If we assume I'm a contractor charging $100 per hour and take the cash as salary:
(100/1.3142) * 0.5 = $38 left after payroll tax and the top income tax rate (50%).
So if I'm just as fast and good as a professional, the professional needs to charge $38 per hour or less for it to be worth it. But in reality, a professional is probably at least 2x as fast as me, making it $76. That's probably less than they charge, so it's worth paying for a professional.
Then you also need to add some cost of doing business.
Said in another way: The 100SEK you earn becomes 25SEK the contract can use (assuming 50% tax rate) – that's the first factor of 4. The last factor can be found in the details.
After all, if the contractor had some strange anomaly where he pays 100% of his income in tax, why would that matter to you?
Do it yourself: Miss out on that hours worth of salary
Subcontract: 2 times tax is paid.
Obviously this has implications on negotiation. This is exactly the reason why services are considered very expensive in the Nordics (as in 80USD to get your hair cut).
Note that this needs to be compared with a company getting their stuff fixed. Their contractor costs are fully deducted from their income.
In my example, a contractor who's twice as fast needs to cost $76 or less per hour . Thrice as fast is $114 or less.
You're right in principle though, just not on that calculation. In Sweden we have tax deductions for private citizens exactly to combat this issue: up to a certain amount per year can be deducted from your income, just like a company can, for certain services (such as cleaning or house repairs).
Said in another way: you don't pay income tax when you paint your own house.
(Also discussed recently on HN.)
In Denmark the tax system is such that if you subcontract out of personal money they need to be 5 times fast than you.
If we say that you can make your deck in half the time a professional would have don it, the factor is still 2.5x.
Ig. assuming a contractor would do it for 50 USD/h, this would translate to "making" 125 USD on hour by doing it yourself, 250 USD/h if you know what you are doing.
Obviously these things change with tax regimes.