[SOUND] So let's compare tax and expenditure decisions in democracy and autocracy which can be obtained from these two optimization problems. Let us start with autocracy first. Let's have a look at the budget constraint in the case of autocracy. Our first observation is that this budget constraint will not be binding. That means that it will not be held as equality. It will be held as straight inequality. That makes perfect sense because a closer look tells us that the maximand is essential difference between the left-hand side and the right-hand side of the budget constraint, and the very purpose of setting up a fiscal system in an Autocracy is to get some fiscal surplus. And this fiscal surplus is precisely the difference between tax revenues and tax expenditures. That means that budget constraint in the case of autocracy is not binding and, essentially, we can simply drop it. Now let's do that. And then we're back to maximizing this function over two variables t and G with no constraints whatsoever. Let me recall our intuition. We mentioned that an autocrat would still be somewhat restricted in his tax appetites because excessive taxes will excessively shrink the tax base, and for the very same reason we expect some public production input provision in the case of autocracy as well. Let's make this intuition more explicit and precise. Let's start first with taxes. If you want to maximize this expression by t and G, what we can see is that, first, we can maximize this product t*r(t), which is essentially the relative tax yield, and then find what public expenditures will maximize net public revenues with the autocrat. So, let's proceed to maximizing t*r(t) How does this expression depend on tax rate? The answer is given by the famous Laffer curve. And typical Laffer curve is shown here on this picture. When tax rate equals 0, quite obviously tax yield which is t*r(t) is 0 as well. When tax rate goes up there are two effects which are in place simultaneously, and they work in opposite directions. On the one hand, higher tax rate certainly increases tax yield but, the other hand, tax rate, when it goes up, increases the deadweight loss of taxes. And, as a result, the portion of tax base which survives taxation gets relatively smaller. So, of these two components t and r(t), t goes up and r(t) goes down. Recall this graph. When tax rate t is small the first effect that is the effect of the increased tax rate prevails and, as a result, in this curve they have an ascending portion where tax yield goes up. Tax yield levels off at a certain level which is the peak of this curve and if you try to increase tax rate beyond this peak the tax yield will start declining. And you have a descending portion of this curve, and of course this is the famous Laffer curve. It's named after a U.S. economist who described it first, and this curve was a very popular argument in fiscal policy debates in favor of cutting tax rates. The argument was if you cut tax rate, sometimes you can actually get an increase in tax yield enhancing public revenue simply because the tax base expands, and this expansion makes up for the losses of the lower tax rate. Anyway this is an Laffer curve which describes how tax yield t*r(t) depends on the tax rate. When the tax rate goes from 0 here to 1 here, and most of the time this is single peaked curve, so there is a tax rate where the tax yield is at its highest level. And if you go back to the problem of autocracy, its pretty clear for us that this will be precisely the rate chosen by the autocrat because the autocrat is concerned in highest tax yield possible. So, we have this second feature of the autocratic fiscal policy, the first one just to recall, is that the budget constraint is not binding, that the portion of tax revenues are appropriated by the ruling class. The second one is that the tax rate will be far from 100%, but still it's going to be fairly high. It'll be the rate that will put us on the top of the Laffer curve. And then finally, the question about public expenditures, what level of public expenditures the autocrat will choose to maximize his net fiscal surplus. The good news is that this public expenditures are now going to be 0. There will be some public production inputs supplied by the autocrat. And, by the way, the authors of this model and of this theory, McGuire and Olson, call this effect an invisible political hand similar to the invisible hand in the private sector described first by Adam Smith. The invisible political hand prompts even an autocratic regime, too, supply some public production inputs. As you see from this picture, the returns to public production inputs are very steep, at least at the low level of public production inputs, and, therefore, these returns, if we have a look at the autocracy problem right here, will be for the expenditures in public production inputs and will generate some net surplus for the autocrat. However, please notice that the incentives to supply such public production input in the case of an autocrat, while these incentives exist, they are not going to be very powerful. And let me explain why. The best way to explain it is to give you a numerical example. Suppose we contemplate an increase in public production input to the tune of, say, $1 million. This is going to expand the tax base by $2 million, r(t)Y(G) is $2 million. And, by the way, if we compare this with the problem of a democracy, this is something that democracy will certainly appreciate because it will capture the difference between the increase of tax base or or pretax income in $2 million in expenditure of $1 million Autocracy however might be reluctant to approve this move simply because the autocrat is not concerned about the wealth of the private sector entirely. He's concerned about the additional revenues and that such increase in private sector's wealth would generate, and I suppose, for example, that the tax rate is 30%. In that case, if the tax base goes up by $2 million, the revenue increase that will be associated with this increase of tax base will be just $600,000 and although $2 million is more than $1 million and, therefore, the society would approve this measure, $600,000 is less than one million and, therefore, the autocrat will be reluctant to go ahead with this increase in public production input provision. So, this is difference between these two problems, and this coefficient t is really critical. And the presence of tax rate here tells us that the incentives of an autocrat to fund public production inputs, while these incentives exist they are not negligible, they are non-trivial, they are considerably weaker than the incentives to fund public production inputs in the case of democracy. And that leads us to the third conclusion about what we can expect from fiscal policies in autocracies and this conclusion is that we should have some public goods and some public production inputs provision, but they're not going to be a whole lot of public goods, and the incentives to provide public goods should be weaker than in the case of democracy. Let's now turn to democracy and see what we can expect in that political regime. [SOUND]