PART III RISK INFORMATION MARKET FAILURES AND PUBLIC

PART III: RISK, INFORMATION, MARKET FAILURES AND PUBLIC GOODS

Microeconomics II n PART III - INFORMATION, MARKET FAILURES AND PUBLIC GOODS 6. Externalities and Public Goods 6. 1. Externalities 6. 2. Public Goods

Topic 6. Externalities and Public Goods

6. 1. Market Failures & Externalities

Externalities An externality is a cost or a benefit imposed upon someone by actions taken by others. The cost or benefit is thus generated externally to that somebody. n An externally imposed benefit is a positive externality (e. g. Wireless connection). connection n An externally imposed cost is a negative externality (e. g. Pollution). Pollution n

Examples of Negative Externalities Air pollution. n Water pollution. n Loud parties next door. n Traffic congestion. n Second-hand cigarette smoke. n Increased insurance premiums due to alcohol or tobacco consumption. n

Example (Fossil fuels) Consider global warming, a negative externality. Many scientists believe this warming trend is caused by human activity, namely the use of fossil fuels. n These fuels, such as coal, oil, natural gas, and gasoline produce carbon dioxide that in turn traps heat from the sun in the earth’s atmosphere. n Figure 1 shows the trend in warming over the last century. n

Figure 1 15 14. 3 14 13. 6 13. 3

Examples of Positive Externalities A well-maintained property next door that raises the market value of your property. n A pleasant cologne or scent worn by the person seated next to you. n Improved driving habits that reduce accident risks. n A scientific advance. n

Externalities and Efficiency n Crucially, an externality impacts a third party; i. e. somebody who is not a participant in the activity that produces the external cost or benefit.

Externalities and Efficiency n Externalities cause Pareto inefficiency; typically Too much scarce resource is allocated to an activity which causes a negative externality ¨ Too little resource is allocated to an activity which causes a positive externality. ¨

Inefficiency & Negative Externalities n Example: A large factory pumps its waste into a nearby lake. The lake is also used for recreation by 1000 people. - Let X be the amount of waste that the firm pumps into the lake, where X< 10. - Let Yi be the number of hours per day that person i spends swimming and boating in the lake, and let Ci be the number of euros that person i spends on consumption goods.

Inefficiency & Negative Externalities n If the firm pumps X units of waste into the lake, its profits will be: π = 1200 X − 100 X² n Consumers have identical utility functions: U(Yi, Ci, X) = Ci + 9 Yi − Yi² − XYi, and identical incomes.

Inefficiency & Negative Externalities Suppose that there are no restrictions on pumping waste into the lake and there is no charge to consumers for using the lake. Also, suppose that the factory and the consumers make their decisions independently. A) What is the level of waste X that maximizes the factory’s utility function? B) What is the number of hours that a person would spent on the lake?

Inefficiency & Negative Externalities C) Is this equilibrium Pareto efficient?

Inefficiency & Negative Externalities Notice from the utility functions that when each person is spending 1. 5 hours a day in the lake, she will be willing to pay 1. 5 € to reduce X by 1 unit. n Since there are 1000 people, the total amount that people will be willing to pay to reduce the amount of waste by 1 unit is 1500€. n If the amount of waste is reduced from 6 to 5 units, the factory’s profits will fall from 3600 € to 3500 €. Evidently the consumers could afford to bribe the factory to reduce its waste production by 1 unit. n

Externalities and Property Rights n Ronald Coase’s insight is that most externality problems are due to an inadequate specification of property rights and, consequently, an absence of markets in which trade can be used to internalize external costs or benefits.

Externalities and Property Rights n Causing a producer of an externality to bear the full external cost or to enjoy the full external benefit is called internalizing the externality.

