Lecture 30: Tax I and Incidence of Tax

So let's understand specific tax and ad valorem tax a little more. Specific means specific. It is based on the specific quality of an object. For example, the length of an object is based on that length. Or what is its specific gravity? Tax is based on that. So if the government can say that you are selling this thing for P rupees, then you will have to pay T tax on every unit. So the effective price of that thing will be P plus T. From which P plus T will be given by the buyer. The buyer will give P plus T. From that P will go to the seller. And T will go to the government. This is when the tax is on the buyer. Similarly, if the tax is on the seller, then the seller will take P from the buyer. And will keep P minus T with him. P is given by the buyer. P minus T is going to the seller. And the remaining T will go to the government. Right? So this is how the tax will be applied. This is the basis of a specific tax. And the second one is based on your value. Which we called ad valorem tax in English. This tax is based on value. What is the value of this thing? A particular percentage of that will be applied. So if something is being sold for P, then the government will say that whatever is the rate of 5% value or 10% value, you pay tax on the T rate. So instead of P, the price will be P multiplied by 1 plus T. And if the seller is giving P multiplied by 1 plus T, then P will go to the seller. And P multiplied by T will go to the government. So this T is a percentage of the value. This is why it is called ad valorem tax. You will notice that if the price in a specific tax goes above P and becomes 2P, then the tax will still be the same. Because this tax is based on its nature. So it will remain T. Right? Whereas here, the tax that the government is collecting based on the value, if this price increases, the government's tax collection will also increase. So there is a difference between the two. So let's focus on a specific tax. Once we understand what changes occur in the market based on a specific tax, then we will also understand the changes that occur based on the value. So let's start with an example. There is a market. The demand curve in the market is given as P is equal to 30 minus Q. This is your demand curve. Here also, it is 30. You already know. This is the Q axis. And this is the P axis. And similarly, if we say the supply, then P is equal to Q. If we believe it to be true, then we should write Q is equal to P supply. And Q is equal to 30 minus P demand. But that also works. There is no problem with that. It is like this from here. P is equal to Q. And this is P is equal to 30 minus Q. And you will see that there is equilibrium. You must have learned to solve it by now. If you solve both the equations together, then Q star will be equal to 15. And P star will also be equal to 15. So here P star is also 15. Q star is also 15. In this market, there is no government intervention. There is no tax. Now the government says that the traders will have to pay tax. Right? T is a specific tax. The more units are sold, the amount multiplied by T will have to be deposited by the government. So this will undoubtedly affect the sellers. Because the seller's willingness to supply how many units they want to sell, their marginal cost, which depends on the minimum demand, if the government is asking for Rs. 2 per unit, then the marginal cost of each unit will increase by Rs. 2. So the willingness to supply will decrease. Those who wanted to supply 15 units at Rs. 15, will now want to supply at Rs. 17. Because they will get only 15 out of 17. They will go to the government for Rs. 2. Earlier, they wanted to supply 10 units at Rs. 10. Now they want to supply 10 units at Rs. 12. With the same logic, they will get only 10 units at Rs. 12. They will go to the government for Rs. 2. So at every price, the quantity supplied has been reduced by 2 units. So the new supply curve will shift by 2 units. Why only 2 units? Because this is happening at Rs. 2 per unit. So how can we obtain the new supply curve? Earlier, we made a video on the lines, the lines and vertical intercepts. How can we write the equation for that? We wrote that if there is a Y on the Urdwadar axis and an X on the Chhatij axis, then we can write any line as Y is equal to MX plus C. Where M was the slope, and C was the vertical intercept, that is, the curve is like this. This means that the slope is M and this is C. Earlier, you saw that P is equal to Q. What does this mean? The slope is 1 and the intercept is 0. This is why it was passed from the origin. Now these 2 units have risen above. This is 2. Earlier, they wanted to supply 0 on Rs. 0. Now they want to supply 0 on Rs. 2 because they are not going to get anything out of 2. 2 times 2 will go to the government. They are going to get only Rs. 1 out of Rs. 3. Earlier, they wanted to supply 1 on Rs. 1. Now they want to supply 1 unit on Rs. 3. You will get the equation here. P is equal to There is no change in the slope, so 1 multiplied by Q and the intercept will be 2. So P is equal to Q plus 2. This is the new supply curve. The supply curve is basically Q is equal to P minus 2. But you are understanding. So because of this, if you calculate the new balance, then you will get here that only 14 units will be sold in the market. And the seller will have to pay Rs. 16. The seller is paying Rs. 16. And the government is taking Rs. 2 out of Rs. 16. And Rs. 14 is going to the seller. So first see and write. P star, Q star. Earlier it was 15. This was also 15. Now instead of 15, earlier the buyer was also paying Rs. 15. The seller was getting Rs. 15. Now the buyer is paying Rs. 17. And the seller, sorry, the buyer, we are taking out the new one. The buyer is now paying Rs. 16. He is paying Rs. 16 in the new equilibrium. And because he is paying Rs. 16, the seller is getting Rs. 16 minus 2, which will give you Rs. 14. You are getting only Rs. 14. And instead of Rs. 15, you are getting only Rs. 14 in the market. So this tax has created an uproar. Let's understand a few things. This has had an impact on the market. What impact has it had? Here you have some sellers and here you have some buyers. The buyers want to give the price at which the sellers will be happy. They will sell their goods. But now they will not be able to pay this tax. So this area will be a deadweight loss. This will be a reduction in the total surplus in the society. Now to achieve the surplus in the society, we add the surplus of the buyer, the surplus of the seller, and the revenue of the government. Because now the government is also a part of the model. So we see that