an externality is, the two costs, the two curves, the market with numbers, and the name for what went wrong.

An effect on someone outside the exchange.

MIC 1001 Externalities

An externality is an effect of a market exchange on someone outside it, who neither bought nor sold: negative if it harms the third party, positive if it helps. Buyer and seller are both content, and the failure is that a third party's cost or benefit never entered the price.

The two costs it creates.

MIC 1002 Private Cost, External Cost, Social Cost

Private cost is what a firm pays; external cost is what it imposes on others. Social cost is their sum, and supply drawn from private cost alone sits too low. Supply is marginal cost only when every cost is the seller's, and an externality breaks that.

The exam's names for the two curves.

MIC 1003 Marginal Private Cost and Marginal Social Cost

Marginal private cost is what the seller bears for one more unit; marginal social cost adds the external cost. With a negative externality, marginal social cost exceeds marginal private cost, so the market overproduces. Overproduction happens because social cost sits above private cost, not below.

The market with numbers.

MIC 1004 The Negative-Externality Market

From a demand schedule, a private supply schedule and an external cost per unit, build the social supply schedule by adding the external cost to the price at every private quantity. Find the market equilibrium where demand meets private supply and the optimum where demand meets social supply; the difference in quantity is the overproduction, and the market price is too low by less than the full external cost, because quantity adjusts too. In the paint market, demand meets private supply at forty-five dollars and four thousand cans. Adding ten dollars of river damage, social supply offers three thousand at fifty and four thousand at fifty-five, and demand meets it at fifty dollars and three thousand cans: a thousand cans too many, and a price five dollars too low. Add the external cost to the supply price at each quantity, which shifts supply up, not left, and the optimum is not zero pollution; each of the three thousand cans is worth more to a buyer than its full cost.

The name for what went wrong.

MIC 1005 Market Failure

Market failure is a market that, left alone, does not allocate resources efficiently. An externality is one cause: the supply curve omits a cost, so price equals the wrong marginal cost and the quantity is wrong. The failure is in the property rights: nobody owns the river, so nobody can charge for damaging it.

Three entries on a rule or a price: command-and-control, the pollution charge, and the firm's abatement decision under it.

The first remedy.

MIC 1006 Command-and-Control Regulation

Command-and-control regulation sets a legal limit on pollution and often the technology to use. It cut pollution sharply where applied, and economists fault its cost, not its aim. Three flaws: no reward for beating the standard, one rule for firms with different abatement costs, and loopholes won by lobbying.

A price instead of a rule.

MIC 1007 A Pollution Charge

A pollution charge is a tax on each unit emitted. A firm abates every unit cheaper to prevent than the tax and pays on the rest, so the cheapest abatement happens first; the tax is unit four's wedge, aimed at the external cost. Set at the external cost per unit, the charge reaches the social optimum; set too low, it changes little.

The firm's decision.

MIC 1008 The Abatement Decision Under a Tax

Given the cost of abating successive lots of pollution and a tax per lot, compare lot by lot: abate each lot whose abatement cost is below the tax, pay on each lot whose cost exceeds it. Total outlay is abatement cost incurred plus tax on what is still emitted, and the rule is to abate until the marginal cost of abatement equals the tax; a firm with cheap abatement abates more, one with dear abatement pays more. A plant emits five hundred pounds a week, and abating successive hundred-pound lots costs two hundred, four hundred, seven hundred, eleven hundred and eighteen hundred dollars. With a tax of eight hundred a lot, the first three lots are cheaper to abate than to pay for, so the plant abates three hundred pounds for thirteen hundred and pays sixteen hundred in tax on the remaining two hundred. The tax aims at cheap abatement, not zero pollution, and the marginal lot decides, never the average abatement cost.

Two entries on a quantity instrument: the cap with marketable permits, and who sells and who buys under it.

A quantity instrument.

MIC 1009 Marketable Permits

Under marketable permits the government caps total pollution, issues permits for that total, and lets firms trade. The cap fixes quantity, and trading sends abatement to whoever does it cheapest: a cheap abater cuts more and sells spare permits to a dear one. A charge fixes price and quantity varies; a cap fixes quantity and price varies. Both find least-cost abatement.

Who trades.

MIC 1010 Who Sells and Who Buys Permits

Given each firm's emissions, its abatement cost per ton and an equal allocation under a cap, predict the trades. A firm whose abatement cost is below the permit price abates beyond its allocation and sells the surplus; one whose cost is above it abates nothing and buys; the price settles between the low and high costs. Total emissions equal the cap whoever trades, and trades decide only who abates, cutting total cost against a rule making every firm cut equally. Three plants each emit three hundred tons, with abatement costs of ten, thirty and sixty dollars a ton, and a cap of four hundred fifty gives each one hundred fifty permits. At a permit price of thirty, the ten-dollar plant abates all three hundred tons for three thousand dollars and sells its permits; the sixty-dollar plant abates nothing and buys them; the thirty-dollar plant abates its own one hundred fifty. Total abatement is four hundred fifty tons for seven thousand five hundred dollars, where an equal cut would have cost fifteen thousand. The cap sets the environmental outcome and the trades set only the cost.

