Cap & Share - the basic idea
Suppose you’re watering your garden with a hosepipe connected to a sprinkler. If you wanted to save water, what could you do? One way would be to plug up the sprinkler holes, one by one. But wouldn’t it be easier simply to turn the tap off a bit?
With fossil fuels it’s the same. There are only about 100 companies with “taps” - that is, they are bringing fossil fuels into the economy (by importing them or getting them out of the ground). The “sprinkler holes” are the millions of cars, houses and factories all over the country, emitting CO2 by burning these fossil fuels somewhere down the line.

It’s much easier to cap the fossil fuels - coal, oil and gas - entering the economy (on the left-hand side of the picture), than to try to control the emissions they cause (on the right-hand side of the picture).
So Cap & Share is what is called an “upstream system”. The cap is enforced by requiring the fossil fuel suppliers to have permits to bring fossil fuels into the economy. The number of permits determines the size of the cap.
And who’s in charge of the permit system? WE are! So WE get the benefit from the sale of the permits. There are two ways this could work:
In the original, 'classic' version of Cap & Share, each year you get a certificate for your share of the country’s CO2 emissions allowance. It might be for 10 tonnes of CO2, say. It’s free, and every adult in the country gets the same. The fossil fuel suppliers (oil, coal and gas companies) have to buy these certificates (you’d sell them via banks or post offices) and they become the permits. If a fossil fuel company buys your certificate, this allows them to bring in as much fossil fuel as will emit 10 tonnes of CO2 when it’s burnt (somewhere down the line). The more certificates they buy, the more fossil fuels they can bring in. Certificates are in demand, and are worth serious money.
Alternatively, and more simply, the permits are auctioned to the fossil fuel companies and the money is simply shared out equally. This version is called 'Cap & Dividend' in the USA. (There are also other possibilities for distributing the money, for example putting some fraction of it into community projects, which some countries might prefer to adopt).
Either way, in order to pay for the certificates, the fossil fuel suppliers put up the price of petrol, heating oil, coal and gas. Petrol (and the other fossil fuels) would cost more, and the cost of capping carbon is built in to the price of all goods and services automatically (so carbon-intensive goods cost more, encouraging the use of low-carbon alternatives). There’s no need for carbon-trading schemes (let alone rationing) - the cap’s taken care of “upstream”. You can get on with the rest of your life.
Some prices go up, but you’re compensated by the income from the 'share'. If you have a lower than average carbon footprint, you’ll come out ahead.