Let Failure Externalities ctly about another agents consumptio production of a particular good. An externality can be positiue or negativ Negative: Loud mobile phone use in public places. 2. Positive: Pipe smoking in enclosed public places. 1. Negative: Toxic waste dumping reduces fishing yields. 2. Positive: University lecturer who gives course notes to other tutors. Externalities arise when there are missing markets. That is, there is no price for a particular good Market- Market Failture An Example Consider two consumers. One is a smoker and one is a fanatical anti-smoker. Clean air is a good for the latter consumer, but smoke(the absence of clean air) is a good for the former. Money is a good for both. Suppose both consumers start with an equal amount of money m. In the absence of a market for clean air the Neither of these points are Pareto efficient. The first welfare theorem fails due to the missing market. If there were a market for clean air, the consumers could trade money for smoke(or money for clean air)until they rrived at a point like r or r. The prices are given by the slope of the budget constraints These points are Pareto efficient- the first welfare theorem is recovered by providing appropriate property rights
Market — Market Failure 1 Externalities • A consumption externality is a situation where a consumer cares directly about another agent’s consumption or production of a particular good. An externality can be positive or negative: 1. Negative: Loud mobile phone use in public places. 2. Positive: Pipe smoking in enclosed public places. • A production externality is a situation where a firm’s production possibility set is directly influenced by the consumption or production decisions of another agent. Again, some examples: 1. Negative: Toxic waste dumping reduces fishing yields. 2. Positive: University lecturer who gives course notes to other tutors. • Externalities arise when there are missing markets. That is, there is no price for a particular good. Market — Market Failure 2 An Example • Consider two consumers. One is a smoker and one is a fanatical anti-smoker. Clean air is a good for the latter consumer, but smoke (the absence of clean air) is a good for the former. Money is a good for both. . . . . . . . . . . . ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... ... . ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ........................................................................................................................... . .................................................................................................... ...................................................................................................... . .......................................................................................... . ..... ...... ....... ....... ...... ...... ...... ..... ..... ..... ..... ..... ..... .... .... ... .. .. A s B m • • • • ω ω 0 x x 0 • Suppose both consumers start with an equal amount of money m. In the absence of a market for clean air the endowment is either at ω — if smoking is illegal, or ω 0 — if smoking is legal. Why? • Neither of these points are Pareto efficient. The first welfare theorem fails due to the missing market. • If there were a market for clean air, the consumers could trade money for smoke (or money for clean air) until they arrived at a point like x or x 0 . The prices are given by the slope of the budget constraints. • These points are Pareto efficient — the first welfare theorem is recovered by providing appropriate property rights
Let Failure The Coase Theorem Notice that the amount of the externality produced at the efficient point depended on how property rights were assigned. If the smoker started with the property rights, more smoke is generated at the efficient allocation. With starts with property rights -the the externality is produced at the efficient allocation. Consider the last example: A Recall that quasi-linear preferences have indifference curves that are parallel translates of each other s"smoke is produced whatever property rights are assigned. Only m varies between efficient allocations This is the Coase theorem the efficient externality level is independent of the initial distribution Market- Market Failture Production Externalities fish f. The firm aste w in the sea, reducing fish yields. Cost (e, w)=c(e) u)and c,(f, u)=c(f)+u- respectivel ence profits are given respectively by: Te =Pee-d(e)+u(1-u) and T, =prf-cf)-w2 Since the electricity firm alone chooses w it will keep producing waste (which reduces cost ) until no more profits be made from doing so. The benefit increases until w =0.5 and decreases thereafter. 0. 5 the marginal benefit of waste is equal to its marginal cost(zero). Both firms set MR=MC to derive f-pe =c(e)and p=c(') Is this efficient? No. The electricity firm is producing too much waste, damaging the fishing firm
