Commodity Taxes

Today we begin the first of several talks on taxes and subsidies. We're not going to be talking about income taxes and income subsidies. Those are typically topics for macroeconomics. Instead, we'll be talking about taxes and subsidies on goods, like a sales tax or a subsidy for wheat. These are also called commodity taxes and subsidies. So let's get going.

We're going to be emphasizing three important ideas about commodity taxation. First, who pays the tax does not depend on who writes the check to the government. For example, suppose the government is taxing apples. The government could make the buyer of apples pay for each apple that they buy. Or they could require the sellers of the apples pay for each apple that they sell. What we're going to show is that, from the point of view of the buyers or sellers, it actually doesn't matter how the tax is placed. The actual outcomes are going to be identical.

Another way of putting this is that the economic incidence of the tax, who actually pays the tax, does not depend on the legal incidence, who is in law required to write the check to the government. This will become a little bit clearer as we go along. Don't worry about it if it's not clear yet. The second key point, who pays the tax does depend on the relative elasticities of demand and supply. In fact, we can summarize point one and point two by saying, who pays the tax depends not on the laws of congress but rather on the laws of supply and demand. The third point is that commodity taxation raises revenue, but it also takes away some gains from trade, that is, it creates deadweight loss. We're going to be looking at point one in this talk, and then we'll move on to point two, and point three in later talks.

So, let's start with point one. Let's begin our analysis of commodity taxation by assuming the suppliers are the one who have to send the check to the government. That is, the legal incidence of the tax falls on the suppliers. What does a tax on the suppliers do? We can think about a tax on suppliers as increasing their costs. This is going to shift the supply curve up by the amount of the tax, so the supply curve shifts up like this.

Another way of thinking about this, is to remember that the supply curve tells us the minimum amount which suppliers require to offer a given quantity in the marketplace. The tax, that is going to increase the minimum amount that suppliers are requiring to offer that quantity in the marketplace. It shifts up that minimum amount required by just the amount of the tax. With the new supply curve we find the new equilibrium. The market equilibrium moves from point A to point B. What we see is that of course, the quantity which is exchanged goes down, in addition, the price paid by the buyers goes up.

How much do the suppliers get? The suppliers collect this amount, the price paid by the buyers, but now they have to give a certain amount of that, the tax to the government. The suppliers end up receiving this amount after tax, right here. In other words, what the tax does, it means that the buyers pay more than before, and the sellers receive less than before. Without any tax, the price the buyers pay is the same as the price the supplier receives. With the tax, the buyers pay a certain price, but the sellers get less than that. They get whatever the buyers pay minus of course, the tax. That's the situation when the suppliers pay the tax, or the suppliers have to send the check to the government.

Let's now look at what happens when it's the buyers who must send the check to the government. Now, we look at the situation when the legal incidence is on the buyers. We begin just as before with the equilibrium with no taxes. No taxes on sellers or buyers. Again, that equilibrium is at point A. I've also included this supply curve here. This is the supply curve when the tax is on the suppliers. It's the supply curve from the previous problem. It's not relevant for this problem. I've included it rather to remind us of where the equilibrium on the previous problem was. You can think of this as a kind of ghost supply curve. It's a supply curve from the previous problem coming back to haunt us.

So what's the effect of a tax on the demanders? Think about it this way. Suppose the most you were willing to pay for an apple is $1. Again, most you're willing to pay for that apple, a dollar, no more. Now, suppose you learned that the government has instituted a new tax. For every apple you buy, you must now pay 25 cents to the government. Now, how much are you willing to pay to suppliers for that apple? You're only willing to pay the maximum amount that you're going to be willing to pay suppliers is now 75 cents. The maximum amount that apple was worth to you is a dollar. If you know you're going to be taxed 25 cents if you buy that apple, then the most you're going to be willing to pay the supplier is 75 cents, because 75 cents plus the 25 cent tax to the government, that's $1. That's the most you're willing to pay to get the apple. In other words, what a tax on demanders does is it reduces their willingness to pay, and that means the demand curve shifts. Which way? The demand curve shifts down by the amount of the tax.

So let's shift. The tax is exactly the same amount that it was before. Let's shift the demand curve down by the amount of the tax. We find now that the new equilibrium is at point B. Notice first of all, that the quantity has declined. The quantity exchange has declined by exactly the same amount as before in the previous problem. What about the price received by the sellers? The sellers now receive this price. Lo and behold, that's exactly the same price as it was before. How about the price paid by the buyers? The buyers now pay what they paid to the suppliers, plus they must pay the tax to the government. This distance is the tax. Lo and behold, the price after tax paid by the buyers is once again exactly what it was when the tax was on the suppliers. When the tax is on the buyers, the buyers pay more than before. The sellers receive less than before by exactly the same amounts. The quantity declines by the same amount, too. The net price, or the total price paid by the buyers is the same. The total price received by the sellers is the same.

Now that you know the idea, I'm going to show you a simpler way of demonstrating this. What we just showed is that it doesn't matter whether the suppliers must write the check to the government, or the demanders must write the check to the government in order to pay the tax. In other words, we can analyze the tax by shifting the supply curve up, or by shifting the demand curve down. As long as we analyze the same size tax, we're going to get equivalent outcomes. It's going to come out the same whichever choice of tax we make.

There's actually a simpler way of thinking about this. What we can think about such a tax is doing, is driving a wedge between what the buyer is paying and what the sellers receive. When there's no tax, what the buyers pay is what the sellers receive, but when there's a tax, the buyers pay more than what the sellers receive. The difference is what the government gets. The difference is the amount of the tax. So let's think about this as a tax wedge. Let's say this tax wedge, this side is, let's say a dollar. Another way of analyzing the tax is to drive this wedge into the diagram until the top of the wedge hits the demand curve, and the bottom of the wedge just touches the supply curve.

Let's take a look. I'm going to drive the wedge in. What this tells us is that the price the buyer pays will be here, point B. The price the suppliers receive will be point D. The difference is the tax. For instance, if the buyers end up paying $2.65, then the sellers must receive $1.65 if the tax is a dollar. Similarly, if the suppliers receive a $1.65 and the tax is a dollar, the buyers must be paying $2.65. With this wedge, we could read off the diagram the price the buyer pays, the price the seller receives, and the quantity exchanged. We don't even have to shift any curves. We just drive the wedge into this diagram.

Let's do an application. In the United States, under the Federal Insurance Contributions Act -- FICA -- 12.4% of earned income up to an annual limit must be paid into social security, and 2.9%, an additional 2.9% must be paid into Medicare. Half of this amount comes directly from the employee. You can see it on your own paychecks. This is the FICA tax, and half the amount comes from the employer.The question is, does the fact that it's a 50/50 split, does this make a difference? Does this mean for example, that since the employer is paying half that this is necessarily a good deal for the employee? No, it doesn't mean that. What we now know is that we could have 100% of this tax paid by the employee, or we could have 100% of this tax paid by the employer. This wouldn't make a difference, not to wages, not to prices, not to anything. It would change the legal incidence of the tax, but it would not change the final economic incidence.

I haven't said here who actually pays the tax. That's what we're going to be talking about in the next lecture. What I've said here is that it doesn't matter who pays the tax from a legal point-of-view of who is obliged to deliver that money. So the legal incidence again, does not have a bearing on the economic incidence of the tax.What we're going to talk about in the next lecture is what does determine the economic incidence of a tax. It turns out to be elasticities of supply and demand, and that's what we'll take up in the next lecture. Thanks again for listening.