Externalities and Property Rights Neither the factory nor the consumers own the lake. n What happens if this property right is created and is assigned to one of them? n Consider that the lake is the property of the factory. The factory sells entry tickets at a price p. n

Externalities and Property Rights Factory maximizes the following profit function: π = 1200 X − 100 X² + 1000 p. Yi Given consumer’s optimal decision U(Yi, Ci, X) = Ci + 9 Yi − Yi² − XYi – p. Yi Max U (. ) w. r to Yi implies the following FOC: Yi = (9 – X – p) / 2. n

Externalities and Property Rights n Factory maximizes the following profit function: Plugging the consumer FOC into the factory profit function we get: π = 1200 X − 100 X² + 1000 p(9 -X-p)/2 FOCp: p = (9 - X)/2 FOCX: X = 6 - 2. 5 p

Externalities and Property Rights n Corner solution. X = 0, Yi* = 2. 25 and p = 4. 5, Π = 10 125€. X= 10, Yi* = 0, Π = 2000€.

Externalities and Property Rights n Corner solution. X = 0, Yi* = 2. 25 and p = 4. 5, Π = 10 125€.

Externalities and Property Rights n Let us compare the factory’s profit: ¨ Before Property rights: Π* = 1200 X* − 100 X*² = 1200*6 -100*36 = 3600€ ¨ After Property rights: Π** = 1200 X** − 100 X**² + 1000 p(9 -X**- p)/2 = 1000*4. 5/2 = 10 125€

Externalities and Property Rights n Let us compare consumers’ utilities: ¨ Before Property rights: Ui* = Ci + 9 Yi − Yi² − X*Yi = Ci + 9*1. 5 − 1. 5² − 6*1. 5 = Ci + 2. 25 ¨ After Property rights: Ui** = Ci + 9 Yi − Yi² − X*Yi − p*Yi = Ci + 5. 0625

PART III: RISK, INFORMATION, MARKET FAILURES AND PUBLIC GOODS

Microeconomics II n PART III - INFORMATION, MARKET FAILURES AND PUBLIC GOODS 6. Externalities and Public Goods 6. 1. Externalities 6. 2. Public Goods

Topic 6. Externalities and Public Goods

Coase’s Theorem n If all agents’ preferences are quasilinear in money, then the efficient level of the externality generating commodity is produced no matter which agent is assigned the property right.

Coase’s Theorem Illustrations 1. The lake example.

Externalities and Property Rights n Consider that the lake is the property of the people. They sell pollution rights at a price q to the factory.

Externalities and Property Rights Factory maximizes the following profit function: π = 1200 X − 100 X² - 1000 Xq FOCx: X = 6 - 5 q Given the factory’s optimal decision U(Yi, Ci, X) = Ci + 9 Yi − Yi² − XYi + Xq = Ci + 9 Yi − Yi² − (6 - 5 q)Yi + (6 - 5 q)q n

Externalities and Property Rights n We get a corner solution. X = 0.

Coase’s Theorem Applications 2. 3. Airport example. Initial assignment of landing and take-off slots do not affect efficiency. Pollution rights.

Externalities and Pollution Rights The evidence of how well tradable pollution rights (market for pollution) have worked in practice is mixed. Example in Los Angeles: 2 schemes to improve air quality. 1 - Regional Clean Air Incentives Market, RECLAIM, which enables the trading of smog causing nitrogen oxides and sulphur oxides. No significant emissions reductions between 1993 and 1997 when the audit was done. 2 - Companies able to inflate the baseline of allowable emissions, by an additional 40 000 tons of air pollution (1998).

Quasi-linear Utility Functions n so A quasi-linear utility function is of the form U(x 1, x 2) = f(x 1) + x 2.

Quasi-linear Utility Functions n MRS = - f ’(x 1) does not depend upon x 2 so the slope of indifference curves for a quasilinear utility function is constant along any line for which x 1 is constant. What does that make the indifference map for a quasi-linear utility function look like?

Quasi-linear Utility Functions x 2 MRS = - f(x 1’) Each curve is a vertically shifted copy of the others. MRS = -f(x 1”) x 1’ x 1” MRS is a constant along any line for which x 1 is constant. x 1

Quasi-linear Utility Functions n The demand for the good causing the externality does not depend on the distribution of income.