there is a deadweight loss in the society because of this tax. Still, why do we impose this tax? We will discuss this later. But we saw that the government imposed this tax on the seller. But the government is not only giving this tax to the seller, but also to the buyer. The Rs. 2 tax that has been imposed, one of it is coming from the buyer and the other is coming from the seller. So there are two things in this. In English, we call it the impact of tax. In Hindi, we call it Karaghaat. And the other is the incidence of tax. Incidence of tax. This is called Karapaat. Karaghaat is talking about who has been taxed. This is in the legal term. What is legal? The tax has been imposed on the seller. What is Karapaat economically? We can say that it is economic. Who is Karapaat? Both of them have to pay one rupee each. The incidence of tax is on both of them. So we saw that the tax was imposed on the seller, but both have to pay. To complete this discussion, we should also see that if the government had not imposed this tax on the seller, but had imposed it on the buyer, what would have happened? So our entire problem is the same. P is equal to 30 minus Q. This is the demand. And P is equal to Q. This is the completion. And the equilibrium is the same as before. So this comes to 15-15. This is P and this is Q. Now in this case, the government tells the buyer that whatever units you buy, multiply that by T. On one unit, you have to pay T. Because last time we took T is equal to 2, a tax of 2 rupees. So here too, we have to ask for 2. You have to pay 2 rupees tax. So there is no difference on the seller. If you look at the impact of tax, there is no difference on the seller. There will be no change in the supply curve. But there will be a change in the demand curve. Because if P is given to the seller, then T will have to be given to the government too. Right? 2 rupees will have to be given to the government too. Because in 30 rupees, he was not ready to buy anything. Now the same will happen in 28 rupees. Because 28 will go to the seller and 2 will go to the government. Then it will come to 30. So because of this, continue this logic at every price. Then it will shift down parallel. And because it is shifting from 2 units down, then the new green demand will be 28 minus Q. And we will see that the new equilibrium is coming at 14. And here too, the supplier is getting 14. But the buyer has to give 14 rupees to the seller and 2 rupees to the government. So effectively, the buyer's expense is 16 rupees and the seller is getting 14 rupees. So here too, the incidence of tax is the same as before. 1 rupee from 15 to 16 is for the seller. And from 15 to 14 is for the seller. Both have to pay 1 rupee each. Here too, you are getting the same deadweight loss to society. Here too, some people were ready to buy. Some people were ready to sell. But now they will not be able to exchange because this has been taxed by the government. So we can say that the deadweight loss is a cost to the government. It is a cost of the society. The cost due to tax. So let's try to understand this. Let's try to understand one more thing. Don't think that whenever the government will impose a tax, half and half will be divided between the buyer and the seller. This is a special case. It is happening in that. Now what we do is, we take some different types of demand and supplies and see what happens. We will take the first example. Let me tell you beforehand that you will understand by looking at these examples that elasticity plays a very important role in deciding who will pay the tax. The side which is more elastic, we will see this later, the side which is more elastic, that side will pay relatively less tax. Right? So let's take an example in which the demand is completely elastic. It is completely elastic. Demand is perfectly elastic. Right? So you will remember, if you revise and see, that if the demand is completely elastic, then it means that the demand curve is equal to 36. It will be like this. And let's take the first supply. P is equal to Q. We see both cases in this. Once the government imposes a tax of Rs. 2 on the seller, and once the government imposes a tax of Rs. 2 on the buyer. So first we see, that first, see this in black, A is called the impact of tax on the seller. Right? Now, if there is a tax on the seller, we have already seen what happens, that the supply curve will shift upwards by 2 units. We have already discussed this. It will shift by 2 units. So first we see, that P star was the market equilibrium of the price, and Q star was the market equilibrium of the quantity. Q star and P star. What impact does it have, if there is a tax on the seller? Now this Q star, Q star becomes dash, which is less than before. We cannot say that there will be 2 units. It depends on the slope here. But it is clearly less than before. P star, what would the buyer be giving? The buyer will still give P star. But from this P star, P star minus 2, came here. Minus 2, this will be given to the seller, and 2 will be given to the government. So what do we see? There is a complete tax incidence here. The tax incidence is on the seller. On seller. The seller will have to pay the entire tax. Right? If this tax, let's take this example again. This is your Q star, P star. This time we will say that the amount of tax is on the buyer. The buyer has to pay the tax. What did we see? If the buyer has to pay the tax, then the demand curve will shift downwards equal to T. Here, we will do the same thing again. Equal to T will shift downwards. Why will it shift downwards? Because earlier if the buyer was ready to pay Rs. 25, this is Rs. 25. Now the seller will be ready to pay only Rs. 23. Because Rs. 23 will go to the seller and if we have Rs. 2 as tax, then Rs. 2 will go to the government. Then it will come to Rs. 25. So because of this, it will shift from 2 units everywhere. Here again, we will get Q star dash. Whatever will be here, we will get the same thing. And here also, P star minus 2 will be given to the seller and Rs. 2 will be given to the government. So in total, P star will be given to the buyer, seller or government. But the seller will get P star minus 2 which was in the first case. Again, we will see that the impact of tax is not important. What is important? Tax incidence for economics. Legally, the impact of tax is important. Who has to pay? Whose responsibility is it? If you don't pay, the government will catch you. But from an economic point of view, tax incidence is more important. And we have seen here that if the demand is perfectly elastic, then the entire tax will have to be paid by the seller.