Two entries on rights and the efficient level: the remedy that needs no regulator, and how much pollution is efficient.

The remedy that needs no regulator.

MIC 1011 Property Rights and the Coase Theorem

If property rights are well defined and bargaining is costless, the parties reach the efficient outcome themselves, whichever side holds the right; the right decides who pays, not the outcome. Whoever owns the river, the cheapest fix gets bought. The conditions rarely hold with many polluters and victims, so regulators exist, and the theorem still shows what any remedy tries to reproduce.

How much pollution is efficient.

MIC 1012 The Efficient Level of Pollution

Each unit of pollution has a benefit, abatement cost saved, and a cost, damage done. The efficient level equates the marginal benefit of emitting with its marginal cost, and zero is efficient only if the first unit's damage exceeds its benefit; banning carbon monoxide would ban driving. Marginal abatement cost rises with abatement, marginal damage with emissions, and the efficient point balances them.

Two capstones: one polluting market run under all three remedies, and the case that started the property-rights idea.

One market under three remedies.

MIC 1013 One Polluting Market, Three Remedies

The market first: demand meets private supply at too large a quantity, because the seller's marginal private cost leaves out the damage, and the optimum is where demand meets social cost. Remedy one, a rule: every polluter cuts by the amount that reaches the optimum, whatever its abatement cost, so the industry spends more than necessary. Remedy two, a charge equal to the external cost per unit: private supply shifts up onto social supply, the market itself moves to the optimum, and each firm abates until its marginal abatement cost equals the charge, so cheap abatement happens and dear abatement is paid for instead. Remedy three, a cap with permits at the optimal quantity: the total is fixed by law and trading moves the abating to the firms that do it cheapest. The charge and the cap reach the same outcome from opposite sides, and all three can hit the quantity, but the two market tools hit it at the lowest cost and keep rewarding cheaper abatement. The paint market makes four thousand cans at forty-five dollars and should make three thousand at fifty. A rule orders each of ten plants to cut a hundred, whether cutting costs five dollars a can or fifty. A charge of ten dollars a can lifts every plant's cost by ten and the market clears at three thousand and fifty dollars, with the plants whose abatement costs less than ten abating and the rest paying. A cap of three thousand with tradable permits lets the five-dollar plants sell permits to the fifty-dollar plants, so the same thousand cans are cut where cutting is cheapest. Same quantity three times; the cheapest total cost twice. Three cautions. The optimum is three thousand cans, not zero. The charge must equal the external cost per unit to land on the optimum; a charge chosen for revenue lands elsewhere. And the cap's permit price is revealed by trading, not set by the regulator, so a cap and a charge differ in who bears the uncertainty when abatement costs turn out different from expected.

The case that started the property-rights idea.

MIC 1014 Coase's Field and Railroad

A railroad's sparks set a farmer's field alight, and who should stop it is the case that reorganized how economists think about externalities. First, harm is reciprocal: either party could prevent the loss. Second, price the options: the spark arrester costs eight hundred a year, moving the crop three hundred, and the fire damage a thousand, so the efficient fix is the cheapest, moving the crop. Third, the theorem. If the farmer holds the right to be free of sparks, the railroad will pay the farmer up to a thousand to move the crop, cheaper than the arrester; the crop moves. If the railroad holds the right to run trains, the farmer will move the crop for three hundred rather than lose a thousand; the crop moves. Whichever way the right runs, the same fix is bought, and only who pays changes. Fourth, the conditions, which make it a theorem and not a policy: the right must be clear and bargaining must be cheap. With one railroad and one farmer that may hold; with a thousand emitters and a million breathers it does not, since nobody can gather a million people to bargain. That is why taxes, permits and rules exist: each tries to make polluters face the cost a defined right would have imposed. With the farmer holding the right, the railroad offers five hundred to move the crop, both gain, and the crop moves; with the railroad holding it, the farmer moves for three hundred and bears the cost. The fix is identical; the three hundred lands on different shoulders. Three cautions. The theorem is about efficiency, not fairness; who holds the right decides who is richer, and the theorem says nothing about which is fair. The conditions are the point: bargaining costs are the normal case, so the theorem argues for defined rights and market tools, not against regulation. And reciprocal harm does not mean nobody is responsible; it means the remedy must be chosen from both sides' options, not assigned by assumption to the emitter.

Look at what you can now do. You can define an externality as a cost or benefit to someone outside the exchange, add external to private cost for social cost, and find a market's overproduction by shifting supply up by the external cost. You can name the three flaws of command-and-control, and take a firm lot by lot under a charge, abating until the marginal cost of abatement equals the tax. You can predict, under a cap, that the cheap abater sells permits and the dear abater buys, and that the trades change only who abates and what it costs. You can state the Coase theorem with its two conditions, and say why the efficient level of pollution is rarely zero. And you can run one market under a rule, a charge and a cap, and work the field and the railroad both ways to the same fix. Unit twelve turns to the externality that runs the other way, and to goods nobody can be kept from using.