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Cap and trade

October 18, 2011 Comments off

“Cap and trade” systems are market based solutions to negative externalities like pollution. They work by creating a market for the externality (and solving the issue of missing markets for externalities). A typical cap and trade system will use permits that allow firms to produce a certain amount of pollution, and if they want to produce a level of output that will mean they end up producing more pollution than they have permits, they have to buy some permits from other firms.

The market solves the issue of firms having different costs of abatement. These are the costs incurred by a firm when it reduces its pollution by a certain amount. Some firms produce more efficiently than others (they produce more units of output per unit of pollution) and so they have lower costs of abatement. It makes sense for them to purchase extra permits from less efficient firms as they will be able to get more profitable output from being allowed to pollute more than the less efficient firms. Similarly, it is better for society if the less efficient firms produce less and the more efficient firms produce more as part of an overall pollution reduction strategy. Under a cap and trade system, the less efficient firms are incentivised to produce less because they can sell some of their pollution permits to more efficient firms. By creating a market for the externality, the more efficient firms will naturally end up producing more and the less efficient firms will produce less, which would not be the case if the government just imposed restrictions on the amount each firm could produce – unless government knew EXACTLY how efficient every firm was, which would be difficult to achieve in practice.

It may seem less complicated if we look at an example.

We can show this by setting up a model where there are three firms, A, B and C, which are all producing pollution and all have constant (but different for each firm) costs of abatement.

Firm A is initially producing 350 units of pollution, and has a cost of abatement of £40 per unit.
Firm B is initially producing 400 units of pollution, and has a cost of abatement of £50 per unit.
Firm C is initially producing 250 units of pollution, and has a cost of abatement of £20 per unit.

The initial total amount of pollution is 1000 units. Suppose the government wants to reduce total pollution levels by 400 units. This means total pollution will have to be no more than 600 units.

We can consider three options here:
1) limiting each firm to producing 200 units of pollution
2) giving each firm 200 ‘pollution permits’ (1 permit allowing production of 1 unit of pollution), and allowing firms to buy and sell the permits from each other
3) auctioning off 600 ‘pollution permits’ in a second price auction (like ebay, the winner pays the second highest bid price)

Option 1: limiting each firm to producing 200 units of pollution.

Firm A would have to reduce its pollution by 150 units, costing £40 x 150 = £6000
Firm B would have to reduce its pollution by 200 units, costing £50 x 200 = £10000
Firm C would have to reduce its pollution by 50 units, costing £20 x 100 = £2000

The total reduction of pollution is 400 units, hitting the government’s target, and the total cost of abatement is £18000.

Option 2: issuing each firm with 200 ‘pollution permits’ and allowing them to trade the permits between them. If any firms want to produce more than 200 units, they need to buy permits from another firm (so the other firm has to produce less). This creates a market for pollution, and there will be a market price for a unit pollution at which these permits will trade.

We can analyse this market by looking at the demand and supply for permits and see if we can determine an equilibrium market price.

First look at the demand. Any firm will be willing to pay up to its cost of abatement for a permit. For Firm A, for instance, the cost of abatement is £40, so if it can buy a permit for £39 it may as well do that and be allowed produce an extra unit of pollution rather than lose £40 in abatement costs by not producing it.

So firm A will be willing to pay up to £40 for a permit, firm B will be willing to pay up to £50 for a permit and firm C will be willing to pay up to £20 for a permit.

This means that if the price, P < 20, then all firms will want to buy permits and demand for them at that price will be 600.
If 20 < P < 40 then firms A and B will want to buy permits but C will not. A was originally producing 350 units of pollution and has 200 permits from the government so needs another 150 permits to produce its original level. B was originally producing 400 units and has 200 permits from the government so needs another 200 permits.The total demand for permits will be the 550 permits.
If 40 < P 50 then none of the firms will want to buy permits.

Now consider the supply. Any firm will be willing to sell a permit if it is worth more than the cost of abatement. For Firm A, for instance, the cost of abatement is £40, so if it can sell a permit for £41 it may as well do that and pay the £40 abatement costs for reducing a unit of pollution.

