[SOUND] Economist named James Mirrlees, for this contribution he received a Nobel prize in economics in the late 1990s. Consider a simple economy whereby every agent has the same utility function U which depends on her consumption x and her labor. This time L stands not for leisure as it used to be before but for labor. And labor is only source of income for this agent. So, her income z equals to omega, or w, whichever you prefer, l. Alright, let's draw an indifference curve of this utility function and this is what is done on this chart. So this is X, this is L, and along this line the agent's utility is constant. X is a source of utility and labor is a source of dis-utility, so you see this curve. Now Mirrlees suggested a simple transformation of this utility function, instead of the initial function U, lets introduce another utility function U-tilda which still depends on consumption x, but instead of labor L, it depends on income z which, of course, is proportional to labor, and this time because agents differ in their productivity, it also depends on this parameter w. So, for different agents, this modified utility function will actually be different. And it's related to the initial utility function by this very simple formula. You can draw indifference curves of this modified utility function in axis x, and x is still consumption as it was before, but instead of using the second axis for labor, use the second axis for income z. And this time for different agents, indifference curves will be different because agents will be different in their productivity w. These are indifference curves for two different agents, and one of them is steeper, and the other one is flatter. And I invite you to think which of these agents is more productive? And after thinking a little bit about this, you should conclude that most likely this agent is more productive than this one. So, w2 is greater than w1. So, this is what Mirrlees economies are all about. You have a community of agents which differ in their productivities at the same utility function, and you can assign to each of these agents this modified utility function. Now, let's see how this Mirrlees economy can be used to choose the best tax schedule. Such best optimal tax schedules would usually be non-linear. And this slide, unfortunately, format of this lecture doesn't allow me to introduce to you the optimal taxation theory, of which James Mirrlees was one of the founders, to the full extent, but at least I will give you some ideas as to how this theory works. Suppose first that you confine yourself to very simple linear taxes. Well, it's not proportional taxes anymore, this time tax schedule is calculated as T of z equals to minus D plus tz. So, D is a subsidy which every agent pays. And then on top of this subsidy, an agent pays taxes according to the tax rate t. In that case, if z is income, then consumption will be related to income according to this formula. And in this graph, I show this straight line which is a graph of consumption as a function of income. And this is diagonal where consumption equals to income. And this diagonal, of course, corresponds to the situation where there are no taxes, when consumption equals income. And we assume that the only purpose of using of earning income is to consume. And, therefore, for every point on this budget line, so to say, you can calculate taxes. Taxes are the differences between what corresponds to this point along the vertical axis x and the diagonal. So, if this is the optimal choice of a taxpayer, then every taxpayer makes a choice on this curve, on this straight line. And these choices will be different reflecting tax payers productivities because, recall that, tax payer's indifference curves will be different as well. So, every tax payer finds the best place on this line, the most preferred point on this line, and this choice will reflect this agent's income and this agent's consumption. And each of such choices will entail tax liabilities. This agent will pay that much of taxes, and this agent will pay that much of taxes, and this is the best that you can do by using this simple tax schedules which are linear in income. Suppose, however, that you want to deploy more sophisticated tax schedules. And, in that case, this graph isn't going to be a straight line anymore. The relationship between consumption and income will not be linear any longer, it will be some sort of a function which is more complex than just a simple straight line. And if you expand your choice of tax schedules to include non-linear taxes, see how powerful you can expand your capacity to earn revenues. Here is a curve that you can see. And on this curve for a relatively low productivity agent, the optimal choice will be here and we still have the same tax revenue from this agent as before. But here is the choice of a high productivity agent, and she makes her choice here on this curve, and, as you can see, tax revenues expand significantly in relation to what was available when you use simple tax rules. You can develop full theory and describe completely such optimal tax schedule. It might have some unexpected properties. For example, one can show that for the highest productivity agent, the optimal marginal tax rate should be zero. Because this agent is such a powerful income earner, you have to create strong incentives for this agent to make as much money as he or she can and this agent will still be paying a lot of taxes. Although the marginal tax rate is zero, but the accumulated tax liabilities would still be quite significant. And, of course, in real world you rarely find tax schedules where high income earners pay zero marginal tax rate. You can find some traces of this conclusion of our theory, for example, when it comes to payroll taxes because, as you probably know, in most countries payroll taxes are payable up to a certain level of your annual salary. And if your salary exceeds this level, then the payroll tax rate drops to zero. But other than that, this prediction of the normative theory is rarely met in practice. And the reason is quite obvious because, as we mentioned before, your tax schedules are driven by a number of considerations. And one of those is redistribution, the societies want to tax high income earners more heavily than low income earners. And, as a result, this redistributional rationales prevail over what normative theory sometimes predicts. So, we were arguing that income taxes are introduced to the arsenal of tax tools of modern governments because they allow to deal with informational asymmetry. But let's recall now another constraint which, as I was arguing, was restricting governments choices of taxes, and this is the administrative constraint. Complex tax schedule are quite difficult to administer. Let's see and understand why. Suppose you have a tax schedule that has several tax brackets and several tax rates. How this system has to be administered? One immediate implication of this system, is that almost every tax payer has to file a tax return, to submit a tax declaration at the end of the year. Why? Because if you have a flat tax rate, then every employer... Suppose that income comes only from employment. That's a simplification, but just for simplicity sake, let that be the case. In that case, say in Russia, every employer deducts from an employee's income 13% of her salary and remits this money to the state budget. It's that simple. And no one has to care about that any longer because the agent is full certain that her tax liabilities are implemented in full because she has to pay 13% of her income from all sources. And if she earns income from several sources, suppose she has another part-time job, her second employer will do the same. And, as a result, 13% of her total income will be sent to government. Now, if the tax schedule is more complex, it's not the case anymore because it depends on what the total income is, and deductions at source, as this is called, which are deduction by employers, will not be sufficient to implement this tax requirements because no single employer does know how much total income of this agent's will be. So, what this agent will have to do at the end of the year, is to collect her salary receipts from all sources and to add receipts from all other sources which are taxable. And then to calculate using a formula what her tax liabilities are, and if there is a balance between what has been deducted at source and what has to be paid, she will have to make that payment to the government. Or if, perhaps, she was taxed more heavily than she was supposed to, she will submit her tax return and the government will pay the difference. But as you see, if you have this non-linear tax schedules, the immediate implication is that every tax payer, in principle, has to file a tax return. And filling a modern tax return is not a simple thing, this is something that requires habit, culture, understanding, experience, perhaps, help of tax professionals. Worse yet, every taxpayer's situation has to be processed by a tax official. And that also requires some capacity, some knowledge, some skills, some data processing technologies that governments might not have. So, this non-linear systems might be beautiful, might be powerful but might be fairly complex to administer. And, as a result, administration costs sometimes could be prohibitively high. In this case, a natural choice for government would be to sacrifice some other gains that this complex tax schedule would produce for the sake of simplicity. And this precisely what happened in Russia almost 15 years ago when progressive tax schedule was, in the way of tax reform, eliminated and replaced by a simple flat income tax with a flat rate of 13% which made the Russian tax system much simpler, much simpler to comply for tax payers, much simpler to administer for the government. It also made it a little bit better protected against tax evasion because lower tax rates reduce the appeal of tax evasion. And, as a result, it's a known fact that after that reform was implemented in Russia, where tax rates were reduced and made flat, and at the same time the tax base was made quite a bit broader, revenue collection, personal income tax collection actually went up. [SOUND]