Market — Market Failure 3 The Coase Theorem • Notice that the amount of the externality produced at the efficient point depended on how property rights were assigned. If the smoker started with the property rights, more smoke is generated at the efficient allocation. • With quasi-linear preferences, it does not matter which consumer starts with property rights — the same amount of the externality is produced at the efficient allocation. Consider the last example: ....................................................................................................................................................................................................................................................................................................................................................................................................................... ....................................................................................................................................................................................................................................................................................................................................................................................................................... . ....................................................................................................................................................................................................................................................................................................................................................................................................................... ................................................................................. . ............................................................................... ................................................................................. . ............................................................................... A s B m • • x 0 x s ∗ • Recall that quasi-linear preferences have indifference curves that are parallel translates of each other. • s ∗ smoke is produced whatever property rights are assigned. Only m varies between efficient allocations. • This is the Coase theorem — the efficient externality level is independent of the initial distribution. Market — Market Failure 4 Production Externalities • Suppose there are two firms, one producing electricity, e, and one producing fish f. The electricity firm dumps toxic waste w in the sea, reducing fish yields. Costs are ce(e, w) = c(e) − w(1 − w) and cf (f, w) = c(f) + w 2 respectively. • Hence profits are given respectively by: πe = pee − c(e) + w(1 − w) and πf = pf f − c(f) − w 2 • Since the electricity firm alone chooses w it will keep producing waste (which reduces cost) until no more profits can be made from doing so. The benefit increases until w = 0.5 and decreases thereafter. • At w ∗ = 0.5 the marginal benefit of waste is equal to its marginal cost (zero). Both firms set MR = MC to derive optimal e ∗ and f ∗ — pe = c 0 (e ∗ ) and pf = c 0 (f ∗ ). • Is this efficient? No. The electricity firm is producing too much waste, damaging the fishing firm
Let Failure ternalising Externalities To see this inefficiency, consider a merged firm producing both electricity and fish Profits are given by T=Pee+prf-c(e)-c(f)+w(1-a)-w2. How much waste would such a firm produce? Profits are maximised by choosing waste. w, so that the marginal benefit to electricity production equals the marginal cost to fish production. Is when mB= MC or 1-2w0= 2w. That is, when ur'=0. 25. Notice this is less than MC MCr MB=MC One solution to externalities is to internalise them in this way. This will result in a socially optimal (efficient) Market- Market Failture Tragedy of the Commons Consider an economy by the ocean. Each agent is a fisherman. They can buy a boat at cost c and go fishing. eans more fish. but at a decreasin rate- overcrowding reduces the number of fish each fisherman catches. Each fisherman takes home fish to a value of f(b)/b. This is auerage benefit, and it is decreasing. A new fisherman would go to sea if the value of fish they would get exceeds the cost of a boat: f(b)/b>c. Hence, an equilibrium is reached when f(b)/6=c. No fisherman would join or leave the market. The government would maximise social welfare which is the total value minus the total cost. f Is there over-fishing or under-fishing relative to the social optimum? Recall that f '(b)is marginal benefit. fficiency occurs, as usual, when
Market — Market Failure 5 Internalising Externalities • To see this inefficiency, consider a merged firm producing both electricity and fish. • Profits are given by π = pee + pf f − c(e) − c(f) + w(1 − w) − w 2 . • How much waste would such a firm produce? Profits are maximised by choosing waste, w, so that the marginal benefit to electricity production equals the marginal cost to fish production. • This occurs when MB = MC or 1 − 2w = 2w. That is, when w 0 = 0.25. Notice this is less than w ∗ . ............. ............. ............. ............. ......... . . . . . ................................................................................................................................................................................................................................................................................. . 0 MC w • • w 0 = 1 4 w ∗ = 1 2 MBe = MCf MBe MCf • One solution to externalities is to internalise them in this way. This will result in a socially optimal (efficient) amount of the externality. Here it is impossible to make one firm better off without making the other worse off. Market — Market Failure 6 Tragedy of the Commons • Consider an economy by the ocean. Each agent is a fisherman. They can buy a boat at cost c and go fishing. • If there are b boats at sea the total value of fish caught is f(b). More boats means more fish, but at a decreasing rate — overcrowding reduces the number of fish each fisherman catches. • Each fisherman takes home fish to a value of f(b)/b. This is average benefit, and it is decreasing. A new fisherman would go to sea if the value of fish they would get exceeds the cost of a boat: f(b)/b > c. • Hence, an equilibrium is reached when f(b ∗ )/b∗ = c. No fisherman would join or leave the market. • The government would maximise social welfare which is the total value minus the total cost. max b f(b) − cb =⇒ f 0 (b s ) = c • Is there over-fishing or under-fishing relative to the social optimum? Recall that f 0 (b) is marginal benefit. (Efficiency occurs, as usual, when marginal benefit equates to marginal cost)
