we're going to briefly discuss some features of tax codes to get a better understanding of how they work let's start by asking why we have taxes there are four main factors first raising revenues to fund programs that might not be easily provided by markets examples include defense and education the next reason is transfer payments that redistribute income at this point the federal government spends well over half of its budget on transfer programs with by far the largest being for the elderly mostly social security and medicare and the remainder being income support programs for low income households third financing its own operations it is the actual running of the government including salaries for government workers and finally correcting market failures this is an important issue related to what i said earlier about how markets might not get us the optimal amount of certain goods now governments use a number of different taxes to raise revenues the federal government primarily uses individual income taxes which is that complicated form that you fill out once a year payroll taxes which fund transfer programs like social security come directly out of your paycheck that's the fica line that you see on your paycheck every other week and corporate income taxes which are levied on the profits of corporations now the corporate income tax is a really interesting place to consider economic incidents after all a corporation isn't a living breathing entity doesn't eat food or make any decisions for itself it's made up of people and only people can bear attacks this is a statement that gets mixed up in politics pretty frequently which is unfortunate because it's a really important concept a corporation or any business is a group of people the owners are shareholders and the workers including managers they sell goods and services to consumers when a corporation is taxed the money for that tax can only come from those three groups lower profits for the owners lower wages for the workers or higher prices for the consumers the true economic incidents will depend on a lot of different elasticities and other factors but the fact remains that only people can bear attacks the notion of statutory incidents of taxing a corporation is particularly unsatisfactory in this case now how about state and local governments states use a mix of income taxes and sales taxes which you're probably familiar with these are percentage of the price of an item and are generally added to your cost when you purchase the item but remember just because the statutory incidence is on you the consumer doesn't mean that the economic incidence is on you as well finally local governments in some states rely on property taxes which are assessed on the value of land and structures now let's define a few more terms the average tax rate is the total amount of taxes paid divided by income that is it's just taxes over income now the marginal tax rate is the amount of taxes paid on an additional dollar earned the change in taxes for a change in income where usually the change in income is one dollar now what's the big difference well let's imagine a very simple tax system for the first fifty thousand dollars of income the tax rate is zero so zero to fifty thousand the rate is zero percent so here's the rate and these are the income levels everything above fifty thousand dollars the tax rate is fifty percent now notice this tax code has two moving parts the marginal tax rate which we've discussed but also the threshold of the tax bracket that is the amount of income at which that rate kicks in that threshold is really important though it's often ignored by journalists and policy makers they only focus in on the marginal rate for example a marginal tax rate of 70 that kicks in at a hundred thousand dollars of income might have a very different impact than that same seventy percent rate that only kicks in at ten million dollars now in this simple tax system if you earn forty thousand dollars you pay zero dollars in taxes the marginal and average rates are both zero because the tax on an additional dollar is zero now at exactly fifty thousand dollars the tax bill is still zero dollars but the next dollar you earn faces a tax rate of fifty percent the average rate is still zero percent but the marginal rate is now fifty percent now suppose you earn a hundred thousand dollars you pay zero dollars on the first fifty thousand and fifty percent on the remaining 100 000 minus 50 000. so your total tax bill is 25 000 therefore your average tax rate is 25 let's actually write that out so if your income is a hundred thousand dollars your tax bill is zero dollars for the first fifty thousand plus a hundred thousand minus fifty thousand times the fifty percent rate that gets you a twenty five thousand dollar tax bill so your average tax rate is twenty five thousand dollars over one hundred thousand the average tax rate is 25 percent but the marginal rate it's 50 percent it's marginal rates that affect decisions after all we make decisions on the margin so let's take tracy who's thinking about taking on a side gig that will pay her a hundred dollars for five hours of work so tracy can earn a hundred dollars for five hours that's twenty dollars an hour the opportunity cost of her taking the job is five hours of leisure let's make that example concrete and say that tracy's leisure is worth 12 dollars an hour to her so her opportunity cost is the five hours of leisure at 12 each so that would be 60 she's willing to do the job because it pays more than what her leisure is worth to her hundred dollars is more than sixty dollars now if tracy earns forty thousand dollars a year already then her average tax rate is zero and her marginal tax rate is zero the tax system doesn't affect her decision because the marginal rate is zero now if she earns fifty thousand dollars a year her average rate is still zero she hasn't paid a single dollar in taxes but her marginal rate is now fifty percent so let's think about tracy's decision the job pays twenty dollars an hour minus taxes after taxes she gets to keep fifty dollars for that five hours the hundred she was paid minus fifty percent in taxes that's ten dollars an hour but we know that her leisure is worth twelve dollars an hour to her and now she won't take the gig because it pays less than her opportunity cost it's the same story if she earns a hundred thousand dollars a year her average rate in that case is 25 but her marginal rate is still 50 percent average tax rates don't really matter for decisions because decisions are made on the margin and it's marginal tax rates that affect our decisions to work and save in this case tracy wouldn't take the job she wouldn't earn that hundred dollars and whoever was willing to hire her wouldn't have gotten their services for which they were willing to pay a hundred dollars that's deadweight loss a transaction that didn't happen now when economists talk about a progressive tax a progressive tax or progressive tax code they mean that it has increasing average rates a proportional tax code has constant average rates while a regressive tax has decreasing average rates i should point out increasing or decreasing what in income the progressive tax code the higher your income is the higher your average rate is regressive tax the higher your income is the lower your average tax rate now notice that even though our simple tax code has just two marginal rates 0 and fifty percent it's a progressive tax since the average tax rate increases with income it was zero for someone earning fifty thousand and twenty five thousand for someone earning or excuse me twenty five percent for someone earning a hundred thousand dollars and someone earning a hundred million dollars would basically be paying pretty close to fifty percent because they're paying this marginal rate on almost all of their income now the united states has as it turns out an extremely progressive federal tax code in fact much more so than nearly any other country if you're interested in these topics the study of the economics of taxes and government policies about spending which is called public finance or public economics we offer a full course that focuses just on these topics