Cap and Trade. Solving Negative Externalities Using Marketable Permits.

Cap-and-trade is a system of marketable permits that are used to address negative externalities. So I want to give you a specific negative externality. Let's talk about pollution and in particular, we'll talk about sulfur dioxide emissions. So sulfur dioxide leads to acid rain and acid rain can kill fish and insects. So let's say it's killing fish in a nearby stream and that there are people who fish in that stream and catch that fish, now a cost has been imposed on them. So let's say that the factory that is producing electricity or whatever they are creating this sulfur dioxide with their production, it's creating acid rain, it's killing the fish and imposing costs on the people who do the fishing and so that's the nature of the negative externality and so there's going to be a market failure in that there's gonna be more sulfur dioxide produced than what is socially efficient.


How does Cap and Trade Works?

Cap-and-trade says well we're gonna do a couple of things to stop that and what we're gonna do is first of all we're going to put a cap on the total amount of sulfur dioxide emissions. So you might say "Look we're gonna have a cap, I don't know how sulfur dioxide is measured but let's say 1 million tonnes is the cap on sulfur dioxide. So firms cannot produce or generate more than a million tons of sulfur dioxide in any given year. So that's the cap but the second part of cap and trade is you say "Now that we're gonna set up a market where firms can actually trade and buy and sell permits to emit sulfur dioxide.


Example of Cap and Trade

So here's how this would work, so let's say that we have an industry with three firms. We have firm A we have firm B and then we have firm C and we allocate initially let's say that firm A is given 200,000 and firm B is 200,000 and then firm C is 600,000 tonnes of permit. Now, these could have been allocated based on historical emissions and say "This firm C sees a lot larger, we should give them larger credit but this could be crazy." Somebody might say "Look that's rewarding, they were emitting a lot they should be punished." but you could also auction the credits, in any event, these are the initial allocations of credits. So firm A, in any given year, has credits given to it so it can produce up to 200,000 tons of sulfur dioxide. Now here's the thing, let's say firm A gets really good they have cleantech they invest in clean technology and they say "If we do a really good job here and we can actually get our emissions of sulfur dioxide below 200,000 tons, then we will speak and sell the difference because we only we got credit for 200,000 tons but we are able to invest in technology and get where we only produced 100,000 tons of sulfur dioxide.


Maybe firm C hasn't invested much in technology and so firms C say "Well look we would like to buy 100,000 tons of credits because maybe we think we're gonna be at 700,000 tons." Now you might think "Hey that's a bad thing because now this firm C hasn't done a really good job and now they're actually admitting more than they were supposed to." but look at the total amount of emissions the total cap is unchanged. We said as a society we could deal with a million tons and so even though firm C might not have done a good job investing in clean technology but firm A did. So firm A can treat firm C and buy and sell them and so there's an incentive for firms to do cleaner technology and so forth and then we also as a society get the peace of mind of knowing that a million tons are the amount of sulfur dioxide can be produced and that's it.


Cap and Trade Vs Pigouvian Tax

Now I want to show you with a graph how this is basically equivalent to using a pigouvian tax which we talked about in another article. It is setting a corrective tax and that will get us to ultimately to the same outcome. So let's say we've got the price in the x-axis and we've got quantity in the y-axis and let's say that we have the marginal social cost of pollution and then let's say that we also have the marginal benefit of pollution. I know it's hard to think of a marginal benefit of pollution, you can also think of is the marginal cost of cleanup or marginal cost. Now we'll just say where our marginal social cost equals the marginal benefit that should be our optimal point, that's our socially efficient quantity. This Q* is our socially efficient quantity of sulfur dioxide. Let's that was we said a million tons.


Now we also can look at the marginal private cost to the firm, so their marginal private cost is lower than the marginal social costs because the firm doesn't internalize the cost to the people doing the fishing who have fewer fish to catch. So that equilibrium, without cap-and-trade and pigouvian tax, is going to be at Q'. So Q' let's say that it's 1,500,000 tons of sulfur dioxide which is inefficient because we're overproducing sulfur dioxide more than a socially optimal point because the factory did not have any incentive to take in the external cause to the people doing the fishing and so forth. So we said when we talked about a pigouvian tax we can actually set an amount of tax that is equal to the difference between Marginal Social Cost (MSC) and Marginal Private Cost (MPC). So basically the marginal external cost, cost of the externality could be set equal to a tax right so that that could be set equal to a tax and that would bring about the socially efficient quantity. So we call that tax would be a price mechanism, this is a way we change the price. We force the factory to face the full social cost of its actions and then because we changed the price to the firm it naturally adjust to the socially efficient quantity.

However, in cap-and-trade we're doing the reverse we're setting the quantity and say we're gonna set Q* at a million instead of taxes, and then we're just gonna set the quantity which is nice because we're gonna set the quantity based on science. Maybe we know the scientists' thoughts a million tons is the absolute maximum limit for sulfur dioxide. With that tax theory you end up at the socially efficient quantity but if you didn't set the tax right or something like that or where there could be issues but in any event now we're gonna be cap-and-trade set the quantity and then let price adjust. So pigouvian tax is a price mechanism and then cap-and-trade is a quantity mechanism. In cap-and-trade, we're setting the quantity and then allowing price to adjust through the sale of the marketable permits and so forth but with the pigouvian tax we're using a price mechanism and then the quantity will naturally adjust as firms change their behavior based on down the fact that they're internalizing the social cost but in theory in theory both the corrective tax and the cap-and-trade, the system of marketable permits both lead to the socially efficient equilibrium.