The person you contract also pays income tax on the amount. So you need to doubly add the tax.

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.

I think that's a logical error; I don't care about how much the contractor makes after tax, I only care what the cost to me is.

After all, if the contractor had some strange anomaly where he pays 100% of his income in tax, why would that matter to you?

On the contrary: My initial statement had nothing to do with price negotiation. All I was trying to assert was how the tax implications are when you do something yourself vs. when you subcontract.

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.

The contractors tax situation is irrelevant to you. The only thing that matters is income vs expenditure. Or in this situation, "how many hours do I have to work to pay the contractor's hourly fee?" and "how much faster is the contractor?". The tax stuff are just details around this.

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).