When the government levies an income tax, it requires individuals and corporations to transfer some of their income in a particular period to the government. They are usually expressed as percentages, and are often graduated meaning that different portions of someone’s (pre-tax) income are taxed at different rates.
For example, suppose an income tax has two brackets with a rate of 10% for income up to $10,000, and 20% for income above $10,000 A person with a pre-tax income of $100,000 would thus owe the government (10% x $10,000 + 20% x $90,000) = $1,000 + $18,000 = $19,000.
One of the major distortions it causes is allowing particular expenses to be deducted (or excluded) from one’s taxable income. E.g. if someone had a pre-tax income of $100,000 but pays $5,000 in interest on the loan he got from the bank to buy his house, he will only report to the IRS that he has $95,000 in taxable income. The appropriate bracket tax rates will then be applied to this lower amount, not to the true $100,000 in income. Such a “loophole” in the income tax code arguably brings the economy closer to the market outcome overall (by limiting the applicability of the distortionary income tax), but it clearly causes large distortions between individual sectors, especially if marginal income tax rates are high. In the case of mortgage interest deduction, the distortion gives people an artificial incentive to prolong the length of their mortgage, and to use their money in other investments rather than paying back the bank as quickly as they otherwise would have.
Another distortion happens with health insurance. Income taxes make it cheaper when the employer pays health insurance for his employees rather than having the employees getting a higher income and paying it themselves.
The biggest distortion happens with the income itself. People will obviously work less if the reward for working is taxed more heavily. Students may prolong their educations and older workers may retire earlier. The hours worked, particularly during holidays, will fall, because of the change in incentives. This is because people will both truly work less, but also because they will work “under the table” and not report their earnings to the government.
Income taxes also make people rethink which jobs to take and which not to take. They have to take in account how much they are going to get taxed and if it is still worth it after the taxation.