Coase’s Theorem & wealth effects Intuition 1. The lake example. What if the users of the lake can buy bigger boats as they get richer? Instead of going to the lake they may prefer to boat on the sea.

Coase’s Theorem & wealth effects Intuition 1. The lake example. What if the users of the lake can buy bigger boats as they get richer? Instead of going to the lake they may prefer to boat on the sea. Ui* = Ci + 9 Yi − Yi² − X*Yi

Coase’s Theorem & wealth effects Intuition 1. The lake example. What if the users of the lake can buy bigger boats as they get richer? Instead of going to the lake they may prefer to boat on the sea. Ui* = Ci + [ 9 Yi − Yi² − X*Yi ] / Ci

PART III: RISK, INFORMATION, MARKET FAILURES AND PUBLIC GOODS

Microeconomics II n PART III - INFORMATION, MARKET FAILURES AND PUBLIC GOODS 6. Externalities and Public Goods 6. 1. Externalities 6. 2. Public Goods

Topic 6. Externalities and Public Goods

6. 1. Externalities

Production Externalities A steel mill produces jointly steel and pollution. n The pollution adversely affects a nearby fishery. n Both firms are price-takers. n p. S is the market price of steel. n p. F is the market price of fish. n

Production Externalities q Steel Mill and Fishery Steel mill River Fishery

Production Externalities n c. S(s, x) is the steel firm’s cost of producing s units of steel jointly with x units of pollution. n If the steel firm does not face any of the external costs of its pollution production then its profit function is:

Production Externalities The first-order profit-maximization conditions are: and

Production Externalities states that the steel firm should produce the output level of steel for which price = marginal production cost. is the marginal cost to the firm of pollution reduction.

Production Externalities is the marginal cost to the firm of pollution reduction. What is the marginal benefit to the steel firm from reducing pollution?

Production Externalities is the marginal cost to the firm of pollution reduction. What is the marginal benefit to the steel firm from reducing pollution? Zero, since the firm does not face its external cost. Hence the steel firm chooses the pollution level for which

Production Externalities E. g. suppose c. S(s, x) = s 2 + (x - 4)2 and p. S = 12. Then: and the first-order profit-maximization conditions are and

Production Externalities The steel firm’s maximum profit level is thus:

Production Externalities n The cost to the fishery of catching f units of fish when the steel mill emits x units of pollution is c. F(f, x). Given f, c. F(f, x) increases with x; i. e. the steel firm inflicts a negative externality on the fishery.

Production Externalities The first-order profit-maximization condition is Higher pollution raises the fishery’s marginal production cost and lowers both its output level and its profit. This is the external cost of the pollution.

Production Externalities E. g. suppose c. F(f; x) = f 2 + xf and p. F = 10. Since the fishery has no control over x it must take the steel firm’s choice of x as a given. The fishery’s profit function is thus: FOC:

Production Externalities q The steel firm, ignoring its external cost inflicted upon the fishery, chooses x* = 4, so the fishery’s profit-maximizing output level given the steel firm’s choice of pollution level is f* = 3, giving the fishery a maximum profit level of:

Production Externalities Are these choices by the two firms efficient? n When the steel firm ignores the external costs of its choices, the sum of the two firm’s profits is 36€ + 9€ = 45€. n Is 45€ the largest possible total profit that can be achieved? n

Production Externalities

Coase and Production Externalities Coase argues that the externality exists because neither the steel firm nor the fishery owns the water being polluted. n Suppose the property right to the water is created and assigned to one of the firms. n Does this induce efficiency? n

Coase and Production Externalities Suppose the fishery owns the water. n Then it can sell pollution rights, in a competitive market, at px each. n The fishery’s profit function becomes n

Coase and Production Externalities n Given pf and px, how many fish and how many rights does the fishery wish to produce? (Notice that x is now a choice variable for the fishery. )

Coase and Production Externalities The profit-maximum conditions are and these give (fish supply) (pollution right supply)

Coase and Production Externalities n The steel firm must buy one right for every unit of pollution it emits so its profit function becomes n Given pf and px, how much steel does the steel firm want to produce and how many rights does it wish to buy?

