This is a work in progress:
Sectors are considered to add value to each other. However, sectors combine in nonlinear manner. That is they do not just add value between each other, they also multiply between each other, and with themselves.
Consider transportation. Transporting an object across country does not add value to that object. It multiplies that object’s value, say by a factor of, for example, 1.3. This would ‘add’ 30% to the value of the object, but the real process is not addition. If the process were addition, then driving an empty truck across country would add value to nothing. (Unless the truck were more valuable on one side of the country than the other. Then the truck’s value would be multiplied.) But this is absurd. On the other hand, multiplying with nothing still gives you nothing.
Manufacturing a good is multiplicative. Each step in the manufacturing process multiplies the value of factors, and the value of the final product is the ‘product’ of these steps.
Profit is multiplicative. Where nothing is produced, no profit can be made. A product or service is sold at a multiple of its value: Greater than one for a profit, less than one for a loss.
Government, then, which is basically in the business of redistributing, transferring, demand, is multiplicative. It is in the business of rearranging factors, seeking to maximize the total produced by the economy. However, it can really only tax agriculture and other extractive sectors, mineral mining and energy extraction. This implies that the product of the tax (a factor less than one), and the subsidy (greater than one), is always less than one, because of the cost. That is the cost is always greater than the benefit. But where the government transfers demand from non-productive sectors to productive sectors, that is, where the subsidy is fictitious, an economy can experience real benefit.
There are cross terms And powers of terms. The church (charity) is another. It transfers demand down the social scale, thus expanding the base of consumption and giving more members of society a stake in that society.
Libertarian states minimize the government source of cross terms, and thus cannot compete against larger effective governments which increase cross terms, and thus greatly magnify the economy.