So firm A will be willing to sell permits at any price over £40, firm B will be willing to sell at anything over £50 and firm C will be sell at anything over £20.

This means that if the price, P < 20, then no firms will be willing to sell.
If 20 < P < 40 then firm C will be willing to sell but A and B won't, so the total supply of permits will be the 200 that firm C were given.
If 40 < P 50 then all firms will be willing to sell so the total supply of permits will be 600.

The supply and demand curves here are stacked, there is a zigzagging upward sloping supply curve and zigzagging downward sloping demand curve. The price of £40 is the tipping point at which there will be possibility of market equilibrium. At £39, demand will exceed supply as A and B want to buy permits meaning a total demand of 550, but only C will be willing to sell meaning a total supply of 200. The excess of demand over supply will push the price up. At £41, only B wants to buy, meaning total demand is 200, while A and C want to sell, meaning total supply is 400. This excess of supply over demand will push the price down.

So if the market price of permits was £40, what would happen? A would be indifferent about buying, selling or doing nothing. B wants to buy 200 permits. C wants to sell 200 permits. So the market trade is that B buys 200 permits from C.

Now the total pollution and abatement would be that:
Firm A would have to reduce its pollution by 150 units, costing £40 x 150 = £6000
Firm B does not have to reduce its pollution at all as it buys enough permits from C to produce its original level of pollution, costing £0.
Firm C doesn’t have any permits to allow it to pollute so would have to reduce its pollution by 250 units, costing £20 x 250 = £5000.

The total reduction of pollution is 400 units, hitting the government’s target, and the total cost of abatement is £11000. This is less than the £18000 that the original plan cost.

What has actually happened there is firm C has stopped producing, it has made £40 x 200 = £8000 selling permits to B and so is better off not producing and selling permits.

Option 3: auctioning off the ‘pollution permits’ in a second price auction.

Suppose the 600 permits just went straight to a government auction. Firm B would be the highest bidder as it was willing to pay £50 per unit, with firm A the next highest bidder, willing to pay £40 per unit. So being a second price auction, B would win this at a price of £40 (technically there would be a slight amount over eg if this was on ebay B would win it at £40.50 but I am discarding that here). So firm B would get the 400 permits it wanted to allow it to produce its original level of 400 units of pollution, paying £40 each (total price to government of £16000).

That means there are 200 permits left and A and C still to bid. A would be willing to pay £40 per permit and C willing to pay £20 so as it’s a second price auction, A wins at price £20. A wants 350 permits but there are only 200 so it just gets the remaining 200 and the government gets £4000).

Now the total pollution and abatement would be that:
Firm A would have to reduce its pollution by 150 units, costing £40 x 150 = £6000, it has also just paid £4000 for its permits, so the total cost to A is £10000.
Firm B does not have to reduce its pollution at all as it buys enough permits from the government to produce its original level of pollution, costing £0, it has paid £16000 for its permits so total cost to B is £16000.
Firm C doesn’t have any permits to allow it to pollute so would have to reduce its pollution by 250 units, costing £20 x 250 = £5000.

The total reduction in pollution is again 400 which hits the government target. The total costs for the three firms are now £31000 but the government has received £20000 so the total net cost to society of the pollution reduction is £11000.

So comparing the three options, all three deliver the government’s pollution reduction targets but option 1 – stipulating a set and equal amount that each firm can produce – is the most expensive. Option 2 – distributing pollution permits and allowing firms to trade them, and option 3 – auctioning off pollution permits – both have the same net cost to society which is lower than option 1. The difference between them is that distributing the permits is better for the firms and auctioning off the permits is better for government.

Externalities and the Coase Theorem

October 17, 2011 Comments off

The Coase theorem is a method of tackling the inefficiency caused by an externality, by awarding property rights to the externality to one party and allowing the parties concerned to bargain their way to an efficient solution. In the case of a negative externality such as pollution, the property right to pollute could be awarded to the polluter, and the victim of the pollution would have to offer to pay to get the polluter to reduce their output. Alternatively, the property right to clean air/water/whatever else is being polluted, could be awarded to the victim, so the polluter would have to offer to pay the victim to be allowed to pollute.

