# carbon tax vs cap-and-trade

in order to compare a carbon tax to cap-and-trade, we must first describe what a negative externality is.

imagine a single unit of two products or services, X and Y.

X costs 2$ and Y costs 3$.

alice values X and Y both at 4$.

thus if she buys X, that increases GDP by 1$ more than if she buys Y. (note, this ignores the sellers’ subjective value for the sake of simplicity.)

and if she buys X, she personally earns that 2$ of profit. whereas if she buys Y, she earns only 1$ of profit. so she’s incentivized to make the purchase that *also* maximizes GDP. she buys X.

but suppose the producers of Y find a way to transfer 2$ of the cost to the public in the form of a negative externality, switching the costs to 1$ for Y, so now the relative costs are 2$ for X and 1$ for Y.

thus if she buys X, she earns 2$ of profit. whereas if she buys Y, she earns 3$ of profit. so *now* she’s incentivized to buy Y, and reduce GDP by 1$ relative to where it would have been if she’d bought X. we have deadweight loss. that is, GDP is lower than it could be.

# pigou

but what if we add a tax to Y in the exact amount of that negative externality of 2$? we thus make Y cost 3$ again, so she buys X, and GDP is maximized.

this is the point of *pigovian taxation*. to optimize GDP.

# caps

another way to get this same behavior would be to set production limits on X and Y, such that the same amount would be produced (and the same market price would be set) as if we’d implemented the tax. we’d be back to optimal GDP just the same. but the problem with that idea is that we don’t know what that optimal cap *would be*. the only way to know would be to add the tax and see what amount the market produces. in which case, we might as well just set the tax and let the market *objectively* determine the output that would flow from that price.

# the cost uncertainty fallacy

it’s common to see an objection like this.

the fallacy here is that in order to calculate the correct cap, you’d do the following:

- estimate the correct SCC (social cost of carbon).
- estimate how much carbon the economy would emit at that cost.

observe that step 2 is an *additional* source of estimation error above and beyond the SCC estimation error that you’d get with a carbon tax. this is strictly worse.

# two ceilings

a great point raised by this reddit user, M4mb0, however is that the *effective* cost of a negative externality is whichever is lower between either its real cost *or* the cost to address it. so if the cost of carbon sequestration is lower than the SCC, we can just use the sequestration price. which is radically easier to determine with certainty. some estimates put the SCC around 180$ per ton, while the cost of carbon sequestration using current technologies can range from 50$ to 100$ per ton of CO2 captured and stored. this is remarkable, because it means objections that it’s too hard to measure the SCC evaporate with this knowledge.

# hypothecation

it is generally incorrect to associate a specific income source with a particular expenditure, known as “hypothecation.” for example, even if the social cost of carbon (SCC) is $50 and the cost of sequestration is $100, it would not be cost-effective to use carbon tax revenue specifically for sequestration. instead, the money should be added to the general fund.

but in the case where the SCC exceeds the sequestration cost, we actually get alpha (excess returns) through sequestration. in this example, we spend 50$ to get 100$ worth of value.

# conclusion

cap and trade is brain dead stupid. just set correct prices via a pigovian tax.