Public goods g (and priva priv t a e t ones) From Fr Marke Mark t e failur f e ailur to optimal taxation

Transcription

1 Public goods (and private ones) From Market failure to optimal taxation

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3 Outline 4 problems pobe for markets Public Bads Review of public goods Externalities The problem of social cost The tragedy of the commons Remedies Mandates Taxes Markets

4 Public bads Is Smog different from National Defense or the national highway system? In one case PG the individual enjoys the public goods whatever the level he contributes. Market leads to under provision because the social value is much larger than individual value In the other case PB the individual imposes a cost (pollution) that everyone (including himself bears) Market leads to excess provision (too much pollution) because the social cost is larger than the private cost.

5 Review of public goods Population of n individuals, all identical Max U(G,c) where G is public goods c is consumption sbjt to g+c Y where G=G i +g U(G, c) =G α +c Voluntary contributions optimize! Under private provision, G is a constant

6 Private provision is inefficient G is a constant and individual contributions are falling with n. What should we do? Total utility is ng α so we want to max ng α G Not transparent but G is increasing in n. (and so is g)

7 Problem 1: Public bad Population of n individuals, all identical Max U(B, b, c) where B is public bad, b i is individual i s isproduction of the public bad c is consumption sbjt to γ+c Y where B=B i +b(γ i ) γ(b) is the investment tthe individual id makes in reducing b. γ is decreasing in b Max U(Bbc) U(B,b,c) = B α γ(b) +c

8 Public bads B is a constant and individual contributions are falling with n. So what is the problem. Individual bears the whole private cost γ but only part of the social benefit So individual underprovides

9 Problem2: Externalities Public goods are non rival and non exclusive Goods with externalities are similar il One individual s utility depends on another individual s consumption Extreme is parent child. Happiness is clearly inter related But there are many other situations. Classic: river, at top water is abundant and clean If irrigation then at bottom no water? If manufacturing then at bottom water is dirty If settlement uses river as sewer.

10 Irrigation Critical issue in the history of the West Early rules are English and in England the law comes from water wheels (can take the water out of the river but you need to put it back) Works for mining i but not for agriculture Later rules come from Spain (so back to an earlier set of rules) If you own the river up to some point you can draw some water for irrigation and not put it back. (claim is proportional to how much of the banks of the river you own) Works for agriculture and for Los Angeles

11 Manufacturing and Cities Two cities. Albany and NY Pittsburg and Cincinnati Paris and Rouen City up river can put in pollution control equipment but that equipment does not affect the quality of its water, just that of the city down river What is the private solution? In this case the market equilibrium is even worse than public goods (because decider gets zero social benefits)

12 Problem 3 The Tragedy of the Commons Suppose there is a forest F. There are n lumberjacks. They each cut f trees a year The size of the forest is a function of its current number of trees F t+1 =G(F t ). We want to know how many trees will be cut what will be the steady state size of the forest. That occurs when G(F) F=nf Assume that a tree not cut this year can be cut next year. If there is only one lumberjack Max= f+δg(f f) FOC =1+δG =0 G =1/ / δ.

13 The commons (2) If there is only one lumberjack FOC =1+δG =0 G =1/ δ. I If there are many lumberjacks Max= f+(δ/n)g(f f) FOC =1+(δ /n) G =0 G =n/ n/δ. The more lumberjacks the more trees are cut down. Again the private cost of not cutting a tree is clear, but each bears only a fraction of the social cost (Fewer trees next year)

14 The problem of social cost Suppose I have some cattle and you plant corn. We have no fences What is likely to happen Solution build a fence. Should a fence be built? Who should ldbuild the fence? Does the law matter?

15 Coase: the solution The fence will be built if it pays to do so The farmer with the lowest cost will build it (even if the other farmer has to pay him) Property rights align incentives. Once incentives i are aligned then the two farmers have an incentive to minimize costs?

16 Solving the tragedy of the commons Mandates Keep some fraction F of the forest out of bounds Set a maximum limit on the number of trees a lumberjack can cut Taxes Tax forest product (reduce demand for them). Affects variable cost Force lumberjacks to pay a fee to log in the forest Affects fixed costs Markets Fix the number of lumber jacks, give each of them 1/n of the forest and allow them to buy or sell their land.

17 Solving Externalities Mandates Require cities to return water down stream to the same quality as it was when it entered their territory Let the down stream city decide on quality Taxes Tax water consumption (because its correlated with sewage) and use the money to build Water treatment plants Tax sewage releases Markets

18 Solving Public Bads Mandates Car emission rules Power plant emission rules Taxes Fuel taxes (indirect) Carbon taxes (and other pollutant taxes) Markets Create a property right and then let it circulate

19 Comparing the solutions Recall the lumber jack problem 1+(δ /n) G =0 G =n/ δ. Efficient is G = δ Recall the public bad solution efficient is Solutions can help but they are only efficient if Solutions can help but they are only efficient if they take into account both social and private costs and benefits

20 Comparing the solutions Mandates. Force everyone to do the same thing. but that is Taxes unlikely to be efficient if there are differences in private costs Again there is such a thing as a Pigouvian tax (one the gets the individual d to bear the social cost of their action, but difficult Markets Allows the low cost solution to occur. What does this mean

21 Implementing solutions Mandates When we want to eliminate a public bad (smoking on planes) Taxes When there are economies of scale in remediation (water treatment) Markets When there is a lot of heterogeneity (air Pollution in Los Angeles)