Consider the situation where we have a firm, firm A, producing some good in a competitive market that causes some pollution as a result of its output. Another firm, firm B, which produces a different good in a different market, is directly harmed by this pollution. It could be something like A being a factory and B being fisheries, and the factory pollutes the water and reduces the number of fish.

Anyway we consider the market for firm A. We said that it was a competitive market so it is a price taker , it faces a horizontal demand curve at the market price, Pc, and can produce as much output as it likes at this price. As the market price is constant and does not vary depending on the output the firm produces, the marginal revenue is also equal to the price. Assume as well that firm A faces an upward sloping (private) marginal cost curve, the more output it produces, the greater its marginal costs.

Firm A will produce up to the point where its marginal revenue equals its private marginal costs, here MR=PMC at Qc, the competitive output quantity.

However also on that diagram is a social marginal cost curve (here ‘society’ includes firm A and firm B), this is higher than A’s PMC curve because it includes the cost of the externality (the pollution) on firm B. By producing at Qc, firm A is producing output above the social optimum. This is because the joint benefit as a result of this output is simply the total revenue gained by firm A (Pc x Qc), firm B does not get any benefit. But the joint social cost is greater. The cost to firm A is (Pc x Qc), and the cost to firm B caused by the externality is ((SCc – PC) x Qc), making the total social cost (SCc x Qc). As (SCc x Qc) > (Pc x Qc) then there is a net loss incurred by this level of production.

The Coase solution offers us two options, either we could
i) award firm A the right to pollute or
ii) award firm B the right to clean resources.

Consider situation i) first, awarding firm A the right to pollute.

Here if A has the right to pollute, then firm B must offer some form of bribe payment to A in order to get A to reduce its output, ie B has to pay A not to produce. Lets call this bribe payment x.

At any output level, the marginal gain to firm A to produce another unit of output is MR – PMC. When the marginal gain is positive it is going to produce another unit of output so it will keep producing until its marginal gain is 0. But each unit that A produces delivers a marginal loss to firm B of MD, the marginal damage produced by the externality for that unit of A’s output.

Now if firm B offers firm A a payment of x in order to stop production at that output, then the marginal gain to firm A is x instead of being MR – PMC, so as long as x > MR – PMC, then A will stop producing.

From firm B’s perspective, if the value of the payment, x, is less than the value of the marginal damage done by the externality for producing that extra unit of output, then it makes sense for firm B to pay x to firm A not to produce it. So by thinking at the margin, firm B will be willing to increase its value of x up to a point where x = MD, the payment equals the amount of marginal damage that the pollution would do to it.

If x = MD, then we can say that as long as MD > MR – PMC, then there is the opportunity for a bargain to stop A producing more output. Even if the MD to firm B is just marginally greater than MR – PMC for firm A, it is worth B making the offer of payment, so we can effectively say they will bargain up to the point where MD = MR – PMC.

Now remember the definition of the social marginal cost is SMC = PMC + MD, it is the private marginal cost of production to firm A plus the marginal damage of the externality to firm B. So this means that we can rewrite that as MD = SMC – PMC.

Substituting this into our equation above we can say SMC – PMC = MR – PMC, hence SMC = MR. That means that after bargaining, production will take place at the point where SMC = MR, the socially efficient level of output.

Now consider situation ii) where firm B is awarded the right to clean resources

This time A does not have the right to pollute, it has to instead compensate B for producing an extra unit of output. This time the payment, x, will be made by A to B.

Now at any output level, the marginal gain to firm A to produce another unit of output is MR – PMC – x. To firm B the marginal loss suffered as a result of firm A producing another unit of output is MD – x. So firm B will accept payment x if x > MD. At any level where x is marginally greater than MD, there exists the opportunity to bargain and A can produce another unit by paying x to B, so they will be able to bargain up to the point where x = MD.