Let Failure Pigouvian Taxes Recall average revenue(demand) and marginal revenue. M R lies below AR and is downward sloping when AR is decreasing. This is analogous to average and marginal benefits in the current model. Cost is a constant c. f(b)/b The social optimum, ', is smaller than the equilibrium value, b. There is over-fishing. How can this be prevented? There are many possibilities 1. Property Rights: Sell the sea to one agent. they will act just like the government. 2. Quota: Only allow b boats on the sea, and enforce by law. 3.Pigouvian Tax:A tax on boats t to increase the cost to c+t Now fisherman will buy the socially optimal number of boats. A Pigouvian tar is a tax to correct an externality. t is given by the dotted line Market- Market Failture Public goods A public good is a good that is provided in the same amount to all consumers if it is provided at all. A pure public good is non-erchudable and non-rival Once provided it is impossible to prevent agents from consuming it. Moreover, one agents consumption of the good does not reduce the amount available to other agents. 1. Excludable Rival: Regular private goods, like apples and bananas 2. Non-Excludable Rival: Free-for-all goods, like the roads. Goods like satellite TV and mobile phone networks. 1. Non-Excludable Non-Rival: Pure public goods like BBC World Service radio When should a particular public good be provided? When the benefit exceeds the cost. If the benefit to each consumer is b1 and b and the cost is c then a good should be provided if b1 +b>c If both bi c and by c then neither consumer would buy the good individually. Even when b1> c and b>e
Market — Market Failure 7 Pigouvian Taxes • Recall average revenue (demand) and marginal revenue. MR lies below AR and is downward sloping when AR is decreasing. This is analogous to average and marginal benefits in the current model. Cost is a constant c. . . . . . . . . . . . . . . . . . ............................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................ . 0 f(b) b • • c f f(b)/b 0 (b) b ∗ b s • The social optimum, b s , is smaller than the equilibrium value, b ∗ . There is over-fishing. • How can this be prevented? There are many possibilities: 1. Property Rights: Sell the sea to one agent, they will act just like the government. 2. Quota: Only allow b s boats on the sea, and enforce by law. 3. Pigouvian Tax: A tax on boats t to increase the cost to c + t. Now fisherman will buy the socially optimal number of boats. A Pigouvian tax is a tax to correct an externality. t is given by the dotted line. Market — Market Failure 8 Public Goods • A public good is a good that is provided in the same amount to all consumers if it is provided at all. • A pure public good is non-excludable and non-rival. Once provided it is impossible to prevent agents from consuming it. Moreover, one agents consumption of the good does not reduce the amount available to other agents. 1. Excludable Rival: Regular private goods, like apples and bananas. 2. Non-Excludable Rival: Free-for-all goods, like the roads. 3. Excludable Non-Rival: Goods like satellite TV and mobile phone networks. 4. Non-Excludable Non-Rival: Pure public goods like BBC World Service radio. • When should a particular public good be provided? When the benefit exceeds the cost. If the benefit to each consumer is b1 and b2 and the cost is c then a good should be provided if b1 + b2 ≥ c. • If both b1 < c and b2 < c then neither consumer would buy the good individually. Even when b1 ≥ c and b2 ≥ c provision is not guaranteed, due to the problem of free riding
Let Failure Fre Consider the following. Each player has bi c, but b, >c/2. Hence the good should be provided. Each player houses whether to pay(contribute toward the public good or not. Free riding results. ay Dont b2-c/2 This is the Prisoners'Dilemma again. The only equilibrium is for both players to not pay. When both agents have bi >c, they could still attempt to free ride by waiting for the other to purchase the good. Then there is a coordination problem. Both player might claim that they do not value the public good Can the true valuations of the agents be revealed Market- Market Failture Efficient Provision How much of a public good, g, should be provided? ppose here are two goods, a private good and a public good. Two agents have income m1 and m2 and spend it To achieve a Pareto efficient allocation, fix agent 2s utility at t2 and maximise u1: max u(z1, g) such that u2(r2, )=y and I1+I2+c(g)=mi+1 The solution lies where [MRS1 +[MRS2= MC(g). The sum of the marginal rates of substitution between the private and public goods is equal to the marginal cost of the public good. could be made better off by a change in the amount of prow If preferences were quasi-linear, u(i,9)=r+v(g), then the equation simplifies. Replacing MRS with marginal utilities for the public good: do/dg +duz/dg= de/dg