Coase and Production Externalities The profit-maximum conditions are and these give (steel supply) (pollution right demand)

Coase and Production Externalities In a competitive market for pollution rights the price px must adjust to clear the market so, at equilibrium, The market-clearing price for pollution rights is thus

Coase and Production Externalities So if ps = 12 and pf = 10 then This is the efficient outcome. 45

Coase and Production Externalities Q: Would it matter if the property right to the water had instead been assigned to the steel firm? n A: No. Profit is linear, and therefore quasilinear, in money so Coase’s Theorem states that the same efficient allocation is achieved whichever of the firms was assigned the property right. (And the asset owner gets richer. ) n

Production Externalities & the Pigouvian Tax n n A tax scheme to correct the efficiency loss created by the production externality. Place a tax on the pollution generated by the firm, t€ per unit of pollution.

Production Externalities & the Pigouvian Tax n FOC. E. g. suppose c. S(s, x) = s 2 + (x - 4)2 , p. S = 12 and pf = 10. n Efficiency will be obtained for

Production Externalities & the Pigouvian Tax n FOC.

The Tragedy of the Commons Consider a grazing area owned “in common” by all members of a village. n Villagers graze cows on the common field. n When c cows are grazed, total milk production is f(c), where f’>0 and f”<0. n How should the villagers graze their cows so as to maximize their overall income? n

The Tragedy of the Commons Milk f(c) c

The Tragedy of the Commons n Make the price of milk 1€ and let the cost of grazing a cow be h. Then the profit function for the entire village is n and the village’s problem is to:

The Tragedy of the Commons The income-maximizing number of cows to graze, c*, satisfies i. e. the marginal income gain from the last cow grazed must equal the marginal cost of grazing it.

The Tragedy of the Commons hc Milk slope = f’(c*) f(c) slope = h c* c

The Tragedy of the Commons hc Milk f(c) slope = f’(c*) f(c*) Maximal income hc* slope = h c* c

The Tragedy of the Commons n For c = c*, the average gain per cow grazed is n because f’ > 0 and f” < 0.

The Tragedy of the Commons hc Milk f(c) f(c*) c* c

The Tragedy of the Commons n For c = c*, the average gain per cow grazed is n because f’ > 0 and f” < 0. So the economic profit from introducing one more cow is positive. Since nobody owns the common, entry is not restricted. n n

The Tragedy of the Commons n Entry continues until the economic profit of grazing another cow is zero; that is, until

The Tragedy of the Commons hc Milk f(c) f(c*) slope = h c* c

The Tragedy of the Commons hc Milk f(c) f(c*) slope = h c c* The commons are over-grazed, tragically.

The Tragedy of the Commons The reason for the tragedy is that when a villager adds one more cow his income rises (by f(c)/c - h) but every other villager’s income falls. n The villager who adds the extra cow takes no account of the cost inflicted upon the rest of the village. n

The Tragedy of the Commons n Any solution?

The Tragedy of the Commons n Modern-day “tragedies of the commons” include ¨ over-fishing the high seas ¨ over-logging forests on public lands ¨ over-intensive use of public parks ¨ urban traffic congestion.

6. 2. Public Goods

Public Goods Definition n A good is purely public if it is both nonexcludable and nonrival in consumption. ¨ Nonexcludable: all consumers can consume the good. ¨ Nonrival: good. each consumer can consume all of the

Public Goods Definition n A good is purely public if it is both nonexcludable and nonrival in consumption. ¨ Nonexclusive: difficult or impossible to charge people for using the good. ¨ Nonrival: the marginal cost of providing the good to an additional consumer is zero.