Firm A will produce up to the point where its marginal gain is 0, ie MR – PMC – x = 0. If x = MD then MR – PMC – MD = 0, so MR = PMC + MD. As we know that MD = SMC – PMC, this means MR = PMC + SMC – PMC so MR = SMC. Again we have reached a situation where firm A produces up till the level where MR = SMC, the socially efficient output.

The conclusion is that with the Coase theorem, it does not matter whether the property rights are allocated to the polluter or to the victim of the pollution, the socially efficient output level will result either way.

However there are some problems with the Coase solution to externalities. Whilst an equilibrium reached through Coasian bargaining may be good in terms of efficiency there may be other concerns in terms of equity. In the case above, if firm A was awarded the property right to pollute then firm B is in an undesirable situation either way, it either has to suffer the pollution or pay A not to pollute. Alternatively if firm B was awarded the property right to clean resources then firm A will be less well off because B is now insulated against damage, either it gets compensated for the pollution produced or it doesn’t produce and pollute.

Instinctively most people would probably say it was more fair to award the property rights to clean resources to firm B. One advantage of this is that by making firm A face the full social costs of production, rather than just the private costs, it is having to internalise the externality and this may encourage it to invest in cleaner production techniques. There is no incentive to invest money in cleaner production techniques if the costs caused by the dirty production are incurred by someone else. However the Coase theorem doesn’t make these sorts of judgements, it simply says that awarding the property rights to one party will lead to the efficient output through bargaining.

There are other problems with the Coase solution:
Bargaining costs may be too high. It is easier when there are just two parties involved but what if there were many parties, for instance if a firm was polluting a coastline and there were hundreds of fishermen and residents that could be harmed by it. It may be difficult and costly to get all of the fishermen and residents together to actually bargain a solution. Some people may also not bother taking part, hoping that their fellow residents will put the case forward (free riding), and this may mean proper negotiations don’t take place.
– There may be difficulties obtaining information on the relative source and size of the damages, and there may be asymmetric information where each party does not know how much the other party really values the relative MD and MB.

To conclude, the things to remember about the Coase solution are:
– If property rights are clearly defined then bargaining can lead to the optimal levels of pollution and output
– Efficiency is achieved regardless of who gets the property rights, but the income distribution is affected by who gets the property rights
– To work it relies on there being no impediments to bargaining, the costs of bargaining can’t be prohibitive, all parties need to have full information and not engage in strategic bargaining behaviour

In reality a fully efficient Coasian solution will not be possible in most situations but the theory is relevant to things like ‘cap & trade’ systems of managing pollution.

The Pigouvian tax

October 16, 2011 Comments off

The Pigouvian tax is a way of tackling a negative externality. If we consider the case where we have a competitive market and a negative externality, then the competitive market leads to an inefficiently high output level compared to the social optimum. So we want to reduce the output and we can do this with a tax.

The gap between the social marginal cost curve and the private marginal cost curve is the amount of marginal damage caused by the externality.

So if you know the level of marginal damage at the socially optimal amount, you can apply a specific tax (quantity tax) of value t. This shifts the supply curve up by the value of the tax, t, which means that the supply curve will now intersect the demand curve at the socially optimal level.

In reality it is going to be difficult to set the level of a Pigouvian tax exactly right, as you would need to be able to measure the exact about of the marginal damage in order to know the social optimum. However the government may still apply a Pigouvian tax even if it knows it is unlikely to result in the exact socially optimal amount, if it can bring the output level closer to the social optimum than it would have been without the tax then it will at least be a welfare improvement.

Externalities with monopoly

October 16, 2011 Comments off

When a firm produces a negative externality (like pollution) then the social marginal cost will be greater than the private marginal cost so a competitive market will produce an output higher than the socially optimal level of output.

Negative externality and competitive market

But what would happen if the firm concerned was a monopoly?

In the example here, the output produced by the monopoly firm is now lower than the socially optimal level of output.