Market — Market Failure 9 Free Riding • Consider the following. Each player has bi c/2. Hence the good should be provided. Each player chooses whether to pay (contribute toward the public good) or not. Free riding results. Pay Don’t Pay b2 − c/2 b1 − c/2 b2 b1 − c Don’t b2 − c b1 0 0 . • This is the Prisoners’ Dilemma again. The only equilibrium is for both players to not pay. • When both agents have bi > c, they could still attempt to free ride by waiting for the other to purchase the good. Then there is a coordination problem. Both player might claim that they do not value the public good. • Can the true valuations of the agents be revealed? Market — Market Failure 10 Efficient Provision • How much of a public good, g, should be provided? • Suppose there are two goods, a private good and a public good. Two agents have income m1 and m2 and spend it on private goods worth x1 and x2 and the public good which costs c(g). • To achieve a Pareto efficient allocation, fix agent 2’s utility at u2 and maximise u1: max x1,x2,g u1(x1, g) such that u2(x2, g) = u2 and x1 + x2 + c(g) = m1 + m2 • The solution lies where |MRS1| + |MRS2| = MC(g). The sum of the marginal rates of substitution between the private and public goods is equal to the marginal cost of the public good. • If this were not the case both agents could be made better off by a change in the amount of provision. • If preferences were quasi-linear, ui(xi , g) = xi + vi(g), then the equation simplifies. Replacing MRS with marginal utilities for the public good: dv1/dg + dv2/dg = dc/dg
Let Failure Voting and Demand Revelation All this relies upon agents revealing their true valuations for the public good. Would they Recall agents would like to free ride. They would like the good to be provided but they would rather not pay for it. Private provision of the public good is therefore unlikely to take place. Voting for a particular level of the public good might be a way to reveal the preferences of individuals. But remember Agent 1 Agent 2 Agent 3 If a, b and c represent different levels of the public good, then there is majority who prefer a to b, a majority whe prefer b to c and a majority who prefer c to a Social preferences are not transitive. More generally, even when transitivity is imposed on a voting system, the level of public good provision voted for is the median preferred level - which is not necessarily the efficient level Valuation mis-representation to manipulate the vote remains an issue. How can true valuations be revealed? Market- Market Failture a Revelation mechanism There is a solution: Revelation mechanisms. Suppose there are n agents, each with a true valuation for the public good of ui. Each will pay a commonly known share si of the cost c if the good is provided Their net valuations are v=ui-sic. Consider the following mechanism 1. Each agent is asked their net valuation vf. They report a valuation bi which may or may not be their true valuation. (They can misrepresent their preferences if they wish) 2. The public good is provided if i_, bi>0. If the reported valuations add to more than zero the good is prowided -this would be efficient if everyone told the truth 3. Each agent a side-payment equal to the sum of the other agents reported valuations(2i+b). Each agent will tell the truth. The incentive to do so is provided by the side-payments at the end. Given that eac agent tells the truth the public good will be provided efficiently. This mechanism is expensive, however. There are cheaper alternatives: The Clarke tar is similar but only gives side-payments to pivotal agents. As an exercise, show why no agent has an incentive to report b i vi in the abowe mechanism
Market — Market Failure 11 Voting and Demand Revelation • All this relies upon agents revealing their true valuations for the public good. Would they? • Recall agents would like to free ride. They would like the good to be provided but they would rather not pay for it. • Private provision of the public good is therefore unlikely to take place. Voting for a particular level of the public good might be a way to reveal the preferences of individuals. But remember: Agent 1 Agent 2 Agent 3 a b c b c a c a b • If a, b and c represent different levels of the public good, then there is majority who prefer a to b, a majority who prefer b to c and a majority who prefer c to a. Social preferences are not transitive. • More generally, even when transitivity is imposed on a voting system, the level of public good provision voted for is the median preferred level — which is not necessarily the efficient level. • Valuation mis-representation to manipulate the vote remains an issue. How can true valuations be revealed? Market — Market Failure 12 A Revelation Mechanism • There is a solution: Revelation mechanisms. Suppose there are n agents, each with a true valuation for the public good of ui . Each will pay a commonly known share si of the cost c if the good is provided. • Their net valuations are vi = ui − sic. Consider the following mechanism: 1. Each agent is asked their net valuation vi . They report a valuation bi which may or may not be their true valuation. (They can misrepresent their preferences if they wish). 2. The public good is provided if Pn i=1 bi ≥ 0. If the reported valuations add to more than zero the good is provided — this would be efficient if everyone told the truth. 3. Each agent receives a side-payment equal to the sum of the other agents’ reported valuations ( P j6=i bj ). • Each agent will tell the truth. The incentive to do so is provided by the side-payments at the end. Given that each agent tells the truth the public good will be provided efficiently. This mechanism is expensive, however. • There are cheaper alternatives: The Clarke tax is similar but only gives side-payments to pivotal agents. • As an exercise, show why no agent has an incentive to report bi 6= vi in the above mechanism
