So when a government designs a tax system, they need to design it to be as efficient as possible. Let's go ahead and see what tax efficiency implies. When we discuss tax efficiency, this implies that one tax system can be more efficient than another. So, what are some problems that we run into? We've talked about deadweight loss a bit. As we increase taxes, there are going to be trades that do not occur when we have taxes. Therefore, the taxes restrict trade and that's going to be an efficiency loss we have because of the tax system. Taxes raise the prices consumers pay and they also lower the revenues of the producers.

The other side here is the administrative burden. This means that there are resources used in compliance with the tax system and enforcement by the government. Filling out taxes can be pretty difficult. Some people have their parents do it, or they hire an accountant to do it, especially once taxes start to get complicated. Business taxes, with all sorts of write-offs and deductions, make it even more complex. This administrative burden places a demand on consumers because they have to fill out these forms and deal with all this paperwork correctly. So, there are multiple layers of administrative burdens which are inefficiencies. If the tax system weren't there, there wouldn't be this time wasted by the taxpayers, nor this money wasted by the government ensuring taxes are done correctly. These are essentially deadweight losses and wasted resources.

When we talk about tax efficiency, we discuss two different tax rates when creating a tax system. The two most important calculations are the average tax rate and the marginal tax rate. The average tax rate is the average rate you pay on all your income, and the marginal tax rate is how much more in taxes you would have to pay if you were to make a little more money. Let's calculate both for an example where the government taxes the first $50,000 earned at a rate of 20%, while all income above $50,000 is taxed at 50%. Suppose this person made $80,000.

To calculate the total taxes paid:

- Taxes on the first $50,000: \(50,000 \times 20\% = 10,000\)
- For income above $50,000, i.e., $80,000 - $50,000 = $30,000, the tax is \(30,000 \times 50\% = 15,000\)

The average tax rate is calculated with \( \frac {25,000} {80,000} = 31.25\% \).

The marginal tax rate is straightforward because any income above $50,000 is taxed at 50%. So, the marginal tax rate is 50%. If this person were to earn an additional dollar beyond $80,000, 50% of that dollar would be taxed.

Let's pause here and let's discuss a hypothetical best, most efficient tax system in the next video.