Defining pure and impure public goods Is the good rival in consumption? Yes Private Good Yes Ice cream No Crowded city sidewalk No Cable tv Is the good excludable? National defense Public Good

Charging a price for a non-rival good prevents some people from enjoying the good (pay TV). n Not charging a price for a non-rival good means that there will be no incentives for supplying the good. n Two basic forms of market failure: underconsumption and under-supply. n

Public Goods Examples n Nonexclusive and nonrival: provide benefits at no marginal costs. n Publicly provided goods may not be public goods! (e. g. Education is rival).

Public Goods Examples Broadcast radio and TV programs. n National defense. n Public highways. n Reductions in air pollution. n National parks. n Legal system. n

Example (Trash collection) For example, in Dhaka, Bangladesh, public trash collection is fairly inefficient, but attempts at privatization have not fared any better. n The key problem with private collection of garbage is the free rider problem–with a private, voluntary system, each resident could simply sneak his garbage into his neighbor’s garbage and avoid making payments. n

Reservation Prices A consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it. n Consumer’s wealth is n. Reservation price r is defined Utility of not having the goodby: is n Utility of paying p for the good is n

Reservation Prices; An Example Consumer’s utility is Utility of not buying a unit of good G is Utility of buying one unit of good 2 at price p is

Reservation Prices; An Example Reservation price r is defined by I. e. by

When Should a Public Good Be Provided? One unit of the good costs c. n Two consumers, A and B. n Individual payments for providing the public good are g. A and g. B. n g. A + g. B c if the good is to be provided. n

When Should a Public Good Be Provided? n Payments must be individually rational; i. e. and n Therefore, necessarily and

When Should a Public Good Be Provided? n And if and Then it is Pareto-improving to supply the unit of good, so is sufficient for it to be efficient to supply the good.

Private Provision of a Public Good? Suppose and. n Then A would supply the good even if B made no contribution. n B then enjoys the good for free; free-riding. n

Can Private Providers Overcome the Free Rider Problem? n Examples of private provision of a public good: ¨ Privately financed fireworks displays. ¨ Christmas lights. ¨ Privately owned British lighthouses until 1842.

Private Provision of a Public Good? n n Suppose and. Then neither A nor B will supply the good alone. Yet, if also, then it is Pareto-improving for the good to be supplied. A and B may try to free-ride on each other, causing no good to be supplied.

Free-Riding Suppose A and B each have just two actions: individually supply a public good, or not. n Cost of supplying the public good, c = 100€. n If both supply the good, they share costs (50€ each) n Payoff to A from the good = 80€. n Payoff to B from the good = 65€. n 80€ + 65€ > 100€, so supplying the good is Paretoimproving. n

Free-Riding Buy Player A Don’t Buy Player B Don’t Buy

Free-Riding Buy Player A Don’t Buy Player B Don’t Buy

Free-Riding Player B Don’t Buy Buy Player A Don’t Buy Nash equilibrium but not efficient

The Free Rider Problem in Practice n There are some interesting examples of the freerider problem in practice. ¨ Only 7. 5% of public radio listeners in New York contribute to the stations–that is, there is a lot of free -riding. In the United Kingdom, the BBC charges an annual licensing fee for all television owners.

The Free Rider Problem in Practice n There are some interesting examples of the freerider problem in practice. ¨ Many users of file sharing services never contribute uploaded files; they only download files. Some of these services, like Kazaa, give download priority to those who contribute.

The Free Rider Problem in Practice n Ten people have dinner together at an expensive restaurant and agree that the total bill will be divided equally among them. (a) What is the additional cost to any one of them of ordering an appetizer that costs 20€? (b) Explain why this may be an inefficient system. (c) Give another example of such situation?

