> the value that money represents is a single value. But why is it a scalar and not a vector? For example, why isn't everything priced with a value and a carbon cost? That would make prices vectors instead of scalars

Suppose for the sake of the argument that the main countries making up the world economy agree to re-price everything in terms of length 2 vectors (standard_cost, carbon_cost). The former element is measured in units of USD say, and the latter is measured in units of kg CO_2(e), say.

Suppose I go to shopping to buy a new CPU. Vendor A offers CPU_A for ($200, 15 kg CO_2(e)) while vendor B offers an equivalent product CPU_B for ($198, 50 kg CO_2(e)).

In the current economy, where externalities of global warming caused by market participants are not priced or regulated, I will purchase CPU_B, as it costs me $198, and I save $2 . I choose the product with the additional CO_2(e) footprint of (50 - 15) = 35 kg CO_2(e). The negative impact of that additional 35 kg CO_2(e) pollution is amortized over 8 billion humans [1], so everyone in the world pays the price of an additional 35 kg CO_2(e) / 8 billion = 4.375e-7 grams CO_2(e) per person. Myself as the end-user and the counterparties in the transaction (merchant, distributor, manufacturer, suppliers, etc) get to share in the value generated from the transaction, but most of the 8 billion people in the world do not get a cut of the value or utility, they only pay the cost.

As well as making the prices vectors, it would be necessary to add some other kind of limited resource into the vector-money economy, to constrain individuals from making decisions with large carbon pollution externalities, otherwise we're back to the same situation where we started, but with a lot more bookkeeping that nearly everyone will ignore.

One way to do this could be introduce regulation for a greenhouse gas pollution rationing system: for argument's sake, suppose we allocate each of the 8 billion people in the world an equal quota of kg CO_2(e) / year pollution they are permitted to emit [2]. Suppose there's roughly 40 gigatons of CO_2(e) pollution per year, and roughly 8 billion people in the world. That gives a quota of 5000 tons of CO_2(e) pollution allowance per year per person. Assuming humanity manages to hold the rate of carbon emissions steady and hold population steady, that gives a quota of 5000 kg CO_2(e) per person per year. Each time you purchase a good or a service, the carbon cost is deducted from your personal carbon budget. For efficiency, suppose we also allow carbon quotas to be traded between market participants. Now we have a carbon market where people exchange $ for CO_2(e) carbon emission allowance.

Now, arguably, we can go back to having scalar prices: Instead of the price of CPU_A being the vector ($200, 15 kg CO_2(e)), it can be the scalar $200 + carbon_price * 15 kg_CO_2(e) . Similarly for CPU_B .

If we assume a carbon price of around $200 / ton of CO_2(e) , as has been proposed in Canada for ~ 2030, that gives prices of $200 + 15 kg * $ 0.2 / kg = $203 for CPU_A , and a $198 + 50 kg * $0.2 / kg = $208 for CPU_B . So as a selfish individual trying to make choices that are good for me, now I am incentivised to pick CPU_B , which is also (relatively) a better choice for the rest of society.

[1] conservative working assumption that the current generation of 8 billion humans is the last generation, and no new humans are born. if we assume future generations, then there's even more humans to amortize the cost of pollution over.

[2] in the real world, not everyone is going to get an equal carbon quota. we don't have a world-scale regulator able to regulate a world scale problem. as has been demonstrated throughout human history, individuals and groups with more power will use that power to wrangle a better deal for themselves at the expense of others. we're not all in it together, even if it is a problem with a global pollution sink becoming full. e.g. i am an australian, in our country we have a per-capita carbon footprint of around 21,000 kg / CO_2(e) per person per capita. That's over four times higher than the pollution per-capita if everyone in the world polluted an equal amount. No domestic politician is going to get elected running on a platform of "unilaterally reduce everyone's carbon footprint by 75%" - the stakeholders who would benefit most from that are the 99.6% of humanity who live in other countries, and they aren't allowed to vote in Australian domestic elections. Dear reader, if you have read to the end of this rant, please lobby your government to put tariffs on your trading partners until they introduce carbon taxes -- particular us in australia.