Tossing out numbers is idiotic at best, but since you fabricated numbers it's pure propaganda. The establishment of a tax system is based on percentages, not dollar amounts. Why? Because this is the only way to make the system fair. If I make 1 billion dollars and pay 10% tax, and you make 50 dollars and pay 10% tax, the system would be fair. What is unfair, is that someone holds the ability to make a billion dollars while other people in the same society starve.
Actually no, what you have described is the most repressive and unfair tax system possible in all cases where the cost of living is higher than 45 dollars. Let's, for the sake of the argument, say that the cost of living is 50 dollars. Now the person earning 50 dollars pays 5 dollars of tax and is thus 5 dollars short and can't afford the basic necessities. The person earning 1 billion dollars will pay 100 million dollars and thus still keep 899950 dollars above the cost of living. Hardly fair and clearly put in place for the profit of the people in charge. That is actually as close to the medieval model as you can get in modern society.
Let's for a second posit that not all money is equal in utility... money below the cost of living is way more useful than money above the cost of living, and the usefulness progressively decreases the further you get from the cost of living. I mean, if the cost of living is 50 dollars you don't want to keep less than those 50 dollars. That is why usually the tax system is working with progressive brackets (from 10% to 39.6% currently in the US) instead of a flat tax. Money below the cost of living should be taxed less than money above the cost of living, which is why the brackets and effective taxation rates depend on your situation (single, married filing taxes together, married filing taxes separately, head of household).
Practical example, at the current US tax rates, for a head of household earning 100000 dollars and not doing any fiscal optimization. The tax bracket is 25% but the effective tax rate is below that. The brackets are as follows: 10% for money between 0 and 12750, 15% for money between 12750 and 48600, 25% between 48600 and 125450. So he's effectively paying 10% for the first 12750 dollars he's earned (1275), 15% on the next 35850 dollars (5377.5) and 25% on what's left (51400, so 12850) for a grand total of 19502.5 dollars. That is an effective tax rate of 19.5%.