## Saturday, 21 July 2012

### 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.

Lola said...

L, sign up at yppuk.blogspot.co.uk, and stand as a candidate at whatever elections are going. It's our only hope, all this campaigning and raising awareness has proven to be for nought.

Bayard said...

It occured to me that if LVT is a tax on land rent (actual and imputed), then it would be an easy move, philosophically, to extend it to that other thing that is rented out, money. So if LVT is x% of the rental value of a piece of land, then it could also be x% of any interest earned. Now, what would be the unintended consequences, I wonder?

Edward Spalton said...

It has always struck me as odd that one of the most highly taxed activities is paid employment, bearing income tax plus employers' and employees' National Insurance contributions. So , one cheer for the idea of land taxation.

However, some activities by their nature take up only a very small space in relation to the amount of profit they generate (i.e. jewelry and diamond cutting) whilst others need a very large area of land proportionate to output (i.e. farming). So by the logic of universal LVT, jewelry would be very cheap and food very dear.

Having adjusted to the EEC's Common Agricultural Policy in 1973, I don't doubt that the adjustment could be made but I feel it would somehow be the wrong way round.

B, yes, a bank asset tax is another good idea.

EdS, "by the logic of universal LVT, jewelry would be very cheap and food very dear."

For three reasons, no.

1. The price of food is whatever people will pay for it, if UK farmers try and charge more, then food will be imported. So that price is fairly fixed. A farmer has to cover his running costs and has to make at least as much money as he could earn doing something else. That is also fairly fixed.

The bulk of what is left over is not really 'profit margin' it is 'rent'. And it is also a fairly fixed figure - and this is the amount that a tenant farmer has to pay over in rent.

Tenant farmers do not charge higher prices than owner-occupier farmers, so therefore, if they paid no income tax/NIC and their landlord paid tax on that rent instead, then the tenant farmer is unaffected and food prices definitely do not go up.

2. Owner-occupier farmers currently pay Council Tax, a bit of business rates, income tax/NIC, benefit from CAP subsidies, which nets off to one figure.

It is not going to be too difficult to ensure that the LVT they pay (on house and land) works out equal to or less than their net tax bill under current rules.

So they are no affected either and prices do not go up.

3. In practice, full-on LVT on forestry and farm land would be somewhere in line with current rents for farm land, i.e. between £10 and £200 per acre, depending how good the land is, i.e. about one penny per square yard per year.

Full-on LVT on commercial land would be approx double current Business Rates bills, i.e. about £30 per square yard per year, and the rate for Hatton Garden or Bond Street where the jewellers all hang out would be £100s per square yard per year.

JJ said...
This comment has been removed by the author.
JJ said...

Mark what's with the use of square yards and acres? Surely metric measures would be more relevant?

Chr, that's just for fun because I'm old fashioned

Edward Spalton said...

Mark,
Long may you continue to be old fashioned and continue with good, traditional, people-sized measures.

I am all right with metric weights and with metric area measurements but when I combine the two (i.e. kg/ha instead of hundredweights or pounds per acre), I really have to work it back to Christian measurement to make sure I'm right.

As an Australian farmer complained about metrication - "The farm's twice as far from town and half the size".

I was in a seed merchant's store a while back and there were some pre-packed seed mixtures. As it used to be my trade, I had a look at them. Whilst the weights were all in metric, the sowing rates were PER ACRE - as any right-thinking man would want!

Kj said...

Graphmaster M does it again!

Ed, ta. Acres are easy to remember - the UK is about sixty million people and about sixty million acres; one acre is the size of a typical football pitch so everybody know what it means etc. And sq yards are much the same size as square metres anyway.

Kj, ta. Except for not making the x axis entirely clear.

Lola said...

The real beauty of this post is that it clearly demonstrates that say 80% of HMRC staff are already redundant, i.e. on benefits. They really don't like it when you explain it to them - I am very pleased to say.

Bayard said...

"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"