Rents and taxes - more or less the same thing

NB, for the purpose of this debate, I use 'rent' to mean sources of income that can't be competed away, as opposed to 'normal profits'. The 'rent' of a hire-car or of buildings themselves is not 'rent' for these purposes, but the additional rent that a landlord can charge because the building are on a particular site, or the grey market value of a taxi driver's licence or a pair of take-off and landing slots at a UK airport is.

1. Let's start with a nice simple supply/demand chart, and see how things change if there is an artificial restriction on supply (see 2.) or if a sales tax, such as VAT is introduced (see 3.):
2. I have a grudge against barriers to entry imposed by legal restrictions on the number of competitors (i.e. taxi drivers in London or landing slots at UK airports), especially where that industry is being subsidised and needs barriers to entry to stop those subsidies being competed away (e.g. nurseries, see update at end of this post), and worst of all are those industries that only exist because of a totally unnecessary regulation in the first place (such as removal of nigh-harmless white asbestos from buildings), who also want subsidies and barriers to entry (see update at the end of this post).

As you can see from the chart, if supply is restricted to less than its equilibrium level, the consumer (that's all of us, by the way, not some abstract concept) has to pay higher prices, generating super-profits for incumbents and people who would otherwise have entered the market are unemployed (or are forced to do something less profitable elsewhere). The super-profits have a significant capital value, for example a London taxi driver's permit or a landing slot at Heathrow.
3. All these bad effects are more or less exactly the same as what happens when you introduce a sales-tax, unless demand is very price inelastic, which applies to fuel, alcohol and tobacco duties. Politicians get away with imposing such 'sin-taxes' because nobody dares stand up for drivers, drinkers or smokers, but they get a tick from economists as well because these duties don't affect behaviour very much.

Apart from that - where supply and demand are both elastic, imposing VAT is not some harmless 'tax on consumption' (despite what decades of brainwashing by the EU says, or centuries of brainwashing by British governments before then) but reduces the profits of business and puts people out of business, as the chart illustrates:
The only difference between the second and third charts is that in the second chart the incumbents are getting the extra revenue and in the third it is the government, but from the point of view of consumers or people who are prevented from earning their livelihood, the effect is more or less the same.

Which is yet more evidence to support the generalisation that rents and taxes are the same thing, it just depends on how narrowly you define rents.