Taxes and the profit maximising price-quantity (in monopolistic competition)

There are few industries which are complete monopolies or cartels (i.e. one or few producers acting in concert; no substitute goods or services) and there are few which are perfectly competitive (no barriers to entry; no product differentiation or customer loyalty).

So the most realistic and widely applicable model is called "monopolistic competition" (low barriers to entry; some product differentiation; some customer loyalty) where each producer/supplier has some leeway as to which particular price-quantity point he will choose, given the location from which he carries out his business.

Assuming they act rationally, they will choose the price-quantity point which maximises their profits; i.e. if they drop their prices, they can increase output but the increased output does not compensate them for the lower revenue; they can increase their prices but the extra per unit revenue does not compensate them for the fall in unit output.

For explanation of how the charts work, see Tutor2U. They label the x axis "quantity", i.e. quantity increases towards the right; I labelled the x axis "price" because this is the easiest variable for a business to change (and quantity merely follows on from that) so price decreases towards the right.

Fig 1 shows the simplest model, with no marginal costs. The profit maximising point is where the revenue-profit line is horizontal, i.e. parallel to the marginal cost line, i.e. at the top:
In Fig 2, let's be a bit more realistic and include marginal costs. The profit maximising point moves to the left slightly (to where the revenue line is parallel to the marginal cost line) and output falls slightly. This is the optimum point, from the point of view of producers and consumers:
In Fig 3, let's add VAT (the worst tax of all). The profit maximising point moves to the left and output (i.e. production, consumption and employment) falls yet again:
In Fig 4, let's add payroll taxes (for simplicity assume that they are borne by the producer, being employer and employees taken together), this steepens the marginal cost line, so output falls yet again:
In Fig 5, let's add corporation tax on net profits (after VAT and payroll taxes), this steepens the left hand of the total cost curve, so output falls yet again:

In our final Fig 6, let's imagine that all these taxes were replaced with a single flat tax on each location (being some sort of average of the total taxes paid by the business occupying that location or similar locations). The profit-maximising price-quantity point pops straight back to where it was in Fig 2 - unit prices are lower and/or quantity is higher, but the total £ value of output is at its highest. As long as the total tax charged is less than the difference between revenues and marginal costs, output is unaffected and is at its optimum point:
Which leads us on to a KLN: "If businesses had to pay tax proportional to the value of land they occupy (i.e. pay rent) then a lot of them would go out of business" which is not just economic nonsense but mathematical nonsense as well:

i. Under our present tax system, about four-fifths of taxes are borne by producers and workers depending on how much value they add from each business location. There is a huge spillover from this value they add into surrounding residential sites (because those sites have the best earning and spending possibilities) which is collected or enjoyed as rent and taxed very lightly.

ii. If we rolled all these business taxes up and just collected it is a fraction of the land/location value currently used by businesses (however defined), we'd see that the positive effects far outweigh the negative (Fig 6).

iii. Very roughly speaking, that's £400 billion of taxes collected from 0.3 million acres of commercially used land, which averages out at £275 per sq yard.

iv. But what if we collected all taxes, call it £500 billion in round figures, from commercial and residential land, regardless of how it is being used? That would be £500 billion being collected from 2.4 million acres of privately-owned developed land (four per cent of the UK by surface area) or an average of £43 per square yard (this could be anywhere between pennies per square yard for farm land and £1,000s per square yard for shops and offices in central London).

iv. It strikes me as nigh inconceivable that many businesses would see a higher tax burden, if the average tax bill on all businesses has just gone down by eighty-five per cent.* A very few businesses might find that they have to move to a cheaper location (smaller, further away from the high street etc) but even of those very few would actually go out of business (i.e. stop offering goods and services for cash), and their land would be put to more profitable use, i.e. a more efficient business would open up on that site; the land would be used for residential or even turned back into farmland. And maybe some residential land in town centres or at the edge of industrial estates would be used for business instead.

v. Of course, output of the vast majority of surviving and new businesses would increase quite markedly to their new profit maximising point (whether it increases by ten per cent or fifty per cent we do not know; it will be different in different industries), which must be A Good Thing, so everybody will find it easier to earn enough that £43 (as employment income, profits or dividends from a pension fund) to pay the tax due on residential land, which we can regard as consumption-without-production.

* There are some sites which are difficult to value objectively because they are intensively used but out in the countryside, like theme parks or power stations, where the value added or the site rental value is far higher than for surrounding farmland. When these are being valued for LVT, one way of approximating the tax due is to take an average of the total taxes generated by that business over the past few years (VAT, PAYE, corporation tax, Business Rates) and simply multiply it by a fairly arbitrary figure like twenty-five per cent, thus ensuring that no existing business ends up paying more: the shortfall will be made up by LVT on the homes in which the business owner and the workers live.