We can do a welfare analysis to see the welfare effects of producing at the monopoly output compared to the socially optimal level of output:

At the monopoly price-quantity combination:
Consumer surplus = A + B
Private producer surplus = C + D + F + G
Externality cost = 0
Welfare = consumer surplus + private producer surplus – externality cost = A + B + C + D + F + G

At the socially optimal price-quantity combination:
Consumer surplus = A + B + C + D + E
Private producer surplus = F + G + H
Externality cost = 0
Welfare = consumer surplus + private producer surplus – externality cost = A + B + C + D + E + F + G + H

The difference in welfare between the competitive output and the socially optimal output is E + H, this is the deadweight loss of the externality in this monopoly market.

However this is not a general rule that can be said to be true for all monopolies. Look at this case as an example, where the firm faces a more elastic demand curve and the marginal harm of the externality is greater (so there is a greater difference between PMC and SMC):

This time the monopoly is producing an output that is greater than the socially efficient amount, although not by as much as it would be if there was a competitive market. Here the welfare losses caused by the negative externality are less in a monopoly environment than they would be in a competitive environment. This is a point worth remembering when it comes to things like energy markets. People naturally assume that competitive markets are better than ones with market power, but if there is a negative externality of pollution that comes with consuming energy, then the economic welfare effects may be less bad for society if there is a monopoly or oligopoly provider producing a lower amount at higher price for consumers (and enjoying high profits) than if there was a competitive market, prices were forced down for consumers, and an excessive amount of energy was consumed.

When there is a negative externality:
– A competitive market will produce too much output relative to the social optimum.
– A monopoly market may produce too much or too little output relative to the social optimum, depending on two offsetting effects:
Elasticity of demand: high elasticity means low Lerner index and low mark-up, closer to the competitive market so more likely to be producing too much output; inelastic demand means high Lerner index, high mark-up and more likely to be producing too little output.
Marginal harm of the externality: high marginal harm means a big difference between SMC and PMC, so monopoly is more likely to be producing too much output, low marginal harm means a SMC is more in line with PMC, so monopoly is more likely to be producing too little output.

When there is a positive externality:
– A competitive market will produce too little output relative to the social optimum.
– A monopoly market will also produce too little output relative to the social optimum. In this case a monopoly will be worse for society than a competitive market. The elasticity of demand and the marginal benefit of the externality will influence the degree to which society loses out by having a monopoly.

Externalities and market failure

October 15, 2011 Comments off

The first theorem of welfare economics tells us that a competitive market will produce an efficient level of output, but this is not true when an externality exists. This is because the externality means there is a difference between the private marginal cost (PMC) and the social marginal cost (SMC). When there is a negative externality, it means the cost to society is greater than the private marginal cost incurred by the firm producing the externality. When there is a positive externality it means there is some benefit to society so the social marginal cost is lower than the private marginal cost.

Here we have a market where a firm produces a negative externality (eg some pollution). In a competitive market, the firm will produce where demand = private marginal cost (D = PMC), the PMC is basically the firm’s supply curve, so you will get a competitive output of Qc and a price of Pc. However when you take into account the negative externality, the SMC is higher than the PMC at all positive levels of output. The socially optimal output, Qs is where D = SMC and this is at a lower level than Qc.

Notice that just because there is pollution, the social optimum is not to produce at the level where there is no pollution because that is also the level at which there is no output either. There is a benefit produced by creating extra output, and there is damage produced by creating the externality that comes with the output. A cost-benefit analysis will find the efficient point at the level where the marginal benefit of producing another unit of output equals the marginal damage of producing another the amount of externality that comes with producing another unit of output.

Again this leads us to the socially optimal point, it is just another way of thinking about it.

When there is a negative externality a competitive market will produce an inefficiently large amount of output. Conversely, when there is a positive externality, a competitive market would produce an inefficiently small amount of output.

We can look at the welfare effects of the externality by breaking it down into consumer and producer surplus.