Free-Riding Now allow A and B to make contributions to supplying the good. n Cost of supplying the public good, c = 100€. n E. g. A contributes 60€ and B contributes 40€. n Payoff to A from the good = 80€ > 0. n Payoff to B from the good = 65€ > 0. n

Free-Riding Player B Don’t Contribute Player A Don’t Contribute

Free-Riding Player B Don’t Contribute Player A Don’t Contribute Nash equilibria

Free-Riding So allowing contributions makes possible supply of a public good when no individual will supply the good alone. n But what contribution scheme is best? n And free-riding can persist even with contributions. n

Variable Public Good Quantities E. g. how many broadcast TV programs, or how much land to include into a national park. n c(G) is the production cost of G units of public good. n Two individuals, A and B. n Private consumptions are x. A, x. B. n

Variable Public Good Quantities n Budget allocations must satisfy n MRSA & MRSB are A & B’s marginal rates of substitution between the private and public goods.

Variable Public Good Quantities n Pareto efficient allocation (Fix B’s utility function at Ub) and solve the following problem: n Pareto efficiency condition for public good supply is:

Variable Public Good Quantities n Pareto efficiency condition for public good supply is Why? ” n The public good is nonrival in consumption, so 1 extra unit of public good is fully consumed by both A and B. n

Variable Public Good Quantities Suppose n MRSA is A’s utility-preserving compensation in private good units for a one-unit reduction in public good. n Similarly for B. n

Variable Public Good Quantities n is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit.

Variable Public Good Quantities is the total payment to A & B of private good that preserves both utilities if G is lowered by 1 unit. n Since , making 1 less public good unit releases more private good than the compensation payment requires Pareto-improvement from reduced G. n

Variable Public Good Quantities n Now suppose n is the total payment by A & B of private good that preserves both utilities if G is raised by 1 unit. n This payment provides more than 1 extra public good unit Pareto-improvement from increased G.

Variable Public Good Quantities n Hence, necessarily, efficient public good production requires

Public Good (Application I) n n n Muskrat, Ontario, has 1000 people. Citizens of Muskrat consume only one private good, Labatt’s ale. There is one public good, the town skating rink. Although they may differ in other respects, inhabitants have the same utility function. U(Xi, G) = Xi − 100/G, Where Xi is the number of bottles of Labatt’s consumed by citizen i and G is the size of the town skating rink, measured in square meters. The price of Labatt’s ale is $1 per bottle and the price of the skating rink is $10 per square meter. Everyone who lives in Muskrat has an income of $1000.

Public Good (Application I) n What is the Pareto efficient size of the skating rink?

Public Good (Application II) n Suppose that 10 people live on a street and each of them is willing to pay 2€ for each extra streetlight, regardless of the number of streetlights provided. The cost of providing x street lights is c(x) = x². n What is the Pareto efficient number of streetlights to provide?

Free-Riding Revisited When is free-riding individually rational? n Individuals can contribute only positively to public good supply; nobody can lower the supply level. n Individual utility-maximization may require a lower public good level. n Free-riding is rational in such cases. n

Free-Riding Revisited n Given that A contributes g. A units of public good, B’s problem is n subject to

Free-Riding Revisited G B’s budget constraint; slope = -1 g. A x. B

Free-Riding Revisited G B’s budget constraint; slope = -1 g. A is not allowed x. B

Free-Riding Revisited G B’s budget constraint; slope = -1 g. A is not allowed x. B

Free-Riding Revisited G B’s budget constraint; slope = -1 g. A (i. e. free-riding) is best for B x. B

Solutions to free-riding n Under what circumstances are private market forces likely to solve the free rider problem? ¨ Intense preferences. ¨ Altruism (e. g. Donations to private hospitals…). ¨ Peer pressure (e. g. the dinner’s example).

Experiment Each student gets four cards, two red (hearts and diamonds) and two black cards (clubs and spades). Each student will be asked to play two cards by putting them on top of a stack in your hand as you come around the room. n Students "earn" four dollars for each of their own red cards that they keep. They also earn a dollar for each red card placed in the stack, by themselves or by anyone else. n

Experiment A student’s dollar earnings are calculated: Earnings = $4 × (number red cards kept by the student) + $1 × (number of red cards played by all ) n