At the competitive price-quantity combination:
Consumer surplus = A + B + C + D
Private producer surplus = F + G + H
Externality cost = C + D + E + G + H
Welfare = consumer surplus + private producer surplus – externality cost = A + B + F – E

At the socially optimal price-quantity combination:
Consumer surplus = A
Private producer surplus = B + C + F + G
Externality cost = C + G
Welfare = consumer surplus + private producer surplus – externality cost = A + B + F

The difference in welfare between the competitive output and the socially optimal output is E, this is the deadweight loss of the externality in a competitive market.

The missing market for externalities

October 14, 2011 Comments off

Externalities are the non-market impacts of an activity which are not borne by
those who generate them. They are the direct effects of the actions of a person or firm on the welfare of someone else in a way that is not transmitted by the market price system.

Lets say you enjoy the music of a small local band, and usually you can watch them perform live at a local venue for £4. Then suddenly they become ‘big’ and a load of new people start watching them. Now the demand for their music has risen, and you can’t watch them for £4 any more, you have to go and watch them play in the main city arena and tickets are £25. Those new fans of the band have directly affected your welfare, because now it costs you more to watch the bank you like. As this effect on your welfare is transmitted through the price system, it is not an externality.

Now what about if one of these keen new fans moves into the flat next door to you and starts playing their music at top volume all through the night. You like the band, but you don’t like the music so much that you want to be kept up all night. This time your welfare has been affected in a way that is not transmitted by the price system, it’s just the annoyance of the loud music. This is an externality.

Notice as well that an externality is the impact on someone else – a different party – that did not agree to the action causing the impact. Externalities can be either positive or negative, they can be costs or benefits, but they are costs and benefits borne by someone else, not the person or firm carrying out the action causing them.

Positive externalities include the benefits of research and development, or training of new staff. When a firm invents some new technology, it may well enjoy big profits from the sales of the technology, but that technology might enable other firms to now become more productive and these gains aren’t captured by the original firm. When a firm hires a graduate and puts them through an expensive training scheme then the graduate leaves for a rival (common in fields like accountancy and law) the rival firm enjoys the benefit of the graduate’s training, but they didn’t provide it in the first place. So when a firm trains a worker the firm is not only creating a potential benefit for itself while it employs the worker, but there could be some benefit enjoyed by a rival firm down the line.

Negative externalities often come in the form of pollution – environmental damage, noise pollution, visual pollution and so on. When the polluter is affecting the lives of someone else, then it is an externality. A firm might keep down its own costs by not investing in technology to stop polluting the water, but there may be local residents that now have polluted water and face higher costs of getting clean water. The polluter has imposed an external cost on other parties.

Sometimes externalities can be quite subtle. If you put an expensive extension on your house and do your garden up so that it looks good, then one of your neighbours might like looking at it, and it makes him feel good, so it’s a positive externality to him. But one of your other neighbours might hate it or feel jealous so it’s a negative externality to him. It might end up making the street look better which helps push up the value of the neighbours’ houses. This is a positive externality to them because although it is a benefit expressed in prices, it is not expressed through the price of the action taken that caused the externality – the price you had to pay for it wasn’t affected by the way it would change the value of your neighbours houses.

There are four characteristics of externalities to remember:

1. They can be produced by individuals as well as firms.
2. There is a reciprocal aspect – someone might not like noisy neighbours but their complaints might annoy the ones making the noise.
3. Externalities can be positive or negative.
4. Zero pollution is not as a general rule socially desirable, because if you want to eliminate all negative externalities and pollution it often means not producing anything.

Because the effects lie outside the price system there is a missing market for externalities. If someone pollutes the atmosphere, they are effectively using up the commodity “clean air”. If clean air were a typical commodity its price would be determined by supply and demand, and it would be used efficiently because the polluter would have to weigh up whether the benefits of the good produced outweighed the cost of the pollution. But as there is no market for clean air, the polluter does not have to pay anything to use it up, so they treat its price as if it were zero. If the market for a commodity is missing we cannot rely on market forces to provide it efficiently. If somebody owned the resource (eg “clean air”) then they could charge for the privilege of using it, and that would give the polluter an incentive